Hypersonic Aircraft Design Concept - FastForward Project

Space Express: Hypersonic Aircraft

Design Concept

Edward Conbeer Daniel Cummins Jonathan Glass Andrew Mackowski Rochelle Mellish Simon Plucinski (Team Lead) Caroline Teichner Alex van Hoek Brandon Vigil Joseph Vogel Zhen Xia (Team Lead)

In fulfillment of MAE 332 Aircraft Design requirements Princeton University

Spring 2007

Table of Contents

1. Configuration- Simon Plucinski 2. Requirements Compliance Matrix- Zhen Xia 3. Performance and Sizing- Jonathan Glass 4. Aerodynamics- Ted Conbeer and Andrew Mackowski 5. Propulsion- Daniel Cummins and Joe Vogel 6. Aerothermal Analysis- Alex van Hoek 7. Structural Analysis- Zhen Xia and Brandon Vigil 8. Mass Properties- Rochelle Mellish 9. Stability and Control- Jonathan Glass and Andrew Mackowski (integrated with Andrew’s 4) 10. Market and Cost Analysis- Caroline Teichner For introduction and conclusion, please see powerpoint presentation.

Simon Plucinski

Configuration

The objective of the configuration section was to coordinate all the aerospace design disciplines to evolve a design to a point that the vehicle would close and complete the mission in a most fuel efficient and cost effective manner. While the ideal shape for a hypersonic vehicle is one as close to a flat plate as possible, volumetric efficiency was given a relatively high priority to reduce the vehicle’s weight as long as it did not severely hurt aerodynamic efficiency. Limiting thermal stress was a very high priority as well, which was the primary reason for choosing the parabolic shape of the planform. While in the back of the mind, production costs were not given a high priority in the vehicle design; hence, things like flat-wrapping were not considered during the design process. The approach to the configuration design was quite organic. Since most of our analyses were automated by code, a configuration could designed, tested, and then improved a number of times. Performance analysis relying on an aerodynamic database and a propulsive database could accurately predict whether a given concept would work or not. Because of the accuracy of our aerodynamic code in predicting aerodynamic efficiency (as later corroborated by the CFD analysis), we were able to optimize the structure using only engineering analysis so that when it came time to run the model through CFD, the model produced very good aerodynamic values. Key features of the design include an unconventional one vertical tail, drooping horizontal tails, and a particularly innovative nozzle design. As mentioned previously, volume maximization was given a relatively high priority for our configuration. Recognizing that the leading edge of the vehicle must by nature be sharp, the thing most limiting the maximization of our volume was base drag that would be created by abruptly cutting the trailing edge of the vehicle.

I circumvented this problem by recognizing that the nozzle region of the airplane would not experience base drag, no matter how aircraft ended, because high pressure exhaust would prevent base drag. This realization made me realize that aligning the nozzle with the freestream flow as drawn in the above figure without tapering down to the leading edge at the aft plane would maximize volume without any drag penalties. Aligning the surface of the nozzle with freestream flow had the added benefit of exposing the vertical tail to completely undisturbed flow, increasing its effectiveness and excusing us from the structural nightmare of securing two outboard vertical tails. The nozzle was rounded for structural reasons (avoid corners) as well as for aesthetic reasons. The nozzle has side walls which prevent exhaust spillage (which would cause thrust penalties).

Base drag

The vehicle is an accelerator that can fly at a low angle of attack (2 degrees) or it can be a cruiser that flies at a higher angle of attack – this dual functionality is thanks to its waverider-like geometry, which produces a very high L/D ratio for hypersonic speeds. The vehicle has the ability to droop its horizontal tails for high q flight. This is to decrease lift, allowing us to fly at an angle of attack that provides sufficient inlet capture area for the engine. For low q flight, the horizontal tails would not be drooped to provide maximum lift. Wing drooping has the added benefit of the XB-70 drooping winglets – that is to increase stability for high q flight (the drooped horizontal tails effectively act as two more vertical tails).

Zhen Xia

Requirements Compliance Matrix The following compliance matrix was compiled based on requirements specified in the initial design requirements distributed at the beginning of the semester.

Parameter Requirement Our Design Maximum Range 7000 nautical miles >7000 nautical miles Maximum Flight Time <3 hrs 1 hr 24 min Accommodation 2 crew members,

10 passengers 2 crew members, 10 passengers

Structure +- 3 g’s, 2000 psf, SF 1.5 met through structural analysis (see presentation)

Take off and Landing Speed 180 knots 132 knots Balanced Field Length 10,000 ft sea level conditions 1640 ft Sonic Boom No sonic boom except

atmospheric re-entry enters supersonic and hypersonic flight over ocean.

Passenger Ticket Price <$100,000 one way <$200,000 round trip

~$25,000 one way

Development time 10 years 10 years

Jonathan Glass

Performance The vehicle was analyzed for three flight paths. The first included an exo-atmospheric trajectory, the second a period of cruise and the third reached low earth orbit. All flight data is summarized in the chart below. The cruiser and exo-atmospheric vehicles have been closed for 7000 nm. Note that these are simply a few of many possible closing weights and speeds and do not represent optimal closures.

Flight Plan Stages Balanced Field Length

Max Mach

Max dynamic pressure

Take off Weight

Time Max Height

T.O. Speed

Exo-Atmospheric

1 0.55 km 14.4 2200 psf 118000 kg 1:24 913 km 180 knots

Cruiser 1 0.54 km 4.9 2024 psf 125850 kg 2:38 29.12km 185 knots

Orbiter 2 N/A 24.8 4444 psf 50000 kg (orbiter)

N/A N/A N/A

General flight paths: Exo-Atmospheric: Horizontal take-off, accelerate to 2000 psf, accelerate to Mach 8, pull up to 39 degrees, accelerate to max mach number, follow ballistic path, fall back to atmosphere, and maximum efficiency glide. Cruiser: Horizontal take-off, accelerate to 2000 psf, accelerate to max mach, energy climb to max altitude, cruise, and maximum efficiency glide. Orbiter: Conventional aircraft releases at 30,000 ft, accelerate to 2000 psf, accelerate to Mach 8, pull up to 39 degrees, accelerate to max mach number, orbit. Early indications show that a two stage orbiter can be built.

