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Light aircraft lift, drag, and moment prediction: A review and analysis

19750016605 · NASA · 1975

Public domain · NASATechnical Reports

Overview

The historical development of analytical methods for predicting the lift, drag, and pitching moment of complete light aircraft configurations in cruising flight is reviewed. Theoretical methods, based in part on techniques described in the literature and in part on original work, are developed.…

Publisher
NASA
Document
19750016605
Year
1975
Pages
500
Chapters
14

section serves as a guide to the systematic dismantling and conversion of

GENERAL PROGRAM MODIFICATIONS It was mentioned in the introduction to this chapter that the original program STALL consisted of approximately 1700 executable statements. Thls section serves as a guide to the systematic dismantling and conversion of the program to its modified form. The program as supplied to NCSU operated in the overlay mode with a main overlay and three additional overlays of the same sublevel. Since total operation within the core of the IBM 370-165 is less expensive than the time to call in overlays, the program was taken out of the overlay mode and compiled and executed as a unit. Some IBM-CDC incompatibilities noted In the previous section were then removed in order to execute the program on the NCSU 370-165. These changes resulted in a significant reduction in execution time at the expense of increased core requirements. As mentioned previously this trade is quite cost-effective.

A second major modification occurred when portions of the program unneeded for the present investigation were removed. These included all portlons associated with stall calculations as well as those portions having to do with flaps. These routines are THREE, MAIN3, and MAIN5.

See Table 2. These changes reduced the number of executable statements by 550 to approximately 1150, a substantial reduction.

MODIFIED NCSU PROGRAM ORIGINAL PROGRAM (FUNC) (STALL) STALL MINV MINV DAGET AAA AAA ZZZ SSS SSS TERP TERP SETSW SETSW DA?SW DATSW AERDA BR IDG BRI DG ARC LOOK ONE MA IN MA I N MAINI MAINI TWO MA IN2 MA IN2 MA IN4 MA IN4 THREE MAIN3 MAIN5 FUNX FUN Table 2. Comparison of routines contained in the original and modified programs.

A further major reduction was realized by making the Reynoldsnumber

of interest Inherent In the two-dimensional data. An in-depth look at what Is Involved with this assumption may be found in the next section of this chapter. Use of this assumption, however, resulted in a decrease in executable statements by 250 to approximately 900.

Stlll another reduction was made by changing the location of data storage. In addition to saving a tremendous amount of input-output time by expurgatlng the nine peripheral storage devices associated with the table look-up procedure and storing the polynomial coefficients within core, the move reduced the number of executable statements by 100 to a remalnlng 800.

Reductlons to the existing less-than-700 executable statements can be attrlbuted to the clean-up of unused variables and to common block reorganization.

CHANGES CONCERNING REYNOLDS NUMBER In order to locate the two-dimensional value of a given aerodynamic coefficient, say C%, in the original program, three separate interpolations were made. Linear interpolation was performed first for the required value of Reynolds number, then for thickness ratio, and finally for camber. Because of the amount of data being searched, an investigation into a possible deletion of one of these variables was initiated. Deletion of any one of the variables would cut the number of interpolations by forty percent. Since the present Investigation had excluded the stal region because of the inability of the two-dimensional program to predict boundary layer separation effects adequately, a reduction in dependence of the results on Reynolds number was established. Changes in Reynolds number at low angles of attack produce very little variation in lift coefficient and only slight variation in drag coefficient (Ref. 79). These variations were so slight that it was decided to either calculate the two-dimensional characteristics for both tip and root airfoil families at the Reynolds number of the mean aerodynamic chord o_ at the mos_ enter the characteristics at only the root and tip values.

Error encountered by the use of the mean aerodynamic Reynolds number is low because of the averaging effect of the camber interpolation and eventual integration. Error encountered by the use of root and tip families at their respective Reynolds number should be even less since this effort gives the coefficient data an implicit relationship in Reynolds number.

The calculation of the spanwise Reynolds number distribution was left in as a check for the designer. It is suggested that designs using high taper ratios resulting in wide Reynolds number variation employ the root-tip implicit method. Removal of the Reynolds number interpolation allowed the deletion of two routines, ARC and LOOK, from the original program (see Table 2).

CHANGES CONCERNING AIRFOIL DATA STORAGE With the transfer of the Reynolds number to an implicit dependence, half of the minimum data sets were no longer necessary; furthermore, the remaining portions of the data sets could be stored in core, resulting in a substantial reduction in operating time since the comparatively long time required to transfer data from tape or disc files could be eliminated.

Adopting this philosophy removed nine external data files, decreased the execution time further, and eliminated approximately iO0 executable statements among these being the two routines DAGET and AERDA of the original program.

A further reduction in execute time was realized by storing the two-dimensional data not as tables of points but as polynomial function coefficients and thus eliminating tabular interpolation.* A schematic diagram of the storage and evaluation procedure is given in Figure 44. Note that for a geometric configuration with root and tip families different, evaluation of any given aerodynamic coefficient has been reduced to four functional evaluations, two thickness nterpolations, and one final camber interpolation.

* Note from Figure C-2 that the angle of attack versus coefficient of lift polynomial was added in order to predict the angles of zero lift without solving for the zeros of a fourth degree polynomial function.

ROOT FAMILY TIP FAMILY STATION (J) Thickness I Thlckmm I I I I I I I I Alpha( J ) Thicknen ( J ) _J SponwiH ComiC} °l Root Interpolation I _ ClTip

ct(J)

Thickness 2 Thickness 2 Fuselag_ • . " RoOT -TIP.

Figure 44. Schema?ic represenfaflon of the modtfied data look up procedure, DISCUSSION OF PROGRAM RESULTS Results of computations of the three-dlmensional lift and drag of a wing using two-dimensional section data as Input are shown In Figure 37 for both the reduced NCSU pregram and for STALL. Agreement with STALL Is very good for the lift and quite reasonable for the drag, especially when one considers that drag "buckets" found experimentally on 6-series airfolls and used in STALL cannot be fit satisfactorily with just a fourth order polynomial. This fourth order representation was judged adequate, however, because the airfoil aerodynamic characteristics program inherently predlcts relatively smooth drag curves. Since such results were always to be the.

input to the three-dimensional program, the authors saw no need to increase the program complexity.

A comparison of the results of predictions of the entire computation procedure with experiment is shown In Flgures 38, 39, and 40. The llft data for the 6-series airfoils, shown In Figure 38, shows excellent agree- ment up to a CLValue of 1.2. The drag data is quite acceptable to a C value of 0.8. The wing data for the four dlglt airfoils indicates tha_, particularly for lift coefflclents above 0.4, the _iscous effects on these thick airfoils are not properly accounted for. The same behavior Is noted for other thick airfoils of the same family. (See Figures 13_ 14, and 15.)

The prediction is, however, much better on the wing constructed of 230-series airfoils (Figure 40). Here, the lift results agree well with experiment for < 1.0 and the drag predictions are in reasonable agreement for C L < 0.6.

seems reasonable to conclude therefore that for C L< 1.0, the program will provide wing lift data as reliable as the two-dimensional data supplied as input. Wing drag predictions made by the program also seem to be as re- liable as the section characteristlcs used as input, at least for C L< 0.8.

Thus, for low-to-moderate lift coefficients and moderate,to-high-aspect-ratio, unswept wings this procedure Is far simpler computatlonally and of equal accuracy as compared with the more complex vortex lattice or lifting surface methods.

PROGRAMS FOR THE CALCULATION OF BODY

AERODYNAMIC COEFFICIENTS

INTRODUCTION The problem of accurately estlmatlng the lift and drag coefflclents of arbltrary three-dlmenslonal bodies in a rigorous fashion will certainly be recognized as an extremely dlfflcult task. The word arbitrary, for example, Implies that the routine or procedure for estimating these coefficients must be general enough to handle a variety of bodles including bluff ones to be useful to those to whom this work Is dlrected; yet the procedure cannot re- quire an excessively large number of computations. In order to yield the most reasonable solution within the constraints of small computer run times and small computer storage requirements the present authors chose to use the fol- lowing procedure: (I) A program to calculate the inviscld flow about arbitrary three- dimensional bodles was obtained from the Naval Ship Research and Development Center at Bethesda, Maryland. One important reason for selectlng this program was the fact that it was equipped with the capabllity of computing on-body streamlines. Another was the fact that it was already limited to bodies alone. Two other programs which the authors acquired in the process of developing this procedure would have required removing the wing characteristics calculation portion of the programs.

(2) The program was reduced in size as much as posslble and speciallzed to calculate the inviscid flow over bodies at zero angles of attack and sideslip. (As received, it permitted one to calculate the invlscld flow field with onset flow components along all three axes.)

(3) The skin friction drag was estlmated by applying a two-dimensional boundary layer technlque to the on-body streamlines and integrating the resultant wall shear over the body surface.

(4) The viscous form or pressure drag was estimated by considering the body wake to be representable within the framework of an invlscid flow solution in much the same manner as the complete airfoil solution was achieved.

The reasons for choosing this procedure are quite straightforward: (I) It relies heavily on existing Programs or procedures whose ap- plicability and computational problems have been well charted. The time and effort required for program development is thus reduced to a minimum.

(2) The procedure is step-like so that if necessary it can be done in pieces on a small machine with limited storage capacity. In contrast, It would be very difficult to segment an attempt to solve the general three-dimensional Navier-Stokes equatlons for a complex boundary shape.

Theoretlcal justlficatlons for someof the steps In the procedure are glven

at length In earlier sections of the present work.

Of course, In order to obtaln shorter running times and smaller storage

requlrements, It has been necessary, as Is always the case, to llmlt flexl-

blllty and employ certain assumptionswhich are not unlformly valld. The

restrlctlon to _ = 0 cases has already been mentioned. In addition, the

boundary layer routine used Is a two-dimensional one so that stagnation

point flows are not well described nor are cases where cross flows are

present. Further, the boundary layer procedure does not permit one to consider

flow separation, _. e.j it assumes separation does not exist. Although body

wakesare Included In the analysis It has been necessary to assume,In the

absenceof an understandlng at the proper criteria, that they all develop ac-

cording to the sameslmpllfled rules. As a result of these llmltations, so_

dlscretlon should be exercised In applying the results of the computation and

In selectlng cases for computatlon so that the governing assumptionsare not

greatly violated.

The dlscusslon below outlines the computational procedure employed. The

orlglnal program Is described in general so as to provide the reader or user

with a reference for understanding the modificatlons madeto It. The modl_i-

catlons are then discussed In detail. Also discussed In detail are the locally

developed elements of the program, In particular the boundary layer and wake-

bodycomputation procedures. Webegin with a presentation of a very effective

meansto Identify errors In the input data. The section concludes with a

discussion of the results obtained using the programto computethe drag of

three bodies: a sphere, a 3:1 prolate spheroid, and a Cessna182 aircraft

fuselage.

SPECIFICATION OF INPUT DATA WITH VERIFICATION BY PLOTTING When calculating the potential flow over a three-dimenslonal body, one is confronted with the problem of how to specify the shape of the body surface.

Obviously, one would like to have an analytical expression for the body sur- face; however, for general three-dimensional bodies practical analytical representations are usually impossible to obtain. The general practice is therefore to approximate the body surface by a large number of quadrilateral- shaped panels defined by a finite number of points in space; each point is presumably exactly on the body surface. If a computer is to be used to solve for the potential flow over these bodies, someone must input the three coordinates of each point; this is a laborious and error-prone task. In addition, each point must be indexed in such a way that the four corner polnts of each panel are defined in a clockwise fashion. Checking the input for errors is also a tedious process since detecting errors by simply scanning a list of the input data points is extremely difficult. To minimize such errors one would like a simplified, orderly procedure for inputting the data, and an effective procedure of finding errors before lengthy potential flow calcu- lations are made. Probably the simpliest procedure for inputting the data is to specify the shape of the body cross section at various stations along the longitudinal body axis. Among the most effective procedures for detecting input errors is to graph the points as viewed from various directions (See Figure 45).

While the above is true for any arbitrary body, in this report we are con- cerned only with aircraft fuselages which have a plane of symmetry along the longitudinal axis. In 1970 NASA, aware of the problems of specifying and checking numerical data, developed a computer program to generate the neces- sary instructions for automatic plotting of an airplane model in numerical form (Ref. 113). The plotting capability of thls program along with its simplified data input procedure makes it Ideal for producing a final, verified numerical data set describing an aircraft fuselage. The program also has the capability of displaying the complete aircraft configuration Includlng wings, pods, fins, and canards. Using it one may draw three-view and oblique orthographic projections, as well as perspective projections of an airplane. The program even has the capability of plotting stereo frames of the aircraft suitable for viewing in a stereoscope. Because of its versitillty the authors chose to use this NASA program to verify aircraft input data. A copy of the program, written for the CDC 6000 computer, was obtained from NASA Langley Research Center and then modified so that it would run on the IBM 370-165 com- puter at N. C. State University. User instructions, plotting software modi- fication procedures, a program listing, and several sample output plots for the modified plot program are given in Appendix D.

Example of a correct and an incorrect data Figure 45.

set for the Cessna 182 fuselage.

It should be noted that most of the modlflcatlons made to the original program were those necessary to enable the program to run on the NCSU IBM computer. These modifications included: (I) changlng the DECODE form of program Input to ordlnary READ input (2) removlng the OVERLAY procedure used to reduce program size durlng execution at NASA (3) addlng subroutlnes which could call IBM software plottlng in- structions w_ich were equivalent to the specified CDC software instructions" (4) assigning variable names to the Input and output file unlt numbers as well as to data storage flle unlt numbers (the user must there- fore only specify the approprlate flle unlt number requlred at hls computlng faclllty).

For more Information concerning the basic program the reader is advlsed to consult Reference 113 which provides a detailed descrlption of much of the program as well as flow charts of each important Program section.

While the Input to the PLOT program Is as conclse as possible, the Input to the NCSU BODY program (as well as the XYZ potentlal flow program) Is both lengthy and tlme consumlng since three coordinates and two indexes are speclfled on each point input card. Accordingly, a program which converts a data set for the PLOT program Into a properly indexed data set for the NCSU BODY program was developed; thus, once the plot data set Is verified, a correct data set for the NCSU BODY program may be generated. As dlscussed In General Program Theory, one criteria for obtaining a reasonable potential flow solution is that ad- jacent body panels must generally have areas whlch dlffer by less than 50 percent. Therefore, the CONVERT program was also designed to compute the area of each body panel and display these areas In an orderly fashion. Also, the Program displays the ratlo of the area of each panel to the area of the panel below It and the panel to Its right. These ratios slmpllfy the procedure of checking panel areas to see If they meet the crlterla described above. It should be noted that while the CONVERT program produces a data set for the fuselage, It wlll accept the input of a data set for a complete aircraft con- figuration and ignore the unnecessary Information. The program Input Is obviously the same as the input for the PLOT program and its description Is therefore not repeated in Appendlx E; however, the program llstlng and a tSlnce plottlng software Is different at almost every computlng faclllty, the user must elther provlde the original CalComp plottlng software for which the program was designed or provlde three equlvalent dummy subroutines as was neces- sary at the N. C. State faillity. See the Plotting Software Modifications sectlon of Appendix D for detailed instructlons.

Next: appendix. →

appendix.

sampleoutput depicting the capabilities described above are given in the

appendix.

By inspecting Figure D-I and Figure F-I, the reader will discover that

the bodyorientations, with respect to the input axis system, are different for

the PLOTprogramand the NCSU BODY program. In order to overcomethis difficulty

the CONVERT programalso contains the instructions required to invert the body

with respect to the X-axis and approximately center the body about the origin.

These instructions are necessary since the flow is in the direction of the nega-

tive X-axis for the NCSU BODY program.

In order to calculate the boundary layer over the body the NCSU BODY pro-

grammust have the properties of the flow field as well as the body geometry.

The CONVERT programwasdesigned specifically for any plot data set as de-

scribed in the original PLOTprogram, and these data sets describe only the

body shape. It is therefore necessary to insert a flow field parameter card

into the data set created by the CONVERT program before the data set is input into the NCSU BODY program. The card (described in Appendix F), which is inserted behind the first card (identification card), specifies the free stream velocity, density, and kinematic viscosity of the flow field as well as the reference area upon which the coefficients are based and an output control parameter. Failure to Include this card in the NCSU BODY program input will result in an invalid program execution.

GENERAL PROGRAM THEORY FOR INVISCID BODY PROGRAM The XYZ potential flow program, obtained from the Naval Shlp Research and Development Center (Ref. 94) Is a computer program for the computatlon of Irrotatlonal, incompressible potential flow about three-dimenslonel bodles of arbitrary shape. The solution method Is essentlally that developed by Douglas Aircraft Company in References 23 and 83. For a detailed descrlptlon of the program theory the reader is advised to consult these references; however, an excellent brlef descriptlon of the method Is given in Reference 94, major portions of whlch are excerpted below.

The body surface is approximated by a set of plane quadrilaterals, and the solution is constructed In terms of a source density on the surface of the body. Based on the assumption that the source denslty Is constant on each quadrilateral, a system of algebraic equations is Used to approxlmete the integral equation for the source density over the body. The source denslty in each quadrilateral is chosen so that the normal component of the veloclty is zero at one point in the quadrllateral. The matrlx equatlon is solved by a simultaneous displacement iteration scheme with a two-elgenvalue extra- polation procedure to speed up convergence.

The XYZ program received at N. C. State Is divided Into five basic sections Section I reads the input cards, computes the descriptlve parameters for each quadrilateral, and checks for errors. Section 2 computes the matrix elements in the equations for the source density and the velocity for polnts on the body. Section 3 solves the matrix equation for the source denslty. Section 4 computes and edits the velocity and pressure coefficient on each quadrllateral.

Section 5 computes the coordinates of the streamlines on the body surface.

The program actually solves a problem involving a stationary, three- dimensional body in a moving ideal fluid. The fluid Is assumed to have a uniform velocity at infinity (?®) which Is parallel with the x-axls of the body. The velocity potential @ satlsfles the followlng equations: V2_ =' 0 In the fluid (1) on the surface of the body _n = 0 C2) = -x.V -y.V - z.V at infinity (S) oo oo X Z Y

where n Indlcates the directlon normal to the surface. A solutlon to these

equations is constructed In the form of a source density (S) on the surface of

the body, (4)

@(p) = y_Su_r f S(q) I dA - x'V - y-V z.V

Bod ace r(p,q) q _x y z where r(p,q) Is the distance between the point p at which we are Interested In flndlng the potential and some other point q on the body, and A_ denotes the area of the quadrllateral contalnlng the point q. Note that Equations (I) and (3) are satisfied by _ as deflned by Equation (4). The boundary condltlon on the body, Equation (_), can be applied to,obtaln an equation for the source denslty (S).

ff

: -2 S(p) + JJ S(q) ;_ r---L---dA @np Body Surface Bnp r(p,q) q (5) -n "V - n .V - n .V px _ py ® pz x y z Slnce the surface of the body Is approximated by a set of plane quadrilaterals whlch are generated from input points (See Figure 46 ), In the limit the above equation requires that the body surface be represented by an infinite number of panels at each of which the flow normal to the surface is zero. It is important to obtain satisfactory results wlth a flnlte number of panels and to properly slze and posltlon these panels on the body surface. In Reference 23 Hess and Smith state that the proper dlstrlbutlon of elements over the body surface Is largely a matter of Intuition and experlence. Panels should be concentrated In regions where the flow properties, particularly the source density, are expected to vary rapidly. The method glves correct results for convex corners, but concave corners cause dlfflculty that may or may not be serious. Accordingly, they recommend that panels should not be concentrated near unrounded concave corners; but If the corner Is extreme enough to requlre rounding, a very great concentration of panels Is necessary in that region.

The panel sizes also play an Important role in determining the validity of the solution. Hess and Smlth note that If several small panels are in the vlclnlty of a large one, the accuracy Is that assoclated wlth the large panel. Thus, the slze of panels should change gradually when going from a region of highly concentrated small panels to a reglon of sparsely concen- trated panels. They recommend that the characteristic dimensions of a panel should usually be no more than 50 percent greater than those of adjacent elements. 239 X Figure 46. The approximate representation of the body surface.

The source density is assumed to be constant in each of the body panels and is computed by satisfying Equation (5) at one point in each of the quad- rilaterals. The polnt chosen is the panel centrold point. Thus, the integral Equation (5) is approximated by a matrix equation S i = >:CijS j. + V i (6) J = (I____) dA where Cij Qu _ rij "Oil : O, and Vo I - _ (nx'V _ + ny'V_ + n .V_ ).

x y z z

Equation (8) Is solved for S by the lteratlve procedure mentioned above

(see Reference 83 for more detalll. The velocity components at each centroid point are then computed from the following equations: (?)

VX i = _ vlijs J + v= J x (8) VY i = _ V2 + V j IJSJ y (9) v31js j + v VZl = j ®z where V21j Qu _y ( 1_)dA,rlj and V31j = Qu . _ (l_!_)rljdA The pressure coefficient Is then computed from these veloclty components.

An Integral over a quadrilateral Is evaluated by one of three methods, dependlng upon the ratlo of the dlstance of the Ith polnt from the quadrl- lateral to the maxlmum dlmenslon of the quadrilateral. If the ratio is greater than 4.0, the quadrilateral Is approxlmated by a monopole (as If It were concentrated at one polnt). If the ratio Is greater than 2.0 and less than or equal to 4.0, the quadrllateral is approximated by a quadrupole.

If the ratio Is less than or equal to 2.0, the Integrals are evaluated exactly. The approximate methods are used because they requlre much less time than the exact method. The evaluation of the integrals Is extensively discussed In References 23 and 83.

The on-body streamlines are computed once the velocities are known at each quadrilateral centroid. The streamline computation procedure used in the XYZ program is discussed in some detail in a report to be published by Charles W. Dawson and Janet S. Dean of the Naval Ship Research and Develop- ment Center in late 1975. This procedure may be outlined in the following manner: (I) The coordinates of a starting point within a particular quadri- lateral are specified.

(2) The two points at which the streamline, passing through the starting point, intersects the sides of the starting quadrilateral are found.

(3) The intersection point which is in the upstream flow direction is retained.

(4) A search is made of the adjacent quadrilaterals to determine which quadrilateral the streamline is entering in the upstream direction.

(5) Using this quadrilateral as a starting quadrilateral the point at which the streamline leaves this new quadrilateral in the upstream direction is determined.

(6) The above procedure, steps (4) and (5), is continued until the streamline reaches the nose of the body.

(7) The upstream portion of the streamline so traced is now defined by the coordinates of its intersection points on the sides of the quadri- laterals through which it passes.

(8) It should be noted that as each point on the streamline is found, the velocity at that point and the distance from that point to the pre- vlous streamline point are calculated.

(9) After returning to the original starting quadrilateral the same procedure is used to trace the streamline in the downstream direction to the body tail.

(I0) The arc lengths computed from point to point in (8) are then all referenced to the nose of the body so that the distance of any point on a streamline from the nose of the body is known.

GENERAL PROGRAM MODIFICATIONS Many of the changes made in the XYZ potential flow program as obtained from the Naval Ship Research and Development Center may be classified as general program modifications applicable to the entire program rather than a particular subroutine; these general modifications are discussed below.

Throughout the remainder of the text the program as received at N. C. State will be referred to as the XYZ program while the modified viscous flow program will be referred to as the NCSU BODY program.

The XYZ program required only minor modifications in order to execute on the IBM 370-165 computer at N. C. State. Four of the five separate sections of the program were changed to subroutines all of which were calle_ by the first section which was designated as the mainline. It was also neces- sary to modify the input and output file numbers as well as some of the data storage files.

In the interest of saving scratch file space, several of the files in the xYZ program were eliminated or reduced in size. In some cases the information stored on these files was put into a COMMON statement and thus made available to all five sections of the program. Table 3 gives a list of both the original file numbers used in the XYZ program and, if the information on these files was not commoned or deleted, _he new file numbers used in the NCSU BODY program.

Variable names were assiqned to the input and output file unit numbers (JREAD-input, JWRITE-output) and to each scratch file unit number used in the NCSU BODY program. The values of the unit numbers are assigned by specification statements at the beginning of the mainline of the NCSU BODY program (JREAD=I, JWRITE=3, KFILEI=7, KFILE2=8, KFILE3=9, KFILE4=IO, and KFILE5=11). For in- stallations having different input/output unit numbers and file numbers these specifications may be easily changed. The addition of a wake body to the original body required more body panels and therefore more panel geometry storage space on file KFILEI. To prevent recalculating original panel geometry, the appropriate information for the new quadrilaterals was calculated and then added to the original information by using a second file (KFILE2) for panel geometry Inform_tlon. The orlginal panel geometry whlch was unchanged was copied from file KFILEI to KFILE2, and the new information was then added to file KFILE2. This two-file procedure is used to prevent file READ-WRITE incompatibilities at other computing facilities.

In an effort to reduce the size of the XYZ program by specializing it to the problem of interest, several modifications were made. Since the program was to be used for bodies at zero angles of attack and sideslip, those portions of the XYZ program which calculate the contributions to the flow and pressure over the body resulting from the Y-flow and Z-flow components were removed when the NCSU BODY program was created. Thus, the free stream velocity in the NCSU BODY program was specified as -1.0 in the X-direction, 0.0 in the Y-direction and 0.0 in the Z-direction. While the potentlal flow calculations are cor- rectly made using just this unit velocity, the viscous part of the program

requlres the specification of the magnltudeof the free stream velocity/ or the

ReynoldsNumberin order to makethe boundary layer calculations. The magni-

tude of the free stream velocity must therefore be specified (see last

paragraph in this section).

XYZProgram NCSU BODY Program

File Number File Name File Number

I KFILE3 9

2 KFILE4 10

3 Information Commoned

4 KFILEKFILEI 7

KFILE2 8

5 (input) JREAD I (input)

6 (output) JWRITE 3 (output)

7 File Deleted

8 File Deleted

9 File Deleted

11 KFILE5 II

12 File Deleted

16 File Deleted

Table 3. Data file comparisonfor the

XYZand NCSU BODY Programs.

The maximum array size for the quadrilateral input arrays and geometry

storage arrays was set at 650. This maximum input array size coupled with the

addition of the wakebody, which uses part of the geometrystorage arrays, means

that the user should specify the original body using less that 600 panels. The

coefficients of local quadratic representation of the body surface, which were

stored on a scratch file as quadrilateral geometry information in the XYZprogram,

were deleted from file storage in the NCSU BODY program, thereby reducing

the file storage spaceand the size of the file input array B. The WS

array contained in the XYZprogramwas also deleted from the NCSU BODY

program, and the required control variables originally held in this array

were commoned or placed in subroutine argument lists.

The addition of the wakebody to the original body and the assumption

of a plane of symmetrynecessitated two important restrictions on specifying

data for the NCSU BODY program. First, the line of reference with respect

to which the Y-coordina#es of the body are specified must be the Y=Oline.

Second,the line of reference with respect to which the X-coordinates of the

body are specified must be a line parallel to a line from the nose of the

body to the tail of the body (see Figure 47 ). This last restriction was

incorporated in order to determine the direction in which the wakebody

should be addedonto the original body.

Z

Parallel Lines Figure 47. Orientation of body with respect to reference line.

In addition to those mentioned above, there were also other input and output modifications made to the XYZ program. Many of the input integers in the XYZ program were just specified as constant values in the NCSU BODY program: NSE=I, MIX=t50, ISM=I, EPS=O.O001, and ISP=O. The other input integers MIY, MIZ, IUCT, IPS, AND IPF were deleted. While the above input variables were deleted, it was also necessary to add the variables VINF (free stream velocity), VO (kinematic viscosity), ROE (density), REFA (reference area), and IWRITE to the NCSU BODY program input. The first three were added to s_Mply the boundary layer routines with the necessary information

to computethe ReynoldsNumber of the body. REFA wasaddedto provide a

reference area for normallzlng the lift and dragcoefficients. IWRITE was

addedas an output control parameter which has the value O, I, or 2. IWRITE=

0 gives maximum output while WRITE=2 gives minimum output. For an exact

description of the input requ red for the NCSU BODY programthe reader Is

referred to the User Instruct ons in Appendix F.

STREAMLINE MODIFICATION AND BOUNDARY LAYER CALCULATION The only practical method for predicting the viscous flow field about an arbitrary three-dimensional body involves the same procedure as that used for the viscous flow about two-dimensional airfoils. The basic steps for this procedure are: (I) obtain an inviscid flow solution for the basic arbitrary body, (2) obtain a boundary layer solution based on the inviscid flow solution, (3) construct a modified body by adding a wake body to the original body, and (4) obtain an inviscid flow solution for the body plus wake body to obtain the final pressures and force coefficients on the physical body. These steps represent an outline of the procedure used in the NCSU BODY program.

The basic method for obtaining the inviscid flow solution has already been discussed in the section General Program Theory For Inviscid Body Program.

Present methods available for obtaining a three-dimensional boundary layer solutlon over arbitrary bodies are very time consuming, require a large amount of computer storage, and are therefore beyond the scope of this report.

As an alternative, the authors chose to use two-dimensional boundary layer calculations along streamlines to approximate the actual three-dimenslonal case. Justification for this procedure has already been discussed in detail beginning on page 113 of the theory section. This method is ideally suited f_r use with XYZ since the program already provides the capability for computing on-body streamlines. Further, the streamline procedure calculates the absolute velocity and surface length from the nose for each streamline point. Con- sidering the approximate nature of two-dimensional boundary layer solutions along streamlines as applied to this problem, it is appropriate to employ rela- tively simple laminar and turbulent boundary layer calculation procedures. The boundary layer displacement thickness 6* and wall shear T are calculated at w each of the panel centroid points. Assuming T w in each panel is constant over that panel area, and given (I) the axial (X-direction) component of velocity from the potential flow solutlon, (2) the absolute velocity for each panel, and (3) the area of each panel, the skin friction drag coefficient is found by integrating the axial component of T w over the body surface. The values of 6* at the panel centroids are used to construct a wake body which is added to the original body. As in the case of the airfoil, the purpose of the wake body is to model the relief of the stagnation condition at the body tail accompanying the presence of the boundary layer (see page 128 ). The construction of the wake body is discussed In the next section of thls report. Once the wake body is generated, a new Invlscld solution for the body plus wake body is found; this solution represents the viscous flow solution over the original body. There is no i,terative procedure as was the case with the airfoil be- cause of the large amount of computer time required for each solution.

Thus far this section has presented a brief summary of how the vlscous flow solution over an arbitrary body can be obtained by modifying the Inviscld flow solution. Attention will now be directed to (I) the actual modifications made in the streamline section of the XYZ program and (2) the addition of the two-dimensional boundary layer calculation procedures.

Since the inviscid solution calculates the velocities at the panel centro_d

points, the appropriate boundary layer parameters are also estimated at these

centroids. This is accomplishedby the following procedure:

(I) For a given panel a streamline is traced, using the centroid point

as the starting point, from the body nose to three points downstream of

the panel centroid. The reader should note that this represents two

modifications of the original streamline procedure provided in the XYZ

program. First, in the XYZprogram, the coordinates for a streamline

starting point were read in by the user, while in the NCSU BODY program

the streamline starting points are automatically specified as the panel

centroid points; thus, the user no longer has the option of inputting

the starting coordinates for streamlines. Second,the XYZprogram

traced a streamline from the noseof the body to the body tail; however, since the boundary layer information is neededonly at the panel centroid,

computation time is simply wasted by continuing to trace a streamline

far downstream of a panel centroid. In the NCSU BODY programat most

only three points are traced downstream of the panel centroid point.

(2) A cubic spline curve of streamline velocity versus arc length is

fitted to the streamline points. This curve is used to generate a more

finely spaced set of velocity versus arc length points as well as the

derivative of the velocity with respect to arc length. This information

Is required by the boundary layer computation procedure. The cubic

spline curve was used because it maybe differentiated to give smooth

first derivatives from tabulated data.

(3) A boundary layer Is computedalong each streamline with transltion

fixed at the point on the streamline where the arc length Is 5 percent

of the total length of the body. If laminar separation arlses before

this point is reached, the programassumesthat turbulent reattachment

occurs at the point of laminar separation. The laminar bc_dary layer is

computedusing the Holstein-Bohlen formulation of the Karm_n_Pohlhausen

momentum Integral method (Ref. 65). If the velocity for the first point

on the streamline is zero then the laminar routine assumes stagnation

point starting conditions; however, if a nonzerovelocity is found then

flat plate starting conditions are used. These two types of starting

conditions are necessary since the potential flow programdoes not always

achieve a stagnatlon point (zero velocity) at the noseof the body. The

turbulent boundary layer method, derived by Goradia in Reference 31, is

a shortened version of the one used in the airfoil program (AppendixA).

Goradia's methodis designed to remain stable under the influence of

extreme gradients, both favorable and adverse, and provide reasonable

momentum and displacement thicknesses downstream of the turbulent

separation point. Consequently, turbulent separation is never predicted

with this method.

(4) The streamline values of 6* and T. at the point corresponding to

W the streamline starting point (panel centroid point) are retained.

These quantities are later used for the construction of the wake body and the calculation of the skin friction drag coefficient.

The above procedure, steps (I) through (4) are repeated for each panel centroid point except for the triangular panels at the nose and tail of the body.

Initiating streamlines from the centroids of triangular panels is omitted be- cause It was found that the streamline tracing procedure experiences great dlfflculty in the region where apexes of several triangular panels come to- gether (i.e. in the region of the nose or tail). Thus, it is necessary to approximate the values of _* and T w at the centroids of the panels using the following procedure: (I) For the triangular panels at the nose of the body, the values of _* and _L are taken to be one-thlrd of their respective values in the quadrilateral immediately aft of each triangle.

(2) For triangular panels at the tail of the body the values of 6* and T w are taken to be equal to their respective values in the quadrilateral Immediately preceeding each triangle.

The streamline procedure was modified in one final way which has not been referred to as of yet. In the XYZ program a search is made of all quadri- laterals to determine the next quadrilateral into which a streamline is traced.

In actuality, a streamline traced in either the upstream or downstream direction must enter one of five quadrilaterals adjacent to the quadrilateral it is leaving. Consequently, only these five quadrilaterals need to be checked to see which quadrilateral the streamline will enter. To reduce program execution tlme this modified search procedure is incorporated in the NCSU BODY program. Figure 48 illustrates the order in which each of the five quadri- laterals are searched when tracing in either the upstream or downstream direction.

It should also be mentloned that in the original XYZ program the stream- line variables were dime_sloned large enough to provide tor tracing 650 stream- line points. This Is well in excess of Tne number needed for the NCSU BODY program. The array sizes of the appropriate streamline variables were there- fore reduced In the NCSU BODY program in order to reduce overall program size.

2 4 . streamline

/

I b b r _: iine _ ' 5 3 trocin 9 in the down-stream direction tracing in the up-stream direction Figure 48. New panel identification procedure for tracing streamlines.

ADDITION OF WAKE BODY In order to predict the drag of an arbitrary three-dimensional body both the skin friction drag and pressure drag must be calculated. AS seen in the previous section, the skin friction drag coefficient is calculated by in- tegrating the wall shear over the body surface. Unfortunately, estimating the pressure drag using an inviscid flow solution technique is not quite as simple. Actually, the pressure or form drag is a relief of the rear stag- nation condition caused by the presence of the boundary layer. Thus, in order to estimate the pressure drag this viscous phenomenon must be correctly modeled In the inviscid flow solution. The authors chose to model this effect with the addition of a wake body. A detailed discussion of the effect of the wake on the pressure drag, the modeling of the wake with a wake body, and the procedure chosen to construct the wake body is given beginning on page 128 In the theory section and is therefore not repeated here. Accordingly, in this section, attention will be directed toward the programming aspect of adding the wake body to the inviscid solution.

(I) The authors chose to define the wake body as the last two sets of panels (modified to some extent) on the original body plus two ad- ditional sets of panels downstream of the original body (See Figure 49 ).

Body Woke Body Figure 49. Definition of wake body.

(2) For simplicity's sake, the wake body is chosen as a body of revolution with its axis on the llne joining the nose and tail of the original body as shown In Figure 47. The reader should note that the original body must therefore be input using a reference line parallel to the line between the nose and tall of the original body.

(3) The radius of the wakebody is chosen to decreaseexponentially

from the beginning of the wakebody to the end. The particular ex-

ponential shape is calculated using the average radius and initial slope

at the beginning of the wakebody as well as the total length of the

wakebody.

original body denoting ponel centroids

---:-"R. l @ o°

• I (_)

i ' I

Figure 50. Panel boundaries on the orlglnal body and the wake body.

(4) Notlng Figure 50 , the average radlus of the orlglnal body Is computed for the X-coordinate of the panel centroids at statlon 2 and is denoted by AVXCG. The average value is computed for the boundary layer displacement thickness of the panels at station 2 and Is denoted by AVDELS.

(5> The actual radius is computed for each body Input point at statlon I and is denoted by RI. The radius corresponding to each body Input point is computed for each panel at station 2 and is denoted by R2.

Twice the average boundary layer displacement thickness is then added to each of the R2 values computed.

(6) A value for the slope (denoted as SLOPE) at each panel around the circumference of the body is then computed from the equation below: SLOPE = (R2 - RI) / (XHOLDI - AVXCG) where XHOLDI is the X-coordinate of station I.

(7) The average slope (denoted by AVSLOP) is computedby summing each

slope previously calculated and dividing this sumby the numberof

points at station I. This slope is taken to be the initial slope of

the exponential.

(8) The location of the end of the wakebody, XINF, is then computed

from the following equation:

XINF = XHOLDI - AREAT / (3.14159*RAV)

where AREAT = 4.0*AREAAV*2.0*MMAXQD and MMAXQD is the total number of points around the half body.

(9) Since all the parameters needed to determine the exponential curve have been found, the X-stations at 3, 4, and 5 are chosen to give panel areas on the surface of the wake body which are approximately equal to AREAAV. The radii corresponding to these X-stations are then calculated using the exponential curve.

(10) It should be noted that if a non-negative average slope is cal- culated for the initial slope of the exponential, the average slope is calculated from the following equation: AVSLOP = - Absolute Value (RAV / (XINF - XHOLDI) ).

(11) Using the radii values at stations 3 through 6, the X, Y, and Z- coordinate values are generated for surface points on the wake body.

(12) Since the geometric information for the panels on the original body ahead of station I need not be changed, this information is copied from KFILEI to KFILE2 (see page 243)in General Program Modifications).

