Natural laminar flow and airplane stability and control

trailing-edge separation of the turbu- shallow pressure recovery, however, lent boundary layer can occur. This section lift characteristics are not boundary-layer separation results in a influenced by the loss of NLF, as shown loss of section lift, and the resulting in figure 9.

effects on airplane longitudinal and lateral-directional stability and R, million Transition control characteristics are discussed -- [ Free in the following section. In addition, ----- 3 Free ----- 3 Artificial at x/c - 0.075 the influence of winglet airfoil sec- 2.0 v Lower surface separationbubble tion characteristics on airplane lateral-directional stability and con- 1.5 trol characteristics is also discussed.

/

1.0 LONGITUDINAL STABILITY AND CONTROL c rn(C[ ) Generally, longitudinal static Crn-20.[O f 7 stability is required for airplane I i I i I I I I I I .025 -10 0 airworthiness certification. However, lO 20 .005 .010 .015 .020 a, deg cd too much static stability can have a negative influence on the control- lability of an airplane. Dynamic Figure 9.- Calculated aerodynamic stability is associated with the characteristics of supercritical response behavior of an airplane as a winglet airfoil.

result of a disturbance, and therefore, The three airfoil sections discus- the damping and frequency of the response motion are examined.

sed in this paper should not be viewed Generally, airplanes must also have as "inferior" or "dangerous" air- some form of dynamic stability, i.e., foils. These airfoils have been the amplitudes of the motion should developed with certain design objec- diminish progressively as a function of tives and constraints in mind and are time. Motion damping has a strong very successful at meeting these design effect on airplane handling objectives. Airplane designers, how- qualities. If it is too low, then the ever, sometimes select these airfoils airplane is too easily excited by to produce lift in operating conditions disturbances, and if it is too high, which violate the original airfoil then the airplane has a tendency to design conditions.

become too sluggish.

TRANSITION AND AIRPLANE Wind-tunnel experiments have been STABILITY AND CONTROL conducted with the Rutan VariEze. This airplane has a high-aspect-ratio fore- In the previous section, the influ- ence of location and mode of transition plane which uses the GU 25-5(11)8 air- foil section. In references 2 and 15, from laminar to turbulent boundary- wind-tunnel data are presented layer flow on airfoil aerodynamic char- depicting the effect of fixed transi- acteristics has been discussed. It has tion on foreplane lift characteristics been shown that for certain airfoils, and airplane longitudinal aerodynamic if the boundary layer becomes turbulent characteristics. In the previous near the leading edge, extensive

S C C

section, it was shown that transition

= CL (_cg - Yac,C ) "_-- m (% (%,C

location has a dramatic influence on

+ CL (Xcg - Xac,WB ) (2)

the lift characteristics of the GU25-

(%,WB

5(11)8 airfoil section. Notably, a

loss in section lift-curve slope due to

fixed boundary-layer transition was

where Xac,WB > Xcg > _ac,c' and Xcg and

shown (fig. 4). In subsonic flow cond-

are defined as the longitudinal

itions, the lift-curve slope of the

ac location of center of gravity and aero-

foreplane, C L , is a function of the

(%,C

dynamic center, respectively, in terms of airplane mean aerodynamic chord c.

sectional lift-curve slope, c£ , Mach

(%

number, and several planform

A reduction in CL due to flow separ- (%,C

parameters. Therefore, a reduction in

ation on the foreplane makes the first

c£ will reduce the gradient of the

term on the right-hand side of equation fore'plane lift curve CL .

(2) less positive, and consequently,

(%,C

C becomes more negative. Equation m

In figure 10, airplane pitching-

(2)(%can also be written in the

momentcoefficient, C m, results clearly

following form:

demonstrate the large influence of

fixed transition on the longitudinal

static stability of the airplane.

Cm : CL ( cg - ac) (3>

(% oL @ 4 i .... i!i¸.....

I::'_:: :._: :::.: ::::_ Canard transition where C L is defined as airplane lift- -.6 { i:: ii'_'"';'!'!'!;_!!4_;;i: oFree curve sl_pe, and _ac indicates the o Fixed, ix/c) t = 5% 1.8 longitudinal location of the airplane aerodynamic center in terms of the airplane mean aerodynamic chord. The

i i

wind-tunnel results of figure 10 are for a fixed foreplane control surface deflection (6 -- 0o), and therefore, CD.zl :::::::: :::::::::::::: ::;/J/::::: e - X can be defined as stick- cg ac fixed static margin of the airplane.

