Runway Based Space Launch System

8/13/2019 Runway Based Space Launch System

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Georgia Institute of Technology

Final Report

Runway-Based Space Launch SystemAerodynamics

Authors:

Robert Golas and Natsuki Nakano

Professor:

Dr. Narayan Komerath

Integrative AssignmentAE 3021 A - High Speed AerodynamicsMay 1, 2013


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Executive Summary

With the extremely high cost of launching directly to space using rockets, other means of spaceaccess must be explored to make certain space projects financially feasible. The launch vehicle

proposed in this document is a single stage horizontal takeoff and landing vehicle capable ofreaching low Earth orbit. The vehicle will utilize a magnetic levitation rail capable of accelerat-ing it to a speed of at least Mach 1. At this point, the vehicle will ignite its ramjet engine whichwill be used to accelerate to Mach 5 in the stratosphere. The ramjet will then mechanicallybe altered to perform as a scramjet and will be used to accelerate to Mach 15 at an altitudeof approximately 25 kilometers where an air breathing engine is no longer viable. Liquid aircycle engines will be used to maximize efficiency. At Mach 15, the ramjet/scramjet engine inletwill close and the vehicle will fire its rocket engine to accelerate to orbital velocity and reachlow Earth orbit. This vehicle does not require any turbomachinery which makes it lightweightand less complex than other proposed options. The vehicle is capable of carrying 100,000 kg toorbit with only 180,000 kg of fuel. Unfortunately, the high drag incurred cannot be overcome

by current engines available. With a future increase in the thrust capability of engines, thisvehicle will be well suited for single stage horizontal takeoff space access.


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Contents

1 Introduction 4

2 Horizontal Takeoff Space Vehicles 5

3 Hypersonic Airbreathing Vehicles 8

4 Current Heavy-Lift Aerodynamic Vehicles 12

5 Conceptual Design 135.1 Preliminary Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.2 Body and Wing Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.3 Design Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165.4 Wing Loading and Speed Variations . . . . . . . . . . . . . . . . . . . . . . . . . 185.5 Staging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195.6 Preliminary Aerodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195.7 Advanced Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

6 Conclusion 24

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List of Figures

2.1 SpaceShipOne and White Knight Courtesy of Scaled Composites [1] . . . . . . . 52.2 SpaceShipTwo and White Knight Two Courtesy of Virgin Galactic[2] . . . . . . 62.3 Pegasus Launch Vehicle Courtesy of NASA [3] . . . . . . . . . . . . . . . . . . . 6

3.1 DARPA Hypersonic Technology Vehicle 2 Courtesy of Aviation Week[4] . . . . . 8

3.2 NASA X-43 Courtesy of X-Planes Data Site [5] . . . . . . . . . . . . . . . . . . . 93.3 Boeing X-51 Attached to a Boeing B-52 Courtesy of Business Insider [6] . . . . . 93.4 Rockwell X-30 NASP Courtesy of Style of Speed[7] . . . . . . . . . . . . . . . . 103.5 Reaction Engines Limited Skylon Courtesy of Reaction Engines[8] . . . . . . . . 10

5.1 Conically Derived WaveRider Body Shape Courtesy of A. Filippone [9]. . . . . . 155.2 Newtonian Flow Field over a Flat Plate Courtesy of Anderson [12] . . . . . . . . 205.3 Lift and Drag Predictions Derived from Newtonian Theory Courtesy of Anderson

[12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.4 CAD Model of the Body of the Vehicle Including the Payload Section . . . . . . 215.5 Diamond Airfoil Shock Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

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List of Tables

4.1 Heavy-Lift Aerodynamic Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5.1 Total Mass Sizing (kg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165.2 Wing Area Variations (m2) with Different Wing Loads at 10% Mass Contingency 185.3 Wing Area Variations (m2) with Different Wing Loads at 40% Mass Contingency 18

5.4 Skin Friction Drag Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.5 Total Lift During Different Operating Conditions . . . . . . . . . . . . . . . . . . 235.6 Total Drag During Different Operating Conditions . . . . . . . . . . . . . . . . . 23

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Chapter 1

Introduction

Current developments of a horizontal takeoff space access vehicle are still in the conceptual

design phase. There are many difficulties associated with launching from a runway into orbit.The primary issue is that the vehicle must be able to operate well in the subsonic, transonic,supersonic, and hypersonic regimes, and do so very efficiently. Horizontal takeoffs typicallyrequire an airbreathing engine. As of now, there are no engines, whether turbojet, ramjet,scramjet or otherwise, that can operate at orbital speed. This indicates that a rocket of sometype is required. At low speeds, the airbreathing engines are very efficient but the I spand thrustdrops significantly above Mach 5. In order to function efficiently, the payload mass should berelatively small in order to reduce fuel mass. Some of this mass can be reduced by using a liquidair cycle engine (LACE) that collects and liquefies oxygen and stores it as oxidizer on board. Ahypersonic vehicle also must operate under extreme temperature conditions requiring advancedthermal protection systems. This document will discuss how prior aircraft have attempted to

overcome these difficulties, and will discuss a new proposed conceptual design.

