Configuration development study of the OSU 1 hypersonic research vehicle

section of the vehicle. The totals were very close to the volumes predicted by the I-DEAS program, as will be discussed later in this report. The skin fiiction coefficient is also predicted in this routine at certain specified conditions. The WAVEDRAG routine was not used due to problems in running the routine. This routine like VISCOUS gave estimates of the wave drag at certain specified conditions as a function of roll angle.

The actual analysis of the HRV was setup in the APAS program by specifjnng a Mach number, altitiude, and certain angles of attack (a) or sideslip angles ( P ) . For each analysis run, a certain configuration was used. This allowed different geometries to be used and compared. In order to set up an analysis run, several parameters must be input including the center of gravity location, planform area, chord length, and vehicle span.

These reference numbers are used to figure the non-dimensional coefficients (such as lift, drag, and moment coefficients). The Hypersonic Arbitrary Body Program (HABP) was used to analyze the vehicle. This program requires the different methods of analysis be specified in APAS before the program is run. There are two methods specified for each section, one for impact flow and one for shadow flow. Impact flow is where the flow directly hits the panel, and shadow flow is where the flow does not come into contact with the panel. For the foreward part of the vehicle, the empirical tangent cone method for impact flow was used due to the shape of the vehicle. The main body of the HRV used the modified Newtonian method for impact flow. The wings and tails used the empirical tangent wedge method for impact flow due to the 2-D nature of these sections. For shadow flow, the Prandtl-Meyer expansion method was used everywhere on the vehicle except at the base of the HRV. Here, a high mach number base pressure method was used. There are several options which need to be set to run the HAE3P program. These include whether sheilding effects are to be considered. For the nose, a hemispherical nose cap is added to configuration. Sheilding effects can also be considered on any component.

For the HRV, no sheilding effects were considered. The last option considered was with Page 11 regard to skin fiiction effects. For the HRV, skin fiiction effects were included using turbulent flow over the whole vehicle. Turbulent flow was used as a 'worst' case for the vehicle since the drag will be greater for this type of flow. There are also options for a laminar to turbulent transistion based on several different parameters but the design of the HRV was based upon turbulent flow. With all the needed information specified, the HRV w a s analyzed.

The results of HABP can be seen in Appendix 7 for our configuration. The UD at the test conditions was around 2. This is lower then predicted by the AERO program.

Also, there was a problem in trimming the vehicle at the test conditions. From the moment coefficent graph, the vehicle was stable but unbalanced, ie. the C , was not positive, Several different ideas were attempted to get the C , , positive including giving the wings incidence and dihedral. The t w i n tails were also rotated to see the effect on the moment coefficient. The basic result was that giving the wing incidence gave the needed positive C , . There was an attempt to move the maximum cross-sectional area to the midpoint of the vehicle giving it a 'hump' in the middle. This actually deceased the moment curve even more since the CG location was behind the midpoint.

In the end, the HRV was made balanced and stable. The moment, lift, and drag coefficients can be seen in Appendix 7. The AIREZ program was used for the subsonic regime since its data matched those in papers better then the subsonic data from AERO.

AERO predicted much lower IfD for the subsonic region then AIREZ. A l l the curves in Appendix 7 are shown at Mach numbers of 0.3, 0.6, 0.9, 3,6, and 12. Each has been divided up into several graphs for clarity.

Page 12

Thermal Protection Svstem

The temperature contours obtained from APAS, see Appendix 7, indicate that a passive system can be used all over the plane except for the nose and leading edges. Multi wall TPS panels were selected for the passive system. These panels can withstand temperatures of approximately 2400 degrees Fahrenheit. These panels were selected for their high mechanical strength, light weight, and flexibiIity. The only disadvantage to these panels is that they have a high thermal expansion coefficient.

Several active thermal protection systems were studied. The active systems that were studied included a transpiration system, a direct cooling system that circulates the fuel through the leading edges and a heat exchanger system, which utilizes a secondary coolant. The direct system and heat exchanger system were ruled out because of their complexity and high component weight.

The transpiration system injects liquid hydrogen i n t o the boundary layer a t the leading edges and nose. Although the transpiration system can not utilize the engine &el as coolant, it was chosen because of the very short time that active cooling w i l l be required during the mission.

Page 13

Propulsion

Turbojet to Ramjet to Scramjet The turbojet to ramjet to scramjet option offers minimum thrust specific fuel consumption. The turbojet is the most etficient means of propulsion under Mach 3.

Turbofan and turboprop engines are more efficient than the turbojet, but, these two engines usually operate in the subsonic regime. Since the turbofan and turboprop operate over a very limited speed range, they were not considered as a first stage propulsion alternative.

A typical turbojet will have a thrust specific fuel consumption between 1 and 2 pounds of he1 per pound thrust per hour. The typical turbojet weighs approximately 2000 pounds.

The ramjet is the most efficient means of propulsion between Mach 3 and Mach 6.

Turbojets can not be used in this region because the turbine would melt at the temperatures that would be necessary to produce thrust. The ramjet overcomes this problem by not using compressors or turbines. Typical ramjets have thrust specific fbel consumptions of 1 . 7 to 2.6 pounds of he1 per pound thrust per hour.

Theoretically, the scramjet is the most efficient means of propulsion &om Mach 6 to Mach IS. The scramjet has a specific impulse of approximately 1500 seconds at Mach This configuration has a high component weight. This increases the empty weight of the aircraft. This configuration would require two turbojets, two ramjets, and two Page 14 scramjets. T h i s does not include the weight of the heavy variable geometry inlets that would be required. Turboramjets were not considered because they will not be ready by 1998, the required operating date for the aircraft.

This configuration is very complex. No aircraft have been built that utilize three different propulsion systems in this manner. No work has been done with variable geometry inlets that operate fiom Mach 0 to Mach 12. This configuration, in addition to being heavy, would take up a lot of volume. Finally, this option offers a very low reliability due to all of the moving parts involved in the engines and inlets.

Due to the high component weight, and enormous complexity of this option, it was ruled out.

Rocket The rocket option is the simplest of all options considered. Rockets can operate over all Mach numbers. Unfortunately, the rocket offers the lowest speclfic impulse of all alternatives considered. The weight of the engines would be 1,140 pounds. Additionally, since the rocket carries its own oxidizer, inlets are not required.

The one propulsion s y s t e m and no inlet fatures combined make the rocket option the most reliable of the alternatives considered. There have been a lot of rockets developed for previous projects that could be suitable for this project. Using a previously developed engine could drastically reduce the cost of the propulsion s y s t e m . Using a previously developed engine will also decrease the propulsion s y s t e m design time.

Page 15 Turbojet to Rocket The turbojet to rocket mode may offer the best of both worlds. The turbojet is 8 to 12 times as efficient as the rocket in the Mach 0 to Mach 3 regime. This could drastically reduce the fbel required to get to Mach 3. Unfortunately, this option also requires variable geometry inlets for the turbojets, which would have to be closed once the rocket engine(s) started at Mach 3.

The weight of the turbojets plus the turbojet fuel may exceed the weight of the rocket fuel required to propel the vehicle from Mach 0 to Mach 3. This will depend on gross takeoff weight. As gross takeoff weight increases, the turbojet to rocket option becomes more attractive. Most turbojets are fueled by JP. If a Hydrogen Oxygen rocket is selected, the vehicle would have to carry multiple fuels for the propulsion systems.

Hydrogen Oxygen Fuel Hydrogen Oxygen fuel provides the maximum specific impulse possible.

Theoretically, Hydrogen Fluorine provides the highest specific impulse, but Fluorine is highly reactive, making,it impractical as a rocket oxidizer. Although Hydrogen has a high heat capacity per pound of fuel, it has an extremely low density. Hydrogen Oxygen has twice the volume of alternative fhels.

Hydrogen Oxygen fuel is very diicult to store. Hydrogen and Oxygen are cryogenic liquids. Hydrogen is particularly dficult to store. Hydrogen has a high heat capacity, which makes it an excellent coolant for an active thermal protection scheme.

F i l y , the scramjet uses Hydrogen as well, making a multiple fuel system unnecessary.

Page 16 The specific impulse for the RL-10 35K Hydrogen Oxygen rocket engine is 41 5 seconds.

The average bulk propellant density is 20 pounds per cubic foot.

JP Oxygen Fuel J P Oxygen fuel is only 60% as efficient as Hydrogen Oxygen fuel. JP Oxygen fuel is dense, so the required volume is a lot less compared to the Hydrogen Oxygen fbel.

Since JP is not cryogenic, it can not act as a coolant in any active thermal protection scheme that might be necessary. The specific impulse for the H-1 JP Oxygen rocket engine is 295 seconds. The average bulk propellant density is 64 pounds per cubic foot.

Propulsion Selection Atter reviewing all pertinent data, a Hydrogen Oxygen rocket propulsion s y s t e m was selected. The rocket propulsion s y s t e m offers the best reliability. Although the turbojet is much more efficient at lower Mach numbers, it was determined that the weight of the turbojets exceeded the weight of the rocket fbel required to propel the vehicle fiom Mach 0 to Mach 3. If the vehicle weighed more than 65,000 pounds at takeoff, the turbojet to rocket option would have been viable.

Hydrogen Oxygen fbel offers the lowest fuel weight for a rocket system.

Hydrogen Oxygen offers a high enough specific impulse to make up for its low density.

The liing body configuration is well suited for Hydrogen Oxygen fud, due to its high volumetric efficiency. Hydrogen Oxygen fuel was also selected because Hydrogen is an excellent coolant.

Page 17 The rocket's low cost, low complexity, and high reliability made it the clear choice for propulsion. The best rocket for the vehicle is the Pratt and Whitney RL-10 rocket engine. The RL-10 is a proven Hydrogen Oxygen fueled rocket. The RL-10 35K provides 34,000 pounds of thrust. The RL-I 0 has a specific impulse of 415 seconds.