The geometric information for the wake body panels is then calculated and this information is added to KFILE2 in such a manner that body plus wake body appears as one.large pseudo-body.

(13) The pressure coefficients for the panels on the pseudo-body are calculated by finding a new inviscid solution over this body. These pressure coefficients are then applied to the corresponding panels on the original physical body along the normals of the original panels (see pages 127 - 132). The appropriate components of these pressure coefficients are then integrated over the body surface to yield a pressure drag coefficient and a pressure lift coefficient.

As an illustration of the shape and location of the wake body with respect to the original body Figures 51 and 52 are included. Figure 51 depicts a 3-I ellipsoid before and after a wake body is added, while Figure 52 shows the Cessna 182 which has an arbitrary cross-section.

o o_ t- O 0- L_ o_ r- 4- °_ r- .c o_ cO c m L.

r, DISCUSSION OF PROGRAM RESULTS To the time of the present writing it has not been possible to investi- gate the applicability of the NCSU BODY program to as many test cases as the authors would have liked. The greater geometric variability and intricacy characteristic of fuselages (in contrast to relatively simple geometry of airfoil families at least), the paucity of reliable experimental data, the extended development time required for the program, and finally, the cost of running the program (more than 10 times as much as the airfoil program) all served to limit the number of runs made using the final version of the pro- gram. Three bodies, however, were studied.

The first was a sphere. For a Reynolds Number of 2 million (based on sphere diameter) a drag coefficient of 0.041 was computed. This is about I/5 the commonly accepted value for the sphere at such Reynolds Numbers, The reason for the low drag value, however, is easy to explain. It may be re- called that the computer program adds the wake body only behind the last two sets of surface panels in the X-direction. For a sphere the wake obviously emanates from a much larger area than the last two sets of panels if one uses a reasonably large number of quadrilaterals to represent the body. During the course of program development it was readily demonstrated that beginning the wake body at the point where separation is observed experimentally does in fact yield the correct value of drag. However, most streamlined bodies produce proportionately smaller separated flow regions; since the program is intendea for use primarily with streamlined bodies, It was felt that the wake body formation procedure should attempt to model closely only the wakes of such bodies. One might also point out that if one better understood the re- lationships among the direction of and location of the flow separatlon from the body and the body geometry and flow Reynolds Number, then one could in- clude analytical versions of these relationships in the system of equations used to calculate the flow; the appropriate wake body would then come out as part of the solution. In the absence of such knowledge, we can do little more than choose a model representative of one class of bodies.

The second body against which the program predictions were tested was a 3:1 prolate spheroid. In this case a Reynolds Number of 6 million was used in the computations. With 560 panels the calculated drag coefficient was 0.094 With only iO0 panels the drag coefficient was Q. I09 indicating the effect which a poorer representation of the body has on the computed drag value. No direct experlmental data was found for this case but a 2:1 ellipsoid was found (Ref. Ii7) to give CD = .07. There is also some evidence that the 3:1 el- lipsoid should have a slightly higher drag because the surface area (skin friction) increases faster than the wake size, and hence, the form drag, diminishes. At any rate, the drag coefficient computed by the program for prolate spheroids with fineness ratios of 3 to 10 appears to be approximately correct.

The final test case was the Cessna182 fuselage. It was found quite dif-

ficult to represent such a body with 560 or fewer panels of nearly equal area.

As a result, while the rule of keeping adjacent panel areas within a ratio of

1:1.5 was honored, there is substantial variation in panel areas between the nose region (where many panels are needed to represent the geometry satis- factorily) and the aft cabin region (where large panels are adequate). This variation, It Is felt, could be responsible for some error in the computation.

The computed drag coefficient value, based on wing area and a length Reynolds Number of 30 million, was .01245. The body lift coefficient at the same con- dition was 0.00444. The computation, it may be noted, also assumes a tur- bulent boundary layer for most of the fuselage. It is therefore applicable prlmarlly to the hlgher speed portions of the flight envelope.

Of course no test data were avallable against which to compare these figures, but a compufatlon using the CD_ method (Ref. 2) gives a drag co- efflclent .00876, about 30% less than the value given by the NCSU BODY pro- gram. The CD_ method is probably the method most often used for preliminary deslgn in the light aircraft industry. It does not differentiate between lamlnar and turbulent boundary layers but nevertheless it seems to yleld drag values which match measured performance reasonably well. Thus It is to be expected that the drag value given by the NCSU BODY program is approxi- mately correct. A more detailed test of the ability of the NCSU BODY program and the other programs discussed in the present work to predict the ae_o- • dynamlc characteristics of actual aircraft is planned for early 1975. 'A ilght twin with an advanced wing design is being carefully instrumented for a series of performance and stability tests. It will be among the objectives of these tests to develop lift and drag flight test data against whic_ to compare the prediction of the programs given in the present work. Until the results of this and other comparisons are available, the authors suggest that potential users of the NCSU BODY program employ its predictions cautiously until Its range of validity is better defined.

r

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70.

Spence, D. A.: "Wake Curvature and the Kutt_ Condition". Journal of Fluld Mechanics, Vol. 44, 1970, part 4, pp. 625-636.

71.

Riley, N.; and Stewartson K.: "Trailing Edge Flows". J ou rna I of Fluld Mechanlcs, Vol. 39, 1969, part I, pp. 193-207.

72.

Preston, J. H.; and Sweetlng, N. E.: "The Experlmental Determlnatlon of the Boundary Layer and Wake Characteristics of a Slmple Joukowskl Aerofoil, wlth Partlcular Reference to the Tralllng Edge Region". A.R.C. R & M No. 1998, March 1943.

73.

Preston, J. H.; Sweetlng, N. E.; and Cox, Miss D. K.: "The Experlmental Determlnatlon of the Boundary Layer and Wake Characterlstlcs of a Plercy 12/40 Aerofoll, wlth Partlcular Reference to the Tralllng Edge Region". A.R.C. R & M No. 2013, February 1945.

74.

Howarth, L.: "The Theoretical Determlnatlon of the Llft Coefflclent of a Thln Elllptlc Cylinder". Proc. Rov. Soc. _, 149, pp.

558-586, 1935.

75.

Preston, J. H.: "The Calculation of Llft Taking Account of the Boundary Layer". A.R.C. R & M No. 2725, November 1949.

76. Preston, J. H.: "Note on the Clrculatlon in Clrcults whlch Cut the Streamllnes In the Wake of an Aerofoil at Right-Angles".

A.R.C. R & M No. 2957, March 1954.

77. Spence, D. A.; and Beasley, J. A.: "The Calculatlon of Llft Slopes Allowlng for Boundary Layer, wlth Appllcatlons to the RAE 101 and 104 Aerofolls". A.R.C. R & M No. 3137, February 1958.

78.

Bollech, Thomas V.: "Experimental and Calculated Characterlstlcs of Several Hlgh-Aspect-Ratlo Tapered Wlngs Incorporatlng NACA 44-Serles, 230-Serles, and Low-Drag 64-Serles Alrfoil Sectlons".

NACA TN 1677, September 1948, 37 pages.

79.

Dommasch, Daniel 0.; Sherby, Sydney S.; and Connolly, Thomas F.: Alrplane Aerodynamics. Pitman Publishing Corporation, 1967.

80.

8hateley, Ishwar C.; and McWhlrter, Jack W.: "Development of Theoretlcal Method for Two-Dlmenslonal Multi-Element Alrfoll Analysis and Design". AFFDL-TR-72-96, Part I, August 1972, 366 pages.

81. Hess, J. L.: "Numerlcal Solution of the Integral Equation for the Neumann Problem wlth Applications to Aircraft and Ships". SIAM Symposium on Numerlcal Solution of Integral Equations with Physlcal Applications, Madison, Wlsconsln, October 1971, I08 pages. Also Douglas Aircraft Co. Engineering Paper No. 5987.

82. Hess, J. L.: "Higher Order Numerlcal Solutlon of the Integral Equation for the Two-Dimenslonal Neumann Problem". Computer Methods In AppIled Mechanics and EnQIneerlnQ, Vol. 2, 1973, pp. 1-15.

83. Hess, John L.; and Smith, A. M. 0.: "Calculation of Non-Liftlng Potential Flow about Arbitrary Three-Dimenslonal Bodies".

Douglas Aircraft Co. Report No. E. S. 40622, March 15, 1962, 177 pages.

84. Labrujere, T. E.; Loeve, W.; and Slooff, J. W.: "An Approximate Method for the Calculation of the Pressure Distributlon on Wing Body Comblnations at Subcritlcal Speeds". Publication of the National Aeronautical Laboratory (NLR), Amsterdam, Netherlands.

85. Loeve, W.; and Slooff, J. W.: "On the Use of Panel Methods for Predictlng Subsonic Flow about Aerofoils and Aircraft Configura- tlons". NLR MP 71018 U, June I0, 1971.

86. Keith, J. S.; Ferguson, D. R.; Merkle, C. L.; Heck, P. H.; and Lahtl, D. J.: "Analytical Method for Predicting the Pressure Distribution about a Nacelle at Transonic Speeds". NASA CR-2217, July 1973.

87. Hess, J. L.: "Calculation of Potentlal Flow about Arbitrary Three- Dimensional Lifting Bodies". Douglas Aircraft Company Report MDC-J5679-OI, October 1972.

88. Glesing, J. P.; K61m6n, T. P.; and Rodden, W. P.: "Subsonic Steady and Oscillatory Aerodynamics for Multiple Interfering Wings and Bodies", Journal of Aircraft, Vol. 9, No. I0, October 1972, pp. 693-702.

89. Woodward, F. A.: "An Improved Method for the Aerodynamic Analysis of Wing-Body-Tall Configurations In Subsonic and Supersonic Flow.

Part I - Theory and Application. Part II - Computer Program Description". NASA CR-2228, May 1973, 126 pages and 315 pages.

90. Wldnall, Shella: "Subsonic Aerodynamics". Astronautics and Aero- nautics, April 1973, pp. 14, 21, and 28.

91. Otto, H.: "Calculation of Nonlinear Lift and Pitching Moment Coeffi- cients for Slender Wind-Body Combinations". Journal of Aircraft, Vol. II, No. 8, August 1974, pp. 489-491.

92.

Roskam, Jan; and Lan, C.: "A Parametric Siudy of Planforrn and Aeroelastic Effects on Aerodynamic Center, _- and q-Stabi ity Derivatives". NASA CR-2117, April 1973.

93.

Bleekrode, A. L.: "A Survey of Current Cot location :',!ethoc.s n Inviscid Subsonic Lifting Surface Theory. Part I! - £_lculational Aspects of Solving the Large Systems of Linear Algebraic Equations on a Digital Computer". Publ ication ot NLR Ams!erdam, Netherlands.

94.

Dawson, Charles W.; and Dear:, Janet S.: "The XYZ Potential Flow Program". Naval Ship Rer_e_rch _nd [_loveloDrlon? (.enter, _!etheSdd, Maryland, Report 3892, June 1972, 65 pdges.

95.

Hopkins, E. J.: "A Semi-Empirical Method for Calculating the Pitching Moment of Bodies of Revolution at Low Mach Numbers". NACA RM A51CI4. 1951.

96.

Goodson, K. W.: "Effect of Nose Length, Fuselage Length, and Nose Fineness Ratio on the Longitudinal Aerodynamic Characteristics of Two Complete Models at High Subsonic Speeds". NASA Memo I0-I0-58L.

1958.

97.

Pitts, W.; Nielsen, J.; and Kaattari, G.; "Lift and Center of Pressure of Wing-Body-Tail Combinations at Subsonic, Transonic, and Super- sonic Speeds". NACA TR 1307. 1957.

98.

Donovan, A. F., and Lawrence, H. R., editors, Aerodynamic Components of Aircraft at High _, Section C: "Interaction Problems" by C. Ferrari. Princeton University Press, 1957. pp. 281-552.

99.

Cebeci, Tuncer; Kaups, Kalle; Mosinskis, G. J.; and Rehn, J. A.: "Some Problems of 1he Calculation of Three-Dimensional Boundary- Layer Flows on General Confirurations". NASA CR-2285. July 1973.

56 pp.

100.

Henrici, Peter: Elements of Numerical Analysis, John Wiley, New York, 1964. 336 pp.

101.

Allen, H. J., and Perkins, E. W.: "A Study of Viscosity on Flow over Slender Inclined Bodies of Revolution". NACA TR 1048. 1951.

102.

Smetana, F. 0.: "Investigation of Free Stream and Stagnation Pressure Measurement from Transonic and Supersonic Aircraft. Final Report."

WADC TR-55-238. April 1958.

103.

Smetana, F.O., and Knepper, D.P.: "Toward Simpler Prediction of Tran- sonic Airfoil Lift, Drag, and Moment".Journal of Aircraft, Vol. 10, No. 2, Feb. 1973. pp. 124-126.

104.

Truitt, R.W.: "Shockless Transonic Airfoils," AIAA Paper 70-187, New York. 1970.

II Sinnott, C. S.; and Osborne, J.: "Review and Extension of Transonic 105.

Airfoil Theory". A.R.C. R & M 3156. 1958.

Thompson, N.; and Wilby, P. G.: "Transonic Aerodynamics". AGARD Con- 106.

ference Proceedings No. 35 (AD-685270). September 1968.

07. Riger, D. D.; and Rose, N. J.: Differential Equations with Applications, McGraw Hill Book Co., New York, 1968, pp. 545.

08. Milgram, Jerome H.: "Section Data for Thin, Highly Cambered Airfoils in Incompressible Flow". NASA CR-1767, July 1971, pp. 72.

09. Cebeci, T.; Mosinskis, G. J.; and Smith, A. M. 0.: "Calculation of Vis- cous Drag of Two-Dimensional and Axisymmetric Bodies in Incompressible Flows". AIAA Paper 72-I, pp. If.

I0. Cebeci, T.; Mosinskis, G. J.; and Smith, A. M. 0.: "Calculation of Separation Points in Incompressible Turbulent Flows". Journal of Aircraft, Vol. 9, No. 9, pp. 618-62_, September 1972.

II. Granvllle, P. S.: "The Calculation of Viscous Drag of Bodies of Revo- lution". The David Taylor Model Basin Report 849. July 1953.

12. Von Mises, Richard: TheorE_y of Fli___h_, McGraw-Hill Book Co., New York.

1945.

13. Craidon, Charlotte B.: "Description of a Digital Computer Program for Airplane Configuration Plots", NASA TM X-2374, September 1970, pp. 84.

114. Klunker, E. B.; and Newman, P. A.: "Computation of Transonic Flow about Lifting Wing-Cylinder Combinations". Journal of Aircraft, Vol. II, No. 4, April 1974, pp. 254-256.

15. Ahlberg, J. H.; Nilson, Edwin N.; and Walsh, Joseph L.: The Theor_ o_Lf splines and Their Applications. Academic Press, New York , 1967.

16. Marshall, F. J.; and Deffenbaugh, F. D.: "Separated Flow Over Bodies of Revolution Using an Unsteady Discrete-Vorticity Cross Wake: Part I - Theory and Application; Part II - Computer Program Description".

NASA CR-2414 & 2415, June, 1974. Part I - pp. 89. Part II - pp. 152.

17. Rouse, Hunter: Elementary. Mechanics o_f_f Fluids. John Wiley and Sons, New York, 1947.

APPENDICES

Next: APPENDIX A-Two-Dimensional Wing Aerodynamic Characteristics Program →

APPENDIX A-Two-Dimensional Wing Aerodynamic Characteristics Program

APPENDIX A-Two-Dimensional Wing Aerodynamic Characteristics Program

User Instructions

The program is written in FORTRAN IV and is designed to run in single

precision on an IBM 370-165 computer with an average execution time of

20 to 25 seconds for each angle of attack. The program calculates the

two-dimensional viscous flow solution of an arbitrary airfoil and evaluates

its aerodynamic force and moment coefficients. The program requires the

specification of the following input data:

(I) The 80 characters of the array TITLE which are used as a header

for identifying output. Since the program allows more than one

airfoil to be analyzed in a given run, TITLE is used as a control

variable to end execution. Termination of execution is achieved

by following the last set of airfoil data to be analyzed by a

title card having only the word END in the first three spaces

(see last card of the sample data set in Figure A-2).

(2) The number NXU of specified upper surface airfoil coordinates, the number NXL of specified lower surface airfoil coordinates,

the control parameter IWRITE, the control parameter IALPHA, and

the control parameter IPUNCH. The largest allowed value of either

NXU or NXL is 65 and no more than 100 total airfoil points may

be specified (NXU + NXL _ 100). The control parameter IWRITE

(either O, I, 2, or 3) determines the amount of output desired

for each set of airfoil data. IWRITE = 0 yields the maximum

amount of output while IWRITE = 3 yields the minimum (examples

of all the IWRITE options are given in Figure A-3 through Figure A-6).

The control parameter IALPHA specifies the line of reference for

the angle of attack. The line of reference is the x-axis of the

reference system of the input data points. For IALPHA = I the

line of reference is the longest chord line of the airfoil. Thus,

if the user knows the location of the chord line of the airfoil

and specifies the airfoil data points so that the chord line is

parallel to the x-axis of the reference system of the input data

points, he should use IALPHA = O. If the user is unsure of the

position of the airfoil chord line with respect to the x-axis of

the input data system, he may choose IALPHA = I, in which case,

the program calculates the longest chord line and references

the angle of attack to this line. The user will find that for

most cases he will want to use the IALPHA = 0 option. For

further explanation of this option see pagell2. The control

parameter IPUNCH gives the user the option of obtaining punched

data (lift, drag, and quarter-chord moment coefficients for each

angle of attack) which may be used in the program designed to

estimate three dimensional aerodynamic characteristics of wings

(see Appendix C). IPUNCH = I gives punched output while the

default IPUNCH = 0 gives none.

4.

(3) The NXU values of the abscissa XU for the upper surface input

points. The XU array should be monotonic increasing from airfoil

leading to trailing edge with 8 points per data card.

(4) The NXU values of the upper surface ordinate ZU which correspond

to the XU values. The ZU array is specified with 8 data points

per card.

(5) The NXL values of the abscissa XL for the lower surface input

points. The XL array should be monotonic increasing from airfoil

leading to trailing edge with 8 points per data card.

(6) The NXL values of the iower surface ordinate ZL which correspond

to the XL values. The ZL array is specified with 8 data points

per card.

(7) The number NA of angles of attack to be read for which a solution

is desired. NA must be less than or equal to 10.

(8) The NA values of angle of attack, ALPHA, given in degrees, 8

values per data card.

(9) The number NM of free stream Mach numbers to be read for which

a solution is given at each of the NA angles of attack. NM must

be less than or equal to 5.

(10) The NM values of free stream Mach number, FSMACH, 5 values per

data card.

(11) The reference chord CREF in feet and the scale factor SF. The

reference chord is used to non-dlmensionalize all of the output.

The scale factor is a multiplicative constant used to convert

the values of XU, ZU, XL, ZL, XTRAN, and ZTRAN to feet. It

would be advantageous for the user to input the airfoil

coordinates as percentages of the reference chord so that CREF

and SF will have, the same numerical values.

(12) The stagnation temperature TO in degrees Ranklne, the Reynolds

number RN in millions, the Prandtl number PR, and the heat

transfer factor KF. Reynolds number should be calculated based

on CREF, and since it is read in millions, RN = 3.0 corresponds

to a Reynolds number of 3,000,000. (It should be noted that this

Reynolds number specification differs from that used In the

NASA program which used millions per foot.) It is recommended

that a value of 1.0 be used for the heat transfer factor. For

cases where heat transfer effects may be important, the user

should consult Reference 32 to determine an appropriate value

for KF.

(13) The control variable LTRAN which determines whether boundary

layer transition is free (LTRAN = O) or fixed (LTRAN = I), the

x location for transition XTRAN, and the z location for

transition ZTRAN. If free transltlon (LTRAN : 0) Is used both

XTRAN and ZTRAN should be specified as 0.0, and the program will

predict the location of the transition points. It should be

noted that if the flxed transition option is used the program

will still use its own predicted point of transltlen If it

occurs before the specified transition point. Since transitlon

must be specified on both surfaces, two transition cards must

be read (upper surface card flrst).

Statements (I) through (13) represent a complete set of data for a

particular alrfoll. The format specification for thls data is given in

Figure A-I. A sample data set of the 23012 airfoil with IWRITE = 3

optlen is shown in Flgure A-2. The output of this partlcular data set

Is shown In Figure A-3, and In addition, examples of the other IWRITE

optlons are given In Figures A-4, A-5, and A-6.

20 A4

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Flgure A-I. Format specification of Input data for the 2-D characteristics

program.

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Figure A-2. Example data set for the 2-D characteristics program.

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Sample Output

eeele CISE impur leee.

l+aCl Z+o12 llmF01L+ALpI+A.01RN-3.0rlIICH I+Q..0.ZlIW. IIIt-0 NIU mxL lw_Ivt o 11 I| zu • 0°0 0+L25Ccl0f-01 O.eSC_OOE-O! o.50_ool.-Ol O.;,e0oG01-ol 0.104)OO01 00 O.t$00_ O00o_OW _ o.250001_ 00 0.30000_ Ga o._000OOl O0 o.$0t_001 O00._001_0f _ 0.?001_01 00 0ot0_ 00 O._(_OI_ O.4_00OOE O@ O. LOOOOOE 01 ° .

ZU • 0.0 0.26700_-0t 0._610001-01 O._gtOOO_'_L o.seol_e.-o| o.e_,2_4e-oL o.'PLeoe._-oL • _OI_M Ol o._6oooo!oO| o._5_ooi_-¢10.?I_O0OE-Ol o.61t*oo01-oL o.5_r000e-ol 0._oe-ol 0._oel_-ol o°|el_-Ol XL • 0.0 0.|Z_0001-01 0.as00_e°0! 0o$O_OE-OI O.Y_000_°o_ O.lOGOl_e i_ o°t_ oo O.e0ON o._5ool_e 0o o.3oo_o_ co o._,coo©ol_ oo o._o1_oo! i_ Ool, OOC_O_ i1_ o.To_o_ _ 0°IOIN_M O00.mM Oo_5OOOOe oo o.|_! ol z_. o o.o =o.|z_o_e-oL-eot _lol_e-ol'_-_oool-ol°o-|iLooo_'_|-°'_ez°°°l_'°l°°'_'l_'°l'°'_el-°_ __. _ _llol_e°o i_o. ,_6oooe _ ot _ Oo _loooe_o 1..o o _ t ?oooe°ol..o. _6,_oe.o i.o. Io_o_° ol-o o _ 16o_ oOl-O. |e eol_. -ol °o. Toooooe-o_-c. I Jool_e- o2 o°o mm • $_ = O.lOOl_Q! o| ro • o._1_ o_ IN . o._oo_oe ol Pe o o._?o_o| oo RF • OoLI_OOM 01 cJep = o.lc._000! el Ltm_ 0,0 0.0 uPplm SUtF*CE _ 0.0 0.0 L_Em SulFice Nit+l+ 2_01_ AIQF01LIAL_'I+I-0/IIN*_oC/_CI4 ll0°-0.1/Iklllf|"0 IN_Ul *I*F01L POINTS _m+em SUSPICE t_lm SUmFlCl XU ZU XL ZL 0.0 0.O 0.0 0.0 0.011g00 O.O26?OO O°O125OO -0.011_ 0.02_000 0.0e_100 0°OZeC_O -0.ml?10_ o.oe_o¢ 0.0_I0_ 0*0900_H_ -o.0eel_0 0.075_00 O.O51OOO 0.0_5000 -O.Oe61C_ OolOO@OO 0.06_30e 0.I000(_ °o.oeeeoo o.L_0oeo 0.0_|_00 O.15OOOO -o.o_e_3_ 0._000¢0 0o0_$000 o.e_oo -0.03e70_: o.3ooooo o.o_eeea 0o_00 °OoO_+e.N o.5@ooo@ 0.061_00 0.5_._0_ -o.o_IT_ 0o70000_ 0.0*360_ Ooy_ -o.oee_ 0.i0_@ o.o_oeoo Ooe_ -o.olL_ 1.0©oooo 0.00|i_ tou -0._.:I_0 N_¢I I]Oll III+OILIILImI.OIIMIe*CI_IICH I_..O.211MIIIT|"O OlSt_IIUTt© IIRF01L @01mT$ uPpeR SURe,C| Lcr_I_R SU4telCe XU Zu XL ZL o.o015ez o.oo+zl) 0.q_+99_ -o.ool)ol 0.011_ o.oese65 o._oy_oe -0.011_J0 0o0_1| 0.0,_5T6 0.e116_ -0.01046e 0°11_524 0.0815_9 o._3_eee -0.01_?|?

o.eoz??_ 0.075110 0.5t71_6 °0o0_0_?1 o°e?31e_ o.o?_e@l o°3_l_oe -0.g_$_11 0 .*ol_e| o. 0_071_ o° )03_6 --OoO_46ee 0o_4|15 OoOe_?oe o.16ee?_ -0.0+)60_ o._lOleO 0.01e11_ 0.15_T0$ -0o0_11_0 0.$1Tii6 0.060011 o.eol??_ -0o0_4|_ o°71515| OoO_t??o 0.07_5el -0°0114_0 0._0750_ OoOle6_e 0.011_ -.0 °Ol190e o._$e; OoO08eeL 0o00_1_ -0 °00_401 - o 0.t99_4 o.ooL eOl 0.001_6z 0 0_|_1 0°0 0o0

Sample output of the 2-D characteristics program with IWRITE=O

Figure A-3.

(note that only upper surface invlscld and boundary layer

solution information is shown here).

ImVl_Cl0 FL0_ $0LUIION SlCA li01| llm;01L/ALPNI-0/,S*)*01_ICHMC.-0.IIIVRIII*0 _C_ UUNH_ * 0*Z¢000 a_L| 0f ITII(_ - _M! S_IFIGI lllmlll0M IWIII! 0 X ! IV/milK. I VlV0 ICOll_. nL Cp 0°OO116 0.¢¢411 0.04)19 0.04J_g 0.00151 Z.00I|4 0.i0$01 0.01_I$ 0.,6101 0.6511_ 0.0_L)I 0.?q6tl 0.011_I 0.0_Sll 0.8.140 0.IlqlI 0.16?Tl 0oZ_) 0o0|40! 0.0Pl_q | o ¢_14 1.0964T 0.J I_T o0. IOL 14 0o0M*_ @.04411 hLll4t I. 11T)6 0oli?16 -0.4011S 0*0_YSl 0*0SlZ| 1.Z|ISg |o141|q 0of*q00 -0.14O)_ 0.07Tie 0.0H?? loZ6eY_ I.ZYTI4 O.151611 -0._|II?

0.I_I|I 0.06411 I.ZI_) 1.2eI_0 0.210)I -0.610It Io IIISl 0.06i$l L • l_)I |. ](1146 0o1614Z -0. tq_1 ) I.|4711 0.4;160 |.II6C0 I._T$ l.ll_I -I.ITIT?

I.ITIII 0.0?lqJ I._6_41 h Z;T04 0.11+06 -O.61611 I.IIIT? 0.0TS 11 |o l_4t) I* ISI01 0ol_0_I -0o _)6 I.II4TI 0*@T$11 IolISlS I.I_IZ_ 0.I_4_6 *0.$|S?I 1.16Ill 0o0TIqq |.IIII) L.I|II) 0.I4411 -0.481T) 0.N)44 0.@_I41 1.15_01 h I0_44 0.141I_ -0.4,|_ 0.1)II_ I.¢_4_I _.1001? Lo I_)_ O.11411O -0.4117) 0.1T|I? 0.4_lq@ I. IIt_ I. II6T_ 0.1)YT$ -0o_I+0 0.+I144 0.CTOTI LoI_I 1.17_06 0._)61I -o.ln67 o._Ii 4ooI?_i L. l_|IO 1.1474s o.II_i *o. )|_I o.41_1_ o.oliiI [ol_)_i ioO_ o.llglt -o.Io_?

0.$ITI| 0.0600J _.011Sl 1.01_ 0.11T0+ *0oi?$T0 0.S_Sl lo01Ilq I. 1Ol+l I. 10_04 0.III01 -0.Z_4I 0.1_l_l 0o@_Sll I.L|_$I h11_)J 0.II_6_ o0.14TYY 4o4|I)_ 0.0IISq I. I0_)4 I* 10_T_ 0.III |l -0.11(14)'/ 0.671_ 4.046_I 1.10114 |*014|$ 0.116U -0.1?10T 1.71511 0.04|IT I.OI+lY | .06S6| 0.11114 -0. _)S_I 0.T6466 0.01546 I._T|_ 1.041_4 0.|_ITT -0.0_ql I 0olII_@ o.o|_e 1.01170 I.O1911 o.I0_11 -0.oIe4_ 0oIIOT4 @.0_14_ |.0_leI |.001|T 0olOtI$ -0.010_L 0*_?Sl 0.01S61 0.ql$1_ 0._||8) 0. |_IS_ 0ol)|q_ 0.qSlS_ e.¢01tS 0._)_* 0._+l|I 0.Ln)_ 0.1|L_I 0.e_t_ 0.001I¢ 0.eZlTi 0.ql0ZI 0.1I)q4 0o ISI)0 LANIM_R 104_10AIV LAYlR $_SllitV NACA l|0l| AIIF01LIILI_AI0/tRI|.01NACN i0.-0.111MNITII0 lllllll01 ItllH i Slllllll{l Yl+PlIllill • Ill*It 01illlS Rim, Ill ST&GNITI_ HIIII_II • ,t0.111 LI/_0 il FUISTJIIa_41111 . 0.1K¢0 II_F01L ¢_I_ l.I010_ PI • 0.?_II _III YI_ISP|t FICIm K - I.¢0_I0 SIPlIArI01 ¢0tmILlll_ NO* • 0.06_37 SPIII W I0_0 - |I16.t19 FIII/NCN _l_Inall¢ Vl$¢mlT_ • e.0_00Y+| N PTIIIC 611Ll If IYTI_ ¢ILPIMI @.0 H0_IIS STIINaTI0_ aT XI¢ - 0.001|06D STIGI_II0_ IT IIC I/C SIC N 0_I$e¢) H T_|YlIC 0IL$I¢ 01LY_S¢¢ CP CP 8*NIIll 0.II16_? I*_0|il4 Zl. ell)IS _.I0_?|T 0.00_tq 0*0_I Q _I 1.11114 o o l.ellll4 0o01101l 0.0_II|4 T.44_I_ I.$064100 0.00_011 0om$ 0.0_167 0.T_II 0.4|1e14 1.0144TI 0.11T_I_ _.|le_6 l._gk_l 0.000_16 0olli0_ 0o01_lI4 0o_0_I0 o.|I_411 IoJl6_0 I._14_I 0o00_19 IoOiI_T| 0.00_I11 *I.IIII_ 1.0)_ll 0.0ill|? e.l)?lll 0o I|SNI I._III o.0ol0|_ 0.0100_ 0._II_ o0.4111S 0.0S?$|4 0.0_T?I1 0oI_©0 0o_S_III Z._II_II 0.0000+y 0.11111T 0.II_11 *0+ I+014 0.4T?I_I 0.0_llll e.II411? 0.ZlSl)_ _._$T_L 0.00_0_ l._01|IY 0._I)19 o0.6|II?

l._leIll 0.11IIll 0._I0]]] 0.116IT_ I._01H 0.00_064 0.0001IT 0.IIII16 **0 60116 0.111SI_ 0o14411S e.I_14|_ -0.010q_) _.4)IIe? 0.0010T) 0.m111 0. lill0S o0._I| 0.1*?l|l 0o16_?11 0.Zlq611 o0. _)07 Io_TS 0.001014 0oI001_I 0.001141 -1.61|_ 0.I_16_$ O*194165 0.I_6@S6 -4o|I)_q) 1.18511) 0.0000_6 1.01011e 0.14_916 -1.61616 0oI01TT4 0.I|$)00 0*IH_?T -0*L$11L$ Z.|_I|T 0°000110 0.000161 0.NI_ -I. l_k16 I*I)4_II 0.|IT)IT 4.Z46eSq o0.10_Y16 _.)?_$T 0.0_0111 0.0111_) 0.III_ -I+$1IYl 0.IIII_ 0.I_0_0 0._411I -0o011|0T Z.)?T6)S 0.00011_ 0.000Ill 0o0011_ o0.40I_| ICIII/C * 0.ll_?l_ nICAIT . 4SI.51 STtA_ • 0.ZI_0LISq _Isam * 910.+0 I_IT& II¢* 0.00_I Ill_ INITIIILIIY Tt_ISIVlON NIS 0(¢_|0 _! X/C • @.|61)q0 SIC - 0.ZIS011 I_I_LII! 10W4OImY LI_I! SmlIY FOIl I_JIVlLIN! IIRFOIL 160_AOll niT'Oil _I INII AltPOILI_L_-OII_o).OIIC_ _0.'0*Z_IMnlTI-0 ITlllllm lillq • $llllITl01 II'PlIITml - Ill.l! Olilll| nlli lM ITi0mlll0_ PtIISUll - *ltO*61l LIIIt +V flllillllM NI(NIRIIIII 0.|llll IltPOlLmO 1.00010 +t IIVlILN mU o ).IN_ NILLI0_ PmIIIOIL mqlt - o.P_m lml_Irlm +Olml_ sic • O.lllll mlill/C e.ilOll fruit, l_Oil+ FOff_ll PlCIOI I.IS+?+ o.o OlmllS I/¢ SiC m 0_IISICI H lHItd_C 0.I'lL SIC H/I/I/C IF CP i*161110 +*llS011 0.141614 -0*@MqI? |.$S4?45 O.0001H O*001111 +*1611?I O.l_Im 0 .Ill111 -0.0111+? l*$mll 0.00014Y 0.mlOl 0*lill_l O.ml_ -I.+l|I)| i.lOHi6 0*)11061 0,141+14 *e*OTOL5$ 1,131011 0.00_116 O*100_ 0*0_IM+ 0.0_414 -0.44_ O+)H_q) i.lil_) 0.IHI+I -O*illl@+ l*lllSll 0,0001J04 0,000_$ 0*04HI41ST 0*l_lSqll -O, ii)_lt O*Illl61 0*Ifl_l +.llTTAT -0.0_I+4_ I*51_H 0,04)O|?1 0.100S6I 0*001T4T 0.10l_5 -i* tllt4et 0.411_II O*qlllt4 0.I]II11 -0*ll0tl+ I.HI61?

0*0_0ml 0.04H_16 0.0_ITI4 0*mill -0.111661 0*44411I O,4iTOlI i*llqlll -O, 11146+ l*]tOllS O,0_OS4T il000?41 0.mT_l 0,+lit *l. IlSil6 O*4MI_I O.IO|I+t 0.11qII4 -0*1161_¢ l.]_i_l 0.0006IS O,IKl04)_ 0*mill O*OQMIT t 1116 _1 O*Slllll 0,S40415 O*lllO*l O*O_SlJ i.)JlSq_J O,00OTIl 0.ml0_i 0.0_?lil 0._01611 i*IHII4 0*ITtlSl i*l|10|l 0.011741 1.11141i 0,O00TIt 0*0010l) 0,0076?0 0.00)914 -I.IIHII OmSIIIll 0.616416 O*llllll -I*001HI l.$m 0.010ill 0.1_1011 0.0_llll 0.01liT4 0.611161 O.iIIHI 0.II11I| -0.01SiSl |*I06TII O,D4H_li 0*HIll0 0.0_4_I 0.DO$1_1 -lilly l.lllill O.614IPI 0*llllll -0*0_Iil l*l_ISIl 0.Nlm4 1.001m o.olonl o.oossM t*11Jlll 0,T|+HI I*lllill *+*OlTJSl I._ITIIT 0,_1171 O,llllll O.O11411 O.lllilll +.?141_ 0*?IIHI 0.II+??¢ -I.01466| l.mJM 0.001il I*_OITII 0*011161 0*01Jill -o I,I11611 O.ll?+l* 0.10tqll -0,011Y+! t, _OTmS o.001+_ O*Oll_ki_ 0.014111 0*IOHM -I. IlSe_l O,It014+ 0.I161|| 0*10114q -0*0illS) L*ll04+l 0*001ill O*011Ll_ O.OlSl_ O*_ITll l*_l_l O.lllill 0.1qll+0 -0. L_)I@I I. II1161 0*00illl 0._1411 0.OlY_) O.l_illOl I*t1111? t.51_11) O,lltl+l -0. |14qt@ I, 11_16) 0*0011Sl O*lilI?l e*010111 O*011l_0 i. II l_ll I*I_ l.01101T O*ll]q44 -0.01410S 1.3_II01 0o00_)ll O*_lllI 0.0111_) 0.0_I011 I. Illltl F Igure A-3. Continued.

LAM|NAR 001JNOAAV LAYER SUGARY NACA 2]0]2 AINFQ|LI&LPttA'O/_N-3*O/RACH NO.-O.2/IVR|TE-O IT_N_TIOIt It_lniJn 4 TUASL.4.ENT BO_NOAIIy LAyEE SUN_&RY FOR EQUIVALENT AIRFOIL U_pEX su_&ce srAGn*rlo_ _EnPEn_lu_qE - Sle._S o_G:ees _:#KI_E srA_k_T[O_ _essuse . 44To.teo Ce/sQ F_ mETNOLOS _UMS_m - _.OOOaO mlLLIO_ P_ANOTC _U_n ° 0o_7000 (IMIrlJL W_rU_ _ICRNeS$)IC o Q.0_|] INIr. I_COnPI. F0M _ACTOI I.)S_!

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Figure A-3. Continued.