Graphs: Exo-Atmospheric:

0 10 20 30 40 50 60 70 80 900

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1000Height vs. Time

Time (min)

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Range (nm)

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time (min)

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12x 105 Weight vs. Range

Range (nm)

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time (min)

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Acceleration v. Time

-0.20

0.20.40.60.8

11.21.4

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Acceleration m/s 2

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Cruiser:

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time (min)

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Acceleration v. Time

-0.20

0.20.40.60.8

11.21.4

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Acceleration m/s 2

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e (m

in)

Orbiter: (Only acceleration period shown)

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Altitude (km)

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Ted Conbeer MAE 332

Dr. Kevin Bowcutt May 15, 2007

Engineering Aerodynamic Analysis of Space Express

Aerodynamically, we wanted to design Space Express to be as close as possible to a Mach 8 cone-flow waverider shape. However, this proved to be difficult, given the contradicting need of control surfaces, engines, and internal volume. As a result, the design process was a constant back-and-forth between aerodynamic and configuration needs until we reached a vehicle height and thickness that would satisfy both requirements. Other than general sizing, additional aerodynamic considerations forced the rear end of the aircraft to be redesigned, extending the nozzle upward and into the fuselage and gently sloping the wing/body down to the lower edge in order to eliminate base drag. Sizing the horizontal tails gave us additional aerodynamic flexibility, but the induced drag coefficient (and to a lesser extent, lift-to-drag ratio) was fairly sensitive to tail sizing, so most of our energy was spent designing a blended-wing shape that was thick enough for configuration, but had small enough angles for aerodynamics. The impact of each configuration change was analyzed using code written in MATLAB. The code was designed to take advantage of classical aerodynamic analysis for low-speed flight and to use more specialized and advanced impact-wedge methods for hypersonic flight, which required that the outer surface of the plane be broken up into 52 tangent flat-plate surfaces. The analyses in the trans- and supersonic regimes were primarily faired to the sub- and hypersonic curves, and (once a final configuration was found) scaled to match CFD analysis. The overall results were very strong. We were able to design a configuration that maintained efficient flight at hypersonic speeds, generated enough lift to takeoff at the required speed, and did not suffer from extreme transonic drag rise, while being volumetrically efficient in order to minimize weight without limiting the internal capacity. Please see the extended presentation slides for more details about the analysis and final aerodynamic performance of the aircraft.

Andrew Mackowski Aerodynamics, Lateral Stability & Control, Renderings Aerodynamics: Before Professor Martinelli was ready for CFD analysis, I helped Ted perform the engineering aero analysis. We spent time going over data plots, making sure they made sense, and coming up with ways to improve our plane’s performance. During this time, I also helped break our CAD model of the plane into flat plates suitable for the engineering aero program.

Once we had access to Gridgen, I spent hours attempting to create a suitable mesh. I encountered huge problems with bad surfaces in the model, which took the help of Manny and multiple weeks to fix. Once the gridding was done, I determined a series of test conditions and ran the CFD simulation. Often, the results would not converge, and I would have to tweak the parameters and re-run the simulation. Here is a chart of my results:

Configuration Moment Axis (from 0,0)

M alpha A_ref Avg Chord X_mom Y_mom C_L C_D C_M

1.2 -4 5.66E+02 2.38E+01 0 0 -6.22E-02 1.38E-02 7.08E-02 1.2 0 5.66E+02 2.38E+01 0 0 -1.64E-02 1.11E-02 3.35E-02 1.2 4 5.66E+02 2.38E+01 0 0 3.72E-02 1.52E-02 -8.82E-03

2 -4 5.66E+02 2.38E+01 0 0 -3.55E-02 8.03E-03 3.98E-02 2 0 5.66E+02 2.38E+01 0 0 4.55E-03 7.12E-03 8.37E-03 2 4 5.66E+02 2.38E+01 0 0 4.93E-02 1.22E-02 -2.74E-02 3 -4 5.66E+02 2.38E+01 0 0 -2.22E-02 4.90E-03 2.42E-02 3 0 5.66E+02 2.38E+01 0 0 1.22E-02 4.76E-03 -3.37E-03 3 4 5.66E+02 2.38E+01 0 0 4.66E-02 9.51E-03 -3.07E-03 4 -2 5.66E+02 2.38E+01 0 0 -2.03E-03 2.90E-03 6.24E-03 4 0 5.66E+02 2.38E+01 0 0 1.25E-02 3.47E-03 -5.46E-03 4 2 5.66E+02 2.38E+01 0 0 2.69E-02 5.09E-03 -1.69E-02 6 -2 5.66E+02 2.38E+01 0 0 2.81E-04 1.74E-03 2.85E-03 6 0 5.66E+02 2.38E+01 0 0 1.11E-02 2.31E-03 -5.67E-03 6 2 5.66E+02 2.38E+01 0 0 2.19E-02 3.69E-03 -1.40E-02 8 -2 5.66E+02 2.38E+01 0 0 1.19E-03 1.23E-03 1.34E-03 8 0 5.66E+02 2.38E+01 0 0 1.00E-02 1.78E-03 -5.46E-03 8 2 5.66E+02 2.38E+01 0 0 1.88E-02 3.03E-03 -1.22E-02

16 0 5.66E+02 2.38E+01 0 0 6.82E-03 9.03E-04 -4.38E-03 16 2 5.66E+02 2.38E+01 0 0 1.28E-02 1.84E-03 -8.94E-03 16 5 5.66E+02 2.38E+01 0 0 2.40E-02 4.53E-03 -1.74E-02

CD_0

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

1.20E-02

0 5 10 15 20

Mach

CD_0

As the following slides show, our design concept was validated by the CFD runs. At high mach numbers, the drag decreased as the shocks closed in around the body. The fact that our engineering aero estimates underestimated the L/D ratio might hint that we were exploiting the waverider effect. However, in order to actually prove this we would have to run more tests. At low mach numbers, the shock waves spread outwards, creating more drag. At mach 1.2, the bow shock detaches, and we start getting spillage drag as well.

Lateral-Directional Stability and Control

I was in charge of the lateral part of the stability and control section, though both Jon and I worked together for the most part. At subsonic speeds, I simply looked up the values of CN� in a table from Raymer. At hypersonic speeds, I modeled the plane as a 2D cross-section down the centerline. Just like a weathervane, in hypersonic flow this surface pivots around the center of mass. I calculated the center of pressure over the cross section by calculating its geometric center (which should be a good approximation at hypersonic speeds). At all speeds, the center of pressure was behind the center of mass, indicating yaw stability. Our plane was stable in roll as well (helped by the drooping horizontal tails). In the end, we sized the rudder at 9% of the planform area. To size the rudder’s control surface, I calculated the size of a flat plate required to cause enough moment to induce a 5 degree sideslip angle at hypersonic speeds. I arrived at a vertical tail control surface size of 20% of the vertical tail planform area, which causes a 5 degree sideslip angle with a 20 degree control surface deflection.

Renderings

For the final presentation, I was in charge of creating flashy renderings of our finished vehicle. I converted our CATIA model into a 3D Studio Max project, and proceeded to create landing gear and control surfaces. I superimposed the model over various environments to give an idea what the final thing would be like.

Computational Fluid Dynamics Analysis

•We analyzed our model with 3D computational fluid dynamics in order to calibrate our engineering analysis•The simulation we used solved the unsteady Euler equations for compressible flow, giving us lift and pressure drag information.

•Unstructured mesh•Finite volume method with edge-based flux accounting

CFD Results• At high Mach numbers, the shocks fall

close to the plane body, creating the waverider effect.

Top (M=16, a=2) Bottom (M=16, a=2)

CFD Results• At high Mach numbers, the shocks fall

close to the plane body, creating the waverider effect.

Top (M=8, a=2)Design Condition

Bottom (M=8, a=2)Design Condition

CFD Results• At low Mach numbers, the shock waves

spread apart, creating wave drag.

Top (M=3, a=2) Bottom (M=3, a=2)

CFD Results• At low Mach numbers, the shock waves

spread apart, creating wave drag.