-8 0 8 16 24 32 44,4 0 -.6 The effect of fixed foreplane transi- O,deg C m tion on airplane lift-curve slope is relatively small, as shown in figure Figure I0.- Longitudinal aerodynamic 10. In the angle-of-attack range from characteristics of VariEze model as 3 ° to 13 °, the wind-tunnel data show tested in Langley 30- by 60-Foot that airplane static margin (stick Tunnel (ref. 2).

fixed) is approximately 0.10 c in the case of free transition. When For a canard configuration, airplane transition is fixed near the leading longitudinal static stability can be edge of the foreplane, however, the written as follows: airplane becomes much more stable and the static margin is approximately 0.30 c. Thus, airplane aerodynamic center shifts rearward over a distance of 0.20 and Long-EZ airplane both use the GU as a result of foreplane trailing- 25-5(11)8 airfoil for the foreplane.

edge flow separation.

Both airplanes have been tested in flight with and without artificial surface roughness near the leading edge Transition of the foreplane in order to measure =5% the changes in airplane longitudinal aerodynamic characteristics caused by loss of NLF. The changes in foreplane lift characteristics with fixed _e deg transition come into view when examining elevator deflection required I '/max to trim the airplane for a given airspeed, as shown in figure 11. For 1 I t 1 I both airplanes, fixed leading-edge 0 6O 80 I00 120 140 transition induces flow separation on Vi, knots the foreplane, and consequently, increased positive elevator deflection is required to obtain a foreplane lift (a) VariEze airplane.

coefficient which provides longitudinal trim.

2O 18 !

In the case of a canard configura- V . J_ Transition rnm _ © Free tion, the influence of wing lift char- tO ot acteristics on the longitudinal static stability is opposite as compared to 5e. cleg 12 the influence of foreplane lift charac- I0 teristics. Therefore, selection of a wing airfoil section shape with lift characteristics which are affected by transition location will result in reduced longitudinal static stability of the airplane. The longitudinal 0 60 18D 80 lO0 120 140 160 stability and control of both the Rutan Vi, knols VariEze and Long-EZ airplanes appear to be almost unaffected by wing boundary- (b) Long-EZ airplane.

layer transition location.

Figure 11.- Comparison of fixed versus free transition performance and longi- For the VariEze and Long-EZ air- tudinal control characteristics as planes, the effect of fixed transition measured in flight (ref. 2).

on airplane lift-curve slope is shown in figure 12. For both airplanes, the The wind-tunnel-measured changes in gradient of the lift-curve slope airplane longitudinal aerodynamic char- becomes less steep by 7 to 13 percent acteristics due to fixed transition (ref. 2). The wind-tunnel results, have also been observed in flight. The however-, only indicate a reduction in original versions of the Rutan VariEze lift-curve slope of less than 4 percent. The reason for this 1.2 - Transition positive elevator deflection is required for airplane trim, as shown in © Free 0 1.0 - figure 11. Apparently, trailing-edge • --. [] flow separation increases with .8 increasing elevator deflection, and CL consequently the lift loss is augmented .6 " at higher airplane lift coefficients.

A second contributing factor is the .4 -- influence of Reynolds number. Flight data at high lift coefficients are .2 -- obtained at relatively low Reynolds numbers as compared to the Reynolds I 1 ] I 1 [ I numbers encountered at low lift 0 14 2 4 6 8 10 12 coefficients. The following expression a, deg depicts this effect more clearly: (a) VariEze airplane.

R1 CL 2 1.6 lransition (4) © 1.4 [] Fixed, (x/c)t= 5% 1.2 where it has been assumed that airplane r_ Free /__ weight and flight altitude are constant 1.0 and R defines chord Reynolds CL number. The reduced Reynolds numbers .8 at higher lift coefficients enhance the .6 foreplane separation problem.