LONGEST CM_RDLINe SYStEm BASIC AEFEflENCE SYSTEM XI¢ Z/C XI¢ l/¢ S/¢ ¢P ¢_ OILra$/¢ VlVO 0.1_0_ -O.OISI6 O._ea_4 -O.O1616 0.|_00, o.oO07z o.ooags 0.0011_ O._t_ O.ltZ_o -0.0_0,_ O.el_C -0.010,_ o.tl|_l -0.0_.67 0.00)10 0.001_ I.ot2z6 0.6710_ -0.0)211 0.J11¢_ -O.O)_LI 0°_)05_ -O.IO)ZZ O.O0)S_ 0.00100 1.050)_ 0.5_2_1 -0.0)_11 Oo_gZ_e -0.0)_11 0°*0064 -0°1)4_1 0.00)1) _°00010 |.06_L) O°_aOl_ -0.0_,6 0.*e¢19 -¢.0.Z,6 0._6 °0.|I_)_ O.O0)TZ o.O00_* L.OI*_I 0.]_1)0 -o.o_zL O.))o)o -O.O_Zl 0.6_)_ -0°2_19 O.O00S_ o.o00)t |.II_IS o._61al -0.0+_61 0.2cede °_.0.)6_ O.T))S) -o.zs**l 0.00010 O.OOO)Z I.IZO0_ O.a_*71 -0.0.1_ O.a]*_! -a.o_l_q 0._6;|_ +O.Z_Z_O 0.000_0 0.000)0 L.II_II 0.20Z_7 -0.03_1 0._¢_ -o°03_t O._L_ -O.2+)O) 0.0010_ 0°000_$ L.II*_I O.I_)SO -0.03_+ O.l_)6e -Q.O_)S O°IZl)_ -O°_I)Z? O.O011Z O°OC_Z_ k.lO_O_ O.I*TZ) -O.O_*rl O.I_P_3 -_.O)*T! 0.15,_) -0.1_15_ 0.001|1 O.O00Z_ L.O_4_| O.I_Z_2 -o.o_t_| O.I_Z_Z -o.o]lse O.e1_lo °O. IIS_) 0.0011_ O.O0_Z* I°OI*Z_ O.O_T_ -O.Oa_S6 O.@_Z -0.0_)10 O._Z_ o0._01 0.000_] O.O001S I.I1111 O°OZ_OL -0.0|_ 0°0_+©1 -O.O|t_ 0._I_$) -O.)6Z_I 0.00_11 0.00001 I°lt_Z$ 0.01|_ +O.OLL_! 0.011_ -O.Oll_t O._Z_* -O°al_?l O°O0$TO 0°0000_ |.tOl_ O.©OSOI -0°00_! 0.0@_0_ -O.00S_I 1.001_ O.I_OZ| O.O0_SO 0.00005 O._Z_ 0._01_ -O._Ot_ O.O01S* -0.001_5 1.00_0_ O.)IIZ) 0.00_01 0°0000) O.?lt_ 0°0 0.0 0.0 0.0 1.00_ 0.|01_0 0.00100 0.0000) 0._*$)| 0.C01_6 0.00,_$ 0.0015_ 0.00_21 1.01,10 1.0087_ 0°00000 0.0000_ 0.0_1_ O.O0_OI O.OLa_S O.OCSO! O.OIZ_ I.OZ)_ O.|O_Zl 0.000_* 0o00005 O._4_T* 0.0]1_) O.O_Se_ 0.011_ O.OZ_I_ 1.0_107 0._0_1 O°OOZT) O.000O6 O.I)Z_ O.O_]Z 0.06_1_ 0.0_)_ 0.0_|_ 1.1],61 +0o66_1] 0.OOZIO 0.00016 hZ_lt_ O.I_;Z_ O.O;ISO 0.1_] 0.0716e l. LI)la -0.6_76 O.O0|S* O.O00ZO I.al_O_ O.|_il O.OT)_) O.I))6e 0.07)9) I.ZO_7 -0.6|7_ 0°000_4 O.O00Z) I.a_l_a O.ZIIZl O.O_S_ o.z_ea8 o.o?_q I._0+)0 -0._6_0) 0.006_0 0.00010 i._1_04 0.))1)0 O.OT_*2 a.)_l)o o.o?_*z I.]r_3* -0.*16_6 0o00_1 0.000_1 I.I_OIL O°3_)_T 0.0_2_0 O.)_]2T O.aP_90 t.*09)* +0._0|1) 0°00)_$ 0°000_6 I.|1)_ O._Zl 0.00_7| 0._**_1 O.06T?I l.*lO_a -0.)140_ O.O04Zl 0.000_ I.t*6)_ 0o*101_ 0.06_1_ O._eOI9 O.06)|Z |._167_ -O.ZO|*P O.O0)TI 0.000_ 1.0_61Z O.SI_I) O.0600a 0._1_|3 O.0600Z |._)la °O.IT6_ OoO0)t_ 0.0010) |.01_71 O.S_Z O.O_O_ O._*S2 O.OS|Z_ |._12_ -O.ZZ_) 0.00_ O.OO103 |.LOeO) OoS_Z_I O.O5531 O._q2_l 0.0_5_| I._Z_I) -0.Z_)65 0.00_96 0.0010_ I.|151_ 0.6_10_ 0.0_9| 0._10_ O.O_t_e l._OI)| -0.1?_05 O.O0)$Z O.O01)7 |.01_61 0.7_66 0.055,_ O._e*_e 0.0)$*6 1.a0_66 -O.1OO61 0.00_16 0.00|11 I.O_ql_ O.alZTO O.OZ_O_ 0.112P¢ 0o02_0_ I°_|Z -o.otl_? O.OOZ_ O.O0_D| l.o)l_q Oo|tO?4 0.022,_ o.eeo_ 0.02_ 1.a9_6| -O.OZS_I 0.00_10 O.OOZ3S I.OIZ|?

O°_g)_ O.O0165 0._$* a°o016_ 1._34) O°O_Z O°OOZZ5 0.0011_ 0o_+111 ul(a Z)OlZ tIRFOILIILPk_.OIRN.].OINkCN NO,,O.Z/I_iV|-O :....::;:; ............ :_ ............. _;.......... ::;::;;;....::;;;::::::;;..: • 0.o o.l_)eo o.OO6_Zl -0.03_I_7 -O.O01$OZ * ii+iiiiii1411111111111111+iiiiiiiiiii+iii+I+I+1411+ii+Iiiiiiiiiiiiiiiiiiiiiii Figure A-3. Continued.

i /

+ .**.. c_st input ..*..

_ACA _Ol_ A._WOSLIA_p.S.Olmm._.OI..C. NC.-O+a1..*l'_'t mlJ. o.o o._zsooc_-ox o.t+,_ool-c,i o.'JooocoE-oL O.TSOOOOe-Ol o.xoooooE oo o.,soooo+ oo o.zooooot oo o._toccol im e.+ooooo_ co o.+oooooe oo o._©ooool oo o**ooooo_ oo o.Tcooooe oo o..ooooo_ _o o, qoooooE oo o.qloccol oa o.1¢oc¢c+ ©t O.ZS+?OO,O'E-OI 0.)_10001-0l O.4++lO00E-Ot o.snoocol-oI O.**/_qf-Ot O.?lqlO00l-¢l 0._0000t-01 z. - o.o o.T*oo@oi-os o,_$_o©_-<)t c.?s_ooo_-os o.*t_ooot+ot o,_Too_f-Ol o._)6o¢of-ox C.)¢SOO_rOI O.161©O_--01 0.1JOCCOl--©l O. t )000<_'<_ XL " 0.0 O. IZ_004_'OI 0.?SooooI--OI 0*qO0000&'0_ O*Y_00e01--Ot O.I00000_ O0 <).ISO0001 00 0,_0000_ 00 o._sco_ol no o. sco©oot _o c.+oooool oo o.sooooo_ oo o._oooooi oo o._ooooo_ o_ c.+ooooo_ oo o._oooo_ oo o.qq©©ooe 4_o _.LOC0OO_ O_ .o + i ?30OOE.01.0. 171000E .0t -0.1 ?_00e-ol -o. Zl t0001 -ok -0. _000£- 0 t-o- )_o00_ -01 - 0+ I_ roo_ - 01 _°o

imo |

call' • o.l++OCOl ol $+ LVmlm UI'*I+I SO. !1,¢! _ o ,o o.© *m_ClL_L'..-_I*N').OJN_:" _.*O.Ztl_*ttl'l INPUt *I.+OIL .OI.t_ ueell SCIIeICt tO+_ SUIV,C_ "U ZU X_ Z_ 0.0 0.* e.O 00 0,01aSC0 O*O+*_C0 0.OlZS00 -o_oxa )oo o.oI+_o o,oJlioo G.OIS_0 -O.OlflDO O.0S+O00 O.O++100 O.OSO000 -O.0,*O0 O*01_O00 O.OS*00+ O.O+SO00 -0.0ZStO0 0.1+¢e©O 0.0,+)O0 O. lOOOOO -O.O++ZOO 0.1+eOOO O.O'l+00 O+lS0C+0 -O.O_SOOO I.+C0¢00 o.o_s©ae o.zoooo0 -o.os++oo ..zscocc o,o+*e©© o.zsoaoo -o.o++loo o.)1++oo o.o+s+oo -o+o*+*oo 0.+ooooo o.,ooooo o.+oocoo +.o_l*ao -o.o+**oo o.s©cooo o.o+l*oo o.sooooo -0.0+L_OO o.,o+eo+ o.os,+oo o.+ooooo -o.o++_oo o.+ooooo ooo*)1oo o.?ooooo -o.o+oooo O.lO@Ooo o.O|OlOO 0.IOO_oo -o.o+tloo +.++++¢0 o.m*leo o.+ooooo -o.otz)oo o.+s¢oc© e.oo+z+o o.++oooo -o.oo_ooo s.o+_oo o.col+oc i.oooooo -o.oal_oo lu I+ XL +_ o.ools*+ o.o++ii) o.+,++*+ -o.oolsox o.o_l+)_ o,o_s**$ o.+_sos -o.ozls_o o.ol+al4 o.a_s_l, o.l*ol+_ -o.ol*Ist o.o_l* o,o*_sT* o.ltz*_* -o.ozo_*, o.x*+2_I o.ot_s,1 o.s_*z -o.o)71o* o.Io_71, O.O,SlL0 U._IPIZ+ +o.o_iI 0.+o_*_* O.0+S+I7 O._OI_I -o.o*_*** 0.*_*IIS O.O*_0* O._*IZT+ -o.o_+ 0.*II0,I 0.0+*_I+ o.o_q_l -0.0_IZl O.+15151 O.0_IY+0 O.0_tS+_ -O.OZ*++O O.7****O O.O_$+*S O.0S_S_+ -o.o_II*_ O.IIZ*_* O.OI+OI_ 0.Osv*ll -O.0_O_S+ 0.*_* O.OZZ_I+ o+ot,ol+ -o.oI*_++ o.o o o Ll,tm** IOU_0+*+ _*vm, SU_IIV u, pe, +_+*cl Met _JOll III+OILI*Lm-01IM-I.O/MICm ,O.-O.+ll+*ll+-I i t+Raylm _mf! + IWRITE=I.

Sample output of the 2-D characteristics program with

Flgure A-4.

TtllOU+.IlUT IIOnkl,i)MT LA_rlI IUIIII4alv poll |0UI¥&LIIPlr AIIII*IIIL ilOll Jou J IleTNODI ,li<:J ++Nil AatFoII./_LPI-O/I.I.,].0++IU, C,I_ m.,.e.ztuuluve.L stl41llVUll v|np_*tuel . lie.J_ _Nles ta_llU ST_llsrnall pnass_*a • *.7***** ¢8 _,1+ pl_llSl*ali sl+.s iltllNt - o.ilul 611P0IL Cm_t0 ;.O•4we ,v 'w i|v_u M|I I.H411 llLLI_ pmlIIITL llmll| +" o. ??c_ mAY I*mSPll PKV_ t - i.m vR+ur_iriom poinT, i++c e.lJ•zt IlUltlIL mVlm twIClJlUSSI#¢ • e.l_ll Ollll. il_. po_ p+cro+l " 1.)$.-9[ _L! lip 61via ¢_Pm0 - e.0 roll.Ills X#C _C • na#¢SeCl . v*_v*_c otn.slc oe_r*s_c cp ¢P 1.161tl4 0.ZI_Ill 0.141_e -0.el6LLS I.)siq_y _.oe+t_ o.eoetll i.s+s+l+ _.o_t*_ o.lolill o.oo_ll_ o.lo_++ -I.+++Ioi 0. Jel_a_ o.sz$114 oo1_o174 -o.o611u I.INWl e.14_lllt 0.13_61 -0.1_11,6 1.111150 il.mml I. *ill•4 I+llOil i.iOMl I -Lil611 t 0._T_li_ 0.Jt_lll O.Z3tll• -.0 e)141* 1. Sit llli •.lilll I .ollli I 0*01illl i. lli9_ -ililil I o.4o1_11 0.+ll_T e.I]506+ -0.1(_,al I. Vltl.'+ O.010+*Z Cl. _ll I._J'll • . It_ "..41+ o II. Illllillll 0.4,+11! 0. +•64,16 e.n*6+_ -o.llyolc 1. l_ielnl_ i.Io•'l+! O .ll,•i.wi 0.111_.ll t 41 .lll._l I++ -I_iitl e._l.l|N o._)ll! e.ll_*_l -o.t t_tlm I. litili li. mall i i.l 0.lilil i.o01111 -Iolll•li t.llt|Z6 o. _1_11 e.llll_! o.O)l_l I • III,l_l i. •lily• t.4NIIOl_+ I.Olyll 1.04111t -l. 1 Ill, e.s_• o.+vTTIi i.IIiis6 1._4_1 I.Illlli O.MIOYli I.II411 il l. IOlllt i* OIIlPll ._lll?l o.l_m| 0.1asi_ o.ll_SlO -e.ollt_l i. long•+ o.ll_l e*_l_ e.illll+ l.H_ei+ -e.l_i_l 0.6111_ o.611_l 0.zlell6 -I.tl_lt i. Ioli.llidi • .lll<llll I I.NIIII O .IP+I_IIO! l.I Ill+. -i I lillll • Itlul • i+.ll_ o.zltl_ • o_ol • . +.

hml$l o .llllm ll.llill O.Oli/ll II. @Olll$ +L Illllti o._|_ls) o._++z+t_ O+llll_l -.o otlo_ i. le+9+l e.Nlll_l e.eilll_ O.ell4_l o.eelsll -I_ I_141 o.I_ l._1411| 0.ze_|l -o.16_116 I o lillllll I O.llll llolll I.Olitll• I. lltlll &l -41. lIMllil o.lINq_ 0.|It_T _.ll611n -0.0t_lt+ 1.14ill I! •.Ill o. Mlill•l i.llil+l ill. IHIItlWI -li. Illillll I i • ill+it i i .,lIOI I .141.1HM_I i .ill6t<+ •. llllil -.i lie Mill t.4_lINt I._ll_t 0.1*_al -e. lIT_0 I .lllmlll •.lMIll I.lillldi I.Illlll O.llll I. lill I I.IMIII 1.01111•$ i. Ill•0 lolllllil O.0111"+l i. ll 0. q_l+l_'14 n .e164mo I.Illlle +e.ol|*_7 I • _lt'_Y o.IWi li+i l*#llil I.IIt416 o*llill I I_IIW_I Ullllll lllllOll ililt i lilt lilil llll01111LltIl.l/lllll.O/IKl ll+_4.111dlll.l i_lll l_m++cl llllillill llqll * ill.l+ 14Fimll l *•NIIII illillilill milllill - Jill.ill Llltl PT l.licu llllil| Ol01O I .film Pl i .lille llLil01 +limit ll_ln O. _T011 I.I_CN li_tAtlal CnlU_ItlOl _0 0.01*l_t lllll II i Iill.ll+ Ill ilMCOll • llm+tlC YlIC011tV e.o_o_*J _ _v#llc e.l olillll Slllllllll II •ll o.l_lli$11 Syll_ll_ ir zlc o.l_i_si9 I#C s_ , vmlll#c li_ s#c IkR VlS_C CP CP l.l l.llll l.o+lltt Is.zz;ll, Z • _Z• • . el_11 0*01WM 0._II_ e. Im_l l.lll 1.1411111 O.lS_lll loolz_l_ z. +lliol l. l_lil 0 + illlll e.lojl+l e. _I|I_ I. lli4_ l.llllll z.*+i_ OoO_et_ o.m_ _.00+_I+ 0.11Ni I.II II14 I .llllll i .... _I_ • mi* e R o loi_u -l.li_ll l.ll411i l.llll z.*illlo Oollilll i.llal_ l.oeil1* -I. I+I+I o.il+l_M o.mmt OolN|ll ~l.StlOlC z • |_il+l •. oN_ • . IIIi i T 0.I011_ -0. silll o .lmr_t+e+, o.N-lll, i I.Inlll -I_ i_lll_ z._Fitl_ l.ml 0.0_I11 e.lle_i_ -_lilll l.llll l.lllll I o.lll*sl o•. itllll i.ill_l •. llll_ • .li+l ol Oom_ -o.lllll l.llill I I. I lllll I.IIt_lt ol. oll_,_ i.•11slt 0. _ • . oi+ll 6 e.Olill6 -.I iI_Ii l.llilll I+IIIIII I.Iltll_ e._llzl l._itl_ o.mt o.lllli+ e.Nili6 -l.l _ill I.IIIIII I. llllll O.ll_lll I.els_ l.++;lll 0.II0101 0.Nilll 0.01|llr -l.illll I. lllITi I.IIIIII Z._•tUl 0 • 0NIII 0 . Uelll 0.0011|_ -4.11111 I. lill?i l.lllill i.Izllll o._so_l l._illll 0.111111 0. uelll o.l_lli_ -I.I_N| I. I lllill I+ llIMl i.zztie6 eot|_ll_ I.+I_+i_ o.llllzl o.lwill 0. 001_II+ -i. IS•+• I .llil_i I. l_lll I._I+I16 e.llllll I.lwllt o. 011_II -l.ll_o I. Mllm O.llllll t.+It_+o 0.0111+4 O.IIIIN I. 000+i_ -l.lill_ I. II llll l.ll I.n_l| -e.ul_l I. lllll I + Millll e.nl_! -I._lsl l.il+ei+ o.l_li+ l.IIll_ 0.010_ -l.llml I. 411111 l.illl t.lt_N _.olllvo o.l_l_+ o.eeoil+ -e.lli_l l_llllC - O.lilllill n(tl! • l?l. ll I?Ii#C • • .)_+till ii*+l • loll.l+ vwlt_l#c • 0._161_ llllyllltlYy Iti41illlm MII 0CCUIIIi II I#_ - e.lllill _#c • 0.lgl_Ti iUllltlll lltlllli live! ill•Ill • ill llilillllll llllili lllll II lilll I liiCl llill IttPilllllPm.illi-l.lllll, ll0."l*10lltlll-I ITIIIT 101 iltlllll llilillll fl•Pllllill . lll.ll IIIIIII tilllll llliillllll P*lllll I • Jill.ill lOlll li . ptilleyt imlln o. _iloo ) ill41* MILl+lOll I NI41 IIAIISITI011 _lqr, sic • o.i+i+l llllllll llllili lll{J_illll#_ • i.Iii Iiii. llililio FOWI liar01 . l.llil6 ILl II lllli_ IIIP4MI • i.I _II lilt sic ii m+_lS_Cl s IWItA/I Hi.SIC _l_ rll#C cp c+ l.mllll l. lilill O.llllll -l.ililll I. llilll O.i•il61 i .llilll I.lll I.+llll 0.1_414 - II. ml'.6 I.+1 ! .llll4111 I' •.l O.lltll t.15•ll -I.il II l.i41111 l.+lllll l.llllll -l.mll It I. ill•41 1.011111 1.14H_ll l.lilMi i .10_ill -i. llilll I. ill•• I . il i ••Ii I.Illllt -.I mill I.+mll @ . ll4111•41 i.tll 0 o d04111m O.HIIIT -• . ITIIH IIllllll I.IIItH I.Illlil -l+llllll I.II)IH I.ll 1.1Ot411 O.HIIill I.llll -lllli I +lllli t I.Illlll I.lliitl - ol I Ii I'llli. I. llill • .llll II I • tOIIl O. ltlll I I • * HIIM -I_ liMII I" llllli I* llqll O.ll Illl -e.ilm+ll• i.:111 _.+_ o.ml4_y t.lltl i.IOll71 t.llllll .i.iiii11 l.illlll •. mlll loll fill -.• elllm I. llilll i .0111i I o . lilllll o . io_ll 1.101111 -I- IIII 16 • o Illll l.6lllll Iollllll - ,• ill Ill h 111?16 i . I ;'_41 o . Nit •._llll O+lllll -I+ I IIiit I.llllll l ° ?lllll O.llii4l - •. llltll l, Ilill_ •. Ollllt I,NIIH O .lillltl I.lil_lt o,• ill l.ll I.lllll4 loHtl61 -t_llllll I.IIlml O.til t.il•llAll I.I.•l+•lll ill. Nil H -l+lPllll i l*lllHl l. lHili l.l•llll -O°•_li61 l. ll7_i I 1.10 ill I l._lill •.OllIl I.NIIII -4J. i_4_TO I "lll_4 I°l?llll I-lfltll "I-fl_lil 1 • ltllil O°MIlII I.ImPlmZ i.@lll_l O. llill i+ ll0lll • .lillll • . lllll @. llifll -o+ lillll I.IIIIII 0.NIlII l.lillll •.IIII?I o. mill l. gill l'•lllll I'iH_! l'llllll "1"1 1 fill I'l_lll O "lllSll 0 °M_l?l •-Ol_411i o.llll II. I.II411l l.t I,lll_l I*llll_ -I* Ollill h IlM?I I.lO/lll 0 .fllli$ O.•llill 0 ,tlllll _ lilIM

Figure A-4. Continued•

LOll) S_&IY _ll,--[Tfn•Tl_ _MIi 4 ,aC, alOLI ¢JnFOJL_aL_A.01n_.).OtmlC_ mO.-0.ZtUWaJt¢.l nICU mall* • ••liNe tlPltlMCl ¢,_o telSl$ PO¢ I_L C0|_PlCSlmr _0aml_IZ*+lOm! • L.0_ Ft.

flY, It ,0o • 1.01¢00 rolL|IOta A_I 0P AT|at, IVALUl 0W II_NI • 01 • o.e N,.

gI*L_*oO--I_LI eEPlml© v.l.r, tl,l_lUCl Ltml_ Lulesr cmom_l+l • L.e¢<+0 Wllr IIAL_A.I---Ik_L! 01Wlml0 U.*.t. L01_IIT •m0.eLl_ll Im_l elr,llm LNIST C_0_Im! *m© tl_l*t_Cl Llml • 0.0 01_. +_Sltl_l F0* *IFeqRCl LI_I II_0V Tml L0,111V C_m_l_ll _t_L e_l CelW_Cllmt| • LIFT ¢OlPPlClINVS ¢_T_!$1. • e.L1541 , ICL)PlIS_. • O.l|g41 • ¢.l|S_l CL • 0.1|5_1 • i _cllmllSl.. e.ocots qco1_155. • o.o_5 * ¢1 o.o_t+_ cn o.oo_a • cx • -e.e_ls t +,,+*+,++,o++++**+t,,+,,,_+*t,,,,,e.,,,, ii_i Cm,PICIf.T CO_,WTe* iv SeUl*l-vo_i _,,._.* = o.oo**l zlees_ xrl**+n_ pelSsule i**_ • e.NI** T*_,SlTIll _mTSt alClLO.III • e+_e_?_ iJclu_plll • ._ z_c sic cp cp HOt,SIC VlN o._le_ -O.Nn)e o.+eeee -IloOOl)O o,0 o+lei)o 0.Nle* o.eol_l e.*I+LI o ._•7| I, -•.oils) 0.4140151 -i.l||_3 o. _l ill o .0)1434 o .lo,I f$ 0.o_19_ o. 9_14| |+ I|,IT(I -_. (i I_e+? OoI||TG -0o 0104+? •. LII|ll ,-_, 0_46y I1o J@)L4 O,001$l 1.0|||4 o. y_ll .-o.o|_6y o. y41414 -i. I|46y 0.116|I I.4_iII o.ooI_tl o.¢l_l i| i .oz$11 io ?i$|| -I.iii14 leylll_ -•. 0|I14_ f+l i04114 .ND.01_16 0.101+l) I).N||] hl|4lS 1o4_L141 -0.@$II | I*6110'I -fi*O_| I (115|0|7 -0° |O)ll I. Oll|$q 0.001114 |. Olll)ll I._I -*.llTl I _._llll -I.01FI I I._ -I*_I I.I_MI B.10 I.IISII II ._t<+$I -O .il_klll _.|g.l| -l.O)41l 0.4_i?|I -I._416_ 0°10_,) O.00@YO I.I?I*_ 1o_I| -*°Ol,kll 0._|_|| -O. 0411411 I)._I1414 -4. II|01 0o0,|91 O.00_bl h0T?|l 1._I¢14 +4.0,I_6 _._ll1_ -.I 0+I_* o.slls* -0.1,+_4 0._0_I O.NOS_ l.dml+.ll 1.4_+Ii -e.o_e_ 1.4*_ii -l.tm_l+ Oo,S_sl --0. iI+i _ o.oomll o.ec_1 1.041_e 1.44144 -i. 04 t+6 _ @°41144 -Oo_k.• f _I. 4si|14 .-i. i i_41 o. 0,_411 o• 041_)4 l• |gill l.)_|l_ 4.0_SI_ I+|_I_ -@+ I)4_614 •. 6_IIII I -0.II)I 4.IIg04_ 0o004)|11 |. |01|II O*))OM .-li°04S_ I 4.I,I)11 -fl* 0_| 0. _.k|_, -0.llS|4 O.C_IOS _ @. l_01& |* I |404 I. I11_I MI.0q'l¢e •.11144 - fl. l_.+_+e i). _111, .-0. lttl _.I a.ON_0 0.00014 I. 11_k g._lll _.I_I I.IIIII -1.04)61 0* _)IIl _+I_I 0*IIII o._)l I.II I. I¢I_7 -e.O_l l°ICl_ -0.11441 O. _S+|_ -0. I_N) e.NIII •.N01e |.fill g+ IT144 _.01_14 •. |T|tl -O.Ol?1, O° II_PiI| -0°I||17 0.NII_ II°0_ _ _. IINI,II e. I+_11 -e.e_l e.|*+l_ -o.o_l o.es+,s -o. l_ISS 0.NIl6 o.ll_l_ |.e_e (1._II -•.•NII 0.044)I -e.ll_ll 0._I)|* .-+. |I+11 e.HI01 •.NIII l.O_l_ Ooll_lql -Uo01144 1°I?_|4 -I.01144 O.4_i .-0°|I•_| ¢I._•_14 ••41_141 I._41 • olI•_$I MI.41_I16 O.@,T_1 -@.0111_ 0.414•II 4°II10| 1. (l_ql| @.0111| _ hlllll 41°01_1441 Ml.Ollkl$ 11114_I - .a lilO,S II.461441 .=_+)IW_I 1°0¢11|$ 1.04101_ |•|6111qi • .ll,ll -l*lll+,• Io@1441| *_._|61_I 0.'I*_I -._. 1_41 1•4•_II @*IM_II |+11_?I_ l.el&ll -0.0_i_I a.elt, t -•.Oll•l 0.N164 -+O.U,_I e.¢<rs,e e._• 1.1N_ • • 1011411 -•°@•_4 | I. C0|411 -O. Ik0_91 I. ••L%% 0°I_II I° @414_0 o • OlI_ ii • 4_,_ o. ¢141| 14k -0°Ill 142 C.•olll -_|'_ I • I_(i_ o= 10L|) 1.041_46 II.•0001 0 • ?14_ 41.0 •.e e.• i. oo,n+ o, lel_l o,@eloo e .o411ol o,,+_s_| lol)01_l •.N+II 0.0@I$I 41. +0.+11 l.,l•l• I. 14141_l e • m • . I_0+ O.Hl_ l • _I_411 •.0 II'I+ l.Clg,_l O°Ol1_ |.II_| +°NIII • .041@14 O • _,k0_+ 0.464_ I°01141 0.•ISII C +I1111_ O + 01_I_ |o•)I_ •o 101_| 0.0•174 O • II_06 • ° II$14_ O°O_,#| 0.0|_4 Q.01441 II,0$SFSU |+l_Jll| -l)liilil_1 •••04T) 1.410007 I.04_I i,o_ o.044_1 o.lJ_ll I,_!1 Io*?l_J _+Jt_J o,l_8 o,III _.101_ • °o_yJ_ 0.04111 ¢.14_|_ o.•9111 l°l_lil MI. 411|| 0° (141_i_.i o°_| Jt i ° _kl+l • .lj ?yS_l @° os,iJ'l ? I_I@_|Q O, OIIIT? Ioll_J_J -4)061 ? _1 0°•4Ji4 41.116 I._?1_1 I.I'_I/ 0.I_16 1.•4411 e.o_l_ I.l_l -0.+._Ii_ •.oollo e.Nell l.l•l•_ o. 1114_ •°o,ll_ 0.iI|$I o. o•i_l i.i_,_1 4.61111 •°(i0|14 @°014111 i °_•?,1 o. 14711 ii.@_Ii_ O*i4?II o.ll'r|I• |o10)11 "=i)=66171 O°INIL$4 •*_4_11 I•_0_I_ i. IT)6• •. @71_11 0*I?|61 (i, o?$41 | • i._,k T ,-o, 6 |_?1 I1.0o4104 ql =4Ni4,14 _1 | ._71_11 41._l_y? @.0_$| l I°_¢I_7 4.II?111 |._)oy4 M_+ 4|$|4 0°o4141s I 0°o_|6 I°_,?|| l.zl_| e.e+sls o.l_*_ e.e_N _.1?ey) -+. se_ll •.ooos_ e._l* _.Ii147 |._60_I •°4_4_4 Oolt.ll|1 O. OT_4• I._04111 _0°_640); ••1olio 0.4.41411o _°111_I i. roll,++ i,e_) e.lcl,l_ o.eTs+s I. _441 -,.o. <.l?, l e.NS+0 e,N0_4 I. I'WlS |.lien e.1+441 l.lllX 0o1_441 t.)?++)+l .-O°+l*M o.OOlll ii.04@41 l.l_ll O.|?)l_ o.o?lgO 1.|7_I? O.•TI_D 1.60_)<I -•._ll_ +.0|_15 0._4_$, l .1011_I •, 40Od+ •,O_•T0 C .'+1144 l, O?OTI _ • _4_0 _. 11_ 0,O_ I I • _l I, I_ll 1o414111 l°Olill 0.+llll O.ll)ll I•+16_4 -I).NiI¥ O°••ltl @.M+ l.mil • .+IYl) •. 064141 I.$|_|I 4. 0601_ 1•44111 "@. 176_4 O._ If+4 O•@_IO) |.kl_Yl |._J4|l 01@_II|4 0o414|| 0.0111• I +'I•|I| -o•_1775 II.(I¢I_+_4 0°•0101 I ° 11141411 II• _•_4_ 0.021)I 1.41111 O.IIS_I 1.&_4111 "0.14 I+I l).10_r_6 @.Nil@ I• ll_14 4.I)_IY e.e_Is4 e.,lls7 1.0SLS9 l._•4)l "0.1LI_I @.0el+6 •.NlZl 1.I_I o.l_le+ o.e+l+o e.6_11s e.o_•e I.T0111 _.1_les O.NISl e.l_l_ l.0_*l • •IIII_Q ii .... •|'kl_ I)+|1111 O 01411_ 1411J||I 4.14|47 • _41_4 (I 14111)0 1.0111• II.... IIII/+I @°111_4 |•041_4 0+_I|44 I 4_I| 4.11!111 • i_l_llO • II_114 I.•LII_ iJ •4o?_| •°111 J,l+o _.SITSJl 4,11| ill I._&fJ_ 0.0,11_11t • ,10o1_16 11.10_61 O,tO/•J 0,SS_ 0 ..... NII'I e 44_m4 4 NON I._l_l o.e441,1 •.H, II4 o 14n_ o W, IU e .... 44+s+ o.c_1_o 1.•441_ e.+os_• I _,m_ 0.l+Zm+ * NI0_ • II_14 e.,llll 11611 I/_L| hll_l+Oltl_l+P_*i*lJ_l=41/_i_k l_°i6°lll_lil_.l • O.• 0°1141141 I.I_411 -O•_J'_l_T +I).04)IIII_ 4 Continued.

Figure A-4.

_*c+ i1a_l Al,,OlL_*t_..qs*.._.Qt.+C. N_.-o.e,l.mL,l-_ *,I.L F_¢I _©_'I_IlWlS ,,r_lv c_.lclwlv+ o......°,.**,..,o,,.,..,,. ...... ..o,.o, IWRITE=2.

Sample output of the 2-D characteristics program with

Figure A-5.

oo oo

II It

oo oo

gd dg dg g_ _

I| II

oo oo oo oo

IL

b"

&g ...... oo oo oo _

u

t ! t I

0 0

¢-

-t--

O0 O0

e_ °--

N

• .. __ . -

E

oo oo oo ??. _ _

-o ;; -o go O0 _ _ --

oo C_

o

O0 O0 _ 0

o

U')

z

U

,I. 41, _ ,! _1. ,I ,! _1. ,IF _ ,I, _

T

tn

? o ,,, ®,_ o _.-.® ®

"E

o ee_

N

___ :_ o.o.o.o.o.o.o.o. : o

_ oo _ oo •

:: ????????: L.

o

gd gd gg _g g

|J

Z N

O

;g oo'" _g oo'_ g o

II I II _3

9K _ I

IJ o oo _

CO

,ID

4-

dd od od do - o

• • " o _g d

t _

z o o

o

I

+-

_ ''

G.

oooooo g _ _ oo

,,J

O.

.... o dd

.J

o

ooooooooo??? _ _oo

I: O.

It

•lr_j • •

E

oo o_ oo _o • * _ z

z

CO

o

_o

oo

l

oo

L..

i"

_ o_ _

o-

ld_

0000000t_

e_, 00000

o .... oooooo I

.a o _ _.) (.) o (.a

l

Next: APPENDIX B- Polynomial Fit of Two Dimensional Data →

APPENDIX B- Polynomial Fit of Two Dimensional Data

APPENDIX B- Polynomial Fit of Two Dimensional Data

User Instructions

Thls program Is written in Fortran IV and Is designed to run in

single precision on an IBM 370-165 computer. Execution requires 54,000

bytes of core storage and approximately six seconds to fit one set of

two-dlmenslonal airfoil data giving four polynomial curve fits of degree

four. For each airfoil the program requires the following input data:

(I) The 80 characters of the array TITLE whlch are used as a header

for Identifying output. Since the program allows more than one

alrfoll to be analyzed In a given run, TITLE Is used as a

control variable to end execution. Termination of execution

Is achleved by following the last set of airfoil data to be

analyzed by a title card having only the word END in the first

three spaces (see the last card of the sample data set In

Figure B-2).

(2) The number NUM. The largest allowable value of NUM is 20.

This variable specifies the number of angles of attack which

follow.

(3) The flrst element values of the arrays AL, CL, CD, CM. These

are the angle of attack and the two-dlmensional coefficients

of llft, drag, and pitching moment for that angle of attack.

Slmilar cards with successive array elements follow until

the number of points specified by NUM are read in.

In addltlon to the previous input data speclfication an internal

swltch is provlded to suppress the plot of the input points and the

curve flt function. When SWITCH is set to zero, plots are produced;

however, when SWITCH is set to one, the plots are suppressed. Another

internal switch PUNCH which operates similarly allows for the fitted

coefficients to be punched Into card form for use with other programs.

Statements (I) through (3) represent a complete data set for a

particular alrfoll. The format specification for this data Is given In

Flgure B-I. A sample data set of the 23012 airfoil Is shown In

Flgure B-2. The output of thls particular data set is shown In

Figure B-3.

30O

r;t ti r

_////////l_

_. '+I <, A,'//.> t '_ _:<i'_':',> ..... I "<'> """ >

< ' '_" ................ V///III/IIA

I'*, ' t ........ IIi_ I 6' _'5',', .... ' t ' I " Ill' I '6, . '5 " .I I O1 6 . 5 I O 16.$ , ; C,l (_211, .... I , ' ' CI_(I) CM(2) '

_!' ' _ i:': ......... I V/////////AI

'_.. o'I'l-.,_ ,1' _,0.s i, ...... ,i,,_,.._ I a,0._

l_ll( .... 1 1 r " C _ ( ' 3 ) _ I :ell{J3) 1 cM(3) . , + .... L L , , ....

t _,, _ L . . n _ , _i I . ] * L t 't II ..........

i ,' t i t,. / t L _ l [ _ J .... ,

tftt_ t_i,t -tl_t<f_tli4t-_I,-ff',!,',l::[: ,lIll_t_*,*,llll!:llr;_i!l

H

rt'Ii_t4 ')_p[_t- _li]_l qiii'l,p_ ll_il-L._ i i L¢_ll!i,,lii_.Z[ i +1'_;+ ; _:'.(,i"!"l'l)_ 1[ ll_ll/ll'_l :, "* ' " _; .... _Lm_ -_ ........

Figure B-I. Format specification of input data for the polynomial fit of

2-D data program.

/

/

-%

/

7 I I0.000 I • ISSO O. 1404SE-01 -0.1 lltST-OI

/

o.oooo o

/

t.O000 O.TIItll ,_ ,O'lOlT4l'Ol -0.1 1 Itll-OI

4.0000

0.$7321 O .?OSil I I[- O8 -O. II IStE-O I I. 0000 0.34SS2 0 .ll 4St[-Ol -0 • I 0_41[-01 ire..

/

AL(2) CL(2) C0(2) CM(_) - _ .0000 -O. _SIE-OI O.?$4S 9 E-Or _ .lOg 8M-Ot AL(I) CL(I ) CO(I) CM(I) -'_ -4.0000 -0._119S3 {_,]1 S NUll

/

t 2:1_1, TITLE SERIES AIRFOIL / ALPHA,.4,.Z,O,Z,4,1tO,IO 012 / RN, I.4S /MAOH NO ,.8 Itl lilt liAI I!

000000000081000000010000 |OOiO00||l|O|lOiiltll|lllllOlOOllOOllOIIlillllllllllllll |111111111111111111111 1 111111111111111111111111111_1171111111|11111 222222222222222222222 2 333333333333333333333 3 444444444A_4444444444 4 55555555555555555555555 55555555555 555555555555555555555 5 444444444444444,14444444___ 44444444444 E61161616661615616165 6 G66566666_6666666666666 iliiiltillii COMPUTING CENTER 711771177771111171717 1 1111111117111111171171711 _ 1111111111111 181111181181111181888 8 1811lllllSl8llillEl|llSllIIII Illllllllllllllll 919911_99911l_911999199i91|9911lll!!11111!l!!!!911111111 199t9191999tt$t111t_t!99 I 2 ] 4 _ I 1 I I IIII q? ,_ li ,511:r ll l_ ?5 tl ?_!4 i_ li ;1 ]1 7l )l i_ ]? ?) !t _ )l !7 _l _1 4| II A2 l] il 45 15 47 41 i_ _1 _1 !? 51 _l _ _I _7 51 51 II In $? t3 (4 IS II II II n iI _, t_ n it tl ii tl ii _l l

/

HP 106_ Figure B-2. Example data set for the polynomial fit of 2-D data program.

||ll|||||||||||i|||||||||tiliiEillEiE||||||||ill||||/|||||| _

..°J _== ..... ; - .