Top (M=1.2, a=2) Bottom (M=1.2, a=2)

Joe Vogel & Dan Cummins

Propulsion Summary

Our objective for this portion of the design was to analyze the propulsion system and its components. We utilized a turbo-ramjet for our first combustion phase, in turbo mode from takeoff to Mach 2.5, ramjet mode from there to Mach 4. We operated RANS CFD on inlets and used NASA Glenn EngineSim code to analyze combustion. Our vehicle uses two turbo-ramjet engines, selected for safety and economic reasons, with a diameter of 1.76m each. For our initial layout, we generated an unsized engine to provide performance data of thrust and Isp at altitude and Mach number. We then designed the sized inlet flowpath based on a maximum Mach number of 4, using variable geometry. We then ran these at Mach numbers of 1.2, 1.5, 3, and 4 to get inlet conditions and pressure recovery. The inlets were run with a backpressure of zero because of code problems, and then compared these to a run with a backpressure of what it ought to be at Mach 3. This attempt was running successfully for the first shock but did not eventually converge. Our second phase used a ram-scram jet combined cycle, as a ramjet from Mach 4 to 5, and a scramjet from there to Mach 8. We designed our inlet for shock-on-lip conditions and capture area at our maximum air-breathing Mach number of 8. RANS CFD was run on this inlet to obtain combustor inlet conditions at Mach 5, 6, 7, and 8, each at an angle of attack 0 and 2 degrees from the horizontal. The results of this analysis were sent into a provided combustor code to determine thrust and nozzle conditions. The combustor code had some bugs and we had to tweak the area ratio, equivalence ratio and maximum temperature to get supersonic exit velocities. These results themselves were the inputs for a nozzle CFD code. We designed a supersonic nozzle based on expansion ratio by approximating the nozzle with flat surfaces, the initial angle at 20-30 degrees and a final angle at 5 degrees. We ran RANS CFD for each nozzle corresponding to each inlet Mach number and angle of attack. The total results of the combined flowpath CFD from inlet to nozzle exit allowed us to compute aerodynamic forces and moments, which we relayed to our team’s aerodynamics group. We were then able to calculate thrust and plot a thrust vs Mach number curve for our Scramjet for our range of Mach numbers. Our final phase of propulsion utilized a rocket-based combined cycle, with a liquid rocket engine burning LOx and RP-1 as oxidizer and fuel, respectively. We based our rocket on the RD-180, a similarly fueled rocket which is commercially available today. Our thrust and Isp data was determined by scaling data from the RD-180 to our aircraft’s size and propulsion requirements. Included: Sample aerodynamics data set CFD images Mass convergence images

q(psi) inlet lift drag moment C_N C_A C_M

13.825 M5 1006.39 480.959 530469 0.024871 0.011886 13.10974 13.658 M6 718.72 441.148 285856 0.017979 0.011036 7.150877 12.992 M8 145.25 369.7 225138 0.00382 0.009722 5.920684 13.754 2M7 844.32 573.18 281535 0.020974 0.014238 6.993627 12.992 2M8 513.143 512.461 243774 0.013495 0.013477 6.410774 13.842 2M5 1503.317 673.209 847889 0.037107 0.016617 20.92856

371.7886m^2 576 151 in^2

Alex van Hoek

Aerothermal Analysis Introduction One of the greatest challenges of hypersonic flight is protecting the aircraft from the tremendous heat created by friction between the air and the fast-moving aircraft. With

generated temperatures exceeding 1500K on some surfaces, an effective thermal protection system (TPS) is critical in protecting the aircraft structure from the heat. The

main aim of the aerothermal analysis on Space Express is to determine the most appropriate TPS materials for each aircraft component, and to optimize the TPS thickness

at each point so as to minimize aircraft weight and drag whilst completely protecting the structure.

TPS Material Selection Before determining the ideal quantities and thicknesses of the various TPS systems on the aircraft, the ideal TPS material for each surface needed to be determined. To do this, the

surface temperatures were determined at each point along the aircraft at the flight condition that would create the highest temperatures. This flight condition would occur

on reentry at Mach 10 and a dynamic pressure of roughly 500psf, which corresponds to the highest Mach number and highest dynamic pressure combination. Although the

aircraft traveled at higher Mach numbers during the flight, at those speeds the air density and dynamic pressure were so low that maximum heating would not occur. These critical

values were calculated by assuming that at this equilibrium temperature, the convective heat flux into the surface and the radiative heat flux out of the surface were equal.

Shown on the following page are plots of the radiation equilibrium temperature and Stanton number for the upper body centerline and the lower body inlet ramp at the

maximum heating condition. On the upper surface, the maximum surface temperature is 1250K (�1800˚F). From the temperature distribution, an oxide-based ceramic matrix

composite (CMC), with an operating range of 1800-2400˚F, was chosen to be the most suitable TPS system. On the lower surface, temperatures reach 1600K (�2450˚F),

suggesting that the ideal TPS system is a Sic based CMC with an operating temperature range of 2400-2800˚F. Both of these CMC systems are relatively durable and require a

reasonably small amount of maintenance, and so are well suited for application on the Space Express.

Please note the boundary layer transition points on the graphs, which occur at Re = 2.43×107 on the upper surface and at Re = 1.14 ×107 on the lower surface.

Fig.x

Transition point

Transition point

Fig.x

Having determined suitable TPS materials for the upper and lower fuselage surfaces, the aircraft’s wings were analyzed at the critical condition:

Fig.x

Transition point

Transition point

Transition point

Transition point

Fig.x

Using the data in the above plots, it was determined that the wings had similar TPS requirements to the upper and lower fuselage. The upper wing would experience a

maximum temperature of about 1250K (�1800˚F) at the boundary layer transition point, and so an oxide-based CMC would be suitable. On the lower wing, with temperatures

reaching 1500K (�2250˚F), the oxide-based CMC would also be used, which has a maximum operating temperature of 2400˚F. The boundary layer transitions occurred at Re = 1.97×107 on the upper wing surface and at Re = 1.04 ×107 on the lower wing

surface.

The leading edges of the aircraft, including the nose, wings and tail, must be able to withstand extremely high stagnation point temperatures. For this reason all leading edges

would be constructed out of reinforced carbon-carbon (RCC), which has a maximum operating temperature in excess of 2500˚F. To minimize drag, the leading edge radii

should be minimized. Thus the minimum radius that would not lead to stagnation temperatures above 1650K (�2500˚F) was determined at each point. The wings and tail,

with sweep angles of 65°, would need RCC leading edge radii of 0.8cm (�0.3in.) to stay below 2500˚F at the critical flight condition. The curved nose, with an increasing sweep

Transition point

Transition point

angle with the increasing distance from the tip, would require a leading edge radius distribution as shown below:

Fig.x

As the plot shows, the leading edge radius of the aircraft fuselage would decrease from

almost 2.5cm (�1in.) at the tip to less than 0.5cm (�0.2in) at the rear. All leading edges would be composed of the RCC, whose high operating temperature range and high yield

strength make it an ideal choice. The aircraft tail would be composed of a single material, differentiating it from the other

aircraft components in which the aircraft structure is covered with a layer of TPS material. Modeled with a rectangular cross-section of 2in. average thickness (�5.1cm), the tail

would be heated from both sides throughout the flight. The following plots show the temperature distribution through a

section of the tail on the ascent and reentry stages of the flight:

Fig.x – Ascent heating on the tail Fig.x – Reentry heating on the

tail

As the plots show, the greatest heating occurs about 450 sec. into the reentry phase of the

flight. At this hottest point, the temperature in the tail reaches 1250K (�1850˚F) at the edges. To withstand the high temperatures, and to have the necessary structural properties

required, the tail should be constructed out reinforced silicon carbide, which has an operating maximum temperature in excess of 3500°F.