.4 °d_ o The previous results demonstrate the influence of premature boundary- .2 I I l ] I I I I I layer separation on airplane longitudi- 0 2 4 6 8 10 12 14 16 18 nal trim requirements and stick-fixed a, deg neutral point location (center-of- (b) Long-EZ airplane.

gravity location at which C = 0).

m Stick-fixed maneuvering margin is Figure 12.- Effect of fixed versus larger than stick-fixed static margin, free transition on airplane lift- and the difference between neutral curve slope as measured in point and maneuver point is propor- flight (ref. 2).

tional to the pitch-damping stability discrepancy is that the wind-tunnel derivative, Cmq. Therefore, if pitch data of figure 10 have been obtained damping is zero, then the difference for a constant elevator deflection _ = between neutral point and maneuver 0 °, while the flight data of figure _2 point is zero. In the case of canard have been obtained for elevator and conventional configurations, deflections required to trim the reduced gradients of the lift curve due airplane. In flight, lower airspeed to flow separation of airplane wing results in higher airplane lift and/or tail will reduce airplane pitch coefficient, and therefore, more damping and, consequently, reduce the effects are assumed _o oe neg±_lu_, reducing lift-induced drag. Ine ue_n

behavior of an airplane. According to

difference between stick-fixed static

reference 16, the undamped natural

margin and stick-fixed maneuvering

frequency of the short period, margin.

mnsp is approximately proportional

Generally, longitudinal transient

_ ./-r IT whnt"_. T defines the airplanes have used the airfoil section attack and therefore decreased shown in figure 8. As mentioned pre- c_ (point C) for the downwind viously, this airfoil was developed for winglet. For the airfoil of figure 8, winglet application at supercritical, section drag at the onset of the drag high Mach number conditions. Further.

5. Althaus, D.: Influencing Tran- ination and leading-edge separation of sition on Airfoils. Technical Soaring, the laminar boundary layer due to the December 1981, pp. 82-93.

suction peak have a detrimental effect on airplane stability and control- 6. Horstmann, K. H.; and Quast, lability. Therefore, for horizontal A.: Drag Reduction by Means of Pneuma- lifting surfaces such as fore-and tail- tic Turbulators. European Space Agency planes and wings it is essential to Technical Translation 743, September design airfoil section shapes which are 1982.

not susceptible to boundary-layer sepa- ration if no laminar flow exists from the leading edge. For vertical lifting 7. Eppler, R.; and Somers, D.

M.: A Computer Program for the Design surfaces such as winglets which provide and Analysis of Low-Speed Airfoils.

directional stability, an additional NASA TM-80210, 1980.

design requirement is that transition location on the upper and lower surface 8. Eppler, R.; and Somers, D.

should move slowly and steadily with M.: Supplement to a Computer Program changing angle of attack. The examples for the Design and Analysis of Low- given illustrate the importance of Speed Airfoils. NASA TM-81862, proper care in the selection of NLF December 1980.

airfoil characteristics to preclude difficulties with airplane stability 9. Nonweiler, T.: A New Series of and control changes due to the loss of laminar flow. Low-Drag Aerofoils. University of Glasgow, Department of Aeronautics and Fluid Mechanics, Report No. 6801, 1968.

REFERENCES 10. Kelling, F. H.: Experimental Investigation of a High-Lift Low-Drag I. Holmes, B. J.; 0bara, C. J.; Aerofoil. Aeronautical Research Gregorek, G. M.; Hoffman, M. J.; and Council Current Papers 1187, 1971.

Freuhler, R. J.: Flight Investigation of Natural Laminar Flow on the Bellanca 11. Kelling, F. H.: Experimental Skyrocket. SAE paper 830717, April 1 983. Investigation of a High-Lift Low-Drag Aerofoil. University of Glasgow, 2. Holmes, B. J.; Obara, C. J.; Department of Aeronautics and Fluid Mechanics, Report No. 6802, September and Yip, L. P.: Natural Laminar Flow 1968.

Experiments on Modern Airplane Sur- 1.2 -- positive elevator deflection is Transition required for airplane trim, as shown in O Free O 1,0- figure 11. Apparently, trailing-edge flow separation increases with .8 - increasing elevator deflection, and C L consequently the lift loss is augmented .6 - at higher airplane lift coefficients.

A second contributing factor is the .4 - influence of Reynolds number. Flight data at high lift coefficients are °2 - obtained at relatively low Reynolds numbers as compared to the Reynolds I I I I 1 J numbers encountered at low lift

2 4 6 8 10 12 14 coefficients. The following expression

o, deg depicts this effect more clearly: (a) VariEze airplane.

R 1 CL 2 1.6 -- (4) Transition o 1.4- [] Fixed, (x/c)t = 5 % o 1.2 where it has been assumed that airplane r_ Free weight and flight altitude are constant 1.0 and R defines chord Reynolds EL number. The reduced Reynolds numbers .8 f/ o at higher lift coefficients enhance the .6 foreplane separation problem.