Three RL-10 engines will be required, giving a combined thrust of 102,000 pounds. Each RL-10 has an exit diameter of 28 inches. The combined weight of all three engines is 1 140 pounds.

The rocket will require 33,700 pounds of fuel for a 47,8 10 pound vehicle, leaving an initial cruise weight of 14,020 pounds. The fuel and oxidizer combined will occupy a volume of 1492 cubic feet. The weight of the Hydrogen required for the rocket phase is 4,8 14 pounds, which occupies a volume of 1,094 cubic feet. The weight of the Oxygen required is 28,886 pounds, which occupies a volume of 398 cubic feet.

Scram jet Propulsion O n l y one scramjet, producing 7,000 pounds of thrust will be required for the test.

According to the General Electric A i r d Engine scramjet data, 420 pounds of Hydrogen will be needed to power the scrimjet for a 1 minute test. This will occupy a volume of 95 cubic feet.

Methods After ruling out the turbojet to ramjet to scramjet option, a program was developed to analyze rocket fuel consumption. The program assumed level flight and a constant lift over drag. The program asks for initial velocity, final velocity, thrust available, gross weight, and a time step. The program uses this information combined Page 18 with specific impulse and propellant density information for Hydrogen Oxygen and J P Oxygen fbels to arrive at a fbel weight and volume for each hel. Basically, the program applies F=ma for each time step.

The most interesting thing learned from this program is that if you increase thrust available, you decrease he1 required. This is due to the fact that more thrust results in a smaller distance traveled, which results in lower work against drag.

Once it was determined that the rocket might be viable for the entire mission, the program was modified to take into account climbing flight. As a rough approximation, a constant climb angle was assumed. The program proved that there was enough volume available in the plane to allow the use of a Hydrogen Oxygen rocket for the entire mission.

Once the RL-10 35K engine data was obtained, the program was modiied one final time to account for thrust variations due to altitude. The exact specific impulse of the RL-10 was also used in the final version.

The propulsion program proved to be invaluable in determining the fmibiiity of rocket propulsion for this mission. Even with some of the crude assumptions, it still gave remarkably accurate results.

Page 18a

Enpine Inlet

The engine inlet is used to supply the needed air to the scramjet engine. The major performance characteristics of the engine inlet are pressure recovery and air quality. An external compression inlet was used because the design was easier. An internal compression inlet may have been bettered suited for the shortness of the inlet, but no information on design could be obtained. For the initial inlet design the CONIC and GEOM computer codes were used. This gave a starting point for the design. The final inlet was designed using the method of characteristics and geometry.

The inlet that was chosen consisted of two compression ramps. This was chosen, because the inlet needed to be short, but still provide an acceptable pressure recovery.

The inlet was designed to begin at approximately two feet behind to nose of the aircraft.

This gave a small amount of lifting surface on the front of the aircraft. It also provided a fairly two-dimensional inlet surface. The oblique shock from the nose of the aircraft gave a Mach number of 8.4 at the first ramp. Because of this distance the first inlet ramp was at an angle of about nine degrees. The second ramp began at about 330 inches from the first ramp.

The inlet provided conditions at the engine face of Mach 5.5 and a pressure recovery ratio of 0.41. The cowl lip of the inlet is used to straighten the flow to provide clean air to the engine. The cowl lip is also used to cover the engine while the aircraft is climbing to the test altitude.

Page 19

Weight and Structure Analvsis

The optimization of the hypersonic test vehicle, OSU I, is basically an optimization of the weight of the vehicle. The weight is the driving parameter in the design of any aircraft. A reduction in weight results in an increase in performance and efficiency, while decreasing he1 weight and cost. Lighter engines, fbels, structures, and materials are always preferred when designing an aircraft. With a hypersonic aircraft, the weight becomes even more important. Due to the ~omplexity of hypersonic aircraft, their weight tends to be enormous. Some total gross take-off weights for various proposed and operational hypersonic vehicles are listed below: Lockheed Hycat- 1 ........................................ 773,706 Ib Lockheed Hycat-4 ........................................ 959,426 lb .................................... Space Shuttle Orbiter 255,170 Ib

...... General Dynamics Orbiter ...................... .: 891,795 Ib

...................................... H2 Fighter (M = 6) 320,000 Ib The payload weights of these vehicles range fkom 42,000 Ib to 80,000 Ib.

The hypersonic vehicle under consideration in this design has a payload of 1,000 Ib. Common sense says that the weight of OSU I should be meager in comparison. The problem with determining the weight of a hypersonic vehicle, especially one that has no comparison to either operational or theoretical designs, is the method to be used in calculations.

Methods for Calculating the Weight of a Hypersonic Vehicle There are a few analytical computer programs available to calculate the weight of a hypersonic vehicle. Hypersonic Aerospace Sizing Analysis for the Preliminary Design of Aerospace Vehicles (HASA) and Weights Analysis of Advanced Transportation Systems Page 20 (WAATS) were the only two considered. WAATS was discarded due to problems obtaining access to the computer system to run the program. However, HASA was run and results were analyzed. Another method would be to break the vehicle down into components and determine their individual weights from analytical calculations or comparisons with similar structures.

HASA HASA is a program written in Fortran that first iterateatively solves for the size of the vehicle, breaks it down into 14 individual components and then weights each of them.

The program uses statistical weight equations to solve for the 14 individual components.

These components include the propellant, body, wing, horizontal and vertical stabilizers, thrust structure, propellant tank, landing gear, propulsion, thermal protection system, avionics, hydraulics, electronics, equipment, and payload. The program has various inputs for fie1 types and their mass fractions, geometry, payload weight and volume, and the number and types of engines.

The program met with limited success. Almost all the contigurations tried resulted in take-off weights of 100,000 Ib to 200,000 lb. The reason for this is that the program was written for large vehicles and certain values in the program are hard coded with this in mind. In order to change these values extensive work would be required. It was determined that time could be better spent on the component build up method.

However, HASA did reveal that vehicles that used large fuel mass fiaction on the order of 0.6 to 0.8 produced the heaviest vehicles. Also, vehicles that used liquid hydrogen as fuel were nearly 1.5 times heavier and 3.0 times as large as vehicles that used the same mass fraction of JP. Vehicle configurations that used just rocket propulsion Page 2 1 were slightly lighter than vehicles that used other configurations, such as; turbojet/ramjet, turbojedscrarnjet, turbojedrocket, and tuhojedramjet/scramjet.

With the unsuccessful try at using HASA as a means of calculating the vehicles weight, a component build-up method was employed.

Component Build-up Method The component build-up method entails breaking down the vehicle into several components, determining their weight, and then summing the weights together. How to obtain the weights of the individual components is the major stumbling block. This problem was solved by developing a solid model of OSU I on SDRC's solid model and finite element analysis program, I-DEAS.

The reason for using I-DEAS to do the solid model was that it could calculate the properties of the mode quickly and accurately. The break down of components used follows: Internal Structures:

- Fuselage frame

- Wing b e

- Vertical tail frame

- Longerons

sufices:

- Fuselage

- wings

- Vertical tail

Components:

- Rocket engines

- Scramjet

Page 22

- Fuel tanks

- Landing gear

- Payload

- Pressurization System

- Power Supply

- Control Systems

Development of Solid Models From the components list the necessary solid models broke down in two main models. The first and most complicated model was the internal structure solid model.

The next was the outer surface model. Also, solid models for the rocket engines and scramjets were necessary. The solid models for the landing gear, payload, and fuel tanks are to simple to mention.

Fuselage Desim The fuselage design for the internal structure entailed the creation of 16 bulkheads along the length of the vehicle fiom 0.3048 m to 15.24 m. The profile were created using the known points of the outside shape of the vehicle (profiles for the top and bottom of the vehicle were treated separately). Then each profile was extruded 76.2 mm and a solid object of the profile was created. The solid object of the profiles was then scaled down by 90% in both the x and y directions. This new object was then used to cut the original object. This resulted in either the top or bottom portion of the fuselage bulkhead. Finally, the top and bottom bulkheads were joined and the result of creating one bulkhead can be seen in Appendix 5. Once all the bulkheads were created, they were placed at the correct locations and then joined to one another in order to create the fuselage. For the outer surface of the fuselage, only the profiles were necessary. The profiles were placed in the correct locations and a skin was drawn over them.

Page 23 The next step was to make four 15.24 m long beams called longerons. These were created using three square profile sections of variable size, (6.35 mm x 6.35 mm, 12.7 mm x 12.7 mm, and 25.4 x 25.4 mm). The profiles were then placed at the correct x,y, and z locations and a skin was created along the path. The longerons were then joined to the firselage, Figure 3. These longerons were not used in the development of the solid model of the outer surface.

Wing and Vertical Tail Design The procedure for creating the wing and vertical tail structures is the same, so only the procedure for the creation of the wing will be discussed.

The solid model of the outer surface (Figure 8) of the wings was created by using two biconvex airfoil shapes for the root and tip of the w i n g . Between these profiles a skin was drawn. Starting with the outer surface, the internal structure of the wing was created by using a cutting block. Once the block was moved to the appropriate location, a cut was made and one of the vertical spars was formed. The result of six cuts produced six vertical spars. Then the outer surfice of the wing was cut horizontally by another cutting block. The result of nine cuts produced nine horizontal spars. Finally, a large cutting block was oriented so that the leading edge of the wing could be obtained. Finally, the vertical and horizontal spars and the leading edge were all joined together. The final internal structure of the wing is shown in Figure 10. The vertical tail was created by using different cutting blocks, but the same method was applied. The result of the vertical tail structure is shown in Figure 12.

Page 24 Scamjet and Rocket Engine Design The scramjet was designed using a profile of appropriate dimensions and then an extrusion was made in order to obtain the solid model. The rocket engines were created using the top half of the profile of the engine. The comers were filleted for a more realistic effect, and then the entire profile was revolved 360 degrees to form the solid object.