TPS Thickness Determination Having selected suitable TPS materials for each aircraft component, the thickness of the

TPS on the upper and lower surfaces of the fuselage was to be determined. In the previous section, it was assumed that at Tequilibrium the convective and radiative heat fluxes

would be equal. In reality, some heat would diffuse from the hot outer surface through the TPS, ultimately heating the entire material and the raising the temperature at the

opposite TPS boundary. Ideally, the TPS would be thick enough to keep the temperature at the structure surface less than 600K (�620°F), but would not be any thicker than this

because excess TPS would unnecessarily add weight to the aircraft. The maximum

allowable surface temperature is a specification dictated by the structural and material characteristics of Space Express. To determine an ideal TPS thickness, the 1D heat

diffusion over the entire flight time would be carried out on a section of TPS. If the temperature at the structural edge of the TPS exceeded 600K at any stage, the section

would need to be thickened and the process would be iterated until an ideal thickness was determined at that point.

As the plots below indicate, the temperature distribution calculations were carried out for each flight stage: ascent, space and reentry. The final temperature distribution of one

stage would become the initial condition for the temperature distribution of the next stage. In space, since there is no air and so no convective heating, the temperature plots were

created by setting convectiveq⋅

= 0 and determining the results of heat radiation from the hot

body in space.

Fig.x

Fig.x

Fig.x

The three plots above show the temperature distribution through the TPS on the first

section of the upper fuselage. The 10.35cm thickness maintains a temperature below 600K at the structural edge for the entire flight time. Please note that the material

properties of the CMC materials on the upper and lower surfaces was kindly provided by Dr. Kei Lau at Boeing.

The process outlined above was carried out for each of the 7 sections on the upper surface and the 3 sections on the lower surface. Shown below are the

TPS thickess distributions on the upper and lower fuselage surfaces.

Upper Surface Oxide-based CMC Thickness:

Position 1 2 3 4 5 6 7 Thickness

(cm) 10.35 9.85 9.60 9.35 8.80 8.70 8.55

Lower Surface SiC-based CMC Thickness:

Position 1 2 3 Thickness (cm) 11.45 11.05 10.10

7 6

5

4

3 2

1

Zhen Xia Brandon Vigil

Structures and Finite Element Analysis

Objectives The objectives for the structural analysis were to define layouts of both the internal configuration and structure, and the external skin. The structure was optimized to fit the internal configuration, minimize weight, and have excellent thermal and structural properties to close the mission. Approach to Design and Analysis Internal Configuration The first great challenge was to fit the internal configuration. Because our vehicle was a waverider shape and we had to maximize L/D, our internal configuration was limited by height. We first placed the LOx tank at the center of gravity for stability and control. For pressurization reasons, we approximated the tank as an ellipsoid shape with spherical end caps. Next, we placed the passenger cabinet immediately in front of the LOx tank because that was the area of the greatest height. Following, the turbo ramjets were placed so that the LOx tank straddled the engines. The other challenge was the place the large amount of fuel. Based on fuel volume calculations, we optimized the sizing of the fuel tanks to complete the mission and placed the JP-7 and RP-1 compartments in the wings of the aircraft. Finally, we placed cargo bays and landing gear in the remaining sections. The landing gear incorporated a quadricycle configuration and were placed based on comparison with existing aircraft. Internal Structure The internal structure was defined based on the internal layout. We placed two bulkheads to straddle the fuselage and had spars extending from the main bulkheads. The spars were defined based on the location of the compartments and places of highest stress as described in the FEM analysis section. External Skin The external skin was defined based on the configuration. We used an idealized configuration to facilitate FEM.

Loads The required loads that our aircraft was designed for included engine loads, aerodynamic pressure loads, landing gear loads, and maneuver loads. Based on the V-n diagram that was created using the source specified in the slides, we designed the aircraft to satisfy 3g’s of maneuvering loads. Materials Selection The major factors that contributed to material selection were weight, thermal properties, and strength. Initially, we considered titanium, aluminum, and nickel based alloys because they were used conventionally in aircraft and spacecraft. We at first decided on titanium because it had an excellent balance of strength and thermal properties. However, we realized that incorporating titanium as the skin and internal structure would make the vehicle too heavy. Instead we opted for a carbon composite which incorporated a resin polymide system for both the external skin and internal skeleton. Developed by Unitech, RP46 Unidirectional IM7 carbon composite was chosen because it had comparable strength to titanium, excellent thermal properties, and only had a fraction of the weight. The horizontal and vertical tails incorporated carbon composite coated with silicon carbide for heating reasons. Finite Element Analysis Based on the internal structure and materials, we ran finite element analyses using Pro/Mechanica. The mesh incorporated p-type elements in both 2D and 3D elements. The 2D elements were triangles and quadrilaterals, and the 3D solids were tetrahedrons. Based on the mesh, we applied displacement constraints, pressure loads, gravity loads, and landing gear loads to determine performance in static stress analyses. After iterating an FEM run which was accomplished in 40 minutes to an hour, we determined maximum loads of the vehicle. Based on the maximum loads, we resized the internal structure and moved the spars to support them adequately. We used a safety factor of 1.5 of the ultimate strength of the material to optimize weight. As a note, we ignored stress concentrations of maximum stresses and designed for the majority stress level because we realized that stress concentrations could be eliminated by locally adding more structure which would negligibly affect the final structure weight. Key Results and Conclusions Through many iterations of FEM, we were able to optimize our structure to not only accommodate all stresses but also to minimize the weight of the structure to obtain a reasonable structural weight to close the mission. We reached 89% of the allowable weight for the aircraft skin and internal structure and reached 95% of the allowable weight for the silicon carbide tails.

Rochelle Mellish

Mass Properties There are many parameters that affect the overall performance of an aircraft, and one of the most prevalent is the mass properties analysis. Important parameters in mass properties include not only the final weight of the aircraft, but also longitudinal moments, longitudinal inertias, and the center of gravity of both subcomponents and the aircraft at-large. Weights Analysis The weights analysis for the Space Express was completed using the fighter equations of Chapter 15 in Daniel P. Raymer’s Aircraft Design: A Conceptual Approach. These approximation equations were used for vehicle components such as hydraulics, electrical equipment, furnishings, instruments, and flight controls. The weights of structural elements such as the wings, vertical tail, fuselage, and Thermal Protection System (TPS) were compiled from actual measurements. The values I chose for the factors involved in my weights approximation equations are listed below. Kcb = 1.0 I assumed our aircraft would not be using cross beam landing gear. Ktpg = 1.0; For Ktpg, which was also used in the

calculation of the main landing gear, I obtained a value of 1.0 since our landing gear was quadropod instead of tripod.

Wl = 87913 pounds I used the weight of the plane before the

landing gear was added and without propellant for this value.

Ngear = 3 I used 3 because it is the same as that for a

Large bomber. I did not use fighter approximations because fighter aircraft are much smaller in scale than our aircraft.