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Chapter 2

Horizontal Takeoff Space Vehicles

Only a few horizontal takeoff space vehicles have been designed and successfully launched. There

have only been two successful horizontal takeoff space vehicles capable of carrying passengersand neither of them achieve hypersonic speed. The payloads each of these vehicles can carry issignificantly less than the requirements of this project.

Figure 2.1: SpaceShipOne and White Knight Courtesy of Scaled Composites [1]

1. SpaceShipOne (Scaled Composites)

(a) White Knight

White Night was used to launch Spaceship One from the ground to 15 km in altitude.It uses two General Electric J85-GE-5 after-burning turbojest, producing 11 kN ofthrust each and 16 kN if afterburners are used. White Knight is designed to carry

a payload up to 3600 kg with a wingspan of 25 m. Despite being developed as aSpaceship One launcher, White Knight was also used to test other space vehiclessuch as Boeing X-37 spacecraft.

(b) SpaceShipOne

After being launched by White Knight, Spaceship One uses Hybrid Solid rocket en-gine produced by SpaceDev to carry itself from 15Km to 100Km in altitude. Space-ship One only has one engine producing 73.5 kN throughout its burn time of 87seconds. Spaceship One was made for and won the Ansari X Prize for being the firstprivate reusable manned spacecraft, carrying one pilot to the orbit.

2. SpaceShipTwo (Virgin Galactic)

(a) White Knight Two

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White Knight Two was designed as a successor to White Knight One. Unlike WhiteKnight One, it has an ability to carry aircraft other than Spaceship One, allowingthe use with testing other aircrafts. White Knight Two has two fuselages whichsandwiches Spaceship Two connected by the wing. It has an ability to carry 17,000kg payloads to 50,000 ft or 200 kg to LEO with a wingspan of 43 meters.

(b) SpaceShipTwo

Spaceship Two is the improved version of Spaceship One. White Knight Two wouldcarry it up to an altitude of 50,000 ft. Unlike Spaceship One, Spaceship Two hasfuture space touring in mind. Other than two crews, it can carry six passengers whowould sign up for private space travel. The rocket motor onboard Spaceship Twoproduces maximum thrust of 270 kN, accelerating Spaceship Two to 4,000 km/h.Spaceship Two has a wingspan of 8.3 meters.

Figure 2.2: SpaceShipTwo and White Knight Two Courtesy of Virgin Galactic [2]

3. Pegasus (Orbital Sciences Co.)

(a) Stargazer

Stargazer is the modified Lockheed L-1011 commercial aircraft modified to carryPegasus spacecraft under its fuselage. It is designed to carry Pegasus up to analtitude of 40,000 ft where it would be launched.

(b) Pegasus

The Pegasus rocket is launched at 40,000 ft. It has an advantage of avoiding flyingwithin a thick atmosphere by launching it in high altitude. It is designed to carry a443 kg payload using three stage rockets with a wingspan of 6.7 meters.

Figure 2.3: Pegasus Launch Vehicle Courtesy of NASA [3]

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There are a few other horizontal take off vehicles capable of achieving hypersonic speed thathave not yet reached space. Many of these hypersonic vehicles use a techinque similar to thePegasus rocket, or actually use a Pegasus rocket. These vehicles will be discussed in the nextchapter.

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Chapter 3

Hypersonic Airbreathing Vehicles

Hypersonic vehicles are classified as an aircraft that can fly at speeds varying from Mach 5 to

Mach 20. In order for a hypersonic vehicle to use an air-breathing engine, a scramjet mustbe utilized. A scramjet works like a ramjet in that it uses high speed flow to compress anddecelerate the incoming air before combustion. Unlike a ramjet, the flow through a scramjetremains supersonic throughout the entire engine. This allows the scramjet to operate withextreme efficiency at very high speed which is necessary in producing a reusable, low costlaunch vehicle. The fastest air-breathing aircraft to date is the unmanned DARPA HypersonicTechnology Vehicle 2 which utilized a scramjet and reached a speed of Mach 20.

Figure 3.1: DARPA Hypersonic Technology Vehicle 2 Courtesy of Aviation Week [4]

The Hypersonic Technology Vehicle 2 was a joint project between DARPA and the United StatesAir Force. Two HTV-2s were built and then tested in 2010 and 2011. The HTV-2 was launchedon a Minotaur IV light rocket. The first test was purposefully terminated after 9 minutes offlight after it entered a destructive roll behavior. The second test launch experienced a similarfate. As mentioned earlier, this vehicle relied on a rocket to enter the lower atmosphere andthen used its trajectory to provide the initial velocity used to ignite its scramjet engines. Thistype of vehicle is clearly unsuited for a horizontal take off space access vehicle; it must use arocket to reach hypersonic speeds and it also was not designed to land.