Assembly of the Hypersonic Test Vehicle Structure The procedure for assembling the structural solid model and the outer surface solid model was the same except for the scramjet and the rocket engines. With the fuselage, the two wing halves, and the two vertical tails, the final hypersonic test vehicle structure could be assembled. F i r s t , the wings were translated to the correct location and then joined to the fuselage. Next, the two vertical tails were rotated 15 degrees fiom the vertical and translated to the correct positions on the hypersonic test vehicle. Then the vertical tails were joined to the fuselage. The scramjet and the rocket engines were moved to appropriate locations and joined only to the outer d a c e solid model. The final internal structure of the hypersonic test vehicle is shown in Figure 13 and the final outer surface solid model is shown in Figure 14.

Weight Calculations from the Solid Models The weight calculations were obtained directly and indirectly form I-DEAS.

Within I-DEAS, the properties of each component were calculated and are listed in Table 2.1. Note, only the information necessary for the calculation of the weight, volume, and center of mass is listed. By imputing the density of titanium (281 1b/ft3) the weights for Page 25 the internal structures was obtained immediately. The weight of the other components were determined by using trade study data and data obtained from I-DEAS.

The weights of the outer surfaces of OSU I were determined by trade studies and the surface area of the object as determined by I-DEAS. From various aircraft, such as the SR-71 and the Space Shuttle Orbiter, the thickness of the fuselage skin was determined to be 118 " and the thickness of the wing and vertical tail skin was determined to be 1116". This values of skin thickness were averages for the skin thickness over the entire surface. Titanium was used because it is a common material in aircraft construction, and follow the idea that the plane must be low cost and operational by 1999. The procedure for calculating the weight of the wings follows: 1. Obtain the surface area of the wings from Table 1.

2. Convert the 111 6" thickness to feet.

3. Obtain the volume of the material necessary by multiplying the thickness by the surface area.

4. Multiply the volume by the density of titanium.

(Note: The actual calculation gives the mass, but the mass is in Ibm so the conversion to lbf is straight forward) The weights of the landing gear were obtained from a trade study discussed at the end of this section. The weight of the rocket engine was obtained fiom NASA, and the weight of the fuel tanks were obtained by scaling the m a i n fuel tanks on the Space Shuttle.

The weight of the fuselage's internal structure was obtained by an iterative process using I-DEASfinite element anaQsis (FEA). This process was performed on a fuselage bulkhead attached to the wing. The objective of this iteration using I-DEAS was to reduce the weight of the member as much as possible while meeting certain design Page 26 requirements. The specifics of this analysis are in the section Engineering Analysis of Fuselage Wing Bulkhead.

A complete list of the weights calculated for each component and the he1 weights are in Table 2.1 and a partial weight pie chart can be seen in Figure 2.1. From the pie chart one can see that the he1 is 74% of the total weight. The structure of the plane is the next largest at 17%. The remaining weight is taken up by the he1 tanks, payload, engines, and landing gear.

Engineering Analysis of Fuselage Wing Bulkhead Static analysis was performed on a fbselage bulkhead in particular the second to the last bulkhead on the vehicle. This particular bulkhead was attached to the wing. The material used for the bulkhead w a s a titanium-carbon fiber alloy with a density of 28 1 lbm3, a Poisson's ratio of 0.33, and a Young's Moduhs of 1.1 x 10 Pa.

To m i n i m i z e computer resources, only half of the bulkhead w a s modeled. This was a viable assumption, which can be validated by looking at the stress contours and deflections for both the half and whole initial bulkhead configurations (see Appendix 5 and 6, initial bulkhead configurations). These figures show that the whole bulkhead is stressed and deflected in the same manner as the half bulkhead. After the initial configuration, modifications were made to increase the stress over the entire bulkhead, while still remaining below the design requirements of maximum deflection of 6.5 rnm, and maximum allowable stress of 500 MPa. Modifications could be made to any part of the bulkhead, except the outside shape. The outside of the bulkhead had to maintain the dimensions shown in Figure 3.5. The various configurations that were analyzed during the Page 27 optimization process along with their corresponding weights are shown in Appendix 3.

Stress contours and deflection plots can be seen in Appendixes 5 and 6, respectively.

A section of the wing bulkhead is connected to the hselage bulkhead as shown in Figure 5. During flight, lift, drag, and moments acting on the wing are transmitted to the hselage bulkhead via the wing clamp. For this study only forces due to lift and drag and moments due to lift were considered. The derivation of these forces is in Appendix 6.

The magnitude and direction of the loads applied to the clamp can be seen in Figure 5.6.

Even though the case of the pin carrying half the moment is more realistic, the worst case of the clamp carrying all the forces was chosen as an extra margin of safety, . Also a load factor of 9 was chosen to represent the maximum loading the wing clamp would encounter during flight..

The restraints were applied to the top and bottom beams of the bulkhead for configurations 1,2, and 4A An additional restraint in the fiom of a longeron was applied to configuration 3 and B-10. These restraints are shown in Figure 5.7.

The following is a brief description of the major changes made during each iteration and the correspondiig results: Configuration 1 This initial design had a thickness of 101.6 mm and a weight of 771.0 kg. This configuration was considered to bulky. The deflection was 0.12 mm and the maximum tensile and compressive stresses were 3.18 MPa and -1.3 MPa, respectively. A high tensile stress could be seen on the top beam, lower surface, and near the upper comer of Page 28 the clamp. This high stress should have been in the corner of the overhand of the clamp.

The reason for it not being there is that the mesh on the clamp area was to coarse.

Configuration 2 The upper and lower beams were thinned while the thickness of the bulkhead was reduced to 89 mm. The resulting weight was lowered to 494.2 kg. The resulting deflection was 7.1 mm and the maximum and minimum stresses were 43.3 MPa and -9.39 MPa, respectively. Although the increase in the stress over the bulkhead due to the reduction in weight is tolerable, the deflection is above the design goal.

Configuration 3 The inner surfhce was rounded near the clamp and the bottom b e a m w a s shaped to conform more to the outside shape of the fuselage. The rounding of the clamp area was intended to decrease the deflection while still decreasing the weight. The addition of a longeron was placed above the clamp in another attempt at decreasing the deflection. T h i s w a s modeled by using restraint C (see Figure 15, page ). While the maximum and

minimum stresses where increased to 45.1 MPa and - 13.6 MPa, respectively, the

reduction in weight was lowered to 3 18.8 kg. The addition of the longeron proved effective in reducing the amount of deflection in the z-direction. The maximum deflection w a s reduced to 4.7 mm.

Configuration 4A and B These configurations show a much slimmer overall bulkhead along with a reduction in thickness to 63.5 mm, and an overall weight reduction to 181 kg. A 0.1 m Page 29 fillet at the inside comers of the clamp was added in order to spread out the high stress regions near the comers. The purpose of these two configurations is to demonstrate the effectiveness of the longeron over the clamp. Configuration 4A has no longeron and its maximum deflection is 45.0 mm, whereas configuration B has a longeron placed just above the clamp and its maximum deflection is 16 mm.

Configuration 5 This configuration was an attempt to thicken the beam above the clamp in order to reduce the deflection in both the y and z direction without the use of the longeron.

Thickness and weight of this configuration were 50.8 mm and 177.4 kg, respectively. A quick look at the maximum deflection shows that this configuration was a failure because it was much worse than the last configuration, B. The addition of the longeron above the clamp seems to be the only viable solution to keeping the z-direction deflection down.

This iteration is shown because it represents the hct that not all of the ideas that were used worked. There were many other configurations that produced worse results than their corresponding previous configuration. However, these configurations were important because a great deal of knowledge was acquired &om their Mures.

Configuration 6 Configuration 6 shows a greatly increased width in the beam above the clamp.

Since the longeron is going to be used to limit the z-direction deflection, a reduction in the overall thickness to 44.5 mrn w a s made. The result was still another reduction in weight to 135.4 kg. The deflection of this bulkhead, 40 mm, was still way to high. From the 3- view deflection plot one can see that this 40 mm deflection must be in the y-direction. The bulkhead is almost entirely in compression except near the cantilever top beam, the Page 30 rounded comer of the top beam, and the upper inside comer of the clamp. There are also very high compression spots all over the beam. From this configuration and the two previous configuration, a conclusion was made that the only way to reduce the y-direction deflection is to increase the width of the upper and lower beams.

Configuration 7 With configuration 7, another reduction in overall thickness to 38.1 mm was made for a reduction in weight of 159.2 kg. This configuration was a success because the maximum deflection was reduced to 9.8 mm, the weight was reduced, and the stress over the entire bulkhead was more proportional. This configuration would have a much longer life span then configuration 6. The deflection around the longeron is more noticeable in this configuration. Looking at the x-view, the bulkhead deflects about the longeron location. This deflection is due to the drag forces.

Configuration 8 In an attempt to reduce the weight even further the beam thickness was cut to 3 1.75 mrn and the lower beam width was reduced. This configuration at a weight of 123.3 kg was the lightest configuration tested. Like configuration 6, this configuration was a failure. The deflectionjumped up to 12.5 rnm. This meant that the lower beam width had to be increased.

Configuration 9 This was the final configuration because it was below the design limit of a maximum deflection of 6.5 mm. The thickness was cut to 25.4 mm, but the lower beam Page 3 1 width was increased to the size of configuration 7. Also the width around and above the clamp was increased. This resulted in a weight of 141.0 kg, and the final deflection of 6.458 mm.

From the x-view of the deflection plot, one can see how the beam deflects around the longeron. This is also represented in the stress contour; the front or left view shows the tension on this face due to the deflection resulting fiom the drag forces applied to the clamp. The back view or right view shows the corresponding areas in compression. The majority of the beam ranges Erom stress values of 30 MPa to -14.3 MPa. A blow up of the clamp shows the high tensile stress, 1 18 MPa, in the upper inside curve of the clamp. This high stress could be alleviated by increasing the fillet size of the clamp. The top of the bulkhead is blown up in the right view. This view shows the greatest rate of change in stress on the bulkhead. From the bottom, the stress ranges fiom a tensile stress of 96 MPa to a maximum compressive stress of -36.3 MPa.