Nl = Ngear*1.5 Lm = 60 inches Ln = 60 inches T = 191087.6 pounds For thrust, T, I used a maximum value from

our propulsion data, which was 191087.6 lb. Nz = 1.5*3; Here, 3 is the limit load factor. I chose

this value to be 3 because 3g's is the maximum acceleration our vehicle experiences.

Sfw = 645.832 square feet Nen = 1 I assumed that, although we have more than

one engine, they are all part of the same unit in the aircraft.

Kvg = 1.62 Our wings droop downward. Ld = 29.13 feet I referenced the document AIAA 2000 3808 in finding this value. Kd = 1.0 This value was chosen assuming that we have circular cross-sectional ducts. Ls = 14.57 feet I referenced the document AIAA 2000 3808 in calculating this value. De = 5.77 feet This is the diameter given by our

propulsion analysis. Ltp = 1.05; I referenced AIAA Journal, Vol. 36, No. 5,

May 1998 when picking this value. Lsh = 39.37; AIAA-94-0202 ...Using information from this document, I was able to assume Lsh was the same length as the engine. Lec = 12.33; %ft Vt = 26311.5 gallons This is the total fuel volume. Vi = Vt I assumed all of our fuel was stored in integral tanks, and gave the tanks the same volume as the total volume of our fuel. Vp = 0 gallons I assumed that we had no self-sealing

Protected tanks, so my value for Vp was 0. Nt = 1 Since all of our propellant, except the LOx

is in the wings, I made the assumption that there was only the LOx fuel tank.

SFC = 1.0 I used a typical value given for ramjet

engines.1 Te = T

1 “Specific Fuel Consumption,” Wikipedia: The Free Encyclopedia, <http://en.wikipedia.org/wiki/Specific_fuel_consumption>

M = 18 Scs = 31.69 square feet I took the areas of parts of the plane

that would normally contain the rudder, flaps, or ailerons on other planes.

Ns = 3 One flight control system for each side of

the wing's control surfaces, and one for the vertical tail.

Nc = 2 Nci = 2 Nnw = 4 Kvsh = 1.0 Nu = 5 I used the lower limit of Raymer's

suggestion of typical values for this parameter. The range was given on page 462 of the text.

Kmc = 1.0 Rkva = 110 kV*A I used the lower limit of Raymer's

suggestion for typical values for this parameter. The range was given on page 462 of the text.

La = 5 feet I assumed that most of the electronics were

located in the cockpit, and that the generators were located at or near the engines. Hence, my routing distance is estimated to be the distance between the electronics in the cockpit and the aircraft's generators.

Ngen = Nen; According to Raymer, these values are on

the same order. Wuav = 1082 pounds I used the weight determined for our

aircraft's avionics system. The weights of our structural elements were calculated from our structural analysis. The TPS weight was calculated from the thicknesses rendered by the thermal analysis. The TPS thickness varied along the length of the aircraft, and these thicknesses were multiplied by the surface areas of the parts of the aircraft that they corresponded to. Using the density rendered by the thermal analysis, which was 192.22 kg/m^3, a grand total TPS weight of 938.23 kg was obtained.

Center of Gravity Analysis In order to calculate the center of gravity of the aircraft, I needed not only the total weight of the aircraft, but also the moments about a common reference point of all the objects that the plane is composed of. The common reference point I chose was the leading edge of the aircraft; all moment arms were measured from this point. Every object on the aircraft was assigned an “x-location,” and each of these moment arms were multiplied by the weights of their associated objects to yield the moments of every object on the plane about the leading edge. All of the moments were summed together and divided by the plane’s total mass to yield a center of gravity (CG) that was 22.4 meters from the leading edge. Moment of Inertia (Iyy) Analysis The moment of inertia of an object about a given point is defined to be I = mr2 , where I is the moment of inertia, m is the mass of the given object, and r is the distance between the object and its given pivot point. I calculated this value for all of the objects in our aircraft, and chose all distances to be defined as the distance between the given object and the center of gravity of the aircraft. To calculate the total Iyy for the aircraft, I summed all of the individual Iyy’s. The total Iyy was 1, 054, 700 kg*m2. Weight Breakdown Matrix (one the next page):

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Space Express Life Cycle Cost 1 Year of Operation

RDTEMAN & ACQOPERATIONDISPOSAL

Space Express Life Cycle Cost10 Years of Operation

RDTEMAN & ACQOPERATIONDISPOSAL

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Worst-Case: �5% market growth �1/2% express market capture �1.25 million lbs/yr �~$105 million/yr

Best-Case: �10% market growth �5% express market capture �65 million lbs/yr �~$5,500 million/yr

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��H �� clear all %COST ANALYSIS ALGORITHMS %BASED ON DR. JAN ROSKAM'S BOOK ENTITLED "AIRPLANE DESIGN: PART VII: %AIRPLANE COST ESTIMATION: DESIGN, DEVELOPMENT, MANUFACTURING AND %OPERATING" published in 1990 CPI_then = 124.0; %1989; Pick ONE year for comparison sake and stick with it CPI_now = 205.5; %2007; Present year value CEF = 1+(CPI_now-CPI_then)/CPI_then; %Cost escalation factor between past data and % %present year value CPI_1990 = 130.7; %Cost escalation factor for year 1990 CEF_1990 = 1+(CPI_now-CPI_1990)/CPI_1990; %See list of CPI vs. years at http://minneapolisfed.org/research/data/us/calc/hist1913.cfm %See CPI Calculator at http://www.bls.gov/cpi/ %CHAPTER 3: METHOD FOR ESTIMATING RESEARCH, DEVELOPMENT, TEST AND %EVALUATION COST AND A METHOD FOR ESTIMATING PROTOTYPING COST (Skipped) %========================================================================== %========================================================================== %========================================================================== %Section 3.1: Airframe Engineering and Design Cost, C_aedr %========================================================================== %All weights are given in lbs W_E = 6.6875*10^4; %total empty weight W1 = 1.7065*10^3; %weight of main landing gear W2 = 885.9976; %weight of nose landing gear W3 = 106.4786; %weight of engine mounts W4 = 729.7902; %weight of firewall W5 = 32.5746; %weight of engine section W6 = 1.3732*10^3; %weight of air induction system W7 = 14.6633; %weight of tailpipe W8 = 714.7427; %weight of engine cooling W9 = 76.8555; %weight of oil cooling W10 = 36.8826; %weight of engine controls W11 = 2.1567*10^3; %weight of fuel systems and tanks W12 = 53.0561; %weight of starter pneumatic W13 = 399.8676; %weight of flight controls W14 = 200.4969; %weight of instruments W15 = 108.3950; %weight of hydraulics W16 = 570.0245; %weight of electrical subsystems W17 = 1.0822*10^3; %weight of avionics W18 = 435.2000; %weight of furnishings W19 = 230.5095; %weight of A/C and anti-ice %%%%%%%%%%%%%%%%%From Roskam----seen as obsolete % W_E =____________; %airplane empty weight % W1 = ____________; %weight of wheels, brakes, tires and tubes % W2 = ____________; %=W_e, i.e. weight of engines % W3 = ____________; %=W_ess,i.e. weight of starter