.4

°d_o The previous results demonstrate

the influence of premature boundary- .2 t, I I I I I I 1 1 .J layer separation on airplane longitudi- 2 4 6 8 10 12 14 16 18 nal trim requirements and stick-fixed o, deg neutral point location (center-of- (b) Long-EZ airplane.

gravity location at which C = 0).

m Stick-fixed maneuvering margin is Figure 12.- Effect of fixed versus larger than stick-fixed static margin, free transition on airplane lift- and the difference between neutral curve slope as measured in point and maneuver point is propor- flight (ref. 2).

tional to the pitch-damping stability discrepancy is that the wind-tunnel derivative, Cmq. Therefore, if pitch data of figure 10 have been obtained damping is zero, then the difference for a constant elevator deflection 6 = between neutral point and maneuver 0 °, while the flight data of figure _2 point is zero. In the case of canard have been obtained for elevator and conventional configurations, deflections required to trim the reduced gradients of the lift curve due airplane. In flight, lower airspeed to flow separation of airplane wing results in higher airplane lift and/or tail will reduce airplane pitch coefficient, and therefore, more damping and, consequently, reduce the difference between stick-fixed static behavior of an airplane. According to margin and stick-fixed maneuvering reference 16, the undamped natural margin.

frequency of the short period _ , ' nsp is approximately proportional Generally, longitudinal transient airplane response consists of two to /-C m /Iyy where Iyy defines the c_ oscillatory terms. The first oscil- moment of inertia about the airplane Y- latory term is called the short-period axis. Therefore, the influence mode which is highly damped and has a of C on the undamped natural high frequency. The second term m describes a very slowly damped, low frequency can be estimated as follows: frequency oscillation which is called C the phugoid mode. In the case of the nSp, I m , I VariEze, a large change in the vari- : (5) C ation of pitching-moment coefficient nsP,2 m_,2 with angle of attack, C m , is produced Thus, an increase of a factor 3 in the due to premature foreplane separa- value of C , as observed in figure m tion. This stability derivative has a 10, causes the undamped natural very strong influence on the OJ 7- longitudinal transient nsp g 0J 6- nsp 8 Basic 5- c_n, rad/sec 7 airplane rad/sec n' C Basic airplane .50 .25 .5 _ ; SP _P °Jnp -I 11 I, I I -i -2 -3 -4 0 I 2 -3 -4 -5 -I C rad C rad-I m 117' (b) Airplane D at 40,000 ft and (a) Airplane B at 5,000 ft and M = 0.7.

M : 0.31.

Figure 13.- Effect of airplane pitching-moment coefficient curve slope on the dynamic stability characteristics.

24O frequency of the short period to increase by more than 70 percent.

C D _p (6) A complete set of stability 2 CLOT derivatives was not available for a canard-type airplane. Therefore, a According to equation (6), an increase sensitivity analysis was conducted to in drag due to transition near the illustrate the potential influences of leading edge appears to enhance phugoid CD, 0 on stability behavior. The damping.

results appear in figure 13. The stability derivatives used are 6.2 presented in reference 16. Airplane B - Basic airplane (fig. 13(a)) is representative of nsp 6.0 Beechcraft B99 type airplanes, while Airplane D (fig. 13(b)) is representa- .8 tive of Gates Learjet Model 24 type airplanes. The results of figure 13 w n, rad/sec _SP indicate that undamped natural < .6 frequency of the short period is strongly influenced by C . Also, .4 m short-period damping decreases due to .2 enhanced longitudinal static stability.

As previously mentioned, in general .02 .04 .06 .08 .i0 the phugoid mode has a low frequency CD and is lightly damped. The results in figure 13 verify this statement, and Figure 14.- Effect of airplane drag the sensitivity analysis shows that coefficient on the dynamic longitudi- phugoid damping is reduced due to nal stability characteristics of increased longitudinal static airplane B at 5,000 ft and M = 0.31.