The overall optimization process resulted in a reduction of wight &om the initial configuration to the fkd configuration of 8 1%. T h i s reduction in weight is mainly due to the reduction of the bulkhead thickness fiom 101.6 mm to 25.4 mrn. Alone, this is a reduction in weight of 75%. The more proportioned stress contours will result in a longer usable lifetime for the bulkhead. As a whole the optimization process resulted in a more l l l y stressed structure The main design barrier was the deflection of the beam. The maximum allowable stress of 500 MPa was never reached. With new modifications, a fbrther reduction in weight could be achieved if methods for reducing the deflection in the y-direction could be implemented. Possibly a vertical spar could be used to decrease this deflection. If this vertical spar was used, a buckling analysis would have to be performed to guarantee that the spar would maintain its shape. Additional longerons could be used to reduce my fbrther increase in 2-direction deflection. The optimum goal would be a fully stressed structure that had the lowest possible weight. With further time and new ideas, this optimum structure could be achieved using I-DEAS.

Volume The configuration chosen for OSU I was a lifting body. One of the biggest advantages of a lifting body is its volumetric efficiency. OSU I is almost an ellipse. This allows for a large volume of components to fit inside the vehicle. The volume for each component is listed in Table 1 and was calculated by I-DEAS. An inboard planform of OSU I is shown in Appendix 2.

The most challenging structures to fit inside OSU I were the hydrogen and oxygen fuel tanks. Attempts a conventional cylindrical tanks was attempted, but not enough volume was produced to hold the 1,189 ft3 of hydrogen fbel. We only immediate solution that presented itself was to scale down the body of OSU I by a &or of 0.9. This resulted in the shape of the fbel tanks seen in the inboard platform. These tanks were a little to big, but fit fine inside the fuselage. The shape of the fie1 tanks is questionable.

Due to the high pressure of the liquid hydrogen, cylindrical tanks are preferred. An analysis of the shape of these he1 tanks must be performed in order to determine their practicality. AU other components in the inboard platform were checked to make sure they fit inside the vehicle.

A breakdown of the volume can be seen in the volume pie chart Figure 2.2. The volume of the hydrogen fuel is almost half to total volume. The oxygen fuel is about a fifth of the total volume, and the rest of the components occupies 3% of the total volume.

The remaining 30% is due to unusable space, and to components not added to the vehicle.

Page 33 Landing Gear The landing gear for the aircraft was required to be rugged, sturdy, lightweight, and compact. It had to be sturdy due to the fact that the craft is remotely piloted and landing without power. Both of these factors lead to the possibility of hard landings. At the same time the gear must be light and compact so as not to use excessive space and weight which could be more readily used for increased fuel and/or other component storage.

In order to minimize the weight of the gear, unnecessary features and components were omitted. For example, since this is a test aircraft, it will most likely not be flown at night, during inclement weather, or at any other less than optimum condition. This led to the omittance of lights on the nose gear. Since the plane is pilotless, it will most likely be taxied to and fiom the runway, tarmac, and hanger. Because of this no steering actuator was incorporated into the design. The nose wheel, however, can be unlocked for full 360" rotation during taxiing. This reduction in features lead directly to weight savings which allow the gear to be built within weight limitations without sacrificing strength.

The nose gear is rearward retracting with twin wheels and a shock strut. The rearward retraction allows the gear to be located farther forward in the nose. Each of the twin nose tires is a 20 ply 20 x 6.6 -10 manufactured by B.F. Goodrich and inflated to 150 pounds per square inch. The main gear is forward retracting to allow placement farther afl to allow an acceptable maximum rotation upon take-off The main gear also incorporates a shock strut and is capable of withstanding a maximum descent rate of twenty-one feet per second. Each main gear tire is a 24 ply 30 x 1 1.5-1 4.5 manufactured by B.F. Goodrich and inflated to 200 pounds per square inch. The nose gear weighs 150 Page 34 pounds and each main gear weighs 200 pounds, including local hydraulic components, for a total gear system weight of approximately 550 pounds.

Page 35

Traiectory

Given predetermined mission requirements and goals, a trajectory that minimized empty weight was needed. The goals and requirements are as follows: accelerate fiom conventional ground take-off to a Mach 12 cruise at 100,000 feet altitude; test a scramjet for one minute at equilibrium conditions; carry 1000 lbs and 35 cubic feet of payload; and land conventionally. It was decided that an unpowered landing was both feasible and necessary in order to minimize weight.

An optimized ascent trajectory was determined through the use of a computer

program called, "ETO - A Trajectory Program for Aerospace Vehicles," which was

developed at the Aero Propulsion and Power Laboratory of the Wright Research Development Center, Wright-Patterson Air Force Base. This program, which is based on equations of motion and forward time iteration, requires aerodynamic data, propulsion data, initial conditions, and phase parameters as input in a particular form text file. Out of five flight phases available in the ETO program, it was found that Phase I, 11 and V provided the best results. Phase I is the take-off ground roll. Phase I1 is a Rutowski climb at a commanded load factor and axial acceleration. Phase V is a pull up to ballistic ascent.

The input file used for the h a l ascent trajectory analysis can be found in Appendix 8.

This file was produced by the FORTRAN code called SORT.FOR, which reads aerodynamic data produced by the AERO FORTRAN code and writes it, along with the propulsion data, into an input file that can be read by ETO. For the final trajectory, Phase I1 is initiated at Vto= 450 fVs and concluded at a velocity of 900 ft/s and altitude of 5,000 feet, incuning a maximum load factor, UW = 1.6 . At this point Phase V is initiated, at which point the vehicle pulls up to a climb angle of 54 degrees and follows a ballistic ascent until leveling at 106,000 feet altitude and Mach 12. 33,700 lbs of LlWL02 &el is required for climb, giving the vehicle a total take-off weight of 47,8 10 lbs. A maximum dynamic pressure of q = 1,960 psi is encountered during this phase.

The unpowered glide descent trajectory was determine fiom the FORTRAN code called GLIDE.FOR. The code determines the maximum range glide descent using LDmax values, which were determined by the AERO FORTRAN code (with base drag).

A maximum range of 783 nautical miles and total mission time of 27 minutes were calculated. Graphical representation of the trajectory analysis can be found in Appendix 8.

Take-off and Landing The take-off performance parameters of the OSU 1 was calculated by ETO.

Under full power of three RL-10 rocket engines, the rolling distance needed is 2,130 feet.

The velocity at this point is 460 Ws. The distance needed to clear a 50 foot obstacle is 4,250 feet. The velocity at this point is 600 fVs.

The program, GLIDE.FOR, calculates the landing parameters. After clearing a 50 foot obstacle at 210 Ws., the vehicle travels 628 feet before touch down at 211 Ws.

Based on an 8 deg/s second rotation to nose down, the vehicle rolls another 209 feet, and then brakes fiom 208 fVs to stand-still in 2,788 feet. T h i s braking distance is based on a rolling co&cient of 0.2, whereas a typical value for a paved runway is 0.4.

Page 37

Longitudinal Stability

Several parameters were needed to calculate the longitudinal stability of our vehicle. These included the mean aerodynamic chord (MAC), aerodynamic center, tail volume ratio (VH), taper ratio (I), and the center of gravity (CG) location. There were several assumptions made in this initial stability analysis. The planform used was simply a delta wing covering the entire vehicle. The twin tails located on top of the vehicle are at a 15' slant with respect to the vertical. For longitudinal analysis, an effective horizontal tail was assumed to be simply the sine of that angle times the height of the tail. This gives the length of the horizontal tail, and the same width was used. As is common in aircraft analysis, the z-component (vertical) of the tail above the CG was assumed small relative to the x-component (axial). This indeed was the case as the numbers show. Last, the lift curve slopes of the wing and the tail were assumed the same since each is the same type of airfoil.

The analysis began by calculating a MAC. This was done using a formula found in Dvnamics of Flight: Stabilitv and Control by Bernard Etkin. The MAC was found as follows: 2 0 (1+R+L2) MAC = 3(1 + A ) This formula was for a planfonn with constant taper and sweep with any loading distribution. This book also contained graphs which gave the distance of the tip of the MAC from the apex of the planform. These values were found using the following parameter: AR tanA112 Page 38 where the L is the sweep angle of the half chord line. This factor then along with the taper ratio gave the distance fiom the apex in terms of the MAC. The tail volume ratio was then calculated using the CG location, wing area, and tail area. The neutral point is then found using the following: hn = hm + VH The static margin is then found by taking the difference between the neutral point and the CG location as a percent of the MAC. The following table gives the resulting values for our vehicle.

As can be seen, our configuration is stable since the static margin varies within allotted limits. The tail planform area w a s found using the X-24 as a guide. The tail area was within 4% of the planfom area for the X-24 again confixming the tail volume ratio found.

The M A S program was used to perform some stability analysis. The moment and S i coefficientswere used to find our static m a r g i n . As discussed in the Aerodynamics section, the APAS program w a s used only for the hypersonic regime. The stablity analysis here is only for the test conditions where the HRV is practically empty of all &el. Using the appropriate CG location, the S C$6 C, curve w a s made. From the equations on the following page, the static margin can be derived fiom this graph.

Page 39 As can be seen, the value of 6 CJ S C, is the negative of the static margin. From the graph included in Appendix 7, the value of our static margin at the test conditions is around 30%. This shows that our vehicle is stable.

Page 40

Cost Analysis

A cost analysis was performed using the method described on pages 24-8 through 24-1 9 in the course text, Fundamentals of Aircraft Desian (Nicolai), with one modifica- tion. This method consists of a series of equations that determine the number of hours required for a particular aspect of the development phase. This number is then multiplied by the current cost rate for that particular aspect. For example, the equation that determines the number of engineering hours required is: where A is the empty weight, S is the maximum speed in knots, and Q is the number of a i r e d to be developed. However, this method was not developed for hypersonic cruise vehicles, so a correction hctor was introduced so that the method gave figures that was in close agreement with cost figures for the X-24C. It turned out that if the exponent of the S term is multiplied by 0.7 wherever it appears in the method, the cost estimate for the development phase is $245 million in 1986 dollars, which is close to the estimate determined by Lockheed " Skunk-Works" (NASA CR- 145274). Therefore, this 0.7 correction factor was used for the developmental cost determination of the OSU I vehicle, and a total of $465 million was found. It is important to note that this figure is 1993 dollars, and that it does not include the procurement of three GE scramjet engines.