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% W4 = ____________; %Weight of cooling fluid % W5 = ____________; %Weight of rubber/nylon fuel cells % W6 = ____________; %=W_els, i.e. weight of batteries, electrical power supply % W7 = ____________; %=W_iae, i.e. weight of instruments, avionics and electronic equipment % W8 = ____________; %=W_arm, i.e. weight of armament system (=0 in our case) % W9 = ____________; %=W_api, i.e. weight of airconditioning units and fluid % W10 = ___________; %=W_apu, i.e. weight of APU % W11 = ___________; %=W_tfo, i.e. weight of trapped fuel and oil W_ampr= W_E -(W1+W2+W3+W4+W5+W6+W7+W8+W9+W10+W11+W12+W13+W14+W15+W16+W17+W18+W19); %lbs %Aeronautical Manufacturers Planning Report weight %OR: if lacking detailed knowledge of airplane component weights, use %equation W_ampr = exp(0.1936 + 0.8645*log(W_To)), where W_To = takeoff %weight V_C = 2645.88337; %Cruising speed in keas (KNOTS EQUIVALENT AIRSPEED) V_max = V_C; N_rdte = 4; %Number of airplanes produced for RDTE phase %Usually between 2-8 for commercial programs F_diff = 2.0; %Judgment factor; accounts for difficulty %(i.e. complexity) of a new airplane program %Ranges from 1.0 to 2.0 for conventional --> most %agressive use of advanced technology %WARNING: Don't lowball this figure! F_cad = 0.8; %Judgment factor; accounts for effect of CAD %on airframe engineering and design cost %Ranges from 1.2 to 0.8 (1.2 --> CAD learning mode, %1.0 --> manual drawings, 0.8 --> experienced CAD) R_erthen = 92.00; %Engineering dollar rate per hour charged for %airframe engineering activity ('then'); preferred to use %currently hourly rates (see Fig. 3.3) %Includes direct engineering labor, overhead, %general and administrative costs and miscellaneous %direct charges (assume high-level security %requirements) R_er = R_erthen * CEF; %2007$ rate MHR_aedr = 0.0396*(W_ampr^0.791)*(V_max^1.526)*(N_rdte^0.183)*(F_diff*F_cad); %total engineering manhours required to complete phases 1-3 (see Notes) C_aedr = MHR_aedr*R_er %Section 3.2: Development Support and Testing Cost, C_dstr %========================================================================== C_dstr = 0.008325*(W_ampr^0.873)*(V_max^1.890)*(N_rdte^0.346)*(CEF)*(F_diff);

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%Section 3.3: Flight Test Airplanes Cost, C_ftar %========================================================================== C_er = 250000000; %Cost per engine (see Appendix B for help estimating) N_e = 6; %Number of engines per airplane C_Pr = 0; %Cost per propeller N_p = 0; %Number of propellers per airplane C_avionics = 1000000; %cost of avionics equipment per airplane %Mark Gonda: S-Rated, triple redundant for safe %fail-ops condition N_st = 4; %Number of static test airplanes; NOT equipped with engines, propellers %or avionics systems) C_engav = ((C_er*N_e)+(C_Pr*N_p)+C_avionics)*(N_rdte - N_st); MHR_manr = 28.984*(W_ampr^0.740)*(V_max^0.543)*(N_rdte^0.524)*(F_diff); R_mrthen = 51; %(see Figure 3.4)Manufacturing Manhour Rate in 1989$$$/manhour R_mr = R_mrthen * CEF; %manufacturing labor rate in dollars per manhour (2007$) C_manr = MHR_manr*R_mr; %manufacturing cost of the flight test airplanes F_mat = 3.0; %Correction factor; depends on type of material used %1.0 for mostly aluminum alloy airframe, 1.5 for %stainless steel airframe, 2.0-2.5 for conventional %composite materials or Li/Al alloys, and 3.0 for %carbon composite airframes C_matr = 37.632*(F_mat)*(W_ampr^0.689)*(V_max^0.624)*(N_rdte^0.792)*CEF; R_trthen = 66; %tooling labor rate in 1989$$$/manhour(see Figure 3.5) R_tr = R_trthen * CEF; %2007$ N_rr = 0.33; %RDTE production rate in units per month; usually 0.33 units/month MHR_toolr = 4.0127*(W_ampr^0.764)*(V_max^0.899)*(N_rdte^0.178)*(N_rr^0.066)*(F_diff); %tooling manhours needed in phases 1-3 C_toolr = MHR_toolr*R_tr; C_qcr = 0.13*C_manr; C_ftar = C_engav + C_manr + C_matr + C_toolr + C_qcr; %Section 3.4: Flight Test Operations Cost, C_ftor %========================================================================== F_obs = 1.0; %factor that depends on importance of having 'low' observables; %Should be =1.0 for commercial airplane without a stealth %requirement and 3.0 for 'stealty' airplanes C_ftor = 0.001244*(W_ampr^1.160)*(V_max^1.371)*((N_rdte)^1.281)*CEF*F_diff*F_obs;

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%3.5 Test and Simulation Facilities Cost, C_tsfr %========================================================================== C_tsfr = 0; %Assuming no extra facilities are required %RDTE COSTS (minus RDTE profit and cost fo finance the RDTE phases) C_RDTE_pre= C_aedr + C_dstr + C_ftar + C_ftor+ C_tsfr; %3.6 RDTE Profit, C_pror %========================================================================== F_pror = 0.10; %For suggested profit of 10% C_pror = F_pror * C_RDTE_pre; %3.7 Cost to Finance the RDTE Phases, C_finr %========================================================================== F_finr = 0.10; %0.1 to 0.2, depending on available interest rates C_finr = F_finr*C_RDTE_pre; %OVERALL RDTE COSTS (including RDTE profit and cost fo finance the RDTE phases) C_RDTE = C_RDTE_pre + C_pror + C_finr %CHAPTER 4: METHOD FOR ESTIMATING MANUFACTURING AND ACQUISITION COSTS %========================================================================== %========================================================================== %========================================================================== N_m = 450; %Number of airplanes produced to production standard during airplane program N_program = N_m + N_rdte; %Number of airplanes produced during an airplane program % Section 4.1: Airframe Engineering and Design Cost, C_aedm %========================================================================== MHR_aedprogram = 0.0396*(W_ampr^0.791)*(V_max^1.526)*(N_program^0.183)*(F_diff)*(F_cad); R_em = R_er; %Previously defined engineering manhour rate in 'today' dollars C_aedm = (MHR_aedprogram*R_em)-C_aedr; % Section 4.2: Airplane Program Production Cost, C_apcm %========================================================================== C_em = 1000000; %Cost per engine during manufacturing phase; may be different %than during RDTE phase; see Appendix B C_ep = 0; %Cost per propeller during manufacturing phase; may be different