................ _...... __ _n_ n_" "_"

.................................. !i!,

i

llll||i||lll|||i|||-=|ti|i|||||||t|ti|llttl||llit|ttt|i lil||lllli

o_

. ¥_

|

L . _t m_t vt _ °_ _ ....

" _'" 8 ....

.w -!_ ...... :._ : :-- _._....

-... _

i l :}::::::::|::: | -_--- : ....

4mN_(4 ,d .._ -a .a .a -.a .a .a .a ..a .a ._ .a .a .a .._ ._., .,_ .i .a m " .

_o

z 1..¢_ _m w_

ii!

i[

- .,,,. _g_ "'o, T

0 m _ m o m O_OmO_ o _ 0 _0 =; =: . . . . ,

z. . = - "

.-| •

• K • om.

_Z E _o

Lo,L.z

La_L_m m Z • .I[

3O5

Sample Output

_ml: _ oa_a _elaOV$. • • - o.zPe44_ v.o._n_s _lts_t_c.

_e • .............. • ................ . ................ , ................... • .............. ***.., ................... , .........

•x .........................................................., '" .................................................

,._ e, e, .................. 2, ....................................................................................

1 ,. 1

I *e I , ......... • * ................ • ................... , ................. • ................... . .................. . .........

I x*" N 1 "° a_ • ............. • ............... , ................. • ................... , .................. . .........

t--O. |l HIll I. ,,_ .II_IiIi lls I Z. lifO0 @

Figure B-3. Sample output of the polynomial fit of 2-D data program•

v_l_cEo o.la_qa6t-o2 • .................. o ................. • .................. ° ................... _ ............................

°_ ............................................................................ , ................. • ......... o ...................

° ; ......................................................................... _ ............... _--. ....................

; ................. " ........................................................................ 7'--" ..............................

o."

• ., .................. °--, ................ , ................. , ........

.............. _ ..................................... , .... , I *''"* I *..° I I r I I *'*''"*"* x ..,...- I I I • ................... ° ........... x ....... ° ................... • ................... " ................... ° ................... " .........

_. (i. 6._|0E-C2, x--o. 31,_*_o B-3. Continued.

Figure

|IGIII. • mU_4H Of 0Ill * 01mTS- ,+nl+t.Ce* e.l+*o, +st,-•+ cc oi--o. +sL])el- C( I | --i. 71q4)_II-( Cl /;.-o.es*+eJl-c ) cl 31_o.zosel_l-o t ¢i +I- o.*Xl_)ll-O.

X-•ALl+| Y-VAL_I V-PIT x-vll+_ T- VI, I.LI! V'Fll -0.3_ _)00 -0.501_751 _'4Z -0.+e+l_l ZI-eZ II O._T)Zla4 -O. I_ 1)'1001+-01 -0o lZ|!11'+|'41 -0. _4'IS4411_I -0.16_I00 _-gZ +0o4_1135+I-02 10 o._,i,_ o.i)Ltzeot-oi +e.lJS32LH-m • '0.150_3¢I' '+°02 -0.1_T)+I-0Z 0.|ZSI_H II 1.00_I40 --O • | *z_e4|+-41 -o. i )_llO**e-41 0.3+++_04 - 0.I05+I00 c."01 -0.L0_2Z6_-01 u ,..,o_ -o...,_-o_ -o.,.,o,.++_ l.)Sl00e 0. _0255¢_ _+01 -0. I0Z_3_°01 II PLOT Of •°.IX+S1 I_0 '-PlI..I' I°$_ F0CL0V$1 cn vlJsus cc x. ............................... +................ • ................ • ............... o ........... , ......

i • i • i •• i • I +++ I •+ I ++ • +1 I++ • +.

+, , • • + • . + I.

............................ ++-_, .......................................................... .+ .....

• I• ++ xl •j "+• .+ • ................ * ................. • ........... -e----. ............... + ..................... + .+.

.+ ...... +_ --. .___ ol I I i l • f i • Ol I I • e I 0 • + i I + • x I l • I I • 11 I I • • I I • • ............. + ............... . ............. . ...... +• ..... + ................ + ....... • .......... _ .....

". : t .'

n+ i • i + ............... . .............. + ................. + .............. . ................ _ ................ • .......

+-.-4.141S_411-4)|, x--O. +tq_l_3o s,l 1.111414

Figure B-3. Continued•

.u,_4En OF DXTJ pOlmWS- vJnJ_¢_- O. _O_lt4_-O* w_ov ew v..al.$J ANn _-FLT*.(*'Sl FOL_O.Sl JLP_A VEJSUS cL t+ 2 • .................. ,. ,._oo ______::::: ..... _;;y,___...................

• I ** I ** t I . .................. ; .................. ; .................................... _ .................. _;,, ............... : .........

**1 ;.................. ;................. ; ..................................... t-_":; ............ : ................... ; .........

**l *o.

..... o--•x .............. ° .................. * .................. * ........

** I •_ , .................. ; .................. _;.•;;.............. , ................... :................ :................. ;.........

" ................. ;..;: ............. ; ................... , ................ t................... : ................. _ .........

:•'; ............... ; .................. . ......................................................................................

v. -,,.•coo• , x.-o.)|e_so x.L._a.4,0 • I_o Oi.E_SIO_xc ¢umve FIT _u_txo_ _mt_ * • c_ol clan (IZl cl)J cl_ • c_ vl_sus _L_ O.IZ_)_ O.llal_ e._eel_ -o.oooo) -c.ooooo _o,_i,. -+.coco to iz.oooo • • ¢o vlmsus c_ o.ooto_ -o.o_zoz o.oo_e_ o.ooo_ o.ooz_q oO_ll_- -O._le_ to l.)slo o *_ee_._N_ee_e_•_•_*_e_*_*_eee•e_e_e_e_•_e_e_ee_e_e_e_ Figure B-3. Continued.

Next: APPENDIX C- Airfoil-to- Complete-Wing Program →

APPENDIX C- Airfoil-to- Complete-Wing Program

APPENDIX C- Airfoil-to- Complete-Wing Program

User Instructions This program is written in Fortran IV and is designed to run in single precision on an IBM 370-165 computer. Execution requires 60,000 bytes of core storage and approximately eight seconds to produce the three- dimensional lift, drag, and pitching moment for a given wing-body configura- tion. For each configuration the program requires the following input data: (I) The aspect ratio ASPEC, the thickness ratio of the tip TAUT, the thickness ratio of the root TAUR, the taper ratio TAPER, the geometric twist TWIST in degrees (If geometric twist is specified, the aerodynamic twist TWISA must be set to a value of I00.), the number of spanwise stations R (R must be less than or equal to 20.), Reynolds number in millions based on wlnQ mean aerodynamic chord REYND, and a criterion for conver- gence of the lift distribution DISCR.

(2) Fuselage height to wing span ratio A, fuselage width to wing span ratio B, the height of the wing above the fuselage centerline H, again as a ratio to wing span, wing-body incidence angle ALPHR in degrees, x-coordinate of the moment reference point X, z- coordinate of the moment reference point Z, the aerodynamic twist TWISA in degrees (If aerodynamic twist is specified, the geomet- ric twist TWIST must be set to a value of I00.).

(3) The number of airfoil families (two tables per family) to be read in with this configuration IFAM, a control parameter for reading in wing geometric parameters ISWIT(1), a control parameter for printing out intermediate calculations as they are performed ISWIT(2), a control parameter for printing out matrices ISWIT(3), and an indicator that the tip airfoil is or is not of the same family as the root IRT. A yes action is implied when the control parameter or indicator is set to one; otherwise, the appropriate space is filled with a zero.

4) The 80 characters of the array NAME which are used as a header for identifying output.

(5) The 80 characters of the array TITLEI which serve as identifica- tion for the first airfoil table.

(6) The thickness ratio of the airfoil in the first table RTI.

(7) The five coefficients of the lift polynomial CCLRTI for the airfoil in the first table.

(8) The domain for which the coefficients qf CCLRTI are valid XLO(1) and XHI(1).

(9) The five coefficients of the drag polynomial CCDRTI for the

airfoil in the first table.

(10) The domainfor which coefficients of CCDRTI are valid XLO(2)

and XHI(2).

(11) The five coefficients of the moment polynomial CCMRTI for the

airfoil in the first table.

(12) The domainfor which the coefficients of CCMRTI are valid

XLO(3) and XHI(3).

(13) The five coefficients of the alpha polynomial CALRTIfor the

airfoil in the first table.

(14) The domainfor which the coefficients of CALRTI are valid

XLO(4) and XHI(4).

(15) A duplication of (4) through (14) for each additional airfoil

until the correct numberof airfoil coefficient tables are

stored.

(16) The 20 elements of the array ALPHB representing the angles of

attack for which three-dimensional lift, drag, and moment

coefficients are to be calculated. One element of this array

must contain the value 99.0 to insure a later return to the

main portion of the program.

The programallows for additional configurations to be calculated

during the samerun. This maybe accomplishedsimply by repeating the

previous input. The programwill continue execution until it encounters

an ASPEC value of 99.0 followed by a blank card.

Statements (I) through (16) represent a complete data set for a

particular configuration. The format specification for thls data is given

in Figure C-I. A sample data set using a 23020 root-23012 tip wing is

shown in Figure C-2. The output of this particular data set is given

in Figure C-3.

I10 ! 6i.

I i . _O_ Figure C-I. Format specification of input data for the airfoil-to-complete- wing program.

........ o. o. o+ +_

0 O. 0 0 O, O. o. O, O.

r], /,LP_I,I .,.. -- / -4+ "I O. I. 4. • e, io. ii, o Item I 4101 :+" ...... _ /<, .... + , CALItTI(I| ell.

XLO(O) Kill(el I. ll_ll .o411111 . +!.,i!. ...... ,.+iTz. , +o.3!a7.

ML0[? I XH][(?)

0 ItD4O I + 430e o CCNRT|(I) .0+ I TeOTI, 0| -0.10 0711-01 .0 .Otl|ll_)8 0 .I e_l_l.01 0 ?OSI01p 01 / XL0<S) XN2(_ _'_ P.CNTI(S) / GCOIITI(I) I_.

0. ? Till 1441.01 .0,4Tllll.Ol O.Illll_Ol 0. IS4471-4ii .0. II?1101-01 ......... ........ , ....... + ....

RLOle) XNI_) ..... :4;.oooo ........ _t'_° ................. _c_.T_(ll 2_I ............. , , , + ..... .... " -0.IIII| l.l$iO CALITI ll) ili ¢ AIJIITI(I) I O n 4 1 7 _ 4 0 + I S O _ -t. IlSO o,otls - o _SSIiSI-OI XLO(4) XNI(4) I XLO(I] X#I($) -O.$11 OI I.IO_ ...... --_: :' '_um';_ID +_ CalmTiI i ) I_1* -0 ?l 141-01 .o.yO_ll-ol +o os44oe-ol -O,|OS_[.Ol 0 411111-01 -0 11 fill I I. lllO CCORTIII) _1 S CCI_TI(I} *oe Y_++---7^'_+_t -o toIPI41.ol o tessH-ot o.l_ele-ol O.tOOIOI.+I I XLO(1) XNI(I| .4.0000 iI.O00 .....

|¢LflT(I ) 1141 (XI.IIII) 0 llllll 0,I IIII 0.14 IIIII.01 .0. II14011-04 .0,111'111111"(11 • It "I_TLSI |&oil SlNIII AI_II_IL / ALPHA, -4,- t,O,t ,4oO,I, I0, I | / Ilil,_l._ / _N m.,. 8 11O41O R¢_'r SUlIO - 8_1| Imlll TIP IRT llllllJ Zllll_r(i) zIl[T(|) zlwztll) I ........ l ...... 9 . ..... 0 .... .... •

/o: " ....... "

O. O. O. O + I00.

,,,. _,,+ ',,_, ,+,,+,, .... .,, ....... ,_ IlllllllllllOOIlllllllllllllllllllllll IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII 1911]ltllllllellllllllllllllelllli?llllllllifl!7l lllll2:tltlll; iiillllilllllllllllllll]llllll31lllll$ll}ll;+ll _ Illillilllll ............................................... ...........

iiiiiiiiiiillllllllilllll_!lllllllltlllllllllll I slIIIIIIlll t'OMPITI_8 CINI'_i_ Illllllllllllllllllllllllllllllllllllllllllllllli _ r7711111Jflll iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii iiiiiiiiiiiiiiii I III lit lllltlilllllttllltliillilllllltiililiitllllllllilll+lllllillil+lllill ' ...... ._,._ ,+. ............... ,_+, ........................... , .................... ..... , ,,.

Figure C-2. Example data set for the airfoil-to-complete-wing program.

llt||lltllltllltllllllttltitl|ltltllllttlllllllllliiiiiililllill _°_ l,Jd

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Next: APPENDIX D- PLOT Program →

APPENDIX D- PLOT Program

APPENDIX D- PLOT Program User Instructions This program was originally written for a CDC 6000 computer (Ref. 113) and was then modified to run in single precision on an IBM 370-165. Given a set of input data the program generates the necessary instructions for auto- matic plotting of an airplane numerical model and can be used to draw three- view and oblique orthographic projections, as well as perspective projections.

These plots are very useful in checking the validity of numerical model data.

The program has an average execution time of _ minufes and 20 seconds for a job yielding 8 different views of the same aircraft.

In order to be compatable with the potential flow program used in this report (see Appendix F), the body coordinates are specified with the body nose at, or near the origin of the coordinate system, dnd the body's longitudinal axis is extended along the X-axis (see Figure D-I). The origin of the Y-axis must lie in the XZ-plane of symmetry, and the Z-axis must be the vertical axis of the body.

Reference 113 does an excellent job of describing the input data cards; therefore, the data specification given below is taken directly from that description. Additional information on this program is available in the cited reference.

Configuration Cards Since the airplane has to be symmetrical about the XZ-plane, only half of the airplane need be described to the computer. The convention used in pre- senting the input data is that the half of the airplane on the positive Y-side of the XZ-plane is presented. The program then uses this information to con- struct the complete airplane. The number of input cards depends on the number of components used to describe the configuration, whether a component has been described previously, and the amount of detail used to describe each component.

The method of input is by FORTRAN "READ" statements.

FORTRAN Columns Name Description 01 to 03 JO If JO=O, no reference area If JO=1, reference area to be read If JO=2, reference area same as previously read FORTRAN Columns Name Descrlptlon 04 to 06 J1 If Jl=O, no wing data If J1=1, cambered wing data to be read If J1=-1, uncambered wing data to be read If J1=2, wing data same as previously read 07 to 09 J2 If J2=O, no fuselage data If J2=1, data for arbltrarily shaped fuselage to be read If J2=-I , data for clrcular fuselage to be read (with J6=O, fuselage will be cambered; with J6=-1, fuselage will be sym_trlcal with XY-plane; with J6=1, entire configuration will be sym_trical with X_f-plane) If J2=2, fuselage data same as previously read 10 to 12 J3 If J3=O, no pod data If J3=1, pod data to be read If J3=2, pod data sam as previously read 13 to 15 J4 no fin data If J4=O, If J4=1, fin data to be read If J4=2, fin data same as previously read 16 to 18 J5 If J5=O, no canard data If J5=I, canard data to be read If J5=2, canard data same as previously read 19 to 21 J6 Simplification code: If J6=O, Indicates a cambered circular or arbitrary fuselage If J2 # 0 If J6=1, complete configuration Is sy_trlcal with respect to XY-plane, which Implies uncambered circular fuselage If there Is a fuselage If J6=-1, Indlcates uncambered clrcular fuse- lage with J2 # 0 22 to 24 NWAF Number of airfoil sections used to describe the wing; 2_ NWAF_ 20 25 to 27 NWAFOR Number of ordinates used to deflne each wing airfoil section; 3_ NWAFOR_ 30 FORTRAN Name Description Co Iumns NFUS Number of fuselage segments; I _ NFUS _ 4 28 to 30 NRADX(1) Number of points used to represent half- 31 to 33 section of first fuselage segment; if fuselage Is circular, the program computes indicated number of y- and Z-ordinates; 3 _ NRADX(1) _ 30 Number of stations for first fuselage segment; 34 to 36 NFORX(1) 4 _ NFORX(1) _ 30 Same as NRADX(1) and NFORX(1), but for second 37 to 39 NRADX(2) fuselage segment 40 to 42 NFORX(2) Same as NRADX(1) and NFORX(1), but for thlrd 43 to 45 NRADX(3) 46 to 48 NFORX(3) fuselage segment Same as NRADX(1) and NFORX(1), but for fourth 49 to 51 NRADX(4) fuselage segment 52 to 54 NFORX(4) Number of pods described; NP _ 9 55 to 57 NP Number of stations at whlch pod radll are to be 58 to 60 NPODOR specified; 4 _ NPODOR _ 30 Number of fins (vertical tails) descrlbed; 61 to 63 NF NF < 6 Number of ordlnates used to define each fln 64 to 66 NFINOR alrfoil section; 3_ NFINOR_ 10 Number of canards (horizontal tails) described; 67 to 69 NCAN NCAN < 2 Number of ordinates used to deflne each canard 70 to 72 NCANOR airfoil sectlon; 3_ NCANOR_ I0; If NCANOR is given a negative sign, the program will expect to read lower ordlnates also; otherwlse, alrfoll Is assumed to be symmetrlcal Cards 3, 4, . . . - remalnin_ data InDut cards. - The remalnlng data input contain a detailed descrlptlon of each component of the alrplane. Each card contains up to 10 values, each value punched in a 7-column fleld wlth a declmal and may be Identlfled In columns 73 to 80. The cards are arranged in the following order: reference area, wlng data cards, fuselage data cards, pod (or nacelle) data cards, fin (vertical tall) data cards, and canard (or horizontal tail) data cards.

Referencearea card: The reference area value is punchedIn columns

I to 7 and maybe identified as REFA in columns 73 to 80.

Wing data cards: The first wing data card (or cards) contalns the locations

in percent chord at which the ordinates of all the wlng airfoils are to be

specified. There will be exactly NWAFOR locations in percent chord given.

Eachcard may be identified In columns73 to 80 by the symbolXAFj where j

denotes the number of the last location in percent chord given on that card.

For example, if NWAFOR=16, there are I6 ordinates to be specified for every

airfoil, and two data cards will be required. The first XAFcard is identi-

fied as XAF10 and the secondas XAF16.

The next wing data cards (there will be NWAF cards) each contain four

numberswhich give the origin and chord length of each of the wing airfoils

that is to be specified. The cards representing the most inboard airfoil are

given first, followed by the cards for successive airfoils. The Information

is arranged on each card as follows:

Columns

Description

I to 7

x-ordinate of airfoil leading edge

8 to 14

y-ordlnate of airfoil leading edge

15 to 21

z-ordinate of airfoil leading edge

22 to 28

airfoil streamwise chord length

73 to 80

card identification, WAFORGj where j denotes the

particular airfoil; for example, WAFORGI

denotes first (most inboard) airfoil

If a camberedwing has been specified, the next set of wing data cards

is the meancamberline (TZORD) cards. The first card contains up to 10 Az

values, referenced to the z-ordinate of the airfoil leading edge, at each

of the specified percents of chord for the first airfoil. If morethan I0

values are to be specified for each alrfoll (there will be NWAFOR values),

the remaining values are continued on successive cards. The remaining airfoils

are described In the same manner, data for each airfoll starting on a new card, and the cards arranged in the order which begins with the most inboard airfoil and proceeds to the outboard. Each card may be identified In columns 73 to 80 as TZORDj, where j denotes the particular airfoil.

Next are the wing airfoil ordinate (WAFORD) cards. The first card con- tains up to 10 half-thickness ordinates of the first alrfoll expressed as percent chord. If more than 10 ordinates are to be specified for each alrfoll (there will be NWAFOR values), the remaining ordinates are contlnued on successive cards. The remaining airfoils are each described In the same

manner, and the cards are arranged in the order which begins with the most

Inboard airfoil and proceeds to the outboard. Eachcard maybe identified

in columns 73 to 80 as WAFORDj, where j denotes the particular airfoil.

F_selage data cards: The first card (or cards) specifies the x values

of the fuselage stations of the first segment. There will be NFORX(1)

values and the cards maybe identified in columns73 to 80 by the symbol

XFUSjwhere j denotes the number of the last fuselage station given on that

card.

If the fuselage is circular and cambered,the next set of cards specifies

the z locations of the center of the circular sections. There will be

NFOFLX(1) values and the cards maybe identified in columns73 to 80 by the

symbolZFUSjwhere j denotes the numberof the last fuselage station given on

that card.

If the fuselage is circular, the next card (or cards) gives the fuselage

cross-sectional areas, and maybe identified in columns73 to 80 by the symbol

FUSARDj where j denotes the numberof the last fuselage station given on that

card. If the fuselage is of arbitrary shape, the y-ordinates for a half-section

are given (NRADX(1) values) and identified in columns73 to 80 as Yi where i

is the station number. Following these are the corresponding z-ordinates

(NRADX(1) values) for the half-section identified in columns73 to 80 as Zi

where I is the station number. Eachstation will have a set of Y and Z cards

and the convention of ordering the ordinates from bottom to top is observed.

For each fuselage segmenta newset of cards as described must be pro-

vided. The segmentdescriptions should be given in order of increasing

values of x.

Pod data cards: The first pod or nacelle data card specifies the

location of the origin of the first pod. The information is arranged on the

card as follows: Description Columns i to 7 x-ordinate of origin of first pod 8 to 14 y-ordlnate of origin of first pod 15 to 21 z-ordinate of origin of first pod card identification, PODORGj where j denotes 73 to 80 pod number The next pod input data card (or cards) contalns the x-ordinates, ref- erenced to the pod orlgln, at which the pod radli (there will be NPODOR of them)

are to be specified. The first x-value must be zero, and the last x-value Is

the length of the pod. Thesecards maybe identlfied in columns 73 to 80 by

the symbolXPODj where j denotes the pod number. For example, XPODIrepresents

the flrst pod.

The next pod input data cards give the pod radii correspondlng to the pod

stations that have been speclfled. These cards maybe identlfled in columns

73 to 80 as PODRj where j denotes the pod number.

For each additional pod, newPODORG, XPOD, and PODR cards must be pro-

vided. Only slngle pods are described but the programassumesthat If the

y-ordlnate Is not zero an exact dupllcate Is located symmetrlcally wlth

respect to the XZ-plane; a y-ordlnate of zero implies a slngle pod.

Fin data cards: Exactly three data Input cards are used to descrlbe a

fin. The Information presented on the first fln data input card is as

follows:

Co Iumns

Descriptlon Ito7 x-ordinate of lower alrfoil leading edge 8 to 14 y-ordinate of lower airfoil leadlng edge 15 to 21 z-ordinate of lower airfoil leadlng edge 22 to 28 chord length of lower airfoil 29 to 35 x-ordinate of upper airfoil leading edge 36 to 42 y-ordinate of upper alrfoil leading edge 43 to 49 z-ordlnate of upper alrfoll leading edge 50 to 56 chord length of upper airfoil 73 to 80 card identification, FINORGj where j denotes fin number The second fin data Input card contalns up to 10 locations in percent chord (exactly NFINOR of them) at which the fin airfoil ordlnates are to be speclfied. The card may be Identlfled in columns 73 to 80 as XFINj where j denotes the fln number.

The third fln data Input card contains the fin alrfoil half-thlckness ordlnates expressed In percent chord. Since the fln airfoil must be symmetrical, only the ordinates on the positive y side of the fln chord plane are specified.

The card Identification, FINORDj, may be glven in columns 73 to 80, where j denotes the fin number.

For each fin, new FINORG, XFIN, and FINORD cards must be provided.

Only single fins are described but the program assumes that if the y-ordinate Is not zero an exact duplicate is located symmetrically with respect to the XZ-plane; a y-ordinate of zero Implies a single fin.

Canard data cards: If the canard (or horizontal tall) airfoil Is sym- metrical, exactly three cards are used to describe a canard, and the Input Is given In the same manner as for the fin. If, however, the canard airfoil Is not symmetrical (Indicated by a negative value of NCANOR), a fourth canard data Input card will be required to glve the lower ordinates. The Information presented on the first canard data Input card Is as follows: Description Co I umns x-ordinate of Inboard airfoil leading edge 1 to7 y-ordinate of Inboard airfoil leadlng edge 8 to 14 z-ordinate of Inboard airfoil leading edge 15 to 21 chord length of Inboard airfoil 22 to 28 x-ordinate of outboard alrfoll leading edge 29 to 35 36 to 42 y-ordlnate of outboard alrfoll leading edge z-ordinate of outboard alrfoll leading Adge 43 to 49 chord length of outboard airfoil 50 to 56 card identlflcatlon, CANORGj where j denotes 73 to 80 the canard number The second canard data Input card contains up to 10 locations In percent chord (exactly NCANOR of them) at which the canard alrfoll ordinates are to be speclfled. The card may be Identlfled in columns 73 to 80 as XCANJ where j denotes the canard number.

The third canard data Input card contains the upper half-thlckness ordinates, expressed In percent chord, of the canard alrfoll. This card may be Identlfled in columns 73 to 80 as CANORDj where J denotes the canard number. If the canard

airfoil Is not symmetrical, the lower ordinates are presented on a second

CANORD card. The programexpects both upper and lower ordinates to be punched

as positive values In percent chord.

For another canard, newCANORG, XCAN, and CANORD cards must be provlded.

Plot Cards

A single card contains all the necessary Information for one plot. The

avallable options and the necessary Input for each are described In the suc-

ceeding sections.

Orthographlc p rojectlons. - For orthographic projections, the card should be set up as follows (See Figure D-5): FORTRAN Co Iumns Name Description I HORZ "X", "Y", or "Z" for horizontal axis 3 VERT "X", "Y", or "Z" for vertical axis 5 to 7 TEST I Word "OUT" for deletion of hidden lines; other- wise, leave blank 8 to 12 PHI Roll angle, degrees (See Figure D-I) 13 to 17 THETA Pitch angle, degrees (See Figure D-I) 18 to 22 PSI Yaw angle, degrees (See Figure D-I) 48 to 52 PLOTSZ PLOTSZ determines the size of plot (scale factor is computed using PLOTSZ and maximum dimension of configuration) 53 to 55 TYPE Word "ORT" 72 KODE If KODE=O, continue rea_ing plot cards If KODE=I, after processing this plot, read new configuration description An attempt is made to center the given configuration within the specifled field. If the desired plot size is greater than 28 inches, centering is attempted within 28 inches so care must be taken in choosing the view. Minimum values are adjusted so that body axis lines with no rotation angles coincide with grid lines on the plotter paper. Therefore, the plotter pen should always be positioned exactly I inch from the side of the plotting space and on the intersectlon of heavy grid lines at the start of plotting.

Plan,. front L and_si.de views (stacked). - For plan, front, and side views, the _rd should be set up as follows (See Figure D-4): FORTRAN Description Columns Name y-origin on paper of plan view, inches 8 to 12 PHI y-origin on paper of side view, inches 13 to 17 THETA y-origin on paper of front view, inches 18 to 11 PSI PLOTSZ determines size of plot (a scale factor 48 to 52 PLOTSZ is computed using PLOTSZ and maximum dimension of configuration) Word "VU3" 53 to 55 TYPE If KODE=O, continue reading plot cards 72 KODE If KODE=I, after processing this plot, read new configuration description Perspective views. - For perspective views, the card should be set up as follows (See Figure D-IO): FORTRAN Description Name Columns x of view point (location of viewer) in data PHI 8 to 12 coordinate system y of view point in data coordinate system 13 to 17 THETA z of view point in data coordinate system 18 to 22 PSI x of focal point (determines direction and focus) 23 to 27 XF in data coordinate system y of focal point in data coordinate system 28 to 32 YF z of focal point in data coordinate system 33 to 37 ZF Distance from eye to viewing plane, inches 38 to 42 DIST Viewing-plane magnification factor; it controls 43 to 47 FMAG size of projected image FORTRAN

CoI umns

Name Description 48 to 52 PLOTSZ Diameter of viewing plane, Inches; DIST and PLOTSZ together determine a cone which Is fleld of vision; PLOTSZ value Is also relative to type of viewer which Is to be used.

53 to 55 TYPE Word "PER" 72 KODE If KODE=O, continue reading plot cards If KODE=I, after processing thls plot, read new configuration descrlptlon.

Stereo frames suitable for viewing In a stereoscope. - For stereo frames sultable for viewing in a stereoscope, the input Is identical to that for the perspectlve views except that the word "STE" is used in columns 53 to 55.

Speclflcatlon of the cards above represent a complete set of data for a particular body. The format specification for thls data Is given In the above text. A sample data set of a Cessna 182 light aircraft Is shown In Figure D-2.

The output of this particular data set, with different plot cards, Is shown In Figures D-3 through D-14.

Plotting Software Modifications Since plotting software is different at almost every computing facility, this section of the appendix is included to help the user specify the ap- propriate softwareplotting instructions expected by the plot program. To institute a plotting procedure at any computing facility the user's program must first be linked with the plotter. In the original plot program linkage was established by the statement: CALL CALCOMP. The user must provide the necessary instructions to produce the same result at his facility. This instruction is given on card CO0 35 In the Program Listing presented in the next section of this appendix. In addition, at most installations an in- struction must also be given to close the plotter data set (i.e. turn the plotter off) after plotting has been completed. In the original plot program this was accomplished by the statement: CALL CALPLT(O.,O.,999). The user must provide an equivalent instruction for his installation as seen on card CO0 67 in the Program Listing.

The actual plotting in the program is accomplished using three baslc subroutines (CALPLT, NOTATE, and LINE) from the CalComp software package.

For the program to operate properly, the user must either provide the original CalComp routines or provide three equivalent dummy subroutines as was necessary at the N, C. State computing facility. Given below is a description of the arguments to, and the results produced by these sub- routines. Also included are listings of the equivalent dummy subroutines used at N. C. State to produce the same results as the original CalComp subroutines.

Subroutine CALPLT To move the plotter pen to a new location wlth Purpose: the pen either up or down, and to turn off the plotter.

CALL CALPLT(X,Y, IPEN) Use: where are the floating point values for pen X,Y movement.

IPEN=2 pen is moved in a lowered position.

=3 pen is moved in a raised position.

Negative IPEN (-2 or -3) will assign X = O, Y = 0 as the location of the pen after moving the pen to X,Y (create a new reference point or orlgln).

IPEN=999Turns the plotter off, the X and Y

values are ignored.

Restrictions: All X and Y coordinates must be expressed as floating point Inches (actual page dimensions) in deflection from the orlgln.

(Equivalent N. C. State Routlne) SUBROUTINE CALPLT(A,B, I) DIMENSION A(1),B(1) IF (I.LT.O) GO TO 5 J=1-2 CALL PLOT(A,B,J ) RETURN 5 J=IABS(1) J =J -2 CALL PLOT(A,B,J ) CALL ORIGIN(A,B, 1.0) RETURN END Subroutine NOTATE Purpose: To draw alphanumeric Information for annotation and labeling.

Use: CALL NOTATE(X,Y,HEIGHT,BCD,THETA,N) where X,Y are the floatlng polnt page co- ordlnates of the flrst character.

For alphanumerlc characters, the coordinates of the lower left-hand corner of the characters are specified.

HEIGHT specifies the height In floatlng polnt inches for a full-size character.

BCD is the string of characters to be drawn and is usually wrltten In the form: nHXXXX--- (the same way an alpha message is wrltten uslng FORTRAN for-

BCD con't

mat statements). Instead of specifylng

alpha informatlon as above, one mayglve

the beginning storage location of an

array containing alphanumeric infor-

mation.

THETA

is the angle in floating point degrees

at which the information is to be

drawn. Zero degrees will print hori-

zontally reading from left to right, 90°

wlll print the line vertically reading

from bottom to top, 180 °wlll print the

llne horizontally reading from right to left (i.e., upside down), and 270 ° will print vertically reading from top to bottom.

is the number of characters, including

N

blanks, in the label.

(Equivalent N. C. State Routine) SUBROUTINE NOTATE(A,B,C,D,E,I) DIMENSION D(1),DD(21) DATA STOP/4H _/ J=l/4 XI=I XR=XI/4 IF ((XR-J).GT.O.1)J=J+I DO 5 K=I,J 5 DD(K)=D(K) DD(J+I)=STOP CALL SYMBOL(A,B,C,DD,E) RETURN END Subroutine LINE To draw a continuous line through a set of suc- Purpose: cessive data points where the minimum values and scale factors are stored at the end of the data arrays.

CALL LINE(XARRAY,YARRAY,N,K,J,L,S) Use:

where

XARRAY and YARRAY are the names of arrays con-

talnlng the X values and Y values, respectively, to be plotted. Values must be in floating point.

Is the numberof points to be plotted.

K= I

this value of K is constant in the plot

program.

J =0

for llne plot. Only line plots are

used in the plot program.

is an integer describing symbol to be

used. This variable is not used but a

space for it in the calling sequence

must be provided.

is the desired symbol height. This

variable is not used but a space for

it in the calling sequencemust be

provided.

Restrictions:

LINE expects the adjusted minimums and scale

factors. Thesetwo parameters (two for the

XARRAY and two for the YARRAY) are automatically

calculated and provided by the plotting pro-

gram at the ends of the XARRAY and YARRAY

respectively. The points actually plotted by

LINE are

(XARRAY(J) - XARRAY(N+I))/XARRAY(N+2) for J=I,N

and

(YARRAY(J) - YARRAY(N+I))/YARRAY(N+2) for J=I,N.

(Equivalent N. C. State Routine)

SUBROUTINE LINE(A,B,I,J,K,L,S)

DIMENSION A(1),B(1),X(31),Y(31)

XMIN=A(I+I)

XSCALE=A(I+2)

YMIN=B(I+I)

YSCALE=B(I+2)

DO5 11=1,1

X(II)=(A(II)-XMIN)/XSCALE

5 Y(II)=(B(II)-YMIN)/YSCALE CALL PLOT(X,Y,I) RETURN END positive roll angle-PHI positive yaw angle- PSI positive pitch angle-THETA Figure D-I. Orientation of body with respect to body reference axes for the PLOT programs.

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!!

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|o1_ I.I_N I°MgN I° _lYa 1°8_ |o_SlO I. 7141441 I.Jo|_ 0o01110 o _ol_o 0°0 ° 6°_lY_ 0.0 0o361_ 0.?l_ I°L_IT0 8.s4glo I*?1|_ |*16o_a I.IT_g hl?$QO Ioa?_ 0°0 ° 0°0 Io|f$_ I°lf_ I°IY_ t.l_010 L.IS4_ Io?_|?0 |°$_70 L.ISlIO 0o?_8_0 0° _IY0 0.0 |.|rS_ IoO?_ h gYVeD I°NI?I ! ° 14_N Io?Ol_ |.SI_0 I*IIQ_ @° ?_!40 0° _$4_0 0.0 0o0 0o0 0._7_i0 0o SlON 0._IO 1° I1_$0 | ° 41000 I°_YO I o?10O0 h7_10 I. _lO 0.0 0.0 0._0_ 0. S_010 0. ?lJ_0 |.01_ |o_$410 IoStlI0 1°61_ 1°6_00 1.64_10 0°0 0.0 0°_ZON O°450)O O.;OOO0 0._I_10 I._O h_l_f0 8 o_0O_ |°_S0 |._S_0 1._5_10 I°_S_ |°_S_ |o_!1_ |°41_ I.Z_I_0 0._0 0. _S_Q O.$|040 0° _$10 0°0 I._1670 1.41670 1°_1670 L°_6;0 L._Si_ I.ISI_ 0°_00 0._@ 0.*_010 0o _|_10 0°0 0.0 0o0 0.0 _._110 3°_6_ _._I_00 _.+_10 3°$)$4O _.6Z_IO _°?1_ _°_lS0 _°11110 4. _1.,4_O 0.0 _°)lZg0 0.0 0o0 0°0 0.0 0.0 0o0 0*0 0°0 I°0 0°1 O.0 0°0 0°0 0°0 0°0 0°0 0.0 Do0 0.0 O.0 0°0 0o0 0.0 2. $00_ S*@0O_ L0* ¢0000 _0*_O_ |0*_O _Oo0O0g0 60°@0000 $0.¢_0 |_@o C0¢00 PLOT DII_ Y _ _r -_.00000 10°0@000 -30°00_ O.O 0oO g.O O.O go0 ?o_O_T x _T _.0_ 10o0_00 _0°0O@00 0o0 0o0 go0 O°O Q°O I@*0@C0_I Figure D-3. Continued.

Figure D-4. Plotted 3-view of the Cessna182.

BEST CESSNR 182 WITH M=21 RND N=29 YIELDING 560 PRNELS -- COMPLETE R!RPLRNE X Z -_5. i0. -30. 8.5 ORT Flgure D-5.

Orthographic projection of a Cessna 182 rolled -45 °, pltched 10 ° and yawed -30 ° with respect to the X-Z plane of symmetry.

BEST CESSNA 182 WITH M=21 AND N=29 YIELDING 560 PANELS -- COPPLETE AIRPLANE 30. 9.25 OAT Orthograph|c projection with hidden lines removed of a Cessna 182 rolled 45 ° , pitched 10 °, and yawed 30 ° with respect to the X-Z plane of symmetry.

BEST CESSNA 182 WITH M=21 AND N=29 YIELDING 560 PANELS -- COMPLETE AIRPLANE X Z _5. 10. 160. 8.5 ORT Orthographic projection of a Cessna 182 rolled 45 ° , Figure D-7.

pitched 10 ° , and yawed 160 ° with respect to the X-Z plane of symmetry.

BEST CESSNR 182 WITH M=21 RND N=29 YZELDING 560 PflNELS -- COMPLETE X Z -_$. O. --70. 8.5 ORT Figure D-8. Orthographic projection of a Cessna 182 rolled -45 ° and yawed -70 ° with respect to the X-Z plane of symmetry.

BEST CESSNR [82 WITH M=21 £ND N=29 YIELDING 560 PRNELS COMPLETE flIRPt.flNE Y Z OUT -45. 10. -30 7.50RT Orthographic projection of a Cessna 182 rolled -45 °, Figure O-9.

pitched lO °, and yawed -30 ° with respect to the Y-Z plane.