An operational cost of $1 5 million was determined based on 60 maintenance hours per flight hour, $60 per maintenance hour, 0.45 flight hours per mission, a total of 21 0 missions, and $6 per gallon for liquid hydrogen. A cost analysis is shown in the following table.

Page 4 1 A i b e Engineering Development Support Flight Test Airplanes Engines & Avionics 37 Manufacturing Labor 5 1 , Materials & Equipment 76 Tooling 47 Quality Control 66 Flight Test Operations 66 Manufacturing Facilities 15 Subtotal Profit (9%) 37 Figure in Millions Net Total 450 of Dollars (1 993) Mission Operations 15 G r o s s Total 465 Table 3. Cost Analysis Page 42

Conclusion

From the studies and analysis described in this report, a final research vehicle was obtained. It has an overall length of 50 feet, wing span of 25 feet, take-off weight of 47,810 lbs, and empty weight of 13,600 Ibs.

A detailed analysis of the air flow into the scramjet, as well as the exhaust diffiser, needs to performed. A more detailed stability and control analysis needs to be performed, including CdCl versus M, stability and control derivatives, and control block diagrams.

Overall, the hypersonic test vehicle described in this report represents a reliable, near-term, feasible, and cost efficient means of hypersonic research. It is recommended that, in order to insure the h r e development of hypersonic cruise vehicles, this vehicle be developed and built.

Page 43 APPENDIX 1: Develo~ment of Solid Models 1. Figure 1 : Bulkhead profile 2. Figure 2: Solid object of bulkhead profile 3. Figure 3: Cut object of top bulkhead 4. Figure 4: Joined bulkhead 5. Figure 5: All bulkheads in correct z-depth position 6. Figure 6: Longerons 7. Figure 7: Longeronsjoined to hselage 8. Figure 8: Solid object of the w i n g 9. Figure 9: Vertical spares 10. Figure 10: Vertical and horizontal spares joined together 1 1. Figure 1 1 : Solid object of the vertical tail 12. Figure 12: Vertical tail structure 13. Figure 13: OSU 1 internal structure 14. Figure 14: Color Iso 15. Figure 15: Iso 1 16. Figure 16: Iso 2 17. Figure 17: 3-view drawing 18. Figure 18 : Landing gear 3. Cut object of top bulkhead 4. Joined bulkhead 5. All bulkheads in correct z-depth position

-

-

6. Longerons 7. Longerons joined to fuselage 9. Vertical spares 11. Solid object of the vertical tail 13. Hypersonic Test Vehicle's Internal Structure 16. Isometric 2 --- -

OHIO

STATE

I UNIVERSITY I

f i r

- - 18. Landing Gear NOSE GEAR: MAIN GEAR: RETRACTING RETRACTING STRUT STRUT \ 2ox6.61& 150 20 PLY PSI

r F

TOWBAR CONNECTION REARWARD RETRACTING W I N NOSEWHEEL WITH SHOCK STRUT NO LANDING OR TAXI LIGHTS NO STEERING ACTUATOR FREE 360' ROTATION WHEN UNLOCKED FORWARD RETRACTING MAlN GEAR MAXIMUM DESCENT RATE OF 21 FTISEC Page 62

A~pendix 2: Weight and Volume Figures

1. Table 2.1. I-DEAS Properties 2. Figure 2.1. Weight Pie Chart 3. Figure 2.2. Volume Pie Chart 4. Table 2.2. I-DEAS vs. PPDWAP Weight Comparison 5. Figure 2.3. Inboard Planform Table 1 . I-DEAS Properties Components Weight Volume Surface C g ( 9 ~ ~ ~ 1 Area lbs ft3 ft 2 ft Body Frame Wing (2) Frame V. Tail (2) Frame Body Skin Wing (2) Skin V. Tail Skin Scramjet Rocket Engine (3) 0 2 Fuel Tank HZ Fuel Tank Nose Gear Main Gear (2) Payload Pressure System Power Supply Avionics Empty Totals Fuels: 0 2 H2 Figure 2.1. Weight Pie Chart Fixed Engines 5% 5% Payload 2% Figure 2.2 .Volume Pie Chart Fixed Engines 3% 4% Stucture Fuel 85% Table 2. I-DEAS vs. PDWAP Weight Comparison I-DE AS PDWAP Ibs Ibs Empty Body Wing Tail Tanks Pressure System Power Avionics

VTail Leading Edge

Fuel Tanks

\\

0 2 \\ Rocket Engines A

1 Rear Gear

Payload

Leading Edge

Page 68

Appendix 3: Stress Contours

1. Configuration I (half)) 1A. Configuration I (whole) 2. Configuration 2 3. Configuration 3 4. Configuration 4A 5. Configuration 4B 6. Configuration 5 7. Configuration 6 8. Configuration 7 9. Configuration 8 10. Configuration 9 11. Configuration 9 (close-up) 1. Configuration 1 (half) 1A. Configuration 1 (whole) 2. Configuration 2 3. Configuration 3 4 , Configuration 4A 6 . Configuration 5 7. Configuration 6 8. Configuration 7 9. Configuration 8 10. Configuration Y 11. Configuration Y (close-up) Page 82

A ~ ~ e n d i x 4: Deflections

1. Configuration 1 (half)) 1A. Configuration 1 (whole) 2. Configuration 2 3. Configuration 3 4. Configuration 4A 5. Configuration 4B 6. Configuration 5 7. Configuration 6 8. Configuration 7 9. Configuration 8 10. Configuration 9 1 1. Configuration 9 (close-up) 2. Configuration 2 3. Configuration 3 5 . Configuration 4B 9 . Configuration 8

Page 94 APPENDIX 5: En~neerinp Analysis of Fusela~e Winp Bulkhead 1. Figure I : Initial bulkhead configuration and weight 2. Figure 2: Bulkhead configurations and weights for 2-5 3. Figure 3: Bulkhead configurations and weights for 3-5 4. Figure 4: Final bulkhead configuration and weight 5. Figure 5: Fuselage and wing bulkhead connection 6. Figure 6: Loads on wing clamp 7. Figure 7: Restraints on fuselage wing bulkhead Figure 1 : Initial Bulkhead Configuration and Weight Figure 2 : Bulkhead Configurations and Weights for 2-5 * 0

-

Figure 3 : Bulkhead Configurations and Weigh& for 5-9 > a I 2 Figure 4 : Final Bulkhead Configuration and Weight

PIN . - >

Figure 7 : Restraints on Fuselage Wing Bulkhead

Page 102

Appendix 6: Force Calculations

Lift, Drag. and Moment Determination The lift over a wing is not evenly distributed, and it was hoped that the actual lift and drag distributions over the wing could be obtained from a computer program.

However, this program was not available soon enough to be of any use. This meant that for the sake of simplicity the lift force is assumed to be evenly distributed over the wing. A ramp distribution over a spanwise cross section is also assumed. With these simplification, the determination of the forces and moments follows: Equilibrium Equations at Cruise:

= 1/4 * L = 16,680.83

(this is due to the lifting-body configuration)

L , = &, / 2 = 8,340.4 (lift on one wing)

1 1 L ' is the lift contribution due to the shaded region Lift force L' is distributed as follows: A, = 80% of the lift A, = 20% of the lift Determination of Equivalent concentrated loading.

L F i n A x i s 3 4 !

A l l the forces shown are directly carried by the wing clamp. Fc represents the force carried by the pin, which in turn is transmitted to the clamp. A l l of the moment is assumed to be carried by the clamp. The resulting equations follow: The drag force is represented by distributing a force on the upper and lower front sides of the clamp along the axis of the pin. Hence, In the actual application of the forces in I-DEAS, FA, FB, and FD are distributed along a line. If F , was finite it would be distributed over and area. The loading condition for a l l the configurations is as follows: With a load factor of 9,

Lm = n * L ' = 9*(1,390.1) = 12,510.9 N

The maximum moment is The drag force is calculated using the ratio of the wing area over the total area S , = 297.29 m S , = 20.3 m (area of one wing)

D , = S , / S , * T

(drag on one wing) D , = 1,401.2 N The drag on the wing is evenly distributed between the 6 rear fuselage bulkheads D* = D , I 6 = 233.53 N

D , , = n * D ' = 9*(233.53) = 2,101.8 N

solving the equations, P a p 108

A ~ ~ e n d i x 7. Aerodynamic Characteristics

1. Figure 7.1. Configuration Trade Studies - W D vs alpha (Config 1,2,3,4,5)

2. Figure 7.2. Configuration Trade Studies - UD vs alpha (Config 1,6,7,8)

3. Figure 7.3. Configuration Trade Studies - Cm vs alpha (Config 1,2,3,4,5)

4. Figure 7.4. Configuration Trade Studies - Cm vs alpha (Config 1,6,7,8)

5. Figure 7.5. Cm vs alpha (M = 4, 6, 12) 6. Figure 7.6. C 1 vs alpha (M = 0.3,0.6, 0.9) 7. Figure 7.7. Cl vs alpha (M = 4, 6, 12) 8. Figure 7.8. C1 vs Cd (M = 0.3,0.6, 0.9) 9. Figure 7.9. Cl vs Cd (M = 4, 6, 12) 10. Figure 7.10. UD vs alpha (M= 4,6, 12) 11. Figure 7.11. Cdo vs .Mach Number 12. Figure 7.12 dCmtdC1 vs Mach Number 13. Conformal Temperature Map