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%than during RDTE phase; see Appendix B C_avionicsm = 1000000; %Cost of avionics during manufacturing phase; may be different %than during RDTE phase; see Appendix C C_engavm = (C_em*N_e + C_ep*N_p + C_avionicsm)*N_m; F_int_then = 3000; %interior cost factor expressed in USD/pax; this is the value for F_int in %1990 prices for a business jet F_int = F_int_then; N_pax = 10; %Number of passengers C_intm = (F_int*N_pax*N_m)*CEF_1990; %Accounts for interior cost component MHR_manprogram = 28.984*(W_ampr^0.740)*(V_max^0.543)*(N_program^0.524)*F_diff; R_mm = R_mr; %Previously defined C_manm = (MHR_manprogram)*R_mm-C_manr; %Labor cost incurred in manufacturing N_m airplanes %to production standard C_matprogram = 37.632*(F_mat)*(W_ampr^0.689)*(V_max^0.624)*(N_program^0.792)*CEF; %Total matls cost associated with building %N_program airplanes C_matm = C_matprogram - C_matr; %Materials cost incurred while manufacturing N_m %airplanes to production standard R_tm = R_tr; %Previously defined N_rm = 5; %Airplane manufacturing rate in units per month MHR_toolprogram = 4.0127*(W_ampr^0.764)*(V_max^0.899)*(N_program^0.178)*(N_rm^0.066)*F_diff; C_toolm = (MHR_toolprogram*R_tm)-C_toolr; %Tooling cost to produce N_m airplanes C_qcm = 0.13*C_manm; %quality control cost associated with building N_m airplanes C_apcm = C_engavm + C_intm+ C_manm + C_matm + C_toolm + C_qcm; %MANUFACTURING AND ACQUISITION COSTS (cost to finance) C_man = C_aedm + C_apcm; % Section 4.4: Cost to Finance the Manufacturing Phase, C_finm %========================================================================== F_finm = 0.15; %0.1 to 0.2, depending on available interest rates C_finm = F_finm*C_man; %OVERALL MANUFACTURING AND ACQUISITION COSTS (including cost fo finance) C_ftom = 0; %production flight test operation cost; neglect C_man = C_man + C_ftom + C_finm;

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% Section 4.5: Profit, C_pro %========================================================================== F_prom = 0.10; %For a suggested profit of 10% C_pro = F_prom*C_man; %C_pro = 0; %ESTIMATE OF THE UNIT PRICE PER AIRPLANE AEP = (C_man + C_pro + C_RDTE)/N_m %Stands for Airplane estimated price %CHAPTER 5: METHOD FOR ESTIMATING OPERATING COST OF COMMERCIAL AIRPLANES %========================================================================== %========================================================================== %========================================================================== % Section 5.1: Method for Estimating the Program Operating Cost of % Commercial Airplanes, C_OPS %========================================================================== N_yr = 10; %Number of years during which airplane is operated (may be sold/resold) %= 20 for transport, 20 for corporate, 20-40 for personal R_bl = 7000; %Block distance measured in nm; depends on routes flown t_bl = 1.4022; %block time in hours %NOTE: I am neglecting components of block time listed on pgs.71-75 U_annbl = (10^3)*(3.4546*(t_bl)+2.994-sqrt(12.289*(t_bl)^2-5.6626*(t_bl)+8.964)); %annual utilization in block hours; depends on airplane type and routes %flown V_bl = R_bl/t_bl; %block speed in nm/hr V_flt = 2645.88337; %Average flight speed at which airplane is operated (KTS) %See pg. 79 for method regarding calculation of V_flt U_annflt = (U_annbl*V_bl)/V_flt; %annual utilization in flight hours R_blann = V_bl*U_annbl; %total annual block miles % Section 5.2: Method for Estimating the Direct Operating Cost of % Commercial Airplanes (DOC) %========================================================================== % Section 5.2.1: DOC of Flying, DOC_flt n_c = 2; %assume 2 pilots for simplicity K = 0.26; %constant that accounts for vacation pay, cost of training, insurance, payroll tax, etc. %V_bl is expressed in nm/hr SAL_then = 144000; %Salary in referenced year (if year is 1989, see Table 5.5) SAL = SAL_then * CEF; %Annual salary paid to a crew member; depends on seniority, company rules, etc. %2007$ AH = 750; %Number of flight hours per year for crew member (see pg. 84) TEF_then = 11; %USD/block hr; travel expense factor in 1990(see Fig. 2.7) TEF = TEF_then*CEF_1990; %TEF in 2007$ C_crew = (n_c)*((1+K)/V_bl)*(SAL/AH)+(TEF/V_bl);

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% Section 5.2.1.2: Fuel and oil cost per nautical mile, C_pol W_Fused = 171658; %Amount of mission fuel used in lbs W_Fbl = W_Fused; %NOTE: NOT accounting for entire deterioration with time, i.e. increased %fuel use with time %Density of RP-1: 7.51086404 lbs/gallon (0.90 g/ml) (wiki) %Density of JP-7: 6.59286954 lbs/gallon (790 kg/m^3) (wiki) %Density of Liq-Ox: 9.52210652 lbs/gallon (1.141 kg/L) (wiki) %Price of JP-7 (2005): 3.00 = 3.15 $/gallon (DoD) (2007) %Price of RP-1: (1982 = 0.27 $/lb...see website below) = 0.57 $/lb % =4.28 $/gallon (2007) %Price of Liq-Ox: 0.92 $/lb (2007 CPI Calc) (1982: 0.43 $/lb (from http://yarchive.net/space/rocket/fuels/fuel_costs.html) % =8.76 $/gallon (2007) FP = 5.3967; %price of fuel in USD/gallon (US gallon)(average of three fuels) FD = 7.8753; %fuel density in lbs/gallon (average of three fuels) W_olbl = 0.70*N_e*t_bl; %weight of oil and lubricants used in lbs %ESTIMATE: W_olbl = (0.70)*N_e*t_bl (pg. 88) OD = 7.75; %Oil density in lbs/gallon (see pg. 89) OLP = 27.12; %2007$/gal from 15.00 1987$/gal in Roskam section 5.2 C_pol = (W_Fbl/R_bl)*(FP/FD)+(W_olbl/R_bl)*(OLP/OD); %fuel and oil cost per nautical mile %OR: C_pol = 1.05(W_Fbl/R_bl)*(FP/FD); % Section 5.2.1.3: Cost of Airframe Insurance per nautical mile, C_ins f_inshull = 0.030; %annual hull insurance rate in USD/USD airplane price per airplane per year AMP = AEP; C_ins = (f_inshull)*(AMP)/(U_annbl*V_bl); %OR: Estimate C_ins = 0.02*DOC DOC_flt = C_crew + C_pol + C_ins; %DOC of flying in USD/nm % Section 5.2.2: DOC of Maintenance, DOC_maint t_flt = 1.402; %average flight time MHR_mapflt = 8; %estimate from Fig. 5.5 (see pg. 95) MHR_mapbl = (MHR_mapflt)*(t_flt/t_bl); %Number of airframe and system maintenance man hours %needed per block hour R_lap_then = 22.50; %airplane maintenance labor rate per manhour in USD/hr %See Table 5.5; use 'Mechanic with A/P' data R_lap = R_lap_then*CEF; %2007$ C_labap = 1.03*(MHR_mapbl*R_lap)/V_bl; MHR_mengbl = 3; %number of engine maintenance hours needed per block hour per engine %See table 5.6, Figs. 5.6, 5.7 R_leng_then = 22.50; %engine maintenance labor rate per manhour in USD/hr %See Table 5.5; use 'Mechanic with A/P' data R_leng = R_leng_then*CEF; %2007$