BEST. CESSNB i82 WITHM=21QND N=29YIELDING 560 PRNELS -- COMPLETE RIRPLRNE

•-20. 50. SO. 7.0 0.0 5.0 15.0 1.0 10. PER Figure D-IO. Perspective view number 1 of the Cessna 182.

BEST CESSNR 182 WITH PP21 RND N-29 YIELDING 560 PRNELS -- COMPLETE RIRPLRNE -20. -50. -50. 7.0 0.0 9.0 14.0 1.0 10. PER Figure D-If. Perspective view number 2 of the Cessna 182 (The reader should note that the viewer is under the aircraft looking up.)

BEST CESSNA 182 WITH M=21 AND N=29

| Figure D-12. Plotted 3-vlew of the Cessna 182 fuselage.

,w (D o !

o

T

C) N X _d T o o °_ u_ BEST CESSNA 182 WITH M=21 AND N:29 YIELDING 560 PANELS -- FUSELAGE ONLY Y Z OUT -_5. i0. -30.

ii. ORT Figure D-14. Orthographic projection with hidden lines removed of a Cessna 182 fuselage rolled -45 ° , pitched lO °, and yawed -30 ° with respect to the Y-Z plane.

Next: APPENDIX E- CONVERT Program →

APPENDIX E- CONVERT Program

APPENDIX E- CONVERT Program

User Instructions

This program Is written In FORTRAN IV and is designed to run In single

preclslon on an IBM 370-165 computer. Given a set of plot Input data as

descrlbed In Appendlx D, this program (I) produces a properly Ipdexed data

set for the NCSU BODY program, (2) computes the area of each body panel

described by the Input points and displays each area in an orderly fashlon,

and (3) dlsplays the ratlo of the area of each panel to the area of the panel

below It and the panel to Its rlght. It should be noted that while the

CONVERT program produces a data set for the alrcraft body, It will accept the

Input of a data set for a complete alrcraft configuration and ignore the un-

necessary Information (wlng, tail, nacelles, etc.). Execution requlres 92,000

bytes of core storage and approximately 15 seconds to run a case wlth 560

panels speclfled. A descrlptlon of the Input data cards Is not included here

slnce It Is the same as that for the PLOT proAram in Appendlx D. The format

speclflcatlon Is also the same. The program listing Is given In the next

section of this appendlx and Is followed by the sample output (Figure E-I)

corresponding to the Cessna 182 data set glven In Flgure D-3.

!

m ,,J

-; i

!

t..ooS .... _-S- =-- - - |- .........

|t ._|S....3.S ...... 8 .... _ =..o t. oo .=hi.==...

!

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C3D

e-

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.-I

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o

g.

.... o

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37O

_.=......:_:::::.::__ ......... _........._........:_....:....

Somple Output

0•| I•IIII o.*sem 0.?000 ••IIH 1.1141 L.4|OT I.S011 I.II_ l.ilN ).SIlt L.ISO0 I•_41• I*Ht_ |.+HI 1.1111 o*ml 0.1MI O*I)0+ Iol*_ll 0 • t o e O o o o I • o 0 I I 1.01,I Z••161 I.i$0I ).HOT 1.19e) ).016T 1.1114 J.91s+ 1.1111 o*mo 0.0 0.4961 I.IJN i•ooeo z.7_90 5.))_e ).e_40 4°5ooo s.mll g•6961 6.1100 +1•_tt 4.191T I.e191 1.1111 _.SI_I •.1611 S.I+_ S.IlSl O*I_tt 6.1_41.0 6.011141 ;.+9170 ?.9?H 1.5_110 9•|JJse e.?000L0*IT_0lL•_bI01hO•10 1.6*g| 1 i. +S401)•0111114* 1IS015. 41 )0tO. 01101 e• II_oI1.O L_01 h S_elO•_t 70 • .• •.ll•I 0.9111 •.41•| •._11I L*I71_ Io1147 IoSI_ 1.61H 1.6161 0•0 e.e e.e o•o 0.0 o.e o•o o.i e.o o.o 1.616T |.9|•t 1.9147 1.916_ I._SII )*)OH 1.0111 e._rl+ I.OUll 0.11.11 o.o o.o eoo o.e o.o o.o o.e o.1 o•o o.o o.o • .0 6 _.0711 1.9791 I.SLII 1.9194 ).8111 1.1109 I.I1tl I.SlII 1.11H .llII +._T00 _*ZTOI 4•_T00 *.ItH _•ZT0e **Z_IO 4•29oe *.ZT01 _•ZTOO _.lY0e 4.HI) *o1111 +.t)l) I.H11 1.1111 1.4111 So1411 S.SlYS S.SSll I.ITll 4.2)00 4•2?00 e•zl0e 4•|FOI 91.1?01 4•17OO 4*it011 4*IY00 4.1700 4._tr0i S.S•)) *.lvoe 0.0 e.le?_ O.II?$ 0.1910 •.l_le I.•Yl, 1.1911 1.1145 1.HIT t.IM0 I.o I.tJJ) o•11o) o.11_ o.67o1 0.110T 0•9680 I.L01) I•Z016 t.*H) IoiS00 I.ISN ).IN0 |.IH* I.|611 )*•)IS O*I*I_I O*I_I_ Io011I O*IIIS L*$167 i,$_le i.slzs 1•491T |.||9| t.|041 O•00)) 0.661T 0•_!? O•II+T e.o 0.• 6 1.1|Se ).Ill0 ).11_I J.|II4 ).lifo ).I91V ).+*II i._els i._III .1111 )•lmli$ 1•io441 i.i1o@ )•|_4| )•_479 )•41124 )•)Tml ),Toil ),814I <,.i_l$I 9.1111 **sol) +.yol) ..911_ _.i_•) 1.11|i _.6111 0.<911 o*_ols o*oml 6•!101 *•Sllt 4•TTH 5*0101 S*ll0e $.)TOI t.+)_ t.916191 S*4750 9.4791 11.4192 0.• 0.1T_0 •.1914 e.1_T1 0._S00 •o6111 I*•151 1.141'I t*01H I*IIIH o.o o•lloI 0.641o e***is o.oT,o l.ol*z L•1101 1.160_ 1.<4991 1.5191 I•0111 1.0•11 i.n11 1•itso t.HS0 0._Ias •.T_l O*_0)T D.1914 0.1_IT |.6411 1.4661 I•6901 |.1441 |•oTol l.lSoa I•0101 0.;IU 0.1196 0._I00 0.• o•e 1.1111 ).I917 IoI_70 I.H01 ).)I)I )**_II )._l•t I.H_I 4.1115 4.191T I*ITH I.TTS0 |•Ollg I•1191 l.qNlYl 3•II_0 ).I_11 I*OqlY )*TO)| )•'115 *.16.I 6.1111 _.YlI) 6._) $.LN) 1.11_| Io•14, _.611T So61_ O*_I_I $._I11 s.ae+l o.e •.is00 0.10+J •.*41T •.•111 1.10_) 0••114 0.•114 0.1ml_ e.I_11 0•1 00141T 0•5010 0*T6_6 Z•0J7_ |._0 l*+1?,I 1.6081 I*lal)) |•F121 0.I111 •.191• •.l_Ii e*HT_ •.Ill) •.I•II e._sll 0.IiI_ i.l+sl O*IlOT I*119J 1.7291 1.111 II I*OYY l.S+Tq |.1|Iq 1.00YS 0.1_1 0.5011 0*I?S_ •.0 0.0 1.9511 ).,69_ i.+t_0 l.oas• ).11_+ 1.01yl |.ti15 ).NIl _.L|IT 4o1144 4**O+) 6._79 *.4911 9.•_I 1.0M) 1.1119 I.It14 5.nl_ i.II_I •.H_ 4.1451 4•4_|6Y 4•6_?_ 4.90_6 t•_ 96_ )•65o) 'J.sY_ 5+6_'12 '_.t_61 g•4950 I. if+| J*_lJ) • .0 e•iiii 0.1196 i.iii+ 0.I014 o*is)i o.•sl_ O*_0tT O*III+I 0*I 0.0 0•1101 0. llJI O.llJ) 1.1_ 1-_0 1"6_ I'Tl_ I*TY_0 I.TlYL 0._0•I I.ml •*_011 e._0_ e.•soi o*l_o •.•i•7 o*ot_t o*Iv_ 0.1441 l. Tel) 1•T111 l.??)l t.liT_ 1.4117 1.14117 1.1411 0.0154 0.SS10 0*lOOT o•o • .0 6 1.1911 ).•16• •.0_ii hill0 ).l_Itl ).I914 I._9_ _oII11 6o1110 .1446 I•4511 1*6611 1.4401 l.*T_l I•5|04 2•44|; 2.9011 |.1101 ).5419 ).e_Ir _.otel 9••I_I 4.11"I 6.1111 *.9161 I*0YlI •.1141 O*II|• $*mI •.ml 4.1111 4•_II 91._1? 6•1_I $.1111 I.I161 $.1417 s•7o41 I.T14_6 S.TiO_i •.Ills $*T0lT e.e e.|011 •.1111 0.1_IT O*1191 O.9061 0.410_ O*_II 0.6111 I._ll 0.0 0•1_11 0•s$11 0.15411 1.1|16 t.s)|) |•?4511 t•1147 2.0111 1•0111 1.6191 •.41_ 0.+M6 0.*II) e.*I16 0.6111 0._I_I e.H•T O*IUD 0.LILY 1.i_z_ 1.1121 I.011, i•14111 l.Orso 1.4191 1.1_7_ o.e_ol o•111_ o.so+l e.o 0°0 I.H|• |o0111 •.•011 |.15_ *.I_II 6.ti*6 _olII| _.III_ _.I146 4.H4m I*+11+T I.OIOT _•4108 |*+Ill 1.4511 I*_I 1.0_I ).|0IT )._1|I I*11TS 4.11_I 6.S_10 +.0_S0 9.tI_I 4.1619 9.9191 1.01t! O*HS0 S.lSI0 O*III0 1.111• s.o))l • .e O*I I.• o*e o*o o*i o*• 1.0 o*e IoI o.o o.14191 1.911o o.9111 l.Z_o I._11 L•TO_S JII_i l•0711 l.l?_0 o*o e.o o*e 0.e i.• l.i o*o o.o o*e iol hi?S0 hl_e 1.17_0 l.I_ L•1141 l•OeTS |•4001 1.0911 0•7115 0•14_ o.• i.e z.)y_ l•J_so 1•_m) ).4_11 i._479 i.?l_l i.iJJ) )*)YH I*?lle 4.011* 9oY_11 4.1_11 4o_ii? +oi_|) 4.yqll? 9•?•IT 4*TlIT 6o_IT 6.I_II _.)))i 416_0 _._)IJ 5.1T50 _.i_IJ 6•016T +•1111 +.I_OI +*14.17 +.2011 6.T'I?

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Figure E-I. CONVERT program sample output of the Cessna 182

with 560 panels describing the half-body.

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Next: APPENDIX F- NCSU BODY Program →

APPENDIX F- NCSU BODY Program

APPENDIX F- NCSU BODY Program User Instructions The program is written In FORTRAN IV and is designed to run in single precision on an IBM 370-165 computer with an execution time of 10-12 minutes for a half-body with 560 panels (I minute for a half-body with 100 panels).

The 560 panel case required 250,000 bytes of core storage. The program cal- culates an approximate solution of the three-dimensional viscous flow over an arbitrary body and estimates the body lift and drag coefficients. The program was obtained by making major modifications to the XYZ potentlal flow program (Ref. 94) supplied by the Naval Ship Research and Development Center, Bethesda, Maryland. The data input and program logic modifications were employed to specialize the program for light aircraft fuselages; therefore, this modified program no longer has the design Capability of the original XYZ program.

Figure F-I illustrates how the body ordinates should be input to provide the correct body orientation wlth respect to the flow direction.

The program Input data specification is based on the descriptlon glven in Reference 94 except where changes were made. The Input consists of. an identification card, two parameter cards, and several body point cards A description of the program Input is given below.

Card I - Identification - Card I contalns any informatlon to Identlfy the problem in columns I through 80.

Card 2 - Flow Control Varlables - Card 2 contains 3 variables whlch determine the flow Reynolds Number, the reference area upon which the co- efficients are based, and an output control parameter. This Is the only card which must be inserted into a data set produced by the CONVERT program in Appendix E.

Parameter Column Description VINF 1-10 Reference free stream velocity in ft./sec, if the body input points are specified In feet (in general it will be units/second where units are the units in which the body input points are specified).

VO 11-20 Kinematic viscosity o_ the fluid in which the body is moving in ft._/sec, if the velocity is specified in ft./sec.

tAll of these cards except one (card 2) is supplied by the CONVERT program given in Appendix E.

Parameter Column Description ROE 21-30 The density of the fluid in which the body is moving in slugs/ft. 3 31-40 REFA The reference area upon which theAaerodynamic coefficients will be based in ft. Z IWRITE Control variable which denotes the amount of out- put the user desires. IWRITE=O yields maximum output. IWRITE=I deletes information given for each input point. IWRITE=2 deletes streamline and boundary layer information as well as input point information. (See Sample Output).

Card 3 - Control Inteqer - Card 3 contains a control integer which must be right justified.

Parameter Column Qescriptlon I-4 NQE Number of quadrilateral panels to be specified by the point cards. The value of NQE should gen- erally be less than 600 (see page 244).

Cards 4. 5, . . . - Point Cards - Each polnt card contalns the following information for one point on the body surface. If one section is used for the fuselage there should be P points specified where P is equal to the maximum MI times the maximum NI.

Parameter Co Iumn Description Xl 1-12 X-coordlnate of the input polnt.

YI 13-24 Y-coordinate of the input point.

Zl 25-36 Z-coordinate of the input point.

NI 39-40 N body station index (see Figure F-2). For plot- ting purposes NI_30.

MI 43-44 M body station Index (see Figure F-2). For plot- ting purposes MI__Z30.

NS 45-48 Section identification number. The CONVERT pro- gram (Appendix E) supplies a one-section data set with a section number of I.

Last Card - Eqd of Data Set - The last card is a blank card to signify the last card of a particular data set.

It should be noted that the program can be run for more than one data set; the user must simply put the complete data sets he desires to analyze in con- secutive order. For more information about this program the user should see pages 243 - 255 which describe the modifications made to the original program as well as Reference 94 which describes the original program.

Specification of the cards above represent a complete set of data for a particular body. The format specification for this data is given in Figure F-3. A sample data set of a prolate spheroid is shown in Figure F-4. Por- tions of the sample output for the light aircraft data set shown in Figure D-3 and plotted in Appendix D are given in Figure F-5. The light aircraft data set was not used in Figure F-4 as the _amp e data set because of the excessive length of the light aircraft data set (in excess of 600 cards).

Z Figure F-I. Orientation of body with respect to body reference axes for the NCSU BODY program.

Next: SECTION A →

SECTION A

Z

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60 panels describing the half-body, 379

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_ o 0 _ O m om

G

zz.:-_ .... ..-- ii:.i:.i._iiii.:-:liii.:ii-:iiiiiii.:l-_ii_iiiiiiii-:i:-i': -" __-" .... _

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i i i iii

. :::::::: :-_-_-_.-: _-;,_

i ," .... "'"'_'°'-" ....

i" 'f ,o ...... . ............

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| t-. 8,.-.. -- -- *,,- g | 8 _ @0 _:

_____t_

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IiliI "IiiII_Ii : ":llliI_ It :liIll: I

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_ 0_ o_

o

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m

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• ._ ...... L_ _I.Q P_Q • _.a>-i- t- . ILI_. *1 k*l_ 11.* z. |. _.. . _ ....... + ...... _l ...... !o.

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Sample Output

POtI_TIAL _LOb pll_lltll SKYI_ l OEST CISS_A 18J MIrN m-Z1 4_ _Z9 TIEL01_ _60 P_|tS -- _$1LIGI O_Y o_0. 04¢ I roles+ mlXo _0. o@ ITlmAllOmS • FL_ ISO ¥1W - 1_6._e1_1 W • 0•C00|6O m_ • 0.O0Z_YO t|pa • It4,_o011 III IVl - 0 | PLANll OP ST_TR¥ CO_|mltllKl Cl|tlltli , O*O00|O SKt IOtl I Vl _Z Y_ 14 VP VII •L Cll P El 10 l) 14 IP lu CII CII MSTI0_KI POINt -PO01 fit 0._|4_1-01 mMIIIM LONG tram _0J0.

0.0 O,0 0, I III_I O.O O.l110M-01 °.leSlie @•101411 -0• 011111 00 : ..,.-11 ..,.+..0 -0.0,,,00.

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l 0 I 0 °.lt01el O.gl+lSdMl i |HIM O+4_00ll O*l$11e• -0.101lqe °o o .

o ++l?les N -°,41tl0e 00 @ llgS_ll Ol -e•|41071 OL -0.107161 01 -°•4_Sl_dE 0° °.°?ll0_-01 -0.1411_I 00 + . ..... . .............. .. _..,. ..... O.OleS_l O*6?01IN O.l?°e01 0,66ISH 0.61+071 0.+I°+ll 00 @•l@_l_l 00 -0.I14000 H -0.14_$tI -0+ll00el Ol -0•17104_ 01 -0. Lllltl 0l -0.1°gill 01 -0.T014IN 0O 0olllO_-01 0.1611N_01 MITIONAILI POINt -PQ_ Pit 0.Ylse-0Z °MIIIII L01IN YNIN 0US•+ , ..,....+,,,.o, 0.1,,+....,1,.,.° .•,0.0.+:. ,.,,,1,000 -..0,+.,00, I l.i 0.I 0.111tel M 0.170100 0_i 0.411501 0.1°0+M °.II0101 -0.114_M H 1 -0,017111 01 +0•+Itl01 00 -0.111111 01 -0. IliON -0.100171 -°.$°lltl 0.101001 -0.111111 00 00 0• I01750 01 0.10lfM - • °o o.nll,+u 0o o•ont,, co o.nome _ ° ..11 °, 0.610111 l.lll?es 0.10!10Z0 01 O °?_oel 0 15_01 00 00 - • • e.INIIH o.+0$)ll H

1. -..10-- -o.,.,,, 0, -o.1,,,. ,, +.1,,., ,, +.,,,,eS o, -0.,.,,0. ,.,0,,,,_0, +':::;___

: ., 0, ,0 . _ . ; +,°

TI V| Vl Y° _ L CZ!

• l| II ll II IP _ CII ¢16 11111111 LeiN tNIN IN°l.

I ?0•4eS _ I +IN 01 0 •ll_0 01 -41 11011'51 II +4 14JIM 01 0 °eSOqll-°l 0*111111 N 0 l?4leS 0l 1.1.I_I ,.0 + O., °•If.,, 0N_ 0.6,01+0I. 0.,641011 ii tllt_l_t_ IiI -0.1.9?_41-411 01_I 1.641411411 00 0.01_es ee O•OLOell O0 0JOIIes °.$0100e 00 °._00el 041 _ - -°•IZO011-Ol MIIIWk_° POINT oP_I lilt 0*°&ll-ll 1111111111 LONI TNIN OIMt+ o • • o o o 0 •l)Oes _ O q°||_l 01 0 1_01_I 00 _ I_IIIII 01 4 10eSle Ol • 11001 es O•|lql_N 00 -O•l$°qll0-Ol 0. LIIT•I 0°| 0•0 0A 0oHes•I_I •.I0S0el es 0.1451_I 01 -l.lpolel el SM 0*JIll01 es O* $I0_I 00 0. 001041-01 O. 101441_•1 0.201_I 01 0*°?4?eS eS 0.11 llH-°l O.l+llll-ll • I_0IKI 101_• 181 INTUI - S0LI0 IA_LI • II.$es POIINIlIL •L_I P•0_IAN M°IION !

1411 °11111 1O| |ITM kll ANT Nile •IILOI_I _II PINILS -- P_SILIII OIRT Figure F-5.

NCSU BODY program sample output for the

Cessna 182 with 560 panels describing the

half-body using the IWRITE=O option.

pe/IIIIIL _ _lm II¢llll s Mll ¢411111 lu •Ira N*il Lil I_1_ TII@INI 114 PlIIILS *- f_ssLill _T • vlLI¢I_'-I*O v _ILO¢|_ 0.• S vlL_II_= •*• IlllATlll _TAIx 16_1_ ImPl_mjTl_l IIIIITIII Ill _ llilllS i II II _ I.I Ol O,N 01 S I. I_TZlW I_ Ib O.l_|lq 41 S •. |_IIS 0| 11_1414 g I.AIIS lg l*l_l 11 • . IlllNII OI _ l*lOllq •1 • *_eSN N A II I* my•Ill--el 11 I* 14si II1-11 Is I* Ill_ll-II II •.140411-01 19 O* 11lii1-01 l SETA&POLAT | 011 I. lll •0 1.49q O• •*!141 OI 16 O .llSlt*ll*l_l lllll_ll_ ILOl _ SKII0N A PIll • I llSl llSlll Ill ilIM llll Ill l+ll TlllIlll liI PllllS -- IUlILill Ill • llLIll AOI.V Cp _ V P/. _ I VI V| • *lllSl •*lilt! O,•lll* O.SII" I II.,_l 1.0811l -I.EI•IS -O*44Sl, •.IgZl -4.44494 I .lilll -I*IITII •.01IN •*Sil" S II*itll_l •llllgi -h??Tll -O*tASSl •*IN'El 4*44&SB l*JT_411 l*llTi6 I*lllll l* llll + 1 | |* TAAI_ l* II_l) - J * lllkll *l*4_tlll •*l )_l| 4. lSllS hEAl•1 -OoItS41 O.0414• It llll- A II*I'NSS •*liIH -t.TIS_ -0._111n •,,061141 4.4TSEO I*lJlll I. SiAl I_ 0. 0919_ t.IM_ - . • • ii.ll_n o.l_1 -1.1Sill (I *,O1951 •*llilA -4 4_S4_ I*•lI_ -I*Oi_ I O* _ IQs • • ilt_ 6 II*_Sl •*Al_l *I*ITSI6 -8.$01+,4 l*lllll 4*lllSl • =lSlII I*ITTAI 0* ilS_ I.SI_ T II*l_l I. 19Ill -I.0T_0 -*• l_lSl •*•Sill -0.411Z9 hSSII9 *I,SlIT_ I*tI_IT I.IIt o .

0. All14 l.llill II. 141_lkl I. SIS- II.l•lll •*AlIlP I I011_ • 11•lll S*lllll _l*4_lA I|*Ti_ 1._9(,'/_ -I*¢KHITS -O*_,_t*AO 6*llI_ -O.4)l_i O*llil) I*ll•ll _*•_ll I. I1_ 10 ll.l_liT S. lSlll -hl;TSl -0.tS_I •.SSEIS -_).MIS?

Ell ol*Alll? •.4111411 l. $6111 -0o¢lYlO5 *i°11Tlt *O. I061,1 O.91lli 1.0Alll_ -O.Ollll 0*Ill Ill -IS,Still I.IT_ O,lllll 4._TT) 4.10)14 4.1OlTI O.ll_I 0*0TALE -0* li_l O* Ill SiS -l.llll, l 1.4IlSI O**illl -0.4)t*kl+l -4.OilS0 -0.10All O._lllll 1.1lilT -l.lillll • ill SIS - II*11Ill l I*SS_lO I.ITSlS *0,lSl51 4*IIAST -0.1|lll 0*SlOtS O,@TIll - •* 111141 I* 144 EEl *I. fill4 l* ll_IS l.iHPl -I*ITTII -0* 00141 -_, 0_Ill 0*II I_I O.llSTI -I.1111+ I) _*II *o lSl -ll*l_lli 0.11440 0.11444 -_.111AI -l,llAll -O*I+ISS O*lilOI O. iT•14 - •. 14•42 I. Ill lIT -l. 4_I+I H O. ISlIT l*liSll -•* 9111S I *0Ore -l*0lll'l l.El|Of I*SS|I$ -l*lilll -l*|ll 114 -il.lllli O.LIMT A.II_S -•,tSlIS 4*0SIM -0.1I+TE 0,Alibi 1,•llll ' -•,11_II • Io 144 ll_ -l.+llll •. 04k•'l I l,liIll -0.41,I III l, 014IT -l,ml4 0,+1114 O.•|104 I*l_Sl • Ill - + $14 -1•*lllll •.lSt_l O.161TY *O.lil$l +*lillE -O. IllP! O.SAISt l*lll+i *l.ttll I O.lll IISSSUlS LIlY All OIAI C01FPICIINSI e*N_*oe +oo_* ee le **** IO_eo*oe MSSSYll eL - 0.00446 MSSllmS C• o 0.00411 A•PSiI_! _lA = I_o00001 II_0S m_lll • @,10tN 04 o1.1_*o*o **e*o +oo* ** •• e**** el* POISITIIL PL01 IIt01tlA SKTI011 I lilT Cllll_ I illTll 11-11 all n,.*_./i LOIN8 l_) PANIL Iq_S• _1_ OW.-- Pili IIIIIIITI II - -halO*leO*l* C0111r+_IIIIISTASlI_IIIS|ITIATIIIILIISlKI'I'I'IIIIIIL ¢lllli01l IN_IIIT Ll[lll PASSIM l)10b_i _II_ILATlllL S Ii _4 • l ¢P OSL U_ES lh III O.•TI_O -I.61ll_ O.LlS_) i. O._i l fields •*IOl_l *hTTTA2 -0*|ITI6 l.STill 1.04161 S II *l TAll 0* I1411 - I*11TT1 *•* _lT_l 0. Ileal hI_ll 14. II11_ 0.1111" *S* 114li -0. lllS$ l*4'II I l* SliT) e.A_lli $.0?_rlT "lellT_ "0* 14li| S* |AT$1 h Iilll I ¥ •UlS [4MI MI •ELTAI THITA! Till ¢FI 04 1_.11111 ll*IlliS i* $S4_01 O*O l.I lilt .14400 ISll.ECI44 O*llAli HI* TSNI T$* TACIt+ 2*41116 0. O••T_) 0.04441 loOT$_l O*S@Ill l. TIllS II$. ISLES ll.l_lOl I. I_$_k4 O.ll_ 0.01141 0.04111 •.11|1I O.04tlS 4olllil •.¢¢144 I.IISSl lll.il III 11.14444 l.i_lll O*lilll 0.10144 1.L$_4_ t.14liE

Figure F-5. Continued•

LINE _ASSI_ r_ou_m _O_[LIIEIAL ! X V Z Ct SL UllS r_T_s tAu c_ !

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SumtAm£ OF OOU_DARY LATE_ xeero_loarlol p_ OVAORILArERALS _UAO X Y Z OSTAI S_IN 11,_140_ O.O611O -I,ZZOI3 O.O00Z_ 0.0005_ II*ZOO_Z O,IOZO_ -I._TT4Z 0°0007_ 0,001_$ ) LI*Y6*O_ 0.100_ -1.10403 O, O00Z_ O.O00Sa 4 11,1_t_ O*IOZ_O -1.71_60 O.OOO16 0.001_I I1oT640_ O*ZgOtl -1.13_13 O.O00Z_ O*O_O_Z i Ll.l_6gl 0.4_40| -l.6Te16 o.ooo7_ o.ool55 T 11.764o) o,)_sz] -1.oY$6o o.oooz6 o.ooo_ | I1,1_!_! o.6o41T -lo_eeo_ o,oooTe o.ool_r o.oleoz o.oo_lz s_O -|0.2e|l) 0,)0070 O* ITOI7 o.o3eTi o.oozlo SsZ -e._2eor o.tOq*f o.)t)o| o.o31T! o.oozzo o.o_e_ o.oozt| o.o]e_ o.oozlt o.o)e_ o.oo_|_ o,o_e4r o.oozlz o.o)141 o.oo_l] o,o)141 o.oo_|_ o. ote_t o.oo_lz o.o)i_ o.oo_Iz _6o -Io.2_le_ o.o_o9o o._6er7 PmlCYl()N I_(qA; COEFFI£IE_T RZPEA[_E A_EA * l?*.O0000 REY_O_.OS _SER * 0.3000( oe Boor LE_rM ?*,*16qq AV_IJG_ I.C_N_IO[O * -I._ZIZZ ENO OF _oo_ _I x - -LI.Z*ll!

$_¢TIO_ 10o0 I_ IN • ¢I* VP YN •L CZ_ YI _2 YJ Y_ ZP _N CZl ¢t6 I 0,o o.l_s)oe oo O.l©_eE oO O._ZO0_-O_ WAI_ING LON_ IMIN OUAO.

Z O,ZZZO0_-O_ O.109_eE O0 o.eeTgo_-ol o. leo_]E-o5 _AtNII_IG LO_ rMl_ Qu_o.

z -o._6o_! ot -O._O*T,4E OZ -O. qLIl_ OI -O.911_e O| O.||LZ_[ O0 O.ZO|aOe oo o._izgo_ oo O._*6_-OZ _Zl -0.10_16_ OL -o.101ele o_ -O._ILL_ O0 -O.ql6_E O0 -o. Ioo16_ Oa -o._)|g_(-ol o.les_ze oo O.elT_e-oz _AI_I_ LONG r_lm Ou_o.

-O.e)_O*E Ol -O.?_I_E-OI O.telZ61 O0 O.?6L_61-OZ o,z_sTe_ O0 0.)6_II_ O0 o._6|?e! OO -O._TZ_TI O0 I 0.Z_460! OO O. la_oE oo 0._11._ OO o._1607_ O0 -o._6el Oo °o.I_1761 CO -O._I$_-OZ -O.II04L_*O| _z_ -O,lolele o| -o._Tz_o! oo -o.e6_16_ co -o._tZl_ oo Q VAn@I_G _O**G T_lm OU_O, |q -Oo|O_Y%E 02 -0.10q?_11[ OZ -O*|_O?E OZ -O.[_)OTE DZ -O*IZO?BE 02 -O.B?L4ZE-O[ O*tTl2?_ O0 0.1_3_E-03 OolZ_ISE O0 O*_g_E-OZ 0.0 0.0 O,62ellE*Ol 0°1_170_ O0 o._?e_ OL 0.1_41_E-0) Oulo.

-O.LO_I_E OZ -O.1$]OYE O_ -O.IZ_O?_ O_ -O.lZO?eE 02 -O. OTS?t_-OI O.Itlll! O0 -0. I0170_ Ol zo -O.ZO_I_E OZ O.LZ6OOE-O_ O.e_64E-06 0._$_-01 O._el_IE-Ol ' 0.I01_0|-0! 0.IIII_ OL o._zle$_-o$ ou_o.

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PAOIAILf _AAO! |H INPUT - $OL|O iNGLE - 25. L4_ Figure F-5. Continued.

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Figure F-5. Continued.

Next: APPENDIX G- Theoretical Basis of Oeller's Method →

APPENDIX G- Theoretical Basis of Oeller's Method

APPENDIX G- Theoretical Basis of Oeller's Method If an inviscid two-dimensional flow is everywhere parallel to the surface of a closed body, then the surface of the body can be represented by a streamline on which the stream function, _, is constant. Oeller (Ref. 26) used this fact to develop a method for obtaining the potential flow about an airfoil. He replaced the airfoil surface by a vortex sheet and required that the sum of the stream function for a uniform stream and the stream function for the vortex sheet be a constant on the airfoil surface. This requirement is represented by the integral equation (GI) z(s) V cos _- x(s)V sin _- 2_)_((s ') &n [r(s,s')]ds' where _ is the unknown constant stream function value on the airfoil surface, V is the free stream velocity, m is the angle between the free stream and_the x-axis of the reference system, y(s') is the vorticity strength at any point s' on the surface, r(s,s') is the distance between points s and s', and x(s) and z(s) are the coordinates of the point of interest s. s and s' are arc lengths measured along the airfoil surface starting from the trailing edge. s is any fixed point on the airfoil surface while s' is the integration variable point which moves from the trailing edge over the airfoil surface back to the trailing edge.

(See Figure G-I.)

z s Figure G-I. Geometry for potential flow calculation.

Note that the reference system is chosen with its x-axis parallel to the airfoil chord line so that m will be the angle of attack of the airfoil.

To solve Equation (GI) for@ and y(s'), the integral is approximated by a summation. The airfoil is divided into N segments, y(s t) is assumed constant on each segment, and Equation (GI) is applied at the mid-point of

each segmentto yield the following systemof simultaneous linear equations

(see Figure G-2).

N

= zcl V cos _ - Xci V sin _ - j=1_ KI" J Y" J (G2) for i = 1,2,...N where f s' )] ds' • . _---I s J+1 _n [r(Scl K _J 2_ _s.

J and Xc I (xi+1 + xi)/2 Zci = (zi+ I + zl)/2 are the coordinates of the midpoint of the ith segment. This point is called control point Sci, and it is the point where the requirement that have a constant value is enforced.

_ct sl.1 _SN.I Figure G-2. Airfoil approximation by polygon.

Kij represents the influence coefficient for the effect of the vorticity of line segment j at the control point i. The influence of all of the line segments at control point i is obtained by summing over j as is done in Equation (G2) To obtain the required expressions fQr the K.. we must • IJ evaluate the integrals _S sj+1%n [r(Sc.,S')]ds' .

• I J First consider the case where i # j, i.e. the ith control point (Xci,Zci) does not lie on the jth segment of the airfoil as shown in the figure on the following page.

,Zc I) (xj+, ,Z|+l) _ _ cl''] Figure G-3. Geometry for calcu'lation of Kij, i#j.

Now with a change in variables from s' to s (s = s' - s.), J sj+1 _n rr(s ,s')]ds' -- J £n rr(s c ,s)]ds.

(G3) ._ r sj+1-s sj Cl JO l In the above figure, x and z are the coordinates of the movlng Integratlon variable point s which moves from point (xj,z i) to point (xi+1'z'+J 1) as s changes from 0 to sj+ I - sj. Since we are co}fisidering a stPalgh_ line segment = S x xj + (x-i+1 -xi) -s.)

(Sj+1 J (z.i+l - z.i) Z = Z. + S J (s j+ I - % ) (G4) r 2 : (x - x )2 + (z - z )2 c i , c i )(zj+ 1 - zj)]s = s 2 + 2 [(xj - x ) - x.) + (zj z (sj+ I - sj) ci (xj+1 J - Cl _ )2 • )2 + (zj zcl + (xj - Xci = s2"+ bs + a for 0 _s _ sj+ I - sj • Now /_n [r(s c I i (G5) f ,s)] ds ; = ½ _n [rZ(Sci therefore sj+1 _n ,s') ds' = ½ J+1-s F [r(Sc. ] Fs J %n Ir2(Sc.'S)]ds "S . I '#'0 I J = rs'+1-s" [ a] ' __^ J J _n s 2 + bs + ds _U (G6)

., +l'n +,s + a -,s

+ V4a - bz tan -z \/a b2!

The integral has this value provided 4a - b 2 > O. That this is always true for this representation of airfoils can be shown by substituting the expressions for a and for b from Equation ((33) into 4a - b 2 to obtain 4a - b a = 4 (xj )(zj+ 1 - zj) - (zj - )(xj+ 1 - xj)

[ xc zc ]

(sj+ I - sj) > 0 .

Also (xj - Xci)(zj+ I - zj) - (zj - Zci)(xj+ I - xj) ((37) VZ4a - b 2 = 2 (sj+ I - sj) [ = 2C where the absolute value signs are used to insure that the positive square root is obtained.

To obtain a final expression for Equation (G6) we must evaluate the terms s + b/2 and s 2 + bs + a for s = 0 and for s = sj+ I - sj, corresponding to the two ends of the jth line segment. For s = sj+ I - sj = As, = )_ + (zj+ I Zc.

(xj+ _ )2 s 2 + bs + a I - Xc i = R2 (G8) - zj)]/As + (zj+ I - z )(z s + b12 = xj+ I - Xci)(xj+ I - xj) c I j+1 = T2 .

Fors =0 s 2 + bs + a = (x. - x )2 + (z. - z )2 J c i J c i = RI (G9) s + b/2 = [(xj - x )(xj+ I - x.) + (z. - z )(zj+ I c i J J c i =TI .

Substituting the above expressions into Equation (G6) and Equation (G2) = I__ 2 %n (R2) - TI _n (RI) - _-_+ an- TI IT ] As C I _ tan-I (GIO) Kij 4_ we obtain It i_ ) i__i 1 for I # j.

Now consider the case where i = j, _.e. the ith control point lies on the jth segment as shown in the figure below.

(xj+i,zj.,) I ) (x,z) (xj,zj)

Figure G-4 Geometry for calculation of K...

• jj Here we have (letting As = sj+ I - sj) r(s ,s) = As_ s for 0 _ s _< As c. 2 2 J and As A__s _<s _<As r(Sc ,s) = s - _- for 2 J Thus for Equation (G3) we have _0 s'+1-s" _n [r(s c ,s)]ds _s/2 _n [_ s]ds + _12 _n Is--_]ds J J = - j _0 and therefore (812) Equation (G2) represents a systemof N equations in N + I unknowns,

i.e. YI, Y2.... YNandS. The additional equation neededto close the

system is obtained from the Kutta condition which is represented by

(G13)

YN (SN+1-SN) = - YI (s2- Sl)

Although Equation (G13) appears to be a rather odd way to express the

Kutta condition, the discussion below will showthat it is indeed correct.

The solution of the system of Equations (G2) plus Equation (G13)

gives a set of yj's for the N segmentsof the airfoil. These vorticity

strengths, yj's, are the sameas the actual local tangential velocities

at the mid-chord control points. Becauseonly the body points are stored

in the program and all calculations are referred to these body points, one

observes (refer to Figure G-2) that what is actually desired are the

local tangential velocities at the body points which are the end points

of the line segments. Therefore, some form of an averaging procedure is needed to obtain the vorticity at a body point from the vorticities on the two line segments that join at the body point. .Letting _j denote the vorticity (and thus the local tangential velocity) at body point sj, the correct averaging procedure is _j = [y - sj) + Yj-I (s. - s )]/(s - sc ) j (Scj j cj_ I cj j-1 (G14) = [yj (sj+ I - Sj) + Yj-I (sj - sj_1)]/(sj+ I - sj_1).

Since y times a line segment length is the circulation due to a vortex sheet of that length, Equation (GI4] is equivalent to requiring the circulation due to _j on the line segment s c. - s c. be the same as the circulation due to y] I on line segment sj -Jsc_ iJPlus the circulation due to yj on line se_ ent Scj - sj.