The most feasible hypersonic air-breathing aircraft to date are those carried to an initial altitudeby a carrier aircraft. The hypersonic vehicle then separates from the aircraft and fires a rocket

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booster to accelerate the vehicle to a velocity in which the scramjet can be ignited. The NASAX-43 and the Boeing X-51 both utilized this technology. The X-43 is extremely small at just 3.7meters in length. The vehicle uses a lifting body design where the body provides most of theaircrafts lift. The aircraft was brought to altitude using a Boeing B-52. The X-43 was attachedto a Pegasus rocket which was used to bring the vehicle up to the speed in which the scramjet

could be ignited. The first test launch was unsuccessful after the Pegasus booster lost control.The second test launch vehicle reached Mach 6.83 and had a burn time of 11 seconds. After theburn, the X-43 flew for an additional 7 minutes before it was flown into the Pacific Ocean. Thethird test flight achieved Mach 9.68 with a 10 second burn time and a 10 minute glide into anintentional crash. The X-43 primarily used two pounds of hydrogen fuel. Scramjets do not needadditional onboard oxygen which significantly reduces size and mass. In order to deal with theheating problems, the X-43 cycled water behind the engine cowl and leading edges to cool thesurfaces. In the future, a similar technique can be used with the fuel like the SR-71.

Figure 3.2: NASA X-43 Courtesy of X-Planes Data Site [5]

The X-51 performs in a similar fashion as the X-43. It is nicknamed the WaveRider because it

utilizes shockwaves to generate additional lift. It too was carried to an altitude of approximately50,000 feet by a B-52. After separation, it utilized a MGM-140 ATACMS solid rocket booster toaccelerate the vehicle to Mach 4.5. The scramjet engine is lit using ethylene and then transitionsto approximately 270 lbs. of JP-7. The first and third test flights both failed, however, thesecond test flight was successful. The X-51 flew under powered flight for 140 seconds setting anew record for a scramjet. It is about twice the size of the X-43 with a total length of 7.62 meters.A fourth test flight is planned for early 2013. Neither of these vehicles carried passengers, neitherwas designed to actually land, and both had very poor success percentages.

Figure 3.3: Boeing X-51 Attached to a Boeing B-52 Courtesy of Business Insider [6]

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During the heart of the Cold War, the US and Russia both started programs to create hypersonicaircrafts called the Aurora and the Ayaks which are both seen as the precursor to hypersonicvehicles.

Using three stages, an aircraft, a rocket, and a scramjet, is not very practical from a coststandpoint. Due to these issues, there is need for a single-stage, reusable hypersonic aircraft.The Rockwell X-30 NASP was the first conceptual single-stage to orbit (SSTO) aircraft. Thereare no details on how the aircraft would perform under low speed and take-off conditions,however, the X-30 body shape used a waverider configuration. Again, this shape generatedcompression lift from shockwaves. The body has two small wings which were essentially to beused to provide trim and control in high-speed flight. These small wings would have difficultygenerating enough lift to initially get off the ground. The planned dimensions labeled the X-30as being 48.8 meters in lengths with a 22.6 meter wingspan. This concept was scaled downand eventually became the X-43. The Russian Tupolev Tu-2000 and the British HOTOL usedsimilar concepts.

Figure 3.4: Rockwell X-30 NASP Courtesy of Style of Speed [7]

Present horizontal takeoff to orbit hypersonic aircraft are still in the conceptual phase. Thereare two noteworthy designs, namely the British Reaction Engines Limited Skylon and the IndianAVATAR RLV. Both of these vehicles use Liquid Air Cycle Engines. The vehicle takes off froma conventional airfield and collects and liquefies air in the atmosphere. They then separateoxygen and store in on board for flight beyond the atmosphere. The AVATAR has a proposedweight of 20 tons with 60 of the mass composed of liquid hydrogen fuel. It is theorized that itcan carry a satellite up to one ton to a 100 km orbit in a single stage. It is said to be able tobe used approximately 100 times. This would significantly reduce launch costs.