Figure 7.1. Configuration Trade studies - L/D vs alpha

- Original

- Forward Hump

- Wlng 5 deg

dihedral

- V T 5 degout

- VT 5 degin

Figure 7.2. Coniiguration Trade Studies : L/D vs alpha

2.5 T

- Original

- Wing -5 deg

- Wing -10 deg

- Wing - 15 deg

Figure 7.3. Configuration Trade Studies : Cm vs alpha

- Original

- Forward Hump

- Wing 5 deg

dihedral

- VT 5 deg out

- VT 5 deg in

Figure 7.4. Configuration Trade Studies : Cm vs alpha

0.04 T

- Original

- Wing -5 deg

- Wing -1 0 deg

- Wing -1 5 deg

Figure 7.5. Cm vs alpha Figure 7.6. C1 vs alpha Figure 7.7. C1 vs alpha Figure 7.8. C1 vs Cd Figure 7.9. C1 vs Cd Figure 7.1 0. L/D vs alpha Figure 7.1 1. Cdo vs Mach Number Figure 7.12. dCmIdC1 vs Mach Number Page 122

A~pendix 8. Traiectorv

1. Figure 8.1. Weight vs Time 2. Figure 8.2. Rate of Climb vs Mach Number 3. Figure 8.3. Altitude vs Distance 4, Figure 8.4. Thrust Available and REquired vs Mach Number 5. Figure 8.5. Altitude vs Mach Number 6. Figure 8.6. T h r u s t Available vs Altitude 7. ETO Input Listing

Figure 8.1. Weight vs Time

Figure 8.2. Rate of Climb vs Mach Number

Figure 83. Altitude vs Distance

Figure 8.4. Thrust Available and Required vs

Mach Number

-

120000

_ _ _ _ _ _ _ _ -----------------

-- 100000 /#- // / / /

/ ' Thrust Available

/ / 80000 --

I i

I -- J

Figure 8.5. Altitude vs Mach Number

Figure 8.6. Thrust Available vs Altitude

7. ETO Input Listing INPUT DATA FILE "SORT.DATW/5MAY93/ROCKET SSTO PROGRAM ETO TABLE XISPA 0 0 0 0 0 1 4 0 0 0.0, .9,1.5,15.0 4000, 3000,2000,1000 TABLE XPHrMAx O,O,~,O,O

134 ,o ,o

0.0,.9,1.5,15.0 1.0,1.0,1.0,3.0 TABLE XCDO O,O,~,O,O 1,14, 0 ,O ~.0,~.1,0.3,0.5,0.7,0.9,1.1,1.3,1.5,2.0,4.0,6.0,8.0,10.0,12.0 0.0,.00549,.00533,.00566,.0063 1,.00723,.02737,.00884,.00809,.00704,.00523,.00453 .00418,.00398,.00385 TABLE XDELCD ~,~,O,O,O 1,13,0 ,O 0 . 0 , lOOO., llOOO., 21000., 31000., 41000., 51000., 61000., 71000., 81000.

91000.,101000.,111000.

0.0,0.002 1,0.0022,0.0022,0.0023 ,0.0024,0.0026,0.0027y0.0029,0.0030,0. 0032 0.0035,0.0037 TABLE XCLALPHA

o,o,o,o,o

1,15, 0 ,0 0 . 0 , 0 . 1 , 0 . 3 , 0 . 5 , 0 . 7 , 0 . 9 , 1 . 1 , 1 . 3 , 1 . 5 , 2 . 0 , 4 . 0 , 6 . 0 , 8 , 0 , 1 0 . 0 , 1 2 . 0 .005,.005,.005,.005,.005,.005,.010,.008,.008,.008,.009,.007,.006,.006,.006 TABLE XK ~ , ~ , ~ , O , O 1 , 1 5 ,O ,O 0.0,0.1,0.3,0.5,0.7,0.9,1.1,1.3,1.5,2.0,4.0,6.0,8.0,10.0,12.0 3.3855,3.3855,3.4036,3.4413,3.5027,3.5965,2.0971,2.2433,2.3399,2.3243,2.1479 2.6083,2.8917,3.0752,3.1992 TABLE XAOAC O,O,~,O,O 2,4,3,0 0.0,0.8,1.0,15.0

-1o.o,o.o, 10.0

80.0,.15,.15,1.0 80.0,.15,.15,1.0 80.0,.15,.15,1.0 TABLE XISPR ~,~,O,O,O 1,12,0,0 1000.0, 11000.0, 21000.0,31000.0, 41000.0, 51000.0,61000.0, 71000.0 81000.0, 91000.0,101000.0,111000.0 308.5,341.9,366.3,383.6,395.4,402.9,407.5,410.3,412.1,413.2,413.8,414.3 TABLE XWDOTPMAX O,O,~,O,O 194 ,o ,o 0.0,2.0,8.0,13.0 245.783,245.783,245.783,245.783 AIRBREATHER AC AREF FASTOIC 0.0, 625.0, .0292 VEHICLE WLAUNCH WFUEL WFINAL VFINAL STAGE 47810., 33750., 14060., 11981., 1 INITIAL CONDITIONS- M O H O GAMMA ALPHA DT DELPRINT TIMEX 0.001 ,O.OOl ,o.o ,o.o ,o.s ,lo ,o.o PHASE 1 WAKEOFF 350.0 PHASE 2 ALPHAZMAX LOADFAC GAMMAMAX ACCCOMD V02 H02 25.0 ,6.0 ,45.0 , 9.0 , 900.0 , 3000.0 PHASE3 ALPHAMIN ALPHAMAX QOCOMD VOTEMP QOFINAL GAINQ3 GAINGAM3 -15.0 ,10.0 , 549. , 900.0, 820. ,10.0 ,1.0 PHASE 4 - - - - - - SWITCH4 VOCRUISE GAINH04 GAINGAM4 GAINQ4 0 ,O.O ,-20.0 ,O.O ,5.0 PHASE 5 - SWITCH5 V05 ALPHASMAX GAMMA5 ACCCOMDS ENDFILE1 1 , 899.0 ,25.0 ,54.00 ,9.0 ,9999 Page 13 1

A ~ ~ e n d i x 9: Dynamic Analysis of the Wing

1. Figure 9.1. FEM on Wing 2. Figure 9.2. Fist Natural Frequency and Mode Shape 3. Figure 9.3. Second Natural Frequency and Mode Shape 4. Figure 9.4. Third Natural Frequency and Mode Shape 5. Figure 9.5. Fourth Natural Frequency and Mode Shape Figure 1 : FEM on Wing Figure 2 : First Natural Freq. and Mode Shape Figure 3 : Second Natural Freq. and Mode Shape OlVolNAL PAGE IS Of K K l R QUALITY Page 151

A~pendix 10. Prooeram Listings

1. Propulsion Trade Study 1 2. Propulsion Trade Study 2 3. Glide Program 4. ETO Sort Program Propulsion Trade Study 1 program a5 15; const tsfch = 8.4; tsfcj = 12.2; dh = 19.97; djp = 64.29; Id = 2.5; var iv, fv,gw, t s, tavai1:real; procedure fbelwt (tsfc,den,iv,fv.gw,ts,tavail:rd); var f v,acc,wyfkt,accg: real; begin v:=iv; t:=o; w:=gw; w:==o; acc:==(tavail-wAd)/w*32.2; writeln ('time acc vel g fbelwt'); accg:=acc/32.2; writeln (t:7:2,acc:7:2,v: 1 0:2,accg:7:2,&:9: 1); while v<fk do begin t:=t+ts; acc:=((tavail-wAd)/w*32.2+acc)/2; accg:=acc/32.2; v:=v+acc*ts; w:w-tsfd3600*tavail:*ts; ftvt:=fwtYsfc/3600*tavail*ts; writeln (t:7:2,acc:7:2,v: 10:2,accg:7:2,fk&:9: 1); end; writeln; writeln ('Fuel Weight: ',fwt:9:0,' Ibmass'); writeln (Empty Weight: ',w:9:O,' Ibmass'); writeln ('Fuel Fraction: ',(gw-w)/gw:5:3); writeln ('Fuel Volume: ',(gw-w)/den: 7:2,' ftA3'); writeln; writeln ('Hit Enter to Continue'); readln; end; begin write ('Input Initial Velocity: '); readln (iv); write ('Input Final Velocity: '); readln ( f i ) ; write ('Input T h r u s t Available: '); readln (tavail); write ('Input Gross Weight: I); readln (gw); write ('Input Time Step: I); readln (ts); writeln; writein ('Hydrogen Oxygen Rocket'); writeln; fbelwt (tsfch,dh,iv, kgw, ts-tavail); writeln; writeln ( ' J P Oxygen Rocket'); writeln, fhelwt (tsfcj,djp,iv,fv,gw,ts,tavail); end.

Propulsion Trade Study 2 program a5 1 5; const tsfch = 9.83; tsfcj = 12.2; dh = 19.97; djp = 64.29; Id =1.5; procedure helwt (tsfc,den,iv, fv,gw,ts, tavail 1 , theta:real); vaf f v,acc,w,fivt,accg,h,dhdt: real; begin v:=iv; t:=o; w:=gw; fivt:=o; h:=o; acc:=(tavaill -wAd)/w*32.2; writeln ('time acc vel g fbelwt'); accg:=acc/32.2; writeln (t : 7:2,acc:7:2,v: 10:2,accg:7:2,fivt:9: l,h:8:0); while v<ft do begin t:=t+ts; te:-5 18.69-h*3.58e-3; if@ > 37500) and (h < 65000) then te:=389.97; ifh > 65000 then te:=389.97+5.45e-4*h; p:=2.1162e3 *exp(-32.U1716/te*h); tavail:=tavaill-p*3.977; acc:=((tavail-w*cos(theta~d-w*sin(theta))/w*32.2+acc)/2; dhdt:v*sin(theta); h:=h+dhdt*ts; accg:=ad32.2; v:=Y+acc*ts; w:w-245.76*ts; fwt:=finrt+245.76*ts; writeln (t:7:2,acc:7:2,v: 10:2,accg:7:2,fivt:9: l , h : 8 : 0 , t a v a i l : 8 : 0 , p : 5 : 0 , t e : 4 : 0 ) ; end; writeln; writeln ('Fuel Weight: ',fwt:9:0,' Ibmass'); writeln ('Empty Weight: ',w:9:O,' Ibmass'); writeln ('Fuel Fraction: ',(gw-w)/gw : 5 :3); writeln ('Fuel Volume: ',(gw-w)/den:7:2,' AA3'); writeln; writeln ('Hit Enter to Continue1); readln; end; begin write ('Input Initial Velocity: I); readln (iv); write ('Input Final Velocity: '); readln (fir); write ('Input Thrust Available: '); readln (tavail); write ('Input Gross Weight: '); readln (gw); write ('Input Time Step: '); readln (ts); write ('Input climb angle: 3; readln (theta); theta:=theta*3.14 15/180; writeln; writeh (Wydrogen Oxygen Rocket'); writeln, fbelwt (tsfch,d4iv,fi,gw,ts,tavai1,theta); writeln; writeln ('JP Oxygen Rocket'); writeln; firelwt ( t s f c j , d j p , i v , f i , g w , t s , t a v a i l , t h e t a ) ; end.