Now consider the Kutta condition represented in Equation (GI3).

Substituting Equation (G13) into Equation (G14) gives YI = YN+I = 0 and thus there is a stagnation point at the trailing edge which is the Kutta condition.

As discussed on page122 , the program actually uses a modified Kutta condition which states that the upper and lower surface velocities at the trailing edge are equal but not necessarily zero. For this case, the trailing edge velocities 71 and 7N+I are calculated from _ _ Jy1J(s2 - s I) + IyNI(SN+ I - sN) YI = YN+I = (G16) (s 2 - s I + SN+ 1 - s N) All other body point velocities are calculated using Equation (G14).

Next: APPENDIX H-Rapid, Inviscid Computation of the Pressure Distribution of →

APPENDIX H-Rapid, Inviscid Computation of the Pressure Distribution of

APPENDIX H-Rapid, Inviscid Computation of the Pressure Distribution of

Symmetrical Airfoils for Mach Numbers Less Than or Equal To 1.0

Prior to undertaking the present study, the senior author had the

occasion to estimate the characteristics of some unusual symmetrical airfoils

at Mach numbers from zero to unity. These airfoils were reportedly capable

of relatively low drag at transonic speeds. It was the intention of the

research to test models of these airfoils and to develop fairly simple, yet

reasonably accurate, methods for predicting their behavior. The reader will

recognize that the development of such methods usually follows one of two

paths: either some new bit of physical or mathematical insight is uncovered

which permits one to legitimately simplify the formulation of the problem or

its method of solution; or one seeks to find or assemble correlations among

empirical results. To pursue the first path_ertainly the more elegant and

distinctive of the two---requires that the researcher be struck by unusual

inspiration, an occurrence that is not always within his power to command,

at least during a fixed time interval. For this reason many simple, but

reasonably accurate, prediction methods are at least semi-empirical.

In reviewing some of the semi-empirical methods given in the literature

for predicting the pressure distribution on airfoils at free stream Mach

numbers near unity it was found that they require as a starting condition the

pressure distribution at MCRITICAL. Thus in order for one to investigate the

utility of these methods or modifications thereof it would be necessary to

have some fairly reliable means of predicting the M^_ pressure distribution.

The task of mounting the computer program discussedU_n NASA CR-1843 (Ref. 34)

seemed to be more involved than was warranted by the uncertainties of the

final result. For this reason it was decided to obtain the pressure distri-

bution by using the 16-point Weber mefhod (Ref. 20) to which had been added a

K_rm_n-Tsien Mach number correction. This method is easily programmed for

computer solution because Weber, by fixing the chordwise location of the

16 points (see Table H-I) at which the pressure is computed, was able to

determine, once and for all, coefficients by which the airfoil ordinates at

these 16 points could be multiplied and the results summed to find the surface

pressures and velocities. One merely supplies these coefficients (which are

given in Weber's paper and here in Tables H-2 through H-7) as a permanent data

set and the ordinates of the airfoil for which the pressures are desired as a

changeable data set. It must be understood, however, that this form of Weber's

method is restricted to inviscid flow about symmetrical airfoils. Thus it can

be expected to give reasonable lift and moment values only for relatively thin

airfoils at moderate-to-small angles of attack. No drag values can be

obtained.

Becauseof its simplicity the methodpermits the calculations to be

carried out very rapidly by even the smallest computer, it therefore seems

well suited for use by those whowould be satisfied to investigate the

characteristics of newsymmetrical airfoils in a more qualitative fashion,

those whoseaccess to larger machinesor computing funds is restricted, or

those with limited skill or time to mount foreign programs. The accuracy of

the method is quite good except in the immediatevicinity of the leading edge

as can be seen in Figure H-I.

The computer programfor performing the calculations required by the

16-point Webermethodwas given the nameTRINSON.This programprovides the

pressure data upon which a second program, COMPR, operates to modify the

pressure distribution for Machnumbersother than zero. As noted above,

below MC_,a K_rm_n-Tsiencorrection is used. For M> M_ R a series of semi-

empirica_ correlations are used to obtain the pressure d_stribution over the

complete airfoil surface. These are described in moredetail in Ref. 103.

Essentially, the procedure uses an approximate analytical method (by Truitt,

Ref. 104) to locate the shock on the airfoil at M = I. The pressure distri-

bution betweenthe shock and the sonic point at M = 1.0 is found from the

correlation of Thompson and Wilby (Ref. 106). Sinnotts' (Ref. 105) semi-

empirical correlation, which gives the pressure distribution aft of the

airfoil peak in terms of the pressure distributions at M = I and M _tM is

used for intermediate Machnumbers. A spline fit of pressure data _e

airfoil peak and that near the sonic point plus the idea that the pressure

distribution on blunt bodies in supersonic flow "freezes" (does not change

with changes in M ) are used to represent the airfoil surface pressures

betweenthe leading edge and the airfoil peak. The pressure rise through the

shockwaveis then "smearedout" following the empirical result presented in

Schlichting (Ref. 65) that the pressure rise occurs over a streamwise distance

of about 50 boundary layer thicknesses for laminar boundary layers and over

about 12 boundary layer thicknesses for turbulent boundary layers.

Comparisonsbetweenthe predictions obtained through the use of TRINSON

and COMPR and experimental data for one airfoil obtained in the NCSU transonic

wind tunnel are shown in Figure H-2. Note that qualitatively the agreementIs

quite good; quantitatively, however, the predictions do not match the experi-

mental results as closely as one might expect for Machnumbersjust above the

critical. In particular, it is evident that for Mach numbers between MCR

(_ 0.77) and M = 0.85 the pressure rise through the shock is even more

"smeared out" Than that suggested by the 505 criterion. On the other hand, for M > 0.85 this concept seems to give very good results.

On the basis of these results an effort was made to develop a somewhat

more accurate prediction by using the 32-point Weber method, given here as

TRANSON, and a more accurate representation of the pressure rise through a

shock. Experimental data showing pressures during the interaction of very

weak normal shocks with laminar boundary layers seem to be quite scarce as

are correlations identifying the governing parameters in a useable fashion.

As a result, it was not possible to find a model analogous to the 506 concept

which was capable of accurately representing the pressure rise through the

shock at all Machnumbersfrom M to M = 1.0 Also, the 32-point Weber

methoddoes not appear to give r_ults markediy different from those obtained

by the 16-point methodexcept for the first 10 percent of the airfoil chord.

Apparently, off-body viscous effects, which are of course inadequately

described by any potential flow treatment or, for that matter, even by simple

boundary layersadded to potential flows, are sufficiently prominent in the

experimental data to prevent one from achieving a better prediction using this

approach.

Since these computerprogramshave not been previously madeavailable in

any form and since they provide comparatively rapid, at least qualitatively

accurate, predictions of the pressure distribution on a limited, but highly

useable class of airfoils for all Machnumbersless than or equal to unity,

it was felt that inclusion of these programshere mayprove helpful to many

readers: Thosewho, on occasion, maynot wish to incur the expenseof

running the 65-point airfoil programand whoare thereby willing to accept

the inherent limitations of the shorter programs; and those whowish at least

a qualitative prediction of airfoil lift and moment characteristics at Mach

numbersabove the applicable range of the 65-point program. The following

discussion provides listings of three programs, instructions for entering

data, and typical output.

32 Point Weber

NCSU 0010

• 16 Point Weber

Oc= 2.5 °

-...-- Lockheed

-.2

1.0 x/¢

.I

.2

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Figure H-I. Comparison of 16 point Weber, 32 point Weber,

and 65 point Lockheed methods for predlctlng

alrfoll pressure distrlbutlons on the NCSU

OOIO at ¢ = 2.5 ° •

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#or one alrfoll.

User Instructions- TRINSON

This program is written in FORTRAN IV and is designed to run in single

precision on an IBM 370-165 computer. Execution requires 32,000 bytes of core

storage and approximately 3 seconds to produce the two-dimensional zero Mach

number pressure distribution for an airfoil at six angles of attack by the

16-point Weber method. For a given run, the program requires the following

input data:

(I) The 240 elements of the Matrix $I given in A.R.C. R&M 2918 and

listed herein as Table H-2.

(2) The 240 elements of the Matrix $2 also given in A.R.C. R&M 2918

and listed herein as Table H-3.

(3) The 256 elements of Matrix $3 also given in A.R.C. R&M 2918 and

listed herein as Table H-4.

(4) The 72 characters of the array TITLE which are used as a header

for identifying output. It is an alphameric array and usually contains

information about the type of airfoil, run number, and any other such infor-

mation desired by the programmer as a header.

(5) The values of X, the x-coordinates (given as X/C of the airfoil

to be considered) from Table H-I.

(6) The values of Y (the normalized y-coordinate of the airfoil to be

considered) corresponding to the values of X.

(7) The values of angle of attack, A, and airfoil leading edge radius,

RHO, for a given airfoil, followed by a last card indicator giving A a value

of greater than 15.

(8) Additional data sets containing information from item (4) through

item (7), for another airfoil, if needed. Only two airfoils may be considered

per run.

Format specifications for these variables may be found in Figure H-3.

A sample data set of the NCSU 0010 may be found in Figure H-4 and the output

for that data set is given in Figure H-5.

. o'°- ..... ° .....

F9.6 If !Till ............

RHO " A 2,50 0.011 ;t]14Sl_t RHO • /.

I ,71 0.01t RHO 0.01 I ..................... V(o6) • f 0,049 O. 0490 0.04?8 0.0422 0.0)44 0.0230 O, 0120 0.001 y(_) ... "_ 0,0010 0,0040 0.0104 0,017'3 0.0_81 0.0333 0.0403 0.0468 / :;; .................. .,,., .

0 00 O._OIT 0.2222 0.14_4 O.OI4ET 0.03000 O.O09el 0 00001 X(I ) , • • • 0.01 0,9019 0.915 0,863i O.T?Ti 0.6_13 0.5975 0.5 TITLE • NCSU 0010 - • 740 .0 -0.505 ,0 ......... S3( 18, II ) • **, • S3(I,I) "'" 02.013 7.488 0 • • 4.031 0 • 2.00_ O.

0_(18, _) -26.769 .,.

S_(I,I) o..

25.70O I?.llT --4.703 _.010 -1,104 .70S --'800 ... SI110, 10) 01.013 -132.10_ ..° / $1(Is I) * • 1.

02.013 -15.061 O, ".601 O" -.130 O- ______________________________________i_____________________________i___|______i I|111111111111111 IIIlllllllllllllllllllllllllllllllllllllllllllllll 11 llllllll]lll 41111|illl)|i|11313|]3133]lllll]31llllll||||)|3 44444444444 44444444444444444444444444444444444444444444444 I_IISIII|SI SS$S'I|lSS|SIiiS$SS555SSSS|II|$|SlI|ItJ|IlIS$ Ill lllli6111666 lilliililllliiliiliilillil|ilillllilillilili Ill COBPUTING C31_]rB III

Ill o4m|oomoooooooJaoommomoaommosolooooooomoooooommmoa oooaoooooaoaeooao

III ooom_|ooooommoouooooooooooJoouJoooooo,oooooooooooloooo_vqo_,o_o_o#onaoooouoo

Figure H-4. Example data set for TRINSON.

i

w w

__ - = u

--,_ b-o ee .(

. -o

o_ .... ee * _tt o'0 _ _,0 _3:o

z

n,

I-

I

o)

.9.

.J

zzzzzz ZZ zZ_ • • Z _ • •

E

ob

o

.° ........ ° ........ .- :-,- ..- -o - -_........ ,..°

Sample Output- TRINSON

tPKO_eI£SSISL! PltSSUAE COEFFICIINT [_CO_I_qESSI_LE PlES$_l| CO_FF|CIE4f _SU 001o _C$_ 0010 ANGLf OF ATVACK* 1.000000 XtC veC CP-UPPE* 0.9_0000 O*OOtiO0 0.2)IS_T O*_l_O00 O*Ot0400 0.0,04_) 0._1_000 0.0|0_00 0.05_0 O*IS_600 O.OlYJO0 -O°OIBO_Z O. TTTAO0 0.0_00 -O.OT_O_I O. TtTlO0 ¢.0_$Z00 -0.0_0_ 0.6_1_00 0.0_!100 -O*O_Y|_6 O._gP_O0 O*O4O)OO -0.1q?096 O*SO000_ O*O*SlO0 -0._*_? 0._00000 0.0,_100 -0.1_$6 O*60Z_O0 0.04_000 -O*Za_)OZ O._OZ_O0 0.04_000 *n°l|_l_!

O._08TO0 0.0_9_00 -O*_TIAt O._oeTo0 0.0_¢0 °0._0_ O.ZZZZO0 0.0'7100 -0.30_6Z?

0°146_00 O*O*ZZO0 -O._OLO_ 0o1_6400 0.0"_00 *O°I_IP*_ _CSU OoLo A_GCE O_ ATTACK. I*_10000 IIC VlC CP-UP_ER 0._¢000 0.001]00 0._)06)_ O._CO00 O.OCI)O0 O*Z_|OI_ 0°_1_00 0.00"000 O,12]_?f 0._61_00 0.O040OO _*1_ 0._1_000 0.010"00 0.0_0| 0.05_600 O*OtT_O0 -0.07_)_1 0.77V000 0.0_00 -O*OZAO_ O*_t)O0 0.0)))00 -O*OTI_)_ 0._00000 0.04_100 -O._Z)f_ 0._00000 O.O*$_nO -0.13_1_I 0.40_$00 0.040000 -O,3_IL_!

0°_00700 0.04_00 -0._14_6| 0.)0|700 0.0_00 *0.164111 O._ZZZO0 O.O*?lO0 -0o*$|107 0°1_6400 O*O_JO0 -O._BL_OZ 0.1_00 O.O*Z200 -O.|le_ o.ol*zTo o.o)_*oo -o.o_o_o o.oo_,_1o o.nl_oo o._ I_COI_RE$SIg¢E PnESSU_E C_FFICIENI I_¢O*mllS$|qLi PlISSU*! CO_FFICIe_I_ _¢S_ OO_O x/C vie CP-LI_Wll 0.9_0000 O.OOlSO0 0.22064a O, _00_0 O,OOt )00 O. Z4101, 0._1900 O.O0_lO0 O.120Z** O._l_O00 0.OlO40O 0.02_0*e 0.0S$_00 0.0|_)00 -O.O)_n_3 0.05_600 O.OI?_O0 0,0_0|1_ o.Y?_eoo O.02SZO0 -o.1o_6 O. ?_7000 O°OZSZO0 -0,01_01) 0.691_00 0,0_|00 -0,[8_$01 0,_0_ 0.0_0)00 -0.00t0_3 0.500000 0.0._000 -0._0._0 O.5¢OOOO 0.O45|OO -0. IO_ZIO 0._02500 0.0._000 -_.)_0_ 0,30_TO0 0.049,00 -0.414727 Oo |OIYO0 0°0_00 -0. ! I_St I O*ZZZ200 0.o*?00o -o.51_e_ Oo ZZZZO0 O. 0_!_0_ -0. |ore_r O*L*_*O0 O*O_ZO0 -O.S_|Z)O 0*08*2;0 0.034400 -0.6,4113 0.010060 0.0_3000 *0.7447_7 O.O0_6tO 0.012000 -1.009_1 **,**eeoeeo,,** ,,e,• ***eeeeeeoeeeeeeeeeejeeeeeeeeellee,,eo,,*********e, Figure H-5. Sample output for TRINSON.

User Instructions- COMPR

This program is written in FORTRAN IV and designed to run in single

precision on an IBM 370-165 computer. Execution requires 23 seconds and

68,000 bytes of core to produce complete pressure distributions about a two-

dimensional airfoil with a round leading edge for ten Mach numbers from zero

to one at one angle of attack. The calculations are carried out first for

the upper surface and then the lower. For each airfoil the program requires

the following input:

(I) The 72 characters of the array TITLE. This array, which should

contain an accurate description of the airfoil, is printed at the first of

the output for identification.

(2) The variable NNN and the value of JPRINT, an integer from 2 to 10

which specifies the print information. NNN should first take on the value I, which implies that the data to follow is that of the upper surface and later,

the value 2, which implies that the data to follow is that of the lower sur-

face. The number of points printed may be calculated by (10 + 90/JPRINT).

(3) The 28 values of the array X, the x-coordinate (given in fraction

of chord) as measured from the leading edge. These values must be specified

at every one percent chord starting from x/c = 0.01 to x/c = 0.10. From

x/c = 0.10 to x/c = I.QO values at each five percent chord are sufficient.

(4) The 28 corresponding values of the array Y, the absolute value of

a y-coordinate of either the upper or lower surface according to the value

of NNN previously specified.

(5) The 28 values of the array CPI. These are the incompressible

pressure coefficients (for the angle of attack of interest) corresponding to

X and Y above. Note from (2) and (3) above that these values of CPI are not

given at the same points as specified by TRINSON or TRANSON (the 16-point or

32-point incompressible pressure distribution programs respectively, from

which this information is supplied). The data from these programs must be

plotted, smoothed, and the correct values of CPI read off at the specific

coordinate locations of (2) and (3).

(6) The angle of attack A in degrees, the airfoil maximum thickness

in fraction of chord, the airfoil slope, E, given at x/c = 0.01, the airfoil

slope, G, given at x/c = 1.0, the maximum y-coordinate above the chord line

ZMAX in fraction of chord, and CREST, the x-position of the maximum

y-coordinate given in percent chord.

(7) The value of NIN, the number of free stream Mach numbers for which

the calculations are to be made.

(8) The values of a free stream Machnumber XM, a ReynoldsNumber,RE,

corresponding to that Machnumber,and KTPE which takes on the value one to

specify the type of boundary layer as laminar and the value zero to indicate

a turbulent boundary layer. Item (8) is repeated until NIN Machnumbershave

been entered.

(9) Items (2) through (8) should be entered nowfor the lower surface.

Only one airfoil may be considered for each run.

Format specification for these variables maybe found in Figure H-6. A

sample data set of the NCSU 0010 maybe found in Figure H-7 and the output of

that data set is given in Figure H-8.

Figure H-6. Formatspeclflcatlon of Input data for COMPR.

Y(I) O.OI|IDO x(_e) i,oo x(I) O.OIO0 NNN JPRINT O 9 Tt TLE NCSU OOlO AIRFOIL __________$__________________________ii_________________________________________ llllll 1_111111111111111 _]]]]]3]]]3]]33)]]]]]]])_]1]]]]]]]1]]1_||_|_)| )3|3))|||)3| 44444444444444444444444444444444444444444444444 44ttSI44144 IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIllll ISiSS55555_S|S5555555S|S_5_S5||555|555_|| S_SSSS|lSSS IIIIliliil|ililliiiliiilliiiiiiililllllllllllll lllllillllil CO_PU_ING CJN_IR Illllllllllllllllllllllllllllllllllllllllllllllllllll""_'_llllllllllll_llll __i__|_|_|_||__|_|_ Figure H-7. Example data set for COMPR.

IZ: 0.

:E

o

I

'It-- °_

_I

E

o_

IIIIIIIlIIIlIIIIIIIIIIIIIIIIIIIIIIIIlllIIllIIIllllIIlIIIIIIl

-" ~ "- - _ 7_ •

o ---- "-i _. _ 44) i w * .-- _* -- _* * ,.,4 o Z I[_, • OZ I ! -)*- _. t,_ I-- N-- ._D • _40 4• _ • _w ,_ -- "I o -- ,._ el _-. _ _l. *- -- -- '_ -- "J .--. 4 I'_ ._ I) Ii[ ._I IiI.... 0"). w _I -- m _I--_ . . - : ..2 _- ......

lllIlllIIIIIIIIlllllllllIIIIlIllIIlI|IIIIIIIIlllIllIIlllIl_l

. _.,. ; ; 0_ z o .+

+ +=++.. ++,+ +F_+ + ._++ _+

c_ m ,-- u. +o+ o. I i_" . w + • _. _0 _r .,,l. • . >.

• I i.- e--I _ -- + I I I • II---- + • I ,_i_ _.- IiI._ M z I',- x Z+ I--I • I+ wlt _ _ _ olc ,11 w ._x • me i+ ,o w ,._-- --_" ,- ,+ - ,+--- _S -p_-*.? ;_ .2 ; - . .. z. §.

+ -"- =- -]-- o: , ..... m .........

°+# i_ +it-_+ _.oo ++;+:.+= :,,._+_, ++ __+. ___+_.,+__

I'_ ............................

• .oo ....... _++o- *++,.,+L ..... ''-- ; *._,'_ ll_'_.._

...... t.I .... _,,- o ¥.+,o.,._.-,+,_t5+, ,-- ++ ........

----ll i t,.. _. I I --I

+o,.,+.,:,.o.=..,,,,..T.--,-,m +T..+ ......o,.,..,,,.,.,..:.o-,.,- ,,., ..,.,,.-II. ---

_ m Om i..+ _ ',J t,.) _ _I ...+ _

IIIlllIIIIIIlIll

xx •

- _

((I _ .

L _- w_w)- _Iw_Lq '9 ( =)ek v) Q w :* w _[ _- *-- s- _ _ Z w lwI 4I _ _ _. w _IL 0 0

...... ili

,iI _ii i ,qO ,I _,_.

I I I I I I I

_o

t "

;il !i!i!

II_ I. _ _.l. -- ,,J iI .J g kl m

!!!!!!!!!!!!

Q I,(I- )-l-

--'i --'i i"

,.-. lTiii_i

,i ":,.-'=i"

ll.,I _ _li- = l- :) ._ = III i II II lJ h- (ill I I

Sample Output- COMPR

Pi(SSUa£ DIIrQI|UTION nfTvfEh SOklCPOINT AIgOTRAILIIKEOS| FOII n.!

xt¢ vie _11_0 P-LOCAL CP 0.0_000 O.O|aO0 0._166_ I._411B -0._0)02 0.0_000 0.02_C 0.)1_| hZ_)07 -0°)||O$ O.OSO00 0.02_$0 0.15_8S 1._0410 -0._6)_ 0o0_000 0.02_0 ©._6071 1°)00_1 -0._)12 IIC vie CPl o.ozcooo ¢.01Zm00 -0. ql_000 o.o2cooo ¢.01a0C© -0._)Z0¢o o.0)0o00 c.o_t$0o °C._|0000 o.o*c00o c.0Z4_C0 -o.|_o0¢o o.o_cooo ¢.0_T_00 -o.v_60¢0 o.06c00o 0.0Z_500 -o.I_Z00o o.oTc0oo ¢.0_1_¢o -0.11200o o.0e0000 0.0)!_00 -0.10_0e0 o.o_¢000 c.0_¢¢0 -0.6_00©0 o.loc0oo 0.o)8_C0 -0._T00C0 o.1_¢000 C.0_Z7¢o °C.60Z0¢0 o._o00oo _°o_6_CO °0. S_|000 o._¢000 C.0_eT¢0 -o._Q_000 C._O00 C.0)66C ¢.)O_Zl |._Z$1_ -0._0|_6 o._o¢ooo 0.o_|0o -o._)Tooo o._C000 C.0_C@ -0.1_0o0 O.aO000 O.OZ)ZO O._IZl l,_)_) -0._107 0._0C000 ¢.0_Z¢0 -O.)60O¢O O.15OOO C,017_0 0._ L._T_] -0._| 0°_C000 ¢°0_7900 -O.))2OOO o._ooooo ¢.o_co -0.10|0o0 o._5¢000 C.O_1)00 -o.??looc 0.60¢000 ¢.0_0_©0 -©.Z_?000 1,00000 -_.O(OCC C.?|l_e I,_Ce -0.)_160 o.65cooo o.o)6_¢o -o._0_oo0 o._ooooo ©.0)Z_C0 -¢.1_¢00 0._5C000 ¢.0_IIC0 -0.1Z?000 o.ocC0oo C.0Z_2C0 -0. o1_000 o._C0OO c.01_C0 -0.0)_0o0 o._¢C00_ c.ol_oc o.¢1_0_0 I.o0c000 0.¢¢o000 z.¢¢oo©o xIC YIC PlPO _-LOCaL C@ 0.0_000 0.02|10 0._65_ 0._010 -I.2*Z_O _, vv Ply T_ErA O.O9OOO ¢.0_1_0 O._e O.O_OI_ -|.0_1_ 0.010000 0.01Zl00 0._i000 C._Ot)O_ 0.0_000 O,O)|_C ¢oe1$1C 0,16_? -0°_T764 O.OeO00 0.011_0 O.Q_Z_O 0,1_69 -O._ISI 0o0)0000 0.0Zl|0¢ 0._)t_e 0._00_7 0.10000 0o01_0 0.6_1_0 O.a_7_O °o.ePell o._oooo o.o_6_o o._ 0._150) -o.ro_,oL O.O1OOOO 0.0_ltC0 0._t001_ 0.ZCT00_ o.7_000 ¢.o_e?c ¢°_1011 o._6ze_ °O,_ZlI| O.O|O00O O.OlJSO0 O. li4673 0.11911| O.6OOOO 0.0_0_0 O.;_IY? 0.6_ -0._|_0 O,O_O000 O.OtSO00 O.14_Z|a C. ItS?s3 O. rO000 O.O_Z_O o,]_¢0 0.6_0_0 -O.Z060) O.ICO000 0,0_4_00 0.1_0175 O.l$1_t o.ZCOOOO o.o_CO 0.0_1_1 o.061_o_ O,6OOOO O.OZ_C c,77_et o.bzo¢* -0.105t?

o._oo0o O.O_Z)O o.aol)o 0._|_6 O.OZO_ o._co000 O.O_eC¢ 0.0|156_ 0.01|_6_ 0._000 0.OO6)O o.elngo O._t_ 0,11_11 0.600¢00 C.O*C_C¢ -o.oe?Z_ -_°¢_?|*S O,65OOOO 0.0_60o -0.0_9_ -o.07_|1) o°_ooooo o.o)z_co -o.oe_4|_ -o, oo*r|_ c.scoooo o.oz)2co -o,1o16o1 -C.lOlZ6o o.|_oooo o.o_¢o -O.II|ZOZ -o. tto_?

S_GCI Loc_r_c AT _ PEmC(_I C_o_o FOR _CH N_|ER- 0.9_ 1.0ooooo -o.o0oooo -o,olz_ -o.ol_a ¢&LCULITION o_ |_| LOC&L PACH bUrRER N|AR TH| NOSE FCq m-t x_c VtC P/_C _-tOCa_ C_ x/c vlc _1_ _-t_cJt CP O.OlO0O o.o_00 o.o)_o0 c.c_O0 _oO_O0O LOCAL _AC_ _U_EI _A$ _aCE_0_O U_ITV _0_! I PE_CE_T CN_m0 c.o_aoo 0.o;000 o.oacon o.o_ooo o,loooo 0.0|6_0 0.*10_0 I*ZO)_I -0,_1_6| ©.1_ooo _._0000 ¢._5C00 o._oooo O._OOUO 0.*_000 o._oooo C._coo _._0_00 0.0_020 C._la?_ J._egIT -0.6T)_6 0._$_00 0.100o0 _.1_000 O.OZllO C._Z61_ 1.1_6! -0o370_0 O.|O000 o._oo_ O._OCOO 0._00_ |.coooo Figure H-8. Sample output for COMPR.

• RESSUM| OlStlt_+JflOm llfueem SONIC eOImf IMO TnklLIK IV._I _CI P-I I_IGL! OF ATT*CX* 2.50 OEGREeS elPO _-LtX;_L CF xlC YIC LOVEm SUnPlC!

0.15000 _.O*Z?@ c.*_svf t*lSbq| -O.i*q4l T_| &ItPO|L ¢O011O|N&ItS &NO [kCCMPR_SSlaLE PmESSURt Q|$TIIflUVICN 0.20000 0.0,_*0 0.**?15 t.I)?O0 -O*ZlVlq 0.30000 O*04qlO C._Z2q_ _*tlO_ -0._1_1!

XtC VI¢ CPl O._O00 O.O_qO O._OVV9 t.aoez7 -o.)_s_q o.poooo o.0_6o 0.)801_ t._6oL_ -o._qe_2 O.OtO@O0 o.Ol|)O0 C.sO_OCO O.OZeO00 O.OL?L¢O O.4Ooooo o.esooo o.otP_o o.)661+ t.zl_42 °o._l_s 0.0)0000 O.O_OlOO ©.1too¢o 0.0_¢000 O.o_qO0 C._410oo 0.05C000 O.02?SCO 0.[|0000 l.coooo -o.ococ¢ c._$_om i._tl_6 -o._e_6 O.OIO00O O.o_qsO0 o.14)00o O.O?¢W_O0 c.O)llCO C. lO00CO 0.010000 C.o_$0o ¢.07_o00 O.OqCO00 0.0)_¢¢0 o.(SOOOO _ACm NUMEEi" o.q?iOO 0.10041o0 0.o3_q¢0 o.C)Oooo O. ISCO00 c.0427c© -O.CSOO©O o._00000 O.O+s+cO -o.o9*000 O.ZSCO00 C.0417¢0 -O,IlOOO0 0.)00000 ©.04q1¢0 -O.lllO00 I/C V/{ P/PO e-LOC&L CP Q*)5¢@00 C*04qqCC +C.ttlOOO O._O0000 C.04qlCO -0.|10000 0.*$¢000 C.0,_¢0 +O. lO_O00 o._oe_o c.o41q¢o oo.¢qlooo o.5scooo ¢.04_oo -o.oqcoco 0.600000 C.040I¢0 -O.OIOOCO 0._5¢000 0.036600 -O,C_|O00 0.;00000 C.oJ2_(O -¢.o50000 O.06OOO 0.0_0 o.e_e 0._ o.1_6 0.75C000 c.o2elco *o.o_oo¢o O.lO000O C.o_z¢o -O.CO*OOO 0*19C000 C.oIl_O0 0.026000 C.0_¢00 C.O_CC c.eomge o._06 0.06oe3 O.+OCOOO c.ol2]CC C,¢6_0C0 0*49¢000 C.0C63¢C C,l_gOCO 1.¢0¢00o o.ccoooo I.CCcoco V_ C_ITICAL _*C_ NU_E_- o.eq_ o.6OOOO o.o_o_o c._TsqP o._o_16 +o.o_e_ q._ooo 0.o)6_o c.lel_6 o.6o_63 -o.om]vr 0.0[00o0 o.o|_)co o._oeooo o._ooz_ 0.0_o¢oo 0.0171C0 O._CO_q e.,6s_e) 0.0_000o o.o_¢ece o._*o_zl o._aeo_e 0.0.0oo0 o.02_00 o._ n._o4o O.OqO00O o.oi750c c,a]_ c._z_ 0.0_0000 0.019900 o.19_6_ o,lq_tmz O.OtO000 O.o_I_cc o.a_o_a c.ze_+_a o.o_oooo o.o)$sco o.16041_ o.|_voq7 O.O_OCOO o.o_oco c,lel_l c.t_z* O.Ico000 0.0_oo O.l_Ot_* c. le_c_ with _ummEm. o._¢0 O._CO00O o.o_OC O.O_Lq_9 O,06t+O0 o._OOOO o.o,8_Cc C.o_I_ c.c_z_O_ O.)COOOO o.o_ecc o.cl_ C.CI_q 0._0000 o.o_eCO -o.oo_g_* -c.co_ O._Coooo o.o+qtco -o.o_oo_ -c.caooe_ SMCCK LDC_IEO _I la _E_CENI CMC_O FO_ P*C_ NC_S_M* 0.9_ o.q¢oooo o.o_qCC +O.O_SIS -C.C,6_9 O.$_OOOO 0*041_¢_ -O.OS?OS_ -O*Oq6qqS o._qOOOO o.0)6_o0 -o.o;qq4_ -o,o?_ LkWINIA ECUNOkRV LlVe_-*RFVNCLO$ NUNBEe- O.lOOE Ot _lC PIMO M-LOCIt CP 0.I¢000o o.o_a_C© -o.oe_q_o -c.ce_s_ c.clcoo o,?qooon o.o2elCC -o.o_4712 -o.cq_v)q C.c_O0O c.c_ooo c.c_coo C.c6o00 t.cco¢oo -o.oooooo *o.12_ooo -o.t_9 o.o_ooo 0.0_0oo c.oqeoo 0.1o¢0o ¢_LCULJTICN O_ T_ LOCke VlC_ NUMBER NEA_ r'E NO_F _ _'1 o.1_ooo C.;Ocoo 0.7500o XI¢ VlC PI_O _-tOCAt C_ C.30000 o._Iooo C.*ocoo o.+_oon 0.0_0 ©._0_|_ |._1_ °0°_004 o._o000 o._$C00 0.04_0 0.0_0 O.e_lll o.e_ O._|t C._O0OO _._0o0 o. POOOO c.O_mlC ¢._2111 |.¢oe_! -o.c99zl c._qCOO o.om_oo o.o]_c o._ o._o 0°01_ o.eooo_ O,U_OOO ¢.to000 o.oJ6_o ©._s_e O.q_el O.OZTO_ o.qoooo C.q_COO l.co00o Cont inued.

Figure H-8.

User Instructions- TRANSGN

This program is written in FORTRAN IV and is designed to run in single

precision on a IBM 370-165 computer. Execution requires 42,000 bytes of core

storage and approximately 6 seconds to produce the two-dimensional zero Mach

number pressure distribution for an airfoil at six angles of attack by the

32-point Weber method. For a given run the program requires the following

input data:

(I) The 992 elements of the Matrix $I given in A.R.C. R&M 2918 and

listed herein as Table H-5.

(2) The 992 elements of the Matrix $2 also given in A.R.C. R&M 2918

and listed herein as Table H-6.

(3) The 1024 elements of Matrix $3 also given in A.R.C. R&M 2918 and

listed herein as Table H-7.

(4) The 72 characters of the array TITLE which are used as a header

for identifying output. It is an alphameric array and usually contains

information about the type of airfoil, run numbers, and any other such

information desired by the programmer as a header..

(5) The values of X, from Table H-I°

(6) The values of Y, the y-coordinates (given in fraction of chord)

of the airforl to be considered at the previously specified values of X.

(7) The values of angle of attack, A, and airfoil leading edge radius,

RHO, for a given airfoil, followed by a last card indicator giving A a value

of greater than 15.

(8) Additional data sets containing information from item (4) through

item (7), if needed. (>nly two airfoils may be considered per run.

Format specifications for these variables may be found in Figure H-9.

A sample data set of the NCSU 0010 may be found in Figure H-IO and the output

for that data set is given in Figure H-11.

. . .

F 0 . $ ' ' .... I ° ' f s2(_.1) [ FIO. 5 FIG S _ ............. [ .... T " • _

V////////_////L Z

l'_r* _I I

FIO. 5 20A4

I I I

Flgure H-9. Format speclflcatlon of Input data for TRANSON.

A RHO

h

30.0 0.0 f A RHO

/

2. 500 O. 011 A RHO ,730 0.011 1 ._0 O.OI I Y(ES) " ' • " " • " Vl$1) "_ _0 0_$T4 0 03452 O.OISEe 0 014414 0.01000 0 011400 0 00480 0.0 i .,.

0 ;";;,. 0.04,,., o. 0.,,,+ 004_,.. 0.04,,4.0:0+_:.. 0_0+0,:. o.o,+40..

_l) • • • FO.OllSO 0.01540 O.OZS40 0.03330 0. 05703 0.04041 0004_41 0 . 04811 /0.000_0 0,00110 0.00_$0 0.00410 0.00 4 . 0 0 0.0 _110 O.OIT=O ....?7 ........... L .................................... :....... oL+. ....... ,,,. ..........

x(151 ...... x(li) " o, 11380 0. 08427 0.0B_O4 o. O380_ o.o_ 183 0. oot81 o. Onl41 0.0 x(u 7) ' "" 0.4§100 0.40180 0.3_400 0.3001,0 O. |E4_O 0. liilO O. le_eo 0. 14640 / xCt) . ..

0.e1?20 0.771,80 0.1,3870 0. OII_O 0.1481 0 0.801,80 0.54_00 0.50 i ;;;; ......... :'::........................................................................ -,, O,iITIO 0.91040 0.11,080 O,IIIIO 0,14100 0, ll61'0 0, lee6o o. 18_lo TITLE NCSU 0010 il POINT --0. _1'8 O. --0.5 II 0. --I +4§1 0. - 1 _.01"_ 0.

811( I ,i ) ItS. 41,4 it. 44t O. I§ .41,§ O. 1,.3 83 O. 4.21,9 ll(l1,11) "_ - I01.811 + i + I i i + i i m+_.:].mxl+:ima++_ +_+.+]m... l+l;.ll_]li+la+lm.l+.a+llllm_al;+llmVllmlll++Ip_+l+.llll_+_++'+.++_+l $(I ,11 ''+ I03,011 11,713 --I 1,+4151 I',114 "I.11'I l,l++ -I +311 0.III , i i a i o,, • ill_ i+11. n m+Pmmllzl,l "l_limx+_.i_inl= x IIm_llll lillllm"ll"lJll"_"""llll_ll#ll_ililll+llulllli+l_al"+_+_l_l F ''' Iil311ll) 0. -0.41'8 O. -1.410 O. 01 IOI $11.41,4 $li 4 I I I i I l_ll I!1 /':;i:i; ....... ::"................................................................

+'; ;;;+Y,+..0 YL':t °+, ..... +o ......... 7,..+1o ........ o; ........ :o;+;: ..... o: ........ :o_,,+,_..

t111111t11111111111111111 II llihllll IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIlilllllllllll Iiii1111111111111111111111111111111111111111111111111 IIIIIIIIIIIIIIIII lllliili]llllllllllllllllllllllllliillllllillll Illlllllllll 4 I I 444444444444444444441llii14441"llilillllilltl illlililiii Illlllllllllllllltilllllillilllllillllllllllllllllillllllllli IlliltlllilllliSSllSilitSlllllillilllllllllilli lilllilllll III I IIIIIIIIIliilllllillilillllllllllllllllllll illilllillli _OMPUTINO C_l'Jrl 1111111111111111111111111111111111111111111111111 _ I111111111111 IIIIIlilllllilllllllllllllllllllllilllllllllllllilili IIIIlilllllllllll ___________i_i_______i___________________________________i_____i________________ Figure H-IO. Example data set for TRANSON.

Z

z

<I

oc

I--

!

e.- e_

L3

E

A-

•

° o m_ m_ o:.-:_ .... " -'""-- ..... .. =.='-" |i :" =0°---i-i= _=°i=---i"_=_-0= i =_ i =_" -.= i ..==-i _---. _ ..... :.'-;" o _" :__: =

Somple Output- TRANSON

IIKO_m[SSlRLi PllSSUt_ [OlFfl£1ik!