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C_labeng = (1.03*(1.3)*N_e*MHR_mengbl*R_leng)/V_bl; %maintenance labor cost per nautical mile of engines C_matapblhr_then = 350; %airframe and systems maintenance matls cost per airplane block hour in USD/hr %Find it in Fig. 5.8 %C_matapblhr = C_matapblhr_then*CEF; C_matapblhr = 579.62; %2007$ (use CPI calculator) C_matap = 1.03*(C_matapblhr)/V_bl; %cost of maintenance matls for airframe and systems C_matengblhr_then = 250; C_matengblhr = C_matengblhr_then*CEF; %2007$ %See Fig. 5.9-5.11; engine maintenance matls cost per engine per airplane %block hour in USD/hr C_mateng = (1.03*1.3*(N_e)*(C_matengblhr))/V_bl; %cost of maintenance matls for engines per nautical mile f_amblab = 1.40; %overhead distribution factor for labor (pg. 102) f_ambmat = 0.70; %overhead distribution factor for material cost (pg. 102) C_amb = 1.03*((f_amblab)*((MHR_mapbl*R_lap)+(N_e*MHR_mengbl*R_leng))+(f_ambmat)*(C_matapblhr+(N_e)*C_matengblhr))/V_bl; %Cost of applied maintenance burden per nautical mile DOC_maint = C_labap + C_labeng + C_matap + C_mateng + C_amb; % Section 5.2.3: DOC of Depreciation, DOC_depr F_dap = 0.85; %airframe depriciation factor; See Table 5.7 pg. 107 EP = 1000000; %engine price; use Appendix B PP = 0; %price per propeller; use Appendix B ASP = C_avionics; %avionics systems price (use Appendix C) DP_ap = 10; %Airplane depreciation period (See Table 5.7) (years) C_dap = (F_dap)*((AEP - N_e*EP - N_p*PP - ASP)/(DP_ap*U_annbl*V_bl)); %cost of airframe depreciation in USD per nm F_deng = 0.85; %engine depriciation factor; See Table 5.7 pg. 107 DP_eng = 7; %engine depreciation period (See Table 5.7) (years) C_deng = (F_deng*N_e*EP)/(DP_eng*U_annbl*V_bl); %cost of engine depreciation in USD per nm C_dprp = 0; %Cost of depreciation of propellers; assume NO propellers F_dav = 1.00; %avionics depriciation factor; See Table 5.7 pg. 107 DP_av = 5; %avionics depreciation period (See Table 5.7)(years) C_dav = (F_dav*ASP)/(DP_av*U_annbl*V_bl); %cost of depreciation of the avionics systems in USD per nm F_dapsp = 0.85; %airplane spare parts depreciation factor (see Table 5.7) F_aspsp = 0.10 ; %airplane spare parts factor (suggested value) DP_apsp = 10; %airplane spare parts depreciation period (See Table 5.7) (years)

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C_dapsp = ((F_dapsp*F_aspsp)*(AEP-N_e*EP))/(DP_apsp*U_annbl*V_bl); %cost of depreciation of the airplane spare parts in USD per nm F_dengsp = 0.85; %engine spare parts depreciation factor (see Table 5.7) F_engsp = 0.50; %engine spare parts factor (suggested value) DP_engsp = 7; %engine spare parts depreciation period (See Table 5.7) (years) ESPPF = 1.50; %engine spare parts price factor (suggested value) C_dengsp = (F_dengsp*F_engsp*N_e*EP*ESPPF)/(DP_engsp*U_annbl*V_bl); %cost of depreciation of the engine spare parts in USD per nm DOC_depr = C_dap + C_deng + C_dprp + C_dav + C_dapsp + C_dengsp; % Section 5.2.4: DOC of Landing Fees, Navigation Fees and Registry Taxes, % DOC_lnr W_To = 2.3492*10^5; %Takeoff weight (lbs) C_aplf = 0.002*W_To; %airplane landing fee per landing C_lf = (C_aplf)/(V_bl*t_bl); %DOC due to landing fees in USD/nm C_nf = 0; %Assume navigation fees = 0 USD/flight C_rt = 0; %Assume registry taxes = 0 USD/flight DOC_lnr = C_lf + C_nf + C_rt; %DOC of landing fees, navigation fees and registry taxes in USD/nm %DIRECT OPERATING COST (not including financing) DOC = DOC_flt + DOC_maint + DOC_depr + DOC_lnr; % Section 5.2.5: DOC of Financing, DOC_fin DOC_fin = 0.07*DOC; %DOC of financing in USD/nm %NOTE: financing costs typically run to 7% of total DOC %OVERALL DIRECT OPERATING COST (including financing) DOC = DOC + DOC_fin % Section 5.3: METHOD FOR ESTIMATING THE IOC OF COMMERCIAL AIRPLANES, IOC %========================================================================== C_mls = 1000; %cost for meal service; depends on route, level of service, etc. C_paxins = 0; %cost for passenger insurance; based on 'Warsaw Convention' C_cat = 1000; %cost for cabin attendents (see pg. 114 for explanation) C_paxgen = 1000; %passenger handling/baggage handling, sales/reservations, %security, etc. %No reliable quantitative methods exist for these values %Airplane designer can lower baggage costs through good baggage space %designs and efficient cabin layout IOC_pax = C_mls + C_paxins + C_cat + C_paxgen; %IOC for passenger services % Section 5.3.2: IOC for Station Operation, IOC_sta C_mgef = 10000; %cost of maintaining ground equipment & facilities

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C_dgef = 1000; %cost of depreciation of ground equipment & facilities %No reliable quantitative methods exist for these values IOC_sta = C_mgef + C_dgef; %IOC for station operation % Section 5.3.3: IOC for Airplane Service, Airplance Control and Freight, % IOC_ascf C_aps = 10000; %cost of airplane service; dependes on how well airplane was designed %from a gate servicing viewpoint C_apctrl = 10000; %cost of airplane control; depends on amt of equipment and personnel %req'd to push airplane away from gate C_frt = 10000; %cost associated with handling freight; NOT passenger baggage IOC_ascf = C_aps + C_apctrl + C_frt; %IOC for aircraft service, control and freight % Section 5.3.4: IOC for Promotion, Sales and Entertainment, IOC_pse % IOC_pse includes the following: %-Commissions to travel agents %-Publicity and Ad Campaigns %-Entertainment %Airplane designer has no leverge over this item; no reliable quantitative %methods exist for these values IOC_pse = 0; % Section 5.3.5: IOC for General and Administrative Cost, IOC_gaa % IOC_gaa includes the following: %-requirements for administrative and accounting personnel as well as %for their facilities %-requirements for corporate staffers and their facilities %Airplane designer has no leverge over this item; no reliable quantitative %methods exist for these values IOC_gaa = 0; %OVERALL IOC IOC = IOC_pax + IOC_sta + IOC_ascf + IOC_pse + IOC_gaa %IOC in USD per nm for a commercial airplane C_opsdir = DOC*R_blann*N_yr/N_m %Direct OC per operator per plane; USD/airplane %DOC = per nautical mile of airplane flown %expressed in USD/nm (per airplane) C_opsind = IOC*R_blann*N_yr/N_m %Indirect OC per operator per plane; USD/airplane %IOC = per nautical mile of airplane flown %expressed in USD/nm (per airplane) C_OPS = C_opsdir*N_m + C_opsind*N_m C_disp = 0.01*(C_RDTE + C_man) ��

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