stability. This observation matches unpublished flight results obtained Lateral-Directional Stability with the Rutan Long-EZ by Brown, and Control Holmes, and van Dam. When evaluating airplane handling qualities with fixed Wind-tunnel and flight tests have foreplane transition, a noticeable demonstrated that the use of winglets reduction in phugoid damping was can provide increased aerodynamic effi- observed as compared to the phugoid ciency by reducing lift-induced drag damping with free transition on the without overly penalizing wing structu- foreplane. This effect appears to be ral weight (ref. 14). A more recent more dominant than the influence of development in the area of airplane airplane drag coefficient on phugoid design is the utilization of wing-tip- damping. The latter is sketched in mounted winglets to provide directional figure 14. If airplane propulsion stability and control in addition to effects are assumed to be negligible, reducing lift-induced drag. The design then phugoid-damping ratio can be of winglet airfoil sections, however, approximated as follows (ref. 16): has not received much attention and some winglet designs for low-speed attack and therefore decreased airplanes have used the airfoil section shown in figure 8. As mentioned pre- c£ (point C) for the downwind winglet. For the airfoil of figure 8, viously, this airfoil was developed for winglet application at supercritical, section drag at the onset of the drag bucket changes rapidly and abruptly. A high Mach number conditions. Further, this airfoil was designed with the significant profile drag differential between the two winglets is produced assumption that the flow over the entire airfoil would be turbulent, due to the rapid chordwise movement of primarily as a result of roughness of boundary-layer transition on the lower surface of the airfoil. This force construction. However, the pressure differential produces a destabilizing gradients around c£ = 0.6 are favorable to NLF as is also indicated by the yawing moment and can produce undesir- section drag characteristics in figure able airplane handling qualities. The 9. The narrow drag bucket is a concern yawing moment produced by the profile when the winglets also provide direc- drag differential is (g > O) tional stability.

b The sketch in figure 15 shows the N = - AC D q SWL T _ (7) drag polar of the winglet airfoil section and illustrates the potential problem.

where SWL T is the area of one winglet and AC D is the profile drag differen- tial between the two winglets. As a result, the change in yawing-moment coefficient is (g > O) AC D SWL T AC = /- (8) n 4 S Lift coefficient, c[ For conventional airplane configura- tions, the ratio SWLT/(S/2) has a value _13 0,_ of 0.02 to 0.10, and as a result, the effect of this destabilizing yawing :/ o_ moment will be small. Some canard configurations, however, use wing-tip- mounted winglets to provide directional Drag coefficient, cd stability and control, and because of Figure 15.- Drag polar of a winglet the relatively short moment arm, the airfoil with a sharply defined drag winglet area must be large to provide bucket.

sufficient directional stability. In that case, SWLT/(S/2) can be larger Point A in figure 15 indicates the than 0.20. An area ratio of that value cruise condition at a sideslip combined with a AC D of about 50 drag angle, B, of 0 °. A small positive counts can generate a destabilizing excursion in sideslip angle causes an yawing moment (6 > 0) AC _-0.00025.

n increase in angle of attack and as a This is a relatively small value.

result enhanced c. (point B) for the However, it may be produced as a result upwind winglet an_ reduced angle of of a sideslip excursion as small as reduction in C and a 20-percent 0.5 o Therefore, for small sideslip nS,WLT angles, the contribution to the air- reduction in airplane Cn8 The lift plane direction stability derivative characteristics of the VariEze wing- may be of the order of _C _ - 0.03 n 8 lets, however, are not sensitive to the rad -I. This value is large enough to transition location from laminar to produce significant nonlinearities in turbulent boundary layer. Additional the rudder force and rudder deflection information on the design considera- variation with sideslip angle.

tions for vertical wing-tip-mounted lifting surfaces on low-speed airplanes In order to prevent changes in is provided in reference 17.

airplane directional stability, it is important that the lift characteristics CONCLUSIONS of the surfaces which provide direc- tional stability are not affected by The analytical and experimental premature boundary-layer transition results presented in this paper demon- near the leading edge. A reduction in strate that the location and mode of transition from laminar to turbulent the lift-curve slope of such a lifting surface due to leading-edge roughness boundary-layer flow can have a signifi- will reduce the value of the direc- cant influence on the lift and drag characteristics of airfoil sections.

tional stability derivative C signi- n 8 For airfoils with a relatively steep ficantly. This derivative has an pressure recovery, it has been shown important influence on the lateral- that boundary-layer transition near the directional transient response charac- leading edge due to surface contamina- teristics of the airplane. Generally, tion can result in trailing-edge sepa- all three modes of motion (spiral, ration of the turbulent boundary roll, and Dutch roll) are affected by a layer. This premature separation pro- reduction in C n The effects of wing- duces a reduction in section lift-curve slope and it can also affect sectional lets on the lateral-directional stabi- maximum lift coefficient. If the lead- lity characteristics of the Rutan ing edge of the airfoil is relatively VariEze are clearly depicted in the sharp, separation of the laminar boun- wind-tunnel results of reference 15 and dary layer can occur after the leading- these results will be used to provide edge suction peak is formed. Leading- an example. For the angle-of-attack edge stall arises when the boundary range from 0 ° to 8 °, the destabilizing layer after transition does not reat- contribution of the airplane without tach to the surface.