Glide Program PROGRAM GLIDE .

IMPLICIT DOUBLE PRECISION (A-G,K-Y) DOUBLE PRECISION ALT(112),P(112),~(1-12),~~(25,20,7) + ,CD(25,20,7) DOUBLE PRECISION ALMAX(25,20) INTEGER H,I,J,Z,IqZF OPEN(UNIT= 1 ,FILE='ATMOS.DAT', STATUS"OLD') OPEN(UNIT=4,FILE='MOD 1 .DATf, STATUS='OLD1) OPEN(UNIT=7,FILE='AOvTl .DAT,STATUS='OLD') OPEN(WT=~,FILE='MOD~.DAT',STATUS='OLD') OPEN(UNIT=3 ,FILE='AOUT2.DAT1, STATUS='OLD') PI=3.14 1 592654DO -(6,10) 10 FORMAT(ENTER TIME INCREMENT: ') READ(5,') DT DATA G~G,R,ZF/l.387D0,3.216D+1,1.716D+3,1/ DATA S,MUR,B,TIME,W6.25D+2,2D-1,2.5D+l,1.97D+2,8.5D-l/ AR=B *B/S DO 30 1=1,12 DO 28 J=1,8 READ(7, *) DU49,XM9,ALMAX(/J),LDMX,CDO9$5TOT DO 27 H=1,6 READ(4, *)DUANE4,XM 1 ,ALPHAg,CL(I, J,H),CD(I, J,H) + ,CLCD,EE59 27 CONTINUE 28 CONTINUE 30 CONTINUE READ(7,*) ENDM READ(4, *) ENDM2 WRITE(6,*) ENDM,ENDM2 CLOSE(UNIT=7) CLOSE(UNIT=4) DO 60 I=1,12 DO 58 J=9,14 READ(3, *) D4,XM9,W(I,J),LDMX,CM)9,ESTOT DO 57 H=1,6 READ(2, *)DUANE4,XMl ,ALP,CL(I, J,H),CD(I; J,H)

+ ,CLCD,EE59

57 CONTINUE 58 CONTINUE 60 CONTINUE READ(3, *)ENDM READ(2, *)ENDM2 WRITE(6, *)ENDM,ENDM;!

CLOSE(UNIT=3) CLOSE(UNIT=2) DO 100 I=l,lll

READ( 1 ,*I LT(I),T(I),P(I),RHO

100 CONTINUE CLOSE(UNIT=l ) OPEN(UNIT= 1 ,FILE='DEC .DAT',STATUS='UNKNOW) DO 99 I=1,12

LMAx(1, 1 S)=ALMAX(I, 14) -

DO 98 2=1,6 CL(1,l S,Z)=CL(I, 14,Z) CD(1,l S,Z)=CD(I, 14,Z) 98 CONTINUE 99 CONTINUE DO 96 I=1,12 DO 97 J=1,15 CYI, J, 7)=CL(I, J,6) CD(I, J,7)=CDKJ,6) 97 CONTINUE 96 CONTINUE TR=ODO DATA THETMX,THET, W/ODO,ODO, 1.3 7D+4/ DATA ALFMyT~~TMN,M,Y,X/2.4D+ 1,-8D-2,1.2D+l,l.O64256D+5, + 1.21314D+6/ Vl=M*DSQRT(GAMA*R*T(lOl)) V W D O VX=Vl L=W 80 IA=INT(Y/lOOO)+ 1 MIA=Y/ 1000-IA+ 1D O IF(Y.LT. lD+l)GOTO 500 PI =P(IA)+MIA*(l'(IA+ 1 )-P(IA)) T 1 =T(IA)+MIA*(T(IA+ 1 )-T(IA)) RHO=P 1 /R/T 1 I=XNT((Y- 1 D+3)/ 1 D+4)+ 1 MI-- 1 D+3)/ 1 D+4-I+ 1D O IF(Y.LT. lD+3)THEN I= 1 MI=ODO ENDIF IF(M.LT. 1.5DO)THEN J=M((M- 1 D- 1)/2D- 1)+ 1 MJ=(M-ID-1)/2D-I-J+lDO ELSEIF(M.LT.2DO)THEN J=8 MJ=(M- 1.5DO)ISD- 1 ELSE J=INT((M-2D0)/2D0)+9 MJ=(M-2D0)/2DO-J+9 ENDIF AL 1 = A L W ( I , J)+M* (ALMAX(I+ 1, J)-ALMAX(1, J)) ALFA=AL 1 +MJ* (ALMAX(1, J+ 1)-ALMAX(1, J)) F(THET. GT. THETMX)THEN ALFA=ODO ELSEIF(THET.LT.THETMN)THEN ALFA=ALFMX ENDIF Z=INT(ALFA/SDO)+ 1 MZ=ALFA/SDO-Z+ ID0 CL2=CL(I, J,Z)+MI*(CL(I+ 1 ,J,Z)-CL(I,J,Z))/3DO CL32CL2+MJ*(CL(I, J+l ,Z)-CL(I, J,Z))/3DO CLA=CL3+MZ*(CL(I, J,Z+ 1 )-CL(I,J,Z))/3DO CD2=CD(I, J,Z)+M*(CD(I+ 1, J,Z)-CD(1, J,Z))/3DO CD3tCD2+Ur*(CD(/J+lyZ)-CD(1, J,Z))/3DO CDA=CD3+MZ*(CD(I, J,Z+ 1 )-CD(1, JYZ))/3DO CLl-CLA IF(THET. GT. THETMX)THEN CL14DO ELSEE(THET.LT.THETMN)THEN CLI=CLA ENDIF CDIKDA IF(M.LT. 1 .ODO.AND.ALFAGT.ODO)THEN CL1=4,5D-1 CD1=9.OD-2 ENDIF IF(Y.LT. 5. 5D+4)THEN THETMN=3.7D-2 THETMX=ODO ENDIF IF(Y.LT. 1D+3)THEN FI=(l6DO*Y/B)**2 CDI=CDA-~DO/(~DWFI)*CL~ *CLl/PI/E/AR THETMN=2.9D-2 THETMX=ODO F(Y.GT.SD+l)THEN TSO=TIME X50=X V50=Vl ENDIF

ma=

QO=RH012DO*Vl *V1 L=RH0/2DO*Vl *V1 *S*CLl D=RH0/2DO*Vl*VI*S*CDl AL=ALFA*PI/l .8D+2 AX=G/W*(TR*DCOS(THET+AL)-D*DCOS(THET)- + L8DSIN(THET)) AY=G/W *(TR*DSIN(THET+AL)-D*DSIN(THET)+ + L*DCOS(THET))-G X=X+(VX+VX+AX*DT)/2DO*DT Y=Y+(VY+VY+AY*DT)/2DO*DT VX=VX+AX*DT VY=VY+AY *DT Vl=DSQRT(VX*VX+VY*VY) M=Vl/DSQRT(GAMA*R*Tl) A=DSQRT(AX*AX+AY *AY) THET=DATAN(VYNX) TIME=TIME+DT IF(ZF.EQ. 1)THEN WRITE(1,300) TIME,M,Y,X/6.0761033D+3,TR,Q0,ALFA,VY7W + , m , D 300 FORMAT(F6.1,1X,F6.3,1X,F7.0,1X,F6.2,lX,F7.0,1X,F6.1,1X, + F4.1,1X,F6.1,1X,F7.1,1X,F6.3,lX,F7.1) ZF=2 ELSE

m=1

ENDIF GOT0 80 500 OPEN(UMT=2,FILE=TSUM.DAT,STATUS=ZMKNOWN') Y=ODO VY=ODO DATA CLAL, ALDOTII .8D-2,-8.33DOI Pl=P(l) TI=T(l) TR=ODO RHO=P l/R/T 1 FI=ODO TL=TIME XL=X VL=VX 40 IF(J.LT. 1)THEN J= 1 ENDIF ALFA=ALFA+ALDOT*DT CLTO=ALFA*CLAL J=INT((M- I D- 1 )lZD- 1 )+ 1 CDTO=CD( 1, J, I ) D=RHOIZDO*VX*VX* S '(CDTO- 1 DOl(1 DO+FI)*CLTO*CLTOlPWAR) L=RHO/ZDO*VX*VX*S*CLTO QO=RHO*VX*VX/2DO IF(VX.LT. 1 D0)GOTO 888 IF(ALFA. GE. 1 D-3)THEN TND=TIME