IIKOII_|S$IK! PIll|U|| ¢OIFflCI|NT JlCSe 0410 )l POlUV *eCS_ OOlO )2 POI_!

aJeit| of ATTICS- |.QOOOOO _q¢_ nf JTTILCao ].00000(_ • . I)9hb44 O.000)O0 0o))¢Z_e 0._S1600 0.c¢©)00 0.;4_|11 0 qmD40O 0oNI/e0 _o ZS6_65 0. q_eGoe ©.oct_oo n.ZAtl_) 0 • _yes0e I| N_O4H) o. 164|1Z 0oq_M00 _. 0CZI00 n. I_qq_ e.ql6 Im 0.006840 0.1)t61I 0. 961900 0.004_00 0o 14_46 I.qJtlOO0 0. N1,4Q0 0.0e00_ 0.q_1000 0.0©_4@0 0.0'_4_4 0.gllY0e 0o010400 e.04ytql o.91_yoo a.ol0400 c.o_ti 0o808S04 0.01NJO4 0o0100_4 0.01_00 O.01)Q00 ¢.0)|67_ 0.OlY_N o.oi|m -_.06_elT _.e|7_oo c.0_|5¢0 *c.c_nsq.

0.691s00 o.0||)4)e -o.i)_*_ o._l)o0 o.o)l)oo -0.0900_ 1.64S100 0o01TON *0.|6_61) 0._Sl00 0.0J_0_0 -0.11_?0_ • oSm 0.04|_0 o0.Z_|_00 0.$0000_ 0.0_q_0 -0.16111.

0o _$1000 0o04_m -0oZG|IS6 0.4|1@00 C.04V|90 *_.|1_00S • o |$4900 0o04_1)4@ -0.|lSt_0 0.)S.S,00 0.04q4_0 -0._01_l e| 10|I00 0.0*SI_0 o0.)_Z 0ote_0o 0.045)_0 -O.Zl00_ 0.|46400 ¢o04|_00 -0.*iT)_5 0.146,_00 _.0_00 oC*_0_ 00|SO40. 0.0|qte4 -0.4T_0 0.0tq440 0.0_|0 -0.1_*_* 0o0_(eG0 0.01**6*0 -0.$_)_ 0.0_eJ0t4 Uo0_*6_0 *0.0_4_q_ 1.0|tS)0 ¢.O1160O -0.4_I7_ 0.0_ts)0 ©.0|1_¢_ 0.0_l 0.004J6|0 ¢.018_00 -0.1_027_ 0.0Oq4t_ 0.01_C0 0.1_,_0_J S*eGLe OF &TIoCt. Z._O0_00 dtmN.I OP AVV_,_te Z*|O0000 o.q_?4O0 4.0¢0|00 0.))TgS6 0.qe?600 0.c¢c)¢0 c._4252_ 0.W ¢.00tJ00 0._,4tVl 0.S40400 C.0CI_@O 0o_6_ 0.S411_4 0.00_040 0.t_*gq) o.q_l_)00 O.00_A00 O. lSIl*_ 4o94|1ml 0.0@744e _.0_0S_0 0._|000 0.0¢_¢0 0.1061_ 0.04kis00 0.01|e04 -_.C05|_2 0.¢06S00 C.O|IICO _.050e_0 1.01_N4 0.011s0e -0.0|$_ 0.ellZ00 0.0_|$C0 -C.@0S|01 e.yVlr840 0.0_S444 -0.|0_6_ 0.I_800 OoO_40Q -0.0_$nI _o691Ne O.O)|)O4 -0.174_i_ 0.6_t)00 o.o_q)oo -0.05_|_| 0.14_|00 o.0|vlllo -o.lto,_4 0.66|t00 o.o)70Jo oo.4_o_ot O.$9154O 0.040_10 -0.1|?o_t 0.591_s@0 o.o*,_ln *0.¢0_0_* 0oS4t 0.04S4S0 -0o_T866| 0._00 Q.Q_4_0 -0.0_9q1_ e.U 0.04_9|0 -0._0t001 0.$004e0 C.0_0 -0. t00eI) 0._IIe00 0.041m -0.)PJ|)| _._1000 0.0.70_0 -o. tto_*l eo4J4_S44 @.04_144 *0._66810 0._0_$00 0o04_4_ -_ol|_)ql I.|S4'N0 0.041_e40 -|._0|ltt 0.)_.90_ @.0_0 -a.1|l)61 @.)4e_0e o.04q4q_ -0o_),_60| 0.|0|?00 0.0_|0_0 O_o11_1_ i.|641441 0.04_1144 -0.*.6_? 0._64)00 0.0_1_0 -0.10_)4_1 O.lU414e 0.045|t0 -0.$|4e010 o.14_Joo c.o_|)_o -¢.071._ o.084zfo 0o0|_||0 -0o _09_1 0.0e_|To 0.0)4|_0 o.o_l?_ o.eg_ |.||1;Go| *o._GzoP_ 0.0_q4)*0 0.0_610 c.|ol_*_ - .

e.o_|_m 0.1|0600 -Ooie4s_y 0.0|1_0 ¢o010_c_ o._oqsl_ o.oo441o 0.0|_400 -t.1s002_ o.ooqG_o 0o0|_400 o. _i_ OoOOJ_41e ooo04soe o._ts46! 0.00|4_0 _.0¢._00 o._o_z_o Figure H-11. Sample output for TRANSON.

Next: APPENDIX →

APPENDIX

APPENDIX

T_ A Computer Program Providing Rapid Evaluation

of Closed-Form Solution for the Flow About a

Prolote Spheroid Moving Along Its X-Axis

In order to evaluate the accuracy of the method described in the body of

this work for predicting potential flow about an arbitrary three-dimensional

body, a search was undertaken for a suitable body with a closed-form velocity

distribution. The most obvious was the sphere. While the sphere does pro-

vide a means for such comparison, it is a very crude approximation of an air-

craft fuselage or similar type three-dimensional body. A body which had a

higher length-to-width ratio would be more representative; therefore, an

analytical method for generating the potential flow about an ellipsoid was

examined.

The solution for potential flow about an ellipsoid is well known and can

be found in Lamb (Ref. 6) and Munk (Ref. 66). The solution and formulae for

generating the velocity distributions are also given in Tim man (Ref. 49). The

equations in the latter work, originally developed for a yawed ellipsoid, were

degenerated to apply to the case of a spheroid (ellipsoid with y and z axes

equal) in a uniform flow field of velocity Uo at zero incidence to the x-axis

of the spheroid.

The velocity distribution of the spheroid was calculated by a computer

program in the following manner: Knowing the x-axis (a), the y and z-axes (b) of the'spherold, and the x,

y, and z coordinates of the point for which the petentlal flow is to be evalu-

ated, a series of coefficients is then determined:

S = ql - b2/a 2

2 ab 2 -I

so - [ tanh (S) - S]

(a2- b2)_

p = 2 U n

(2 - s o)

x 2 1

G = a -T + __ (y2 + z 2)

b_

Following Timman,one maymanipulate the degenerate form of the

equations to obtain the velocity componentsin terms of these coefficients:

- p z 2

U

(yZ + )

P xy

v = _ (a2b 2 )

P.xz)

W

Given the dimensions of the spheroid and the free stream velocity, the

program then computes u, v, and w at a specified x, y, and z on the surface

of the spheroid by means of the relations above.

From the equations it can be seen that the potential flow about a sphere

may also be generated by letting a be equal to b. Because of the Indetermlnant

form of the solution for this case, it is necessary to obtain a solution

for a sphere by letting a = 1.01b.

Because of its speed and accuracy this program was most helpful in

establishing when the general three-dimensional body potential flow prGgram

was running correctly and how many panels were required and In what distribution

to represent a body adequately. It is presented here so that the reader may

use it for that purpose or as a direct solution for a special class of fuselages.

The latter case may be of special interest to those with limited computing

facilities or those who wish to demonstrate the design concepts related herein

without Incurring the large computing expenses of the general three-dimenslonal

body program. The following discussion provides a listing, instructions for

entering data, and typical output.

Sam_o Output

)--I SPNIt010 YMt 1341E0ilIVICAL YILOCITY SOLUTION POll • SIPHIEIiOlO Ik* |•0004Hi I* i•Q0000 UO_ L.OOHO I X ¥ Z U V II CP L |.00ON o•oeoeo o.oa@oo *e.coooo o•oo¢oe e.eoeee loeceoe I I•SOeOO e.oeoce @.SSLTT -o.e_nntl o.ooeoo o.6so6z -o.o04|o • |.(1000• (l•ooo00 00T44L? -L•OJOll O.00OO0 0oN•6! *0•liSTS 4 $.!41Q04) O•0•000 0.0660| -1t.00190 O.0Oe0O 0•NOSI *0•8iNS J I•M_00 O.O0000 O.SAlSl -I.t06Sq @.Gl¢@@ 0.1J044 -O.|4IM 6 O•lqHBO• 0.000O0 0.90613 -1.111'41 0.00000 0o06NI "0.111401 ? 0.00N0 0.00O0Q h0O¢O0 oh|t1 ? 0•00e0Q 0,000_ -0oH001 Sgmlt| • lie TNIEOIIETICAL V|LOCITY SOLUTION FOIl & SPHlit0lO 1•00100 8* I•Oe000 I I V I U V V CP I 1.00100 0.0O04e 0.00104 *O• 0004)0 0.00000 0.001SS 1.00000 • i.•04100 0•1414100 •.044TZ -@.Q(INI 0.00400 0.01706 O. 9'0S4.9 | 0.99S00 O•00000 0•06|Zl -0,0060| 0o00000 0.0S_?0 0•q_100 4 O• N0e 0•Oe000 0.0?T_I --O. 004NH) O•00eO0 0•1|$14 O.eO6S0 S 0• _T00 O. MM00 O. Oq_J6 -I_ O|S00 0. i4Q00 O• IHS8 0•UN| • 0•_S99 OoN00e O. ,•sol - •. 01_9 •. 00000 0.16e16 o. yv_ • o.q_iq OoOlO00 o. li_J9 -0• 0|_)O 0• 00e00 0.16J19 0• •liHI O II• q_'l_IP •.00000 0el|it | .-41. 0104_ O• 00000 O. LT4k04 0•'I60gT • qk qP91_IP O. 01000 0•1141,1• -0• 1111•4 O• 0G0041 0•10796 0.'16410 tO O. •ql, l•q) O. 04NNIO O. l IIIIIT • 0111s' O. 041000 0•1991t •09S•I.3 . * • 910 0.OlHT O*00000 •••99_ I roll 0.00000 • Olt4l I 14_ - ° • • 91)1 0.00_T •.0000O o••tee• t 49116 • oeeoe o oils1 I _9o ql_5, O.II08416 •. O0000 •*•9996 1 491'11 go00000 • 1114,1 l 144101 • • • • 99J 0* 007q_ 0• 00000 0* 9_SS? 1 11 O•00000 O•0|t•l 1 I400T m 0.00696 O.0e000 O q_l_O 1 4q_Sl • 00000 O tl041 *1.14111 m e.oo_i0• 0.000N 0 ••m I +b9915t go00000 O.00_IPl -l.14.Ol) q_6 1.00446 • 00000 • •_ I 44_JT 0.0e000 O g0•41 -l.l+llS HT 0.0011•4 i.0•O00 • e,19qMl I. 4_I_I+0 i.•0000 • 005HPl -I.I4OIT 090 0.001941, • 00004) I.O0e00 I 4q_ll• • _4_00 Oo004_! I 14019 • 4• •.410196 O•00_I0 I.04HIO0 I 44414,0 O.000•O 0.I01"I$ 1 144110 IIIOI •.000e, t 1014000 I O000e I _+q144+0 O.OlgO0 • OOllbl -I=14+•11 Figure l-3. Sample ou,pu, for SPHEROID.

Program Listing

THE POTENT|AL FLOW &OOUT A SPH4ERO|O AS GERIVEO FRoIqS THE POTINTIAL FLOW AOOUT A YARED ELLIPSOID AT ZERO INCIOENCE |¥! R* TI_RAN - NATIONAL AEROSPACE LA|OAATOR¥ - THE NEIHERLANOS REALO8 S DATA ENO/eENO *l DI NENS|ON T| TLE (ZO!

20 READII,1201 TXTLE 120 FOAIIAT I Z©&_ I IFITITLEIII.EQ.ENO ) GO TO 30 HAl TEI]t2ZS| TITLE LZS FORflAT I ° | *//_OX,20A4 ) RE&O¢ | *I ]0| AtOoUOt IXwN 130 FORHATK3FEO. S,21101 C'R Vll IIE ( -II, 1$@ I A eBvUQ |SO FOflMATIII2OReeTHE THEORETICAL VELOCITY SOLUTION FOR A $PHERO|D I 'llZX. cA-* ,FLO. S/ZXt eB-eoFlO.5/IXl eUO*'eFIO.5I/ 2T4, *| 0,TlO e iXe_TZO e +yi tT30 ! IZl !¥i+01 *Ue e TROt eve, T60 ' +lie t TTO, iCpe jt | &SO'AIR OSQeROR CSQ'COC A4°ASOO& SO ID*oBSOIR SQ C++oC SQOC SO So SORT ( | *-CSO/ASQ I AOo2. Is& e|eC / I ASQ-CS@ ) el I * 5e ( *SeOLOG I ( i * OO*S )/I |. 04_S ! I-S ) Po2° _JOF 12.-AO) Y'0* OXA'|+IN XAe|.4'DXA DO 15 I'|*N IRE IRIT+,T.R T RR- JR-OAR Xt Xl4kA ZeA|S I SORT 11 .-XAIXA ) I GO TO I0 l RE&OR l, I tlOlil,+V.Z |0 XSO-XlX ¥SO*YOY ZSOoE*Z Gs XSOI &4_YSO/II4*Z SQIC_ U _- le/GO ( YSQ/14. Z S01C 4 I VuPJGO(RIY/ASG/RSO) kleP/Ge4 XeI/ASO/CSO!

VSIi+UIIJ4 I_lV*lllll CP" L*-VSIIJUOIUO MR|_I 5*|00I | tX*YvZeU*VeNeCP FOIII4ATI IS. IZ_ lO.Sl 2S CONT INU!

GO TO 20 )0 R! TUmN ImO fEND TITLE _t_ B UO IX N | .00| I • I O IOO41 TITLE _'* X' Y Z _' O. O. I.

Y z "_

X .5 O- .98613

Y z _

/ : O- .94258

x Y z "_

1.5 O. • 86603 X Y Z 2 , O* ,744 I 7 ¥ Z

/ _ -,_

2.5 O- .55f77 3, O. O, A B UO IX N 3- I. I I 7 3- I SPHEROI D Illlllllll$ IIIllllllllll|llll llOllllllllllllll|l|OlllOllOlllOOllllllOlOlllllllll Ilil1111111 II111111111_11111_ Illlllllllllllllllfllitl IIII}111111111111 2_122222222 221?22277211722212 2!21122222!272222271_1222212722222!

11331J333_) _1_331331_33_3113 44|444|4444 44444144444144414 55555555555 5_555555_55555555 iiii|iiiiii i$$iiiillliliiili ilili$1111illlilli _ . 7 ikiiliii|ll6 COMPrJ'TI_G C_NT_R 11117111711 11177111711171111 1111111111111111!111 _,__ 11111111!1111 IIIIIIIIIII llllll|llllllllll IIIIIIIIIIIIIIIIIIIIIIII lllllllllllllllll ttliltllJlll 111|19|1511 i_ll!

lllllllllllllllllll_llllllllllllllll_l_llllllllllll l Figure I-2. Sample data set for SPHEROID.

45O

User Instructions

Thls program Is written In Fortran IV and is designed to run on an

IBM 370-165 computer. Execution requlres 30,000 bytes of core storage and

approxlmately 10 seconds to predlct the velocity distribution and pressure

coefflclent for 1600 points. For a glven run, the program requires the

followlng Input data:

(I) The 80 characters of the alphamerlc array TITLE whlch are used as

a header for Identifying output. It is used to terminate executlon by set-

ting the first four characters to "END_".

(2) The x-axis (a), the y and z-axes (b), the free stream x-velocity,

U o , the mode Indicator, IX, and the number of points for this run, N. The

mode Indlcator, IX, may take on two values. If IX Is zero a meridian solution

of N points Is generated by the program. By indicating IX as one, the

programmer Implies that a merldlan solution is not desired and that N spe-

clflcally selected points will follow.

(3) The points x, y, and z (if IX equals one) at which the solutlon Is

to be calculated.

Format speclflcatlons for these variables may be found In Flgure I-I.

A sample data set of a three-to-one prolate spheroid Is glven In Figure 2-2

and the output for that data set Is given In Figure I-3.

jiil,,ll ill Ii . _,_,,_L, ....

!

,,o._ ,,o _ .... ,,o

H////////I////A

rl

T'i !x,r

!!, i

' ' ' _ ' ' r Y I ..........

l,,i0r

' i

!!_!T_''_'.:II: ,! "

Figure 2-I. Format speclflcatlon for SPHEROID.

Next: APPENDIX d - Supplementary Bibliography →

APPENDIX d - Supplementary Bibliography

APPENDIX d - Supplementary Bibliography Listed below is bibliographic Information on some post-1970 documen÷s In the NASA information collection dealing, at least in a general way, with the estlmatlon of aerodynamic characteristics of subsonic aircraft. The methods described are, for the most part, intended for computer solution. A listing of the appropriate program Is given in quite a number of these documents along with user instructions. The documents are available (except where noted) from the National Technical Information Service by requesting the first number (document accession number) shown in each citation.

The list was assembled from a computer search of the NASA information collection for documents Indexed under both aerodynamic characteristics and computer methods or numerical methods. Results from a second search employing the terms Prediction Analysis Techniques, Flow characteristics, Aerodynamic Drag, Aerodynamic Coefficient, and Performance Prediction are also included.

Titles_d mini-abstracts were then examlned to select those citations given below. The present authors have not seen the complete document in most cases.

The llst is intended to provide some contemporary references for the worker just entering the field as well as an indication of the direction in which contemporary research is moving for the benefit of the more casual reader.

Because the task of assembling this work as a whole necessarily limited the period of preparing the literature review to late 1972 it was not possible to include the.documents listed here in the review.

I • 72BI0618 Langley-11047 Vortex-Lattice Fortran Program for Estlmating Subsonic Aerodynamic Characteristics of Complex Planforms Margason, R. J.; Lamar, J. E.

2. 71BI0153 Lewis-11382 Computer Program for Calculating Aerodynamic Forces on Blade Sections MC Nally, W. D.

.

74A15445 9 pages Computerized Deslgn of Transport Airplane Takao, K.

Japan, Defense Academy, Memoirs, Vol. 13, Sept. 1973, pp. 327-335.

.

73A22433 2 pages Calculation of Forces on Stores in the VIclnlty of Aircraft Serbin, H.

Journal of Aircraft, Vol. 10, Feb. 1973, pp. 123, 124.

go 73A17213 4 pages Leading-Edge Force Features of the Aerodynamic Flnite Element Method Lan, C.-T.; Roskam, J.

Journal of Aircraft, Vol. 9, Dec. 1972, pp. 864-867.

o 73A14377 37 pages Transonic Profile Theory - Critlcal Comparison of Varlous Procedures Eberle, A.; Sacher, P.

Deutsche Gesellschaft Fuer Luft - und Raumfahrt, Symposlum Ueber Tragfluegel-Aerodynamik Be i Schallnahen Stroemungen, Goettlngen, West Germany, Oct. 26, 27, 1972, Paper In German.

o 72A43455 SAWE Paper 908 15 pages An Aerodynamics Model Applicable to the Synthesls of Conventional Fixed-Wing Aircraft Peyton, R. S.

Society of Aeronautical Weight Engineers, Annual Conference, 31st, Atlanta, Ga., May 22-25, 1972.

t 72A16798 AIAA Paper 72-221 A Simple Model for the Theoretical Study of Slat-Airfoil Combinations Llebeck, R. H.; Smyth, D. N.

o 71A24253 SAE Paper 710389 Low Speed Airfoil Analysis Using a Small Digital Computer Koepsel, R. E.; Miller, J. A.; Wentz, W. H., Jr.

New York, Society of Automotive Engineers, Inc., Society of Automotive Engineers, National Business Aircraft Meeting, Wichita, Kan., Mar.

24-26, 1971.

10.

73N70722 GDC-TN-70-AVLABS-09 54 pages Use#sManual for Tilt Wing and Deflected Slipstream Aerodynamlcs Program Pederson, S. K.

74N14741 NASA-TR-R-421 11.

A Study of the Nonlinear Aerodynamics of Bodies in Nonplanar Motion (Numerical Analysis of Aerodynamic Force and Moment Systems During Amplitude, Arbitrary Motions) Schiff, L. B.

Ph.D. Thesis - Stanford University, Calif.

12. 74N14739 NASA-TM-X-62321 31 pages Plotting Program for Aerodynamic Lifting Surface Theory -- User Manual for Fortran Computer Program Medan, R. T.; Ray, K. S.

13. 74N11810 NASA-TM-X-62309 Geometry Program for Aerodynamic Liftlng Surface Theory Medan, R. T.

73N31226

14.

Starting Vortex, Separation Bubbles and Stall -- A Numerical Study of

Laminar UnsteadyFlow Around an Airfoil

Mehta, U. B.

Ph.D. Thesis, lllinois Inst. of Tech., Chicago, Univ. Microfilms Order

No. 73-12222.

73N27890 NASA-CR-2217

15r

Analytical Methodfor Predicting the Pressure Distribution About a

Nacelle at Transonic Speeds

Keith, J. S.; Ferguson, D. R.; Merkle, C. L.; Heck, P. H.; Lahtl, D. J.

73N27889 NASA-TN-D-6933

16.

On the Numerical Simulation of Three-DimensionalTransonic Flow with

Application to the C-141 Wing

Lomax,H.; Bailey, F. R.; Ballhaus, W. F.

73N27212 NAL-TR-309

17.

In Japanese; English Summary

A Numerical Calculation of a Two-DimensionalIncompressible Potential

Flow Around a Set of Airfoils Applying the Relaxation Method

Nakamura, M.

National AerospaceLab., Tokyo,'Japan,

73N25010 ARC-R/M-3487

18.

The Calculation of the SpanwiseLoading of Sweptback Wingswith Flaps

or All-Moving Tips at Subsonic Speeds

Brebner, G. G.; Lemaire, D. A.

19. 73N24997

Kelvin ImpulseTheory Applied to Llft on Airfoils

Delaney, J. A.

Ph.D. Thesis, Cincinnati Univ., O. Univ. Microfilms Order No. 72-31627.

73N24325 SC-CR-72-3i82

20.

Numerical Solution of the Three-Dlmensional BoundaryLayer on a Spinning

Sharp Bodyat Angle of Attack

Watklns, C. B., Jr.

21. 73N243i9 NASA-TT-F-14918 24 pages

The Kutta-JoukowskyCondltlons in Three-Dlmensional Flow

Legendre, R.

22. 73N24302 90 pages

The Three-Dlmenslonal Structure of Transonic Flows Involvlng Llft

Hafez, M. M.

Ph.D. Thesls, Univ. of Southern Calif., Unlv. Microfilms Order No.

72-27661.

23.

73N24054 14 pages

Reviewof TwoMethodsof Optimizing Aircraft Design

Kirkpatrick, D. L. I.

In AGARD Aircraft PerformancePrediction Methodsand Optimization.

24.

73N22998 AFAPL-TR-72-100 124 pages

Lifting Surface Theory for Statically Operating Propellers

Murray, J. C.; Carta, F. C.

25.

73N21952 FTD-MT-24-1646-72 20 pages

ApproximateMethodof Calculating the AerodynamicLoad Distribution on a

Low-Flying Wingwith a Fuselage

Tsvetkov, L. G.

26.

73N21913 NWL-TR-2796 122 pages

BodyAlone Aerodynamicsof Guidedand UnguidedProjectiles at Subsonic,

Transonic, and Supersonic MachNumbers

Moore, F. G.

27.

73N21292 MDC-J5679-02 81 pages

Calculation of Potential Flow About Arbitrary Three-DimensionalLifting

Bodies, User's Manual

Mack, D.

28.

73N19999 NASA-TN-D-7251 35 pages

Steady, Subsonic, Lifting Surface Theory for Wingswith Swept, Partial

Span, Trailing EdgeControl Surfaces

Medan,R. T.

29.

73N18054 FTD-HT-23-834-72 12 pages

Flow Around WingProfile with the Presenceof the Surface of a System

of Sourcesand Sinks

Baev, B. S.; Zhuravlev, V. N.

30.

73N17035 AFFDL-TR-72-26-VOL-3 207 pages

V/STOL Aircraft AerodynamicPrediction MethodsInvestigation, Volume3

Manual for ComputerPrograms

Wooler, P. T.; Kao, H. C.; Schwendemann, M. F.; Wasson,H. R.; Ziegler, H.

31.

73N17033 AFFDL-TR-72-26-VOL-1 238 pages

V/STOL Aircraft AerodynamicPrediction MethodsInvestigation, VolumeI

Theoretical Development of Prediction Methods

Woo ler, P. T.; Kao, H. C.; Schwendemann, M. F.; Wasson,H. R.; Ziegler, H.

32.

73N16985 120 pages

A ComputerProgramfor the Prediction of AerodynamicCharacteristics of

Wing-Body-Tail Combinations at Subsonic and Supersonic Speeds,Part 2

Anders, S.; Bustavsson, L.

Aeronautical Research Inst. of Sweden,Stockholm.

33.

73N15035 32 pages The Avsyn Air Vehicle Synthesls Program for Conceptual Design Sanders, K. L.; Staley, P. A.

34.

73N15004 9 pages Design of Airfoils with High Lift at Low and Medium Subsonic Mach numbers Wortmann, F. X.

In AGARD Fluid Dyn. of Aircraft Stalling.

35.

73N14989 NASA-CR-2186 58 pages Steady Inviscid Transonic Flows Over Planar Airfoils - A Search for a Simplified Procedure Magnus, R.; Yoshihara, H.

36.

73N13007 RIAS-TR-72-166 50 pages On Lifting Wings with Parabolic Tips Jordan, P. F.

37.

73N13006 AFOSR-72-1737TR 50 pages Exact Solution for Lifting Surfaces Jordan, P. F.

38.

73N12315 NPS-59NN72082A 48 pages Flow Studies of Axisymmetric Bodies at Extreme Angles of Attack Smith, L. H.; Nunn, R. H.

39.

73N12224 NLR-TR-70088-U 38 pages Computer Application of Subsonic Lifting Surface Theory Labrujere, T. E.; Wooters, J. G.

National Aerospace Lab., Amsterdam, Netherlands.

40.

73N11999 NASA-CR-2157 115 pages Calculative Techniques for Transonic Flows About Certain Classes of Wing-Body Combinations, Phase 2 Stahara, S. S.; Spreiter, J. R.

41.

73NI0242 MDC-J5264-VOL-2 310 pages Investigation of Aerodynamic Analysis Problems in Transonic Maneuvering, Volume 2 Airfoil Analysis Computer Program Gentry, A. E.

42.

73NI0042 AFFDL-TR-71-155-PT-1 50 pages Takeoff and Landing Analysis (Tola) Computer Program Lynch, U. H. D.

43.

72N32302 NASA-TT-F-14547 20 pages Subsonic and Supersonic Flow Around Nonaxisymmetric Fuselages Rothman, H.

44.

72N31991 18 pages Lift-Curve Slope and Aerodynamic Centre Posltion of Wings in Invlscid Subsonic Flow Engineering Sciences Data Unit, London, England, Avail on Subscription from Engineering Sciences Data Unit, 251-259 Regent Street, London, WIR 7AD.

45.

72N31909 SRL-TR-70-O009 24 pages A Method for Aerodynamic and Propulsion Design Optimization of the Short Range Dogfight Missile Forbrlch, C. A.; Gallington, R. W.; Hatlelid, J. E.; Hyde, J. P.; Murrow, R. C.

46. 72N30264 NASA-TT-F-14538 6 pages Numerical Study of the Influence of the Wing Tlp Shape on the Vortex Sheet Rolling Up Rehback, C.

47.

72N29002 RIAS-TR-72-040 70 pages Complete Solution for Lifting Wings with Parabolic Tips Jordan, P. F.

48. 72N26023 NASA-CR-112065-3 114 pages Theoretical Prediction of Interference Loading on Aircraft Stores, Part 3 Programmer's Manual Danfernandes, F.

49. 72N26003 ONERA-TP-I088 16 pages In French; English Summary Aerofoil Stall Prediction in Incompressible Flow Vincentdepaul, M.

50. 72N26001 26 pages Calculation of Pressure Distributions for an Airfoil in Subcritical Flow Including the Effect of the Boundary Layer Anders, S.; Gustavsson, L.; Hillgren, R. S.; Toll, G. I.

Aeronautical Research Inst. of Sweden, Stockholm.

51. 72N24005 AFOSR-72-OO34TR 19 pages The Discrete Vortex Approximation of a Finite Vortex Sheet Mc_re, D. W.

72N24003 MDC-J5108 AFOSR-72-0370 92 pages 52.

A General Class of Airfoils Conformally Mapped from a Circle James, R. M.

72N22002 ARC-R/M-3630 53.

The Linearized Subsonic Flow Over the Centre-Section of a Lifting Swept Wing Rossiter, P. J.

72N15010 48 pages

54.

In German;English Summary

Downwash Investigations on a Missile Tails

Gregoriou, G.

Messerschmitt-Boelkow-Blohm G. M. B. H., Ottobrunn, WestGermany.

72NI1289 NASA-TN-D-6530 16 pages

55.

Contribution to Methodsfor Calculating the Flow About Thin Lifting

Wingsat Transonic Speeds_ Analytic Expressions for the Far Field

Klunker, E. B.

71N30488 NASA-TT-F-702

56.

The Calculation of the Pressure Distribution on a Cascadeof Thick

Airfoils by Meansof Fredholm Integral Equations of the SecondKind

Martensen, E.

(Translation of Ref. 24).

71N19385 9 pages

57,

A Methodfor Predicting Interference Forces and Moments on Aircraft

Stores at Subsonic Speeds

Fernandes, F. D.

In AGARD Aerodyn. Interference, Jan. 1971.

74N18680 NASA-CR-2334 187 pages

58.

Correlation of Full-Scale Drag Predictions with Flight Measurements on

the C-141AAircraft: Phase2 WindTunnel Tests, Analysis, and Predlctlon

Techniques. Volume2 WindTunnel Test and Basic Data, Final Report

MacWilkinson, D. G.; Blackerby, W. T.; Paterson, J. H.

74N18679 NASA-CR-2333 166 pages

59.

Correlation of Full-Scale Drag Predictions with Flight Measurements on

the C-141AAircraft Phase2 Wind Tunnel Test, Analysis, and Prediction

Techniques, VolumeI Drag Predictions, WindTunnel Data Analysis and

Correlation, Final Report

MacWilkinson, D. G.; Blackerby, W. T.; Paterson, J. H.

74N14716 50 pages

60.

Aircraft Drag Prediciton for Project Appraisal and PerformanceEstimation

Butler, S. F. J.

In AGARD Aerodyn. Drag.

74N14712 11 pages

61.

AerodynamicDrag and Lift of General BodyShapesat Subsonic, Transonic,

and Supersonic MachNumbers

Moore, F. G.

In AGARD AerodynamicDrag.

62.

74N14711 38 pages A Survey of Drag Predictlon Techniques Applicable to Subsonic and Transonic Aircraft Desgin Paterson, J. H.; MacWilkinson, D. G.; Blackerby, W. T.

In AGARD Aerodyn. Drag.

63.

73N15010 16 pages The Effect of Leading Edge Geometry on High Speed Stalling Moss, G. F.; Haines, A. B.; Jordon, R.

In AGARD Fluid Dyn. of Aircraft Stalling.

64.

72N22995 NASA-TM-X-67791 94 pages Nonplanar Method for Predicting Incompressible Aerodynamic Coefficients of Rectangular Wings with Circular-Arc Camber Lamar, J. E.

Ph.D. Thesis, Virginia Polytechnic Institute, Avail. NTIS HC $6.75.

65.

72N11869 NASA-TM-X-67413 9 pages A Comparison of Some Aerodynamic Drag Factors as Determined in Full- Scale Flight with Wind-Tunnel and Theoretical Results Saltzman, E. J.; Bellman, D. R.

In AGARD Facilities and Tech. for Aerodyn. Testing at Transonic Speeds and High Reynolds Number.

66.

74N1423 9 pages New Investigations for Reducing the Base Drag of Wings with a Blunt Traillng Edge -- Effects of Splitter Plates and Splitter Wedges on Aerodynamic Drag Coefficients Tanner, M.

In AGARD Aerodyn. Drag.

67.

74N14719 20 pages Drag of Supercritlcal Airfoils in Transonic Flow -- Comparison wlth Conventional Airfoil Drag Coefficients Kacprzynski, J. J.

In AGARD Aerodyn. Drag.

68.

74N14709 AGARD-CP-124 469 pages Partly in English and Partly in French Aerodynamic Drag Advisory Group for Aerospace Research and Development, Paris, France, Avail. NTIS HC $25.50, Proceedings of Specialist Meeting, Izmlr, Turkey, 10-13 April 1973.

69.

73N31228 ESOL-71020 ESDU-67010 23 pages Aerofoils having a Specified Form of Upper Surface Pressure Distrlbutlon Details and Comments on Design Engineering Sciences Data Unit, London, England, Avail Issuing Activity, Sponsored by Mln. of Defence and Roy. Aeron. Scc.

73N23362 ESDU-BODIES-02.04.02 3 pages 70.

Drag of Streamline Solids of Revolution (Transition at 0.11 Behind Nose (Numerical Analysis of Drag of Streamlined Bodies of Revolution for Various Length to Diameter Ratios) Engineering Science Data Unit, London, England, Avail. Issuing Activity.

71.

74N14729 11 pages The Drag of Externally Carried Stores Its Prediction and Alleviation -- Drag Reduction by Redesign or Development of New Aircraft Installations Pugh, P. G.; Hutton, P. G.

In AGARD Aerodyn. Drag.

72. 74N14728 22 pages The Drag Resulting from Three-Dimensional Separations Caused by Boundary- Layer Diverters and Nacelles in Subsonic and Supersonic Flow Peake, D. J.; Rainbird, W. J.

In AGARD Aerodyn. Drag.

73. 74N14724 15 pages A Study of Flow Separation in the Base Region and Its Effects During Powered Flight -- Interaction Between Propulsive Jet and Free Stream Flow Addy, A. L.; Korst, H. H.; White, R. A.; Walker, B. J.

In AGARD Aerodyn. Drag.

74. 74N14718 12 pages Remarks on Methods for Predicting Viscous Drag -- Aerodynamic Drag Prediction for High Angles of Attack and Multielement Airfoils Smith, A. M. 0.; Cebeci, T.

In AGARD Aerodynamic Drag.

75. 74N14717 9 page_ Appendix A Data Item Service for Aircraft Drag Estimation -- Collection, Dissemination, and Development of Aerodynamic Drag Prediction Data Engineering Sciences Data Unit, London, England, Avail. NTIS, In AGARD Aerodyn. Drag.

74N12704 ESDU-73028 23 pages 76.

Drag of Two-Dimensional Steps and Ridges Immersed in a Turbulent Boundary Layer at Subsonic and Supersonic Speeds Engineering Sciences Data Unit, London, England, Avail Issuing Activity, Sponsored by Roy. Aeron. Soc.

74NI0311 ESDU-BODiES-O2.04.01-AMEND-A 3 pages 77.

Drag of Streamline Solids of Revolution (Transition at Nose) Engineering Sciences Data Unit, London, England, Avail. Issuing Activity.

78.

Not in File 23 pages

Measurements in the Thick Axisymmetric Turbulent BoundaryLayer Near

the Tail of a Bodyof Revolution

Patel, V. C.; Nakayama, A.; Damlan,R.

Journal of Fluid Mechanics, Vol° 63, pp. 345-368, April 1974.

79.

74A19581 13 pages Numerical Solution of the Three-Dim_nsional Boundary Layer on a Spinning Sharp Body at Angle of Attack Watkins, C. B. Jr.

Computers and Fluids, Vol. I, Dec. 1973, pp. 317-329.

80.

74A11957 21 pages The Numerical Solution of the Navier-Stokes Equations for Laminar Incompressible Flow Past a Paraboloid of Revolution Veldman, A. E. P.

Computers and Fluids, Vol. I, Sept. 1973, pp. 251-271.

81.

72A41264 2 pages Lift on Airfoils with Separated Boundary Layers Ness, N.

Journal of Aircraft, Vol. 9, Aug. 1972, pp. 607, 608.

82.

74N13984 AFOSR-73-1265TR-PT-7 45 pages Three-Di,_nsional Laminar Boundary Layer Over Body of Revolution at Incidence, Part 7 The Extremely High Incidence Case Wang, K. C.

83.

73N25006 ARC-R/M-3221 20 pages Numerical Methods for Calculating the Zero-Lift Wave Drag and the Lift- Dependent Wave Drag of Slender Wings (Evaluation of Double Integral Equation for Calculation of Wave Drag Due to Volume and Aerodynamic Lift of Slender Wings) Weber, J.

In Arc Aerodyn. Res., Including Heating, Airfoils, and Boundary Layer Studies, Vol. I, pp. 155-173.

84.

72N32330 200 pages The Optimum Shaping of Axisymmetric Bodies for Minimum Drag in Incompressible Flow (Optimum Hydrodynamic Configurations for Submerged Minimum Drag Axisymmetric Vehicles in Incompressible Fluids) Parsons, J. S.; Goodson, R. E.

85. 72M50104 I page FORTRAN V Program

TRW Vortex-Lattice (N-Surface) SubsonicAerodynamics

(AerodynamicCalculations for Single or Multiple Lifting Surface

Configurations by ImprovedVortex-Lattice Method)

Rome re

National Aeronautics and SpaceAdministration, LyndonB. Johnson

SpaceCenter, Houston, Texas.

86. 71M51203 I page FORTRAN IV Program

SubsonicUnsteadyAerodynamic

(Steady and UnsteadyAerodynamicCoefficients'for Subsonic Lifting

Surfaces)

Harrison

National Aeronautics and SpaceAdministration, Marshall SpaceFlight

Center, Huntsville, Ala., Jan. 1972.