winglets is C _ -0.057 rad -I In n B The two-dimensional results have this angle-of-attack range, the winglets been used to examine the effects of -I produce a C _ 0.115 rad boundary-layer transition behavior on nS,WLT airplane longitudinal and lateral- resulting in an airplane C _ 0.058 directional stability and control. The n 8 analyses indicate that both trailing- rad -I. A 10-percent reduction in wing- edge separation of the turbulent boun- let llft-curve slope due to premature dary layer due to leading-edge contam- flow separation results in a 10-percent

5. Althaus, D.: Influencing Tran-

ination and leading-edge separation of

sition on Airfoils. Technical Soaring,

the laminar boundary layer due to the

December1981, pp. 82-93.

suction peak have a detrimental effect

on airplane stability and control-

6. Horstmann, K. H.; and Quast,

lability. Therefore, for horizontal

A.: Drag Reduction by Meansof Pneuma-

lifting surfaces such as fore-and tail-

tic Turbulators. European SpaceAgency

planes and wings it is essential to

Technical Translation 743, September

design airfoil section shapes which are

1982.

not susceptible to boundary-layer sepa-

ration if no laminar flow exists from

7. Eppler, R.; and Somers, D.

the leading edge. For vertical lifting

M.: A Computer Program for the Design

surfaces such as winglets which provide

and Analysis of Low-SpeedAirfoils.

directional stability, an additional

NASA TM-80210, 1980.

design requirement is that transition

location on the upper and lower surface

8. Eppler, R.; and Somers, D.

should move slowly and steadily with

M.: Supplementto a Computer Program

changing angle of attack. The examples

for the Design and Analysis of Low-

given illustrate the importance of

SpeedAirfoils. NASA TM-81862,

proper care in the selection of NLF

December1980.

airfoil characteristics to preclude

difficulties with airplane stability

9. Nonweiler, T.: A NewSeries of

and control changes due to the loss of

Low-DragAerofoils. University of

laminar flow.

Glasgow, Department of Aeronautics and

Fluid Mechanics, Report No. 6801, 1968.

REFERENCES

10. Kelling, F. H.: Experimental

Investigation of a High-Lift Low-Drag

I. Holmes, B. J.; Obara, C. J.;

Aerofoil. Aeronautical Research

Gregorek, G. M.; Hoffman, M. J.; and

Council Current Papers 1187, 1971.

Freuhler, R. J.: Flight Investigation

of Natural Laminar Flow on the Bellanca

11. Kelling, F. H.: Experimental

Skyrocket. SAEpaper 83071 7, April

Investigation of a High-Lift Low-Drag

1983.

Aerofoil. University of Glasgow,

Department of Aeronautics and Fluid

2. Holmes, B. J.; Obara, C. J.;

Mechanics, Report No. 6802, September

and Yip, L. P.: Natural Laminar Flow

1968.

Experiments on Modern Airplane Sur-

faces. NASA TP 2256, June 1984.

12. Wortmann, F. X.: Experimental

Investigation on NewLaminar Profiles

3. Dwiggins, D. : DangerousWhen

for Gliders and Helicopters. Ministry

Wet?. Homebuilt Aircraft, Part I and

of Aviation Translation TIL/T. 4906, 2, March and April 1983.

1960.

4. Hewes, D.: Effects of Rain and

Bugs on Flight Behavior of Tail-First

Airplanes. Sport Aviation, Part I, 2, and 3, May, June, and July 1983.

13. Althaus, D.; and Wortmann, F.

X.: Stuttgarter Profilkatalog I, Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig, West Germany, 1981.

14. Whitcomb, Richard T.: A Design Approach and Selected Wind-Tunnel Results at High-Subsonic Speeds for Wing-Tip Mounted Winglets. NASA TN D- 8260, July 1976.

15. Yip, Long P.: Wind-Tunnel Investigation of a Full-Scale Canard- Configured General Aviation Airplane.

NASA TP 2382, March 1985.

16. Roskam J.: Airplane Flight Dynamics and Automatic Flight Controls. Published by Roskam Aviation Engineering Corporation, 1979.

17. van Dam, C. P.: Natural Laminar Flow Airfoil Design Considera- tions for Winglets on Low-Speed Air- planes. NASA CR 3853, December 1984.