m = x

VND=VX ELSEIF(ALFA.LT. ID3)THEN ALDOT=ODO ALFA=ODO ENDIF IF(ZF.EQ. 1)THEN ELSE ZF=l ENDIF AL=ALFA*PVl .8W2 AX=G/W*(-D-MUR*(W-L)) DVX=DTVAX X=X+(DVX+VX+VX)l2DO*DT TIME=TIME+DT VX=VX+DVX M=VX/DSQRT(GAMA*R*Tl) GOT0 40 888 WRITE(2,65) V50,XL-XSO,VL,XND-XL,VND,X-XND,X-XSO 65 FORMAT('VSO= ',F7.2,5xXAP.. ',F6.0,5X,'VL= ',F7.2,5X, + XROLL= ',F6.0,/,'VND= ',F7.2,5X,XBR= ',F6.0,5X, + %AND= ',F6.0) STOP END ETO Sort Program PROGRAM SORT IMPLICITDOUBLEPRECISION (A-G,K-2) DOUBLE PRECISION ALT(I12),P(112),~(112),CL(25,20,7) + ,CD(25,20,7),ZEE5(25,20,7),DU4(25),~(20),CD0(25,20) + ,ALPHA(~),K(~O),DELCD(~~),CLAL(ZO),XSP(~~),T~(~~) INTEGER H , I , J OPEN(UNIT= 1 ,FILE='ATMOS.DAT',STATUS='OLD') OPEN(UNIT=4,FILE='MOD3 .DAT, STATUS='OLDt) OPEN(UNIT=7,FILE='AOUT3 .DAT',STATUS='OLD') OPEN(UNIT=2,FILE=MOD4.DAT',STATUS='OLD') OPEN(UNIT-3 ,FILE='AOUT4.DAT1,STATUS='OLD') OPEN(UNIT=6,FILE=WSFOR\SORT. 144',STATUS=ZMKNOW) PI=3.14 1592654D0 1 0 ) 1 0 FORMAT('MPUT DATA F I L E "SORT.DATW/5MAY93/ROCKET SSTO' + ,/,'PROGRAM ETO'J,TABLE X I S P A ' J , ' O 0 0 0 0 ' + 1 4 0 O'/'O.O, .9,1.5,15.01) - ( 6 7 1 1 ) 11 FORMAT('4000, 3000,2000,1000',/,TABLE XPHIMAIC,/, +'0,0,O,0,Ot,/,'1,4 , O , 0 ' , / , ' 0 . 0 , . 9 , 1 . 5 , 1 5 . 0 ' , / , ' 1 . 0 , 1 . 0 , 1 . 0 , 3 . 0 ' + ,/,TABLE XCD0',/,'0,0,0,0,0',/,'1,14,0,0') DO 30 I=1,12 DO 28 J = 1 , 8 READ(7,400 1 ) DU4(I),XM(J),ALMAX,LDMX,CDO(I,J),E5TOT 400 1 FORMAT(F8.1 ,F7.4,F6.3,F6.3,

+ F8.5,F7.4)

DO 27 H=1,6 READ(4,26)DUANE4,XMl ,ALPm,CWJ,H),CDO,J,H) + ,CLCD,ZEES(I,J,H) 26 FORMAT(F8.1 ,F7.4,F7.2,F7.3,F7.3,F7.3,F9.5) 27 CONTINUE 2 8 CONTINUE 30 CONTINUE CLOSE(UN1T-7) CLOSE(UNIT=4) DO 60 I=1,12 DO 58 J=9,14 READ(3,403 1) D~,XM(J),ALMAX,LD~CDO(I,~,E~TOT 403 1 FORMAT(F8.1 ,F7.4,F6.3,F6.3,

+ F8.5,F7.4)

DO 57 H=1,6 READ@, 561DUm4,XM 1 ,ALP,CL(I, J,H),CD(1, J,H) + ,CLCD,ZEES(I,J,H) 5 6 FORMAT(FS.l,F7.4,F7.2,F7.3,F7.3 + ,F7.3,F9.5) 57 CONTINUE 58 CONTINUE 60 CONTINUE CLOSE(UNIT=3) CLOSE(UMT=2) D O 1001=1,111 READ( 1, *) A L T ( I ) , T ( I ) , P ( I ) , R H O 100 CONTINUE CLOSE(UNIT= 1) WRITE(6,lO 1) (XM(J), J= 1 , 1 4 ) 1 0 1 FORMAT('0.0,1,12(F3.1,1,'),F4.1,~F4.1) WRITE(6,lOZ) (CDO(1, J ) , J=l ,14) 102 FO~~AT~O.O,~10(F6.5,','),F6.5,/,2(F6.5,1,1),F6.5,/, + TABLE XDELCD',/,'O,O,O,O,O',/,'1,13,0 ,O') DO 210 J=1,14 CDN= 1 D+2 DO 200 H=1,6 I F ( C D ( 1 , J,H).LE. CDN)THEN K(J)=ZEES( 1 9 J,H) ENDIF 200 CONTINUE 210 CONTINUE DO 220 I=1,12 DSUM=ODO DO 215 J=1,14 DO 2 1 1 H=1,6 DCD=CD(I, J,H)-K(J)*CL(I,J,H)**2DeCDO(l, J) DSUM=DSUM+DCD 211 CONTINUE 215 CONTINUE DELCDO=DSUM/8.4D+l 220 CONTINUE WRITE(6,240) @U40,1=1,12) 240 F O R M A T ( ' 0 . 0 ' , 9 ( : ' , F 7 . 0 ) , / , 2 ( F 7 - O , ' , ' ) , F 7 . 0 ) WRITE(6,250) @ELCD(JJ,I= 1 , 1 2 ) 250 F O R M A T ( ' O . O ' , l O ( ' , ' , F 6 . 4 ) , / , F 6 . 4 , ' , ' , F 6 . 4 , / , T A B L E XCLALPHA1 + ,/,'0,0,O,0,O1J,'1,15 , 0 ,0 ' ) DO 270 J=1,14 CASUM=ODO DO 265 I=1,12 CAL=(CL(I, J , S ) - C L ( I , J , l))/(ALPHA(s)-mHA(1)) CASUM=CASUM+CAL 265 CONTINUE CLAL(J)=CASUM/l.25 1 270 CONTINUE WRITE(6,280) (XM(J), J= 1,14) 280 FORMAT('O.O,',12(F3.1,','),F4.1,',',F4.1) WRITE(6,290) CLAL( 1 ) , ( C L A L ( J ) , J= 1 , 1 4 ) 290 FORMAT(F4.3,14(',',F4.3),/,TABLE XK',/,'O,O,O,O,O',/,

+ ' 1 , 1 5 ,o , O ' )

WRITE(6,300) (XM(J),J=l, 1 4 ) 300 FORMAT('0.0,',12(F3.1,','),F4.1,',',F4.1) W R . I T E ( 6 , 3 10) K ( l ) , ( K ( J ) , J = l , 1 4 ) 310 F O R M A T ( F 6 . 4 , 1 0 ( ' , ' , F 6 . 4 ) , / , F 6 . 4 , 3 ( ' , ' , F 6 . 4 ) , / , + TABLE XAOAC',l,'O,O,O,O,O',l,'2,4,3,0',/, + '0.0,0.8,1.0,15.0',/,'-10.0,0.0,10.0',/,'80.0,. 1 5 , . 1 5 , 1 . 0 1 ) WRITE(6,320) 320 FORMAT('80.0,.15,.15,1.0',/,'80.0,.15,.15,1.0',1, + TABLE X I S P R ' J , ' O , O , O , O , O ' , / , ' l ,12,0,01) DO 340 I=1,12 IC=(I-1)*10+1 TR=3.4D+4-P(IC)/4DO*PI*(2.8D+111.2D+1)**2DO XISP(I)=TR/S. 192771 084D+1 ALT 1 (I)=ALT(IC) 340 CONTINUE WRITE(6,3 50) (ALT 1 (I),I= 1 , 1 2 ) 350 FORMAT(F8.1,7(',',F8. 1 ) , / , F 8 . 1 7 3 ( ' , ' , F 8 . 1 ) ) WRITE(6,360) (XISP(I),I=l, 1 2 ) 360 FORMAT(F5.1,ll ( ' , ' , F S . l),/,TABLE XWDOTPMAlC,I,'O,O,O,O,O'J + , ' 1 , 4 ,O ,0'J,'0.O,2.O78.0, 13.0',/,245.783,245.783,245.783', + ',245.783',/,'AIRBREATHER 'J,'AC AREF FASTOIC') WRITE(6,3 70) 370 FORMAT('O.0, 625.0, .0292',/,'VEHICLE 'J7 + W L A U N C H WFUEL WFINAL VFINAL STAGE1,/,

+ '48000., 35000., 13000., 11981., 1 ' )

WRITE(6,380) 380 FORMAT('IMT1AL CONDITIONS-'J, + 'MO H O GAMMA ALPHA DT DELPRINT TIMEXJ,

+ '0.001 ,0.001 ,O.O ,o.o , 1 . 0 ,10 , O . O ' )

WRITE(6,390) ' , I , WAKEOFF'J,'3 7 5 . 0 ' , 1 , 390 FORMAT('PHASE 1 + 'PHASE2- ' I

+ ' A L ~ H / U ~ L O ~ F A C GAMMAMAX ACCCOMD V02 H02')

WRITE(6,400) 400 FORMAT('20.0 ,8.0 ,30.0 ,9.0 , 900.0 , 18~o.0'J3 + 'PHASE3--- ' 1 9 9 + 'ALPHAMIN ALPHAMAX QOCOMD VOTEMP QOFlNAL GAINQ3 GAINGAM3') WRITE(6,4 10) 410 FORMAT('-5.0 ,5.0 , 549. ,1200.0,2305. ,10.0 ,1.0',/, + 'PHASE 4- ' / 9 , + 'SWITCH4 VOCRUISE GAINHO4 GAINGAM4 GAlNQ4') WRT'IE(6,420) 420 FORMAT('0 ,0.0 ,-20.0 ,0.0 ,5 .O1,/,'PHASE 5-'1, + 'SWITCH5 VOS ALPHASMAX GAMMAS ACCCOMDS ENDFILE1 ',I,

+ '0 ,o.o ,o.o ,o.o ,o.o ,9999')

STOP END