87.

74MI0002 I page CDCFORTRAN Program1,293 cards

Modified Multhopp MeanCamber Program-- MeanCamber Surface Required to

Support Set of Loadings on CompositeWing in SubsonicCompressible Flow

National Aeronautics and SpaceAdministration, Langley ResearchCenter, Langley Station, Va., Price: Program$275.00/ Documentation$15.50.

88.

73MI0132 2 pages FORTRAN IV Program6,594 cards

An ImprovedMethodfor the AerodynamicAnalysis of Wing-Body-Tail

Configurations in Subsonicand Supersonic Flow

(AerodynamicAnalysis of Wing-Body-Tail Configurations in Subsonic and

Supersonic Flow)

Aerophysics ResearchCorp., Bellevue, Wash., Price: Program$600.00/

Documentation$27.50.

89. 73MI0131 I page FORTRAN IV Program960 cards

General Lifting-Line Jet Flap FORTRAN Programfor Estimating Subsonic

AerodynamicCharacteristics

(Estimation of Subsonic Aerodynamic Characteristics of Jet-Flapped Wings)

Northrop Corporate Labs., Hawthorne,Calif., Price: Program$250.00/

Documentation$4.00.

90. 74A25062 ONEIDA, TP No. 1247 14 pages

In French

AerodynamicProblemsof the Short Takeoff and Landing Aircraft

Ceresuela, R.

(L'Aeronautique et L'Astronautique, No. 41, 1973, pp. 43-56).

91. 74A21893 4 pages In Russian

An Optimization Methodfor a Generalized Class of Functionals and Its

Application to the Problemof Determining the Shapeof a BodyExhibiting

Maximum AerodynamicEfficiency

Bunimovich, A. I.; Dubinskii, A. V.

Moskovskii Universitet, Vestnik, Seriia I - Matematika, Mekhanika, Vol.

28, Nov.-Dec. 1973, pp. 87-90.

92.

74A21104 11 pages

The High Subsonic Flow Around a Two-DimensionalAerofoil with a Trailing

EdgeControl Surface

Nixon, D.

Aeronautical Quarterly, Vol. 24, Nov. 1973, pp. 273-283.

93.

74A20765 AIAA Paper 74-106 28 pages Aeroelastic Loads Predictions Using Finite Element Aerodynamics Rowan, J. C.; Burns, T. A.

American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting, 12th, Washington, D. C., Jan. 30-Feb. I, 1974.

94.

74A20280 7 pages Subsonic Potential Aerodynamics for Complex Configurations - A General Theory Morino, L.; Kuo, C.-C.

AIAA Journal, Vol. 12, Feb. 1974, pp. 919-197.

95.

74A19684 36 pages In French Flexible Lifting Surfaces -- In Steady Inviscid Compressib e Flow Vaussy, P.

(Association Technique Maritime et Aeronautique, Session, 73rd, Paris, France, May 14-18, 1973), Association Technique Maritime et Aeronautique, Bulletin, No. 73, 1973, pp. 361-394, Discussion, p. 395.

96.

74A18878 AIAA Paper 74-107 14 pages A Finite Element Method for Potential Aerodynamics Around Complex Configurations Chen, L.-T.; Suciu, E. 0.; Morino, L.

American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting, 12th, Washington, D. C., Jan. 30-Feb. I, 1974.

97.

74A18820 AIAA Paper 74-72 8 pages Odin - Optimal Design Integration System for Synthesis of Aerospace Vehicles Rau, T. R.; Decker, J. P.

American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting, 12th, Washington, D. C., Jan. 30-Feb. I, 1974.

98.

74A18681 13 pages In Russian Calculation of the Aerodynamic Characteristics of a Wing System Moving at Subsonic Speed Near Land or Smooth Water Surface Ermolenko, S. D.; Khrapovitskii, V. G.

Samoletostroenie Tekhnika Vozdushnogo Flota, No. 32, 1973, pp. 3-15.

99".

74A15965 9 pages Exact Method of Designing Airfoils with Given Velocity Distribution In Incompressible Flow Strand, T.

Journal of Aircraft, Vol. 10, Nov. 1973, pp. 651-659.

100.

74A15747 22 pages Note on the Aerodynamic Theory of Oscillating T-Tails. I - Theory of Wings Oscillating in Yaw and Sideslip Ichlkawa, T.; Isogal, K.

Japan Soclety for Aeronautical and Space Sciencest Transactions, Vol.

16, No. 33, 1973, pp. 173-194.

101.

74A15709 7 pages In Russian A Problem of Designing the Optimal External Contours of an Alrcraft Oslpov, V. A.; Tereshchenko, A. M.

Avalatslonnala Teknika, Vol. 16, No. 3, 1973, pp. 11-17.

102.

73A40427 5 pages Simplified Aerodynamic Theory of Oscillating Thin Surfaces in Subsonic Flow Jones, W. P.; Moore, J. A.

AIAA Journal, Vol. 11, Sept. 1973, pp. 1305-1309.

103.

73A37846 7 pages In Russian Integral Equation in the Theory of Lifting Surfaces Poliakhov, N. N.

Leningradskii Universitet, Vestnik, Matematika, Mekhanika, Astronomila, Apr. 1973, pp. 115-121.

104. 73A37545 15 pages In Romanian New Contributions to the Iterative Method for Aerodynamic Calculations of Wings in Subsonic Flows Patraulea, N. N.

Studii Si Cercetari De Mecanica Apllcata, Vol. 31, No. I, 1973, pp. 15-29 15-29.

105. 73A36394 5 pages A Finite-Element Method for Calculating Aerodynamic Coefficients of a Subsonic Airplane Hua, H. M.

Journal of Aircraft, Vol. 10, July 1973, pp. 422-426.

106.

73A31746 4 pages Remarks on Vortex-Lattice Methods (Optimal Grid Arrangement in Vortex Lattice Method of Lifting Surface Aerodynamic Analysls, Comparing Numerical with Kernel Function Results for Simple Wing Planforms) Hough, G. R.

Journal of Aircraft, Vol. 10, May 1973, pp. 314-317.

107.

73A27732 5 pages In German FS-28 - A Contribution to a Possible Develop_nt Trend in Llght- Aircraft Design (Light Motorized Glider-Type Aircraft Design, Development and Flight Testing, Discussing Aerodynamic Configuration, Structural Design and Performance Characteristics) Deutscher Aerokurier, Vol. 17, Mar. 1973, pp. 152-156.

108.

73A26256 440 pages In Russian Design and Stability of Airplanes and Helicopters (Russian Book on Airplane and Helicopter Design and Stability Covering Selection of Wing/Rotor/Configuration and Power Plant, Subsystem Deslgn, Strength, Reliability, Lifetime, Etc.)

Voskoboinik, M. S.; Lagosiuk, G. S.; Milen'Kii, lu. D.; Mirtov, K. C.; Osokin, D. P.; Skripka, M. L.; Ushakov, V. S., Chernenko, Zh. S.

Moscow, Izdatel'Stvo Transport, 1972.

109.

73A24915 4 pages Symmetrical Airfoils Optimized for Small Flap Deflection Wortmann, F. X.

Aero-Revue, Mar. 1973, pp. 147-150.

110.

73A23468 4 pages Estimation of Aerodynamics for Slender Bodies Alone and with Lifting Surfaces at Alpha's from 0 Deg to 90 Deg (Aerodynamic Forces and Moments Estimation for Slender Bodies of Circular and Nonclrcular Cross Section without and with Lifting Surfaces at 0-90 Degree Angles of Attack) Jorgensen, L. H.

AIAA Journal, Vol. 11, Mar. 1973, pp. 409-412.

111.

73A21611 10 pages In Russian Discrete Vortex Scheme of a Wing of Finite Span Vorob'ev, N. F.

Akademiia Nauk, SSSR, Sibirskoe Ctdelente, Izvestila, Serlia Tekhnicheskikh Nauk, Oct. 1972, pp. 59-68.

112.

73A18510 10 pages

Pressure Airships - A Review

(Airships Design, Constructional and Operational Characteristics,

Discussing Aerodynamics,Flight Control, Performanceand Trim)

Hecks, K.

Aeronautical Journal, Vol. 76, Nov. 1972, pp. 647-656.

113.

73A11657 39 pages In German Further Development and Employment of the Subsonic Panel Method (Three-Dimensional Potential Flow Past Arbitrarily Shaped Aerodynamic Configurations, Using Hess-Smith Numerical Method) Kraus, W.

Deutsche Gesellschaft Fuer Luft-Und Raumfahrt, Jahrestagung, 5th, Berlin, West Germany, Oct. 4-6, 1972.

114.

73AI0048 I page Simplification of the Wing-Body Interference Problem Graham, R. E.; McDowell, J. L.

Journal of Aircraft, Vol. 9, Oct. 1972, p. 752.

115.

72A44298 18 pages In German Computation of the Potential-Theoretical Flow Around Wing-Fuselage Combinations and a Comparison with Measurements Koerner, H.

Zeitschrift Fuer Fluqwlssenschaften, Vol. 20, Sept. 1972, pp. 351-368.

116.

72A41150 9 pages Experimental Investigations of Separated Flows on Wing-Body Combinations with Very Slender Wings at Free-Stream Mach Numbers from 0.5 to 2.2 Stahl, W.; Hartmann, K.; Schneider, W.

International Council of the Aeronautical Sciences, Congress, 8th, Amsterdam, Netherlands, Aug. 28-Sept. 2, 1972.

117.

72A41138 9 pages Potential Flow Calculations to Support Two-Dimensional Wind Tunnel Tests on High-Lift Devices Labrujere, Th. E.; Schipholt, G. J.; De Vries, O.

International Council of the Aeronautical Sciences, Congress, 8th, Amsterdam, Netherlands, Aug. 28-Sept. 2, 1972.

118.

72A34060 AIAA Paper 72-682 Analytic Prediction of Dynamic Stall Characteristics (Aerodynamic Stall Characteristic Prediction from Static Experimental Data for Airfoils, Noting Boundary Layer Effects) Ericsson, L. E.; Reding, J. P.

American Institute of Aeronautics and Astronautics, Fluid and Plasma Dynamics Conference, 5th, Boston, Mass., June 26-28, 1972.

119.

72A32250 138 pages Handbook of Airfoil Sections for Light Aircraft (Book on Airfoil Section Designs for Light Aircraft Covering Wind Tunnel Studies of Lift Drag Ratio as Function of Angle of Attacks Rice, M0 S.

Milwaukee, Vis., Aviation Publications, $3.95, 1971.

120.

72A31401 22 pages Vortex-Lattice Method for Calculating Aerodynamic Coefflclents of a Subsonic Airplane (Vortex-Lattice Method for Subsonic Aircraft Aerodynamic Coefficients Calculation, Verifying Results wlth Airbus Lifting Surface Wing Tunnel Test Data) Hua, H. M.

Astronautical Society of the Republic of China, Transactlons, Nov. I, 1971, pp. 1-22.

121.

72A29132 7 pages In Russian Invariant Methods of Determining the Lift Coefficient of Various Aerodynamic Profiles from the Flow Spectrum (Aerodynamic Profiles Lift Coefficient Determination by Empirical Formula Based on Potential Flow Lines Obtained by Conformal Mapplng) Suprun, V. M.

Samoletostroenie I Tekhnika Vozdushnogo Flota, No. 25, 1971, pp. 8-14.

122.

72A25595 SAE Paper 720337 12 pages Consideration of Application of Currently Available Transport-Category Aerodynamic Technology in the Optimization of General Aviation Propeller-Driven Twin Design.

(Transport Aircraft Aerodynamic Design Technology Application to Gen@ral Aviation Propeller Driven Twin Engine Aircraft, Discussing Wlng Loading and Aspect Ratio Optimization) Raisbeck, J. D.

Society of Automotive Engineers, National Business Aircraft Meeting, Wichita, Kan., Mar. 15-17, 1972.

123.

72A18958 AIAA Paper 72-188 16 pages Review and Evaluation of a Three-Dimensional Lifting Potentlal Flow Computational Method for Arbitrary Configurations (Subsonic Three Dimensional Potential Flow Computational Method Llftln 9 Aerodynamic Configurations Analysis and Deslgn) Rubbert, P. E.; Saaris, G. R.

American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting, 10th, San Diego, Calif., Jan. 17-19, 1972.

124.

72A17194 11 pages

In French

Researchand Tests on Laminar Airfoils

(Laminar Flow Airfoils for Gliders, Optimizing Profiles for Favorable

Velocity and Pressure Distribution)

De Lagarde, B.; De Loof, J. P.

L'Aeronautique et L'Astronautique, No. 32, 1971, pp. 29-39.

125.

72A16109 5 pages

Refinementof the Nonplanar Aspects of the SubsonicDoublet-Lattice

Lifting Surface Method

(Subsonic Doublet-Lattice Lifting Surface Method. NonplanarAspects

Refinement, Using Wing-Tail Configurations)

Rodden,W. P.; Giesing, Jo P.; Kalman,T. P.

Journal of Aircraft, Vol. 9, Jan. 1972, pp. 69-73.

126.

72A12723 66 pages Experin_ntal Studies of Aerodynamic Coefficients of a Wing-Fuselage Combination and Comparison with the Results of Linear and Nonlinear Theories at Subsonic Speeds (Wing-Fuselage Combination Aerodynamic Coefficients, Comparing Experi- mental Data with Subsonic Linear and Nonlinear Theoretical Results) Herpfer, E.; Heynatz, J. T.

Deutsche Gesellschaft Fuer Luft-Und Raumfahrt, Jahrestagung, 4th, Baden-Baden, West Germany, Oct. 11-13, 1971.

127.

7iA43312 14 pages Lifting Line Theory of a Wing in Uniform Shear Flow (Minimum Drag and Lifting Line Characteristics of Large Aspect Ratio Wing in Univorm Shear Flow with Velocity Variations Along Span) Morita, K.

JSME, Bulletin, Vol. 14, pp. 550-563.

128.

71A39543 3 pages Equations of an Aircraft's Form (Computer Aided Aircraft Design, Analysis and Production, Discussing Numerical Master Geometry Program Developed by British Aircraft Corporation) New Scientist and Science Journal, Vol. 51, pp. 410-412.

129.

71A24012 332 pages In Russian Preliminary Design of an Aircraft (Soviet Book on Aircraft Preliminary Design Specifications as Function of Performance, Aerodynamic and Structural Parameters. Discussing Tradeo#fs in Operational Requirements for Specific Configurations) Diac_enko, A. A.; Fadeev, N. N.; Goroshchenko, B. T.

_oscow, Izdatel'stvo Mashincstroenie.

130.

71A18511 AIAA Paper71-50 19 pages

Aerodynamicsof Finned Missiles at High Angle of Attack

(Finned Missiles Aerodynamicsat High Angle of Attack, Examining

BodyVortex Wake Region Interaction with Fins)

Nicolaides, J. D.; Oberkampf,W. L.

American Inst. of Aeronautics and Astronautics, AerospaceSciences

Meeting, 9th, NewYork, N. Y., Jan. 25-27, 1971.

131.

71A13737 4 pages

The Lift of a Slender Combinationof a Fuselageof Rectangular Cross-

Section with a High Wing

(Lift of Slender Aircraft with Rectangular Cross Section Fuselageand

High Wing)

Andrews,R. D.

AERONAUTICAL JOURNAL, Vol. 74, pp. 903-906.

132. 74N16700 NASA-TM-X-62325 91 pages

Equation Solving Programfor AerodynamicLifting Surface Theory

Medan,R. T.; Lemmer, O. J.

133.

74N16699 NASA-TM-X-62323 67 pages

BoundaryCondition Programfor AerodynamicLifting Surface Theory --

Using FORTRAN IV

Medan,R. T°; Ray, K. S.

134.

Not in File 13 pages

Sting Free Drag Measurements on Ellipsoidal Cylinders at Transition

ReynoldsNumbers

Judd, M°; Vlajinac, M.; Covert, E. E.

Journal of Fluid Mechanics, Vol° 48, pp. 353-365, July 1970.

135. 74N14710 11 pages

Technical Evaluation Report -- Application of Aerodynamic Drag Research to Design of Aircraft Butler, S. F. J.

In AGARD Aerodyn. DPag.

136. 72A12723 66 pages

In German Experimental Studies of Aerodynamic Coefficients of a Wing-Fuselage Combination and Comparison with the Results of Linear and Nonlinear Theories at Subsonic Speeds (Wing-Fuselage Combination Aerodynamic Coefficients, Comparing Experi- mental Data with Subsonic Linear and Nonlinear Theoretical Results) Herpfer, E.; Heynatz, J. T.

Deutsche Gesellschaft Fuer Luft-Und Raumfahrt, Jahrestagung, 4th, Baden-Baden, West Germany, Oct. 11-13, 1971.

137.

73N27209 NASA-TT-F-14962 34 pages Calculation of Potential Flow Around Profiles with Suction and Blowing (Integral Equations for Calculating Incompressible Potential Flows Aroun Around Profiles with Suction and Blowing) Jacob, K.

Washington NASA Transl. into English from Ing.-Arch., Berl_n, Vol. 32, No. I, 1963, pp. 51-65.

138.

73N27045 AFFDL-TR-72-132 592 pages Optimal Design Integrations of Military Flight Vehicles (ODIN/MFV) (Development of Digital Computing System for Synthesis and Optimization of Military Flight Vehicle Preliminary Designs) Final Report, May 1971 - Sept. 1972 Hague, D. S.; Glatt, C. R.

Aerophysics Research Corp., Bel evue, Wash.

139.

73N25043 ARC-R/M-3279 ARC-22503 46 pages On the Design of Wing-Body Combinations of Low Zero-Lift Drag Rise at Transonic Speeds (Optimum Design of Wing-Body Combinations for Zero-Lift Drag Rise at Transonic Speeds) Lord, W. T.

Ministry of Aviation, London, England In ARC Aerodyn. Res. Progr., Including Turbine, Nozzle, Flutter, and Instrumentation Studies, Vol. 2, pp. 1381-1426.

140.

73N24049 57 pages Parametric and Optimization Techniques for Airplane Design Synthesis (Parametric and Optimization Techniques for Aircraft Design Synthesis to Show Principal Lines of Data Flow for Component Development) Wallace, R. E.

In AGARD Aircraft Performance Prediction Methods and Optimization.

141.

73N24042 AGARD-LS-56 345 pages In English and Partly in French Aircraft Performance Prediction Methods and Optimization (Development) and Application of Aircraft Performance Prediction Methods for Subsonic and Supersonic Transport and Fighter Aircraft) Williams, J. A/ED.

Advisory Group for Aerospace Research and Development, Paris, France, Avail. NTIS HC $19.25.

142.

73N21916 157 pages The Design of a Vertical Takeoff and Landing Aircraft for the General Aviation Market (Design and Development of Vertical Takeoff Aircraft Configuration for Use with Air Transportation Services Between Major Population Centers) Harding, J. C.

Ph.D. Thesis, Dartmouth Coll., Hanover, N. H., Avail Univ. Microfilms Order No. 72-23515.

73N21899 NASA-CR-112231 32 pages 143.

A Parametric Study of Planform and Aeroelastic Effects on Method for Computing the Aerodynamic Influence Coefficient Matrix of Nonplanar Wing-Body-Tail Configurations (Aerodynamic Influence Coefficient Matrix for Nonplanar Wing-Body-Tail Configurations) Roskam, J.

144. 73N15997 222 pages An Optimal Configuration Design of Lifting Surface Type Structures Under Dynamic Constraints (Optimized Design of Supersonic Aircraft Wing Based on Linear Combination of Weight of Wing and Aerodynamic Drag Minimization) Miura, H.

Ph.D. Thesis, Case Western Reserve Univ., Cleveland, Ohio, Avail. Univ.

Microfilms Order No. 72-18717.

145. 73N14004 41 pages In Italian Theory of Subsonic Lifting Surface (Fixed Mode), Some Considerations and Propositions for Improving the Method of Numerical Solution (Improving Method of Numerical Calculation of Aerodynamic Coefficients for Subsonic Lifting Surface) Polito, L.

Pisa Univ., Italy, Faculty of Engineering.

146. 72N32007 12 pages Calculation of the Aerodynamic Characteristics of Lifting Systems Composed of Rectangular Wings (Calculating Aerodynamic Characteristics of Lifting Systems Composed of Rectangular Wings Arranged One Behind Another) Joint Publications Research Service, Arlington, Va.

In Its Rept. from the Higher Educational Inst., Aviation Tech., pp. 15- 26.

147. 72N29016 404 pages Preliminary Design of an Aircraft (Development of Handbook of Basic Principles of Aircraft Design Based on Technical Specifications and Calculation of Aerodynamic Characteristics) Goroschchenko, B. T.; Dyachenko, A. A.; Fadeev, N. N.

Transl. into English from "Eskiznoe Proektircvanie Samoleta", 1970, pp. 1-332, Translation of No. 129.

72N29000 326 pages Unclassified Document 148.

Aerodynamics (Application of Aerodynamic Data to Design of Passenger Aircraft with Emphasis on Laws of Gas Motion Flow and Boundary Layer Theory) Mkhitaryan, A. M.

Transl. into English from the Publ., "Aerodinamika", 1970, pp. 175-428.

]49.

72N23042 AFOSR-72-O369TR 67 pages Theoretical Studies on the Aerodynamics of Slat Airfoil Combinations (Aerodynamic Characteristics of Leading Edge Slats Plus Main Airfoil Combinations), Final Report Liebeck, R. H.

150.

72N18037 AEDC-TR-71-186 68 pages Calculation of Forces on Aircraft Stores Located in Distrubed Flow Fields for Application in Store Separation Prediciton (Aerodynamic Characteristics of Bomb in Steady, Incompressible, Potential Flow Based on Model), Final Report, I Apr. 1970, - 30 June 1971 MacDermott, W. N.; Johnson, P. W.

151.

72N11017 AFOSR-71-1079TR 53 pages On the Aerodynamic Forces of Oscillating Two-Dimensional Lifting Surfaces (Aerodynamic Lift Characteristics of Oscillating Two-Dimensional Airfoil Subjected to Sinusoidal Gust), Final Report Yates, J. E.; Houbolt, J. C.

152.

71N37597 46 pages Calculation of Potential Flow About Arbitrary Three-Dimensional Lifting Bodies (Computer Program Development for Potential Flow Calculation About Lifting Bodies), Final Report, Dec. 1969 - Oct. 1970 Hess, J. L.

153.

71N33016 AFFDL-TR-71-26-VOL-1 208 pages Stol High Lift Design Study, Volume I - State of the Art Review of (Test Data Reduction and Prediciton Techniques for High Lift Aerodynamic and Propulsion System Configurations for Short Takeoff Aircraft Design - Bibliographies) May, F.; Widdison, C. A.

154.

71N29335 22 pages Calculation Methods for Unsteady Airforces of Tandem Surfaces and T-Tails in Subsonic Flow (Numerical Analysis of Aerodynamic Loads and Coefficients for Tandem and T-Tail Surfaces Harmonically Oscillating in Subsonic Flow) Davis, D. E.

In AGARD Symp. on Unsteady Aerodynamics for Aeroelastic Analyses of Interfering Surfaces, Part I, 1971.

155.

71N21973 NASA-TN-D-6243 11 pages Charts for Predicting the Subsonic Vortex-Lift Characteristics of Arrow, Delta, and Diamond Wings (Predicting Aerodynamic Characteristics of Arrow, Delta, and Diamond Wing Platforms Using Prandtl-Glauert Transformation) Polhamus, E. C.

71N20115 80 pages

156.

Calculation of the Three-DimensionalPotential Flow Around Lifting

Non-Planar Wingsand a Wing-BodiesUslng a Surface Dlstributlon of

Quadrilateral Vortex-Rings

(Numerical Calculation of Steady Three Dlmenslonal Potential Flow

Around Lifting Nonplanar Aerodynamic Configurations Basedon Surface

Distribution of Quadrilateral Vortex-Rings)

Maskew,B.

71N13402 ONERA-NT-163 34 pages

157.

In French

Preclse Calculation of UnsteadyAerodynamicPressures in Subsonlc Flow

(Transient Pressures and Aerodynamic Coefficients of Rectangular Wings

in Subsonic Flow Using Linear Equations)

Salaun, P.

Office National D-etudes et de RecherchesAerospatiales, Parls, France.

158. 74A18897 3 pages

In German

Investigations ConcerningWing-Fuselage Interference in the Caseof

Subsonic Velocity

Koerner, H.; Ahmed,S.R.; Mueller, R.

Dfvlr-Nachrichten, Dec. 197_.

159. 74A17270 18 pages

In German

Nonlinear Airfoil Theory wlth Allowance for GroundEffects --- for

AerodynamicInterference ProblemsSolution

Hummel,D.

_J__j_i?_[j__FuerFlugwissenschaften. Vol. 21, Dec. 1973, p. 425-442.

74A17180 DGLR Paper 33 pages

160.

In German

The Effect of Wing Planform Modifications on the AerodynamicPerformances

of Fighter Aircraft

Staudacher, W.

Oesterreichlsch_ Gesellschaft Fuer WeltraumforschungUndFlugkoerpertechnlk

and DeutscheGesellschaft Fuer Luft-Und Raumfahrt, Gemeinsame Jahrestagung, 6th, Innsbruck, Austria, Sept. 24-28, 1973.

74A11606 SAEPaper 730876 9 pages

161.

NowAirfoil Sections for General Aviation Aircraft --- Cruising and Flap

Development Tests

Wentz, W. H., Jr.

Society of Automotive Engineers, National AerospaceEngineering and

Manufacturing Meeting, Los Angeles, Calif., Oct. 16-18, 1973.

162.

73A43028 11 pages In German The Panel Method for the Calculation of the Pressure Distribution on Missiles in the Subsonic Range Kraus, W.; Sacher, P.

Zeitschrlft Fuer Flu_wissenschaften, Vol. 21, Sept. 1973, p.301-311.

163. 73A41192 13 pages The Aerodynamic Development of the Wing of the A 300B Mcrae, D.M.

Aeronautical Journal, Vol. 77, July 1973, p. 367-379.

164. 73A38007 4 pages Prediction of the Lift and Moment on a Slender Cylinder-Segment Wing-Body Combination Crowell, K.R.; Crowe, C.T.

Aeronautical Journal, Vol. 77, June 1973, p. 295-298.

165. 73A34676 SAE Paper 730318 25 pages Applications of Advanced Aerodynamic Technology to Light Aircraft Crane, H.L.; McGhee, R.J.; Kohlman, D.L.

Society of Automotive Engineers, Business Aircraft Meeting Wichita, Kan., Apr. 3-6, 1973.

166.

73A32819 49 pages In French Calculation of the Characteristics of Tail Fins in the Vortical Field of a Wing Yermia, M.

Association Aeronautique et Astronautlque de France, Colloque D'Aero- dynamique Appliquee, 9th, Saint-Cyr-L'Ecole, Yvellnes and Paris, France, Nov. 8-10, 1972.

167.

73A25490 AIAA Paper 73-353 I0 pages Application of Computer-Aided Aircraft Design in a Muitidisclplinary Envlronment Fulton, R.E.; Sobieszczanski, J.; Storaasll, 0.; Landrum, E.J.; Loendorf, D.

AIAA, ASME, and SAE, Structures, Structural Dynamics, and Materials Conference, 14th, Williamsburg, Va., Mar. 20-22, 1973.

168.

73A23856 32 pages Transonic Airfoils - Recent Developments In Theory, Experlment, and Design Nieuwland, G.Y.; Spee, B.M.

In Annual Review of Fluld Mechanics. Volume 5. (A73-23851 10-12) Palo Alto, Calif., Annual Reviews, Inc., 1973, p. 119-150.

169. 73A1419 2 pages

Lift of Wing-Body Combination Yang, H. T.

AIAA Journal, Vol. 10, Nov. 1972, p. 1535, 1536.

74N21645 AD-775538 MDC-J5831 277 pages 170.

Analytical Studies of Two-Element Alrfoil Systems James, R.M.

Interim Report, Feb. 1971 - Dec. 1973.

74N21635 NASA-TN-D-7579 15 pages 171.

On the Use of Thlck-Airfoil Theory to Design Airfoll Famllles In Whlch Thickness and Lift are Varied Independently Barger, R.L.

74N20694 AD-774430 91 pages 172.

Addition of an Arbitrary Body Analysls Capablllty to the Boeing TEA 236 Finite Element Computer Program Westphal, J. L.

M.S. Thesis Air Force Inst. of Tech., Wright-Patterson AFB, Ohlo. (School of Engineering) 173. 74N18654 AGARD-R-614 20 pages Interferlng Lifting Surfaces In Unsteady Subsonic Flow Comparison Between Theory and Experiment Becker, J.

Presented at 37th AGARD Structures and Mater. Panel Meeting, The Hague, 7-12 Apr. 1973.

174. 74N17707 41 pages In German; English Summary Reciprocal Influence of a Body of Finlte Length and a Wlng at Mld-Wlng Position at Subsonlc Speed Gregoriou, G.

Avail. Ntis HC $5.25; Bundeswehramt, Bonn 30 DM 175. 74N13674 24 pages Reynolds Number Effects at Low Speeds on the Maximum Lift of Two-Dimensional Aerofoil Sections Equipped wlth Mechanical High Llft Devices Thaln, J.A.

In Natl. Res. Council of Can. Quart. Bull. of the Div. of Mech. Eng.

and the Natl. Aeron. Estab. p. 1-24 (see N74-13673 04-34)

Next: Section Designed for General Aviation Applications →

Section Designed for General Aviation Applications

176.

74N11821 NASA-TN-D-7428 71 pages Low Speed Aerodynamic Characteristics of a 17 Percent Thick Airfoil Section Designed for General Aviation Applications McGhee, R.J.; Beasley, W.D.

177.

74N11815 NASA-TT-F-15183 25 pages Calculation of Flows Around Zero Thickness Wings with Evolutive Vortex Sheets Rehbach, C.

Transl. into English from Rech. Aerosp. (France), No. 2, Mar. - Apr. 1972, p. 53-61.

178.

74NI0019 NASA-CR-2344 97 pages The Effects of Leading-Edge Serrations on Reducing Flow Unsteadiness About Airfoils, an Experimental and Analytical Investigation Final Report Schwind, R.G._ Allen, H.J.

179.

73N26000 NASA-TT-F-14959 42 pages Airfoil Profiles in a Critical Reynolds Number Region (Force Measurements and Pressure Distributions on Three Gottinger Airfoil Profiles Druing Transition From Laminar To Turbulent Boundary Layer Flow) Kraemer, K.

Transl. into English from Soderdruck Aus der Z. Forsch. Auf Dem Gebiete des Ingenieurwesens' ' (West Germany), V. 27, No. 2, 1961, p. 33-46.

180.

73N25002 ARC-R/M-3180 19 pages Observations of the Flow Over a Two Dimensional 4 Percent Thick Aerofoil At Transonic Speeds (Wind Tunnel Tests to Determine Pressure Distributions for Four Percent Thick, Circular ARC, Biconvex Airfoll at Transonic Speeds) Henshall, R.D.; Cash, R. F.

In ARC Aerodyn. Res., Including Heating, Airfoils, and Boundary Layer Studies, Vol. I, p. 63-81 (see N73-24999 16-01).

181.

73N24040 AD-757813 81 pages An Exact Method of Designing Airfolls with Given Velocity Distribution in Incompressible Flow An Extension of the Lighthill and Arlinger Methods (Application of Conformal Mapping Procedures for Designing Airfoil Shapes with High Design Lift Coefficients) Final Report Strand, T.

15 Jun. - 15 Dec. 1972.

73N24000 ARC-R/M-3238 40 pages 182.

The Pressure Distribution on Two-Dlmensional Wlngs Near the Ground (Numerical Analysls of Pressure Distrlbution In Incompresslble Flow on Two-Dimensional Airfoils Near Ground) Bagley, J.A.

In ARC Res. Progr. on Aerodyn. Heating, Airfoils, Wings, and Alrcraft During 1960, Vol. I, p. 79-118 (see N73-23995 15-01).

73N22977 NASA-CR-112297 233 pages 183.

An Analytical Study for the Design of Advanced Rotor Alrfolls (Design and Evaluation of Two Airfoils for Helicopter Rotors for Reduction of Rotor Power Requirements) Kemp, L.D.

73N21914 AD-755480 MDC-J5679-01 166 pages 184.

Calculation of Potential Flow About Arbitrary Three-Dimensional Lifting Bodies (Development of Method for Calculating Potential Flow about Arbitrary Lifting Three-Dimensional Bodies with Emphasis on Bound Vorticlty and Application of Kutta Condition) Final Technical Report Hess, J.L.

73N21907 NASA-TN-D-7183 41 pages 185.

Low-Speed Wind Tunnel Investigation of A Semispan Stol Jet Transport Wing Body with an Upper Surface Blown Jet Flap (Wind Tunnel Tests to Determine Static Longitudinal Aerodynamic Characteristics of Jet Transport Wing-Body with Upper Surface Blown Jet Flap for Lift Augmentation) Phelps, A.E., Ill; Letko, W.; Henderson, R.L.

186. 73N21054 7 pages Wake Characteristics of a Two-Dimensional Symmetric Aerofoil (Generation of Aerodynamic Noise by Turbulent Wake Behind Rotary Wing Airfoil and Relationship to Drag and Lift Coefficients) Kavrak, I.

In AGARD Aerodyn. Rotary Wings (see N73-21031 12-02) 187. 73N20995 198 pages An Analysis of the Design of Airfoil Sections for Low Reynolds Numbers (Design of Airfoil Sections for Low Reynolds Numbers Based on Requirement to Achieve Transition Upstream of Major Adverse Pressure Gradient) Miley, S.J.

Ph.D. Thesis Mississippi State Univ., State College. Avail Univ. Microfilms Order No. 72-20272.

188.

73N16283 AD-751075 MDC-J5713 63 pages A New Family of Airfoils Based on the Jet-Flap Principle (Air Foils Based On Utilization of Jet-Flap Principle) Bauer, A.B.

Technical Report, Apr. 1971-Apr. 1972.

189.

73N15992 AD-751045 116 pages Circulation Control By Steady and Pulsed Blowing for a Cambered Elliptical Airfoil (Short Takeoff Aircraft Llft Augmentation and Prevention of Airflow Separation on Cambered Ellipitical Airfoil Section Using Circulation Control) Walters, R.E.; Myer, D.P.; Holt, D.J.

190.

73N15050 DLR-FB-72-63 42 pages In German; English Summary Theoretical Parameter Studies of Wing-Fuselage Combinations (Prediction Analysis Method to Determine Influence of Geometry Parameters on Aerodynamic Characteristics of Body-Wing Configuration) Koerner, H.

Deutsche Forschungs- und Versuchsanstalt Fuer Luft- und Raumfahrt, Brunswick (West Germany). (Abteilung Fuer Theoretische Aerodynamik.)

Avail. Ntis HC $4.25; Dfvlr. Porz, West Ger. 11DM.

191.

73N15010 16 pages The Effect of Leading Edge Geometry on High Speed Stalling (Aerodynamic Configurations of Swept Wings to Improve Lift Performance at Stall in Higher Range of Subsonic Speeds) Moss, G.F.; Haines, A.B.; Jordon, R.

In AGARD Fluid Dyn. of Aircraft Stalling (see N73-14998 06-02).

192.

73N15009 12 pages A Simplified Mathematical Model for the Analysis of Multielement Airfoils Near Stall (Development of Procedure for Determining Characteristics of High Lift Systems Where Viscous Effects Dominate) Bhateley, I.C.; Bradley, R.G.

in AGARD Fluid Dyn. of Aircraft Stalling (see N73-|4998 06-02_.

193.

73N15008 12 pages The Low Speed Stalling of Wings With High Lift Devices (Analysis of Aerodynamic Stall Characteristics of Wing Sections With High Lift Devices in Two-Dimenslonal Flow) Foster, D.N.

In AGARD Fluid Dyn. of Aircraft Stalling (see N73-14998 06-02).

73N15007 27 pages

194.

Aerodynamicsin High Lift Airfoil Systems

(Analysis of AerodynamicProcessesOccurring in Flow Past Unpowered

Multi-Element Airfoils in High Lift Attitude)

Smith, A.M.O.

in AGARD Fluid Dyn. of Aircraft Stalling (see N73-1499806-02).

73N14998 AGARD-CP-I02 342 pages

195.

Partly in English and Partly in French

Fluid Dynamicsof Aircraft Stalling

(Proceedings of Conferenceon Fluid Dynamicsof Aircraft Stalling to

Include Stall and Post-Stall AerodynamicCharacteristics of Various

Military Aircraft)

Advisory Group for AerospaceResearchand Development,Paris (France)

Avail. Ntis HC$19.25

Presented at Fluid Dyn. Panel Specialists Meeting, Lisbon, 25-28 Apr. 1972.

73N14051 AD-749726 FTD-HT-23-181-72 36 pages

196.

Application of the Wing ImpulseTheory to the Determination of Propeller

Slip Stream Influence on Wing Aerodynamic Characteristics

(Wing ImpulseTheory Applied to Determination of Propeller Slipstream

Influence on WingAerodynamicCharacteristics, Using Airfoil of Finlte

Span)

Kopylov, G.N.

Transl. into English from Tr. VyssheeAvlationnoe Uchilishche

Grazhdanskii Aviatsil (USSR),No. 24, 1965, p. 24-43.

73N14043 AD-749485 AFFDL-TR-72-96-PT-2 86 pages

197.

Development of Theoretical Methodfor Two-DimensionalMulti-Element

Airfoil Analysls and Design. Part 2 Leading-EdgeSlat Design Method

(ComputerProgramfor Designing Leading EdgeSlats for Producing

Specified Pressure Distribution on Maln Airfoil)

McGregor,O.W.; McWhirter, J.W.

Final Report, 24 May 1971- 12 Jun. 1972.

73NI0242 AD-740124 MCD-J5264-VOL-2 310 pages

198.

Investigation of AerodynamicAnalysis Problems in Transonic Maneuvering.

Volume2 Airfoil Analysis ComputerProgram

(Development of ComputerProgramfor Analyzing Mono-Element and Multi-

ElementAirfoils at Subsonic Speedwith Attached Air Flow - Vol. 2)

Gentry, A,E.

Final Report, Jun. 1970- Aug. 1971.

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Document details

Doc number
19750016605
Publisher
NASA
Year
1975
Pages
500
File size
18 MB
Chapters
14
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