Figure 3.5: Reaction Engines Limited Skylon Courtesy of Reaction Engines [8]

The Skylon is aiming for a reusability of 200 launches. It aims to carry up to 15 tons. It iscurrently planned to be unmanned. After landing, the Skylon would have a turnaround time

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of just two days. All hypersonic engines must use precooling in order to function. The vehicleuses a SABRE engine with a very interesting design. It operates like a conventional jet engineup to Mach 5.5 at an altitude of 26 kilometers. The air inlet closes and then operates as a highefficiency rocket until it reaches orbital speed. Unlike all other aircraft previously listed, theSkylons SABRE engines are not scramjets but rather a jet engine running combined cycles of

a precooled jet engine, a rocket engine, and a ramjet. This is similar to the SR-71 design but itremains an air-breathing aircraft up to a velocity of Mach 5.5 utilizing a state of the air coolingsystem. It has a length of 83.3 meters, a wingspan of 25.4 meters, and can carry a payload of15,000 kg which is still significantly less than the 50,000 kg requirement of this project.

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Chapter 4

Current Heavy-Lift Aerodynamic Vehicles

The five greatest takeoff weight heavy-lift vehicles can be found in Table 4.1. The aircraft

have the potential to carry large hypersonic vehicle carrying a large payload to an initial launchaltitude. All of these vehicles have a relatively low service ceiling of approximately 40,000 feet.The B-52 launched the X-51 at 50,000 feet, so these vehicles may show a slight decrease inperformance at the lower altitude.

Table 4.1: Heavy-Lift Aerodynamic Vehicles

Aircraft Takeoff Weight (kg) Wing Span (kg)

Antorov An-225 640,000 88.4Airbus A380F 590,000 79.75

Boeing B747-8F 448,000 68.45

Antorov An-124 405,000 73.3Lockheed C-5B 381,000 67.89

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Chapter 5

Conceptual Design

5.1 Preliminary Idea

There were two main design considerations and thought processes that were contenders for afinal design construct. The first was a piggyback type aircraft that would use a heavy-lift vehicleto carry it to a certain altitude. At that point it would detach and use a rocket to accelerate tohypersonic speeds where it would then use a scramjet to maintain hypersonic velocity. There arefew main problems associated with this technique. First, a heavy-lift aircraft capable of carryingthe orbital vehicles payload (the power array), the orbital vehicle itself, the orbital vehicles fuel,and its own fuel would be necessary. This is simply outside the realm of current capabilities.Even if it could be carried, an air-breathing scramjet has never been able to be successfullyplaced into orbit. Finally, this multistage technique would require a lot of synchronization, atleast two separate aircraft, fuel for both aircraft, and would more than likely not be able to

meet the payload mass requirements. For these reasons, the following concept has been chosenas the most likely contender.

The plan is to utilize a system similar to the Reaction Engines Limited Skylon. The vehicle willfunction as an all-inclusive horizontal take-off and landing orbital vehicle. The vehicle will beplaced on a mag-lev rail which will be used to accelerate to a velocity of at least Mach 1. At thispoint in time, a ramjet engine similar to the SABRE engine will be ignited producing additionalthrust. The body shape will be similar to the Boeing X-51 with more pronounced delta wingsto create lift at lower flight speeds. The bodys wedge-like shape will create compression liftat high flight speeds. A combination of compression lift and lift from the wings will generateenough total lift to allow the vehicle to take off from the mag-lev rail.

A liquid air cycle engine will be used to conserve some of the initial vehicle mass and storeLOX onboard. The ramjet will be used until LOX tanks are full and the vehicle reaches a speedof approximately Mach 5. Around Mach 5, the shape of the inner air intake manifold will bechanged mechanically. This will change the engine from a ramjet to a scramjet. In the ramjetconfiguration, the intake manifold will slow the flow to subsonic speeds using a combination oframps and baffles. In the scramjet configuration, the effect of these ramps and baffles will bereduced to allow supersonic flow throughout the engine. The scramjet will be used from Mach5 to Mach 15. At this point, like the SABRE, the air intake will be closed and the vehicle willenter a closed cycle rocket booster stage to reach low earth orbit using the stored LOX and LH2.Unlike the SABRE, this engine is simply a ramjet/scramjet and does not require the turbojetengine components which will reduce mass, complexity, and fuel consumption. The aircraft will

require two separate engines unlike the SABRE; one will be the combination ramjet/scramjet,and the other will be a rocket engine mounted in the rear of the aircraft. By separating the

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rocket engine and the ramjet/scramjet, the rocket engine is not subjected to the extremelyhot flow from the ramjet/scramjet engine and can also use a nozzle more suited to a rocketsneeds.

This vehicle will require significant thermal protection and precooling to ensure the aircraft doesnot disintegrate. Due to the delta wing shape, the vehicle will glide similar to the Space Shuttleupon reentry and will be able to land on a runway and slow down with the aid of parachutes.With this technique, it is believed that this vehicle will be extremely efficient, cost effective,will be able to carry heavy loads, and will have a very fast turnaround time.

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5.2 Body and Wing Shape

There is great difficulty in designing a body and wing shape suitable for a speed regime rangingfrom zero to reentry speeds of Mach 30. The body shape must be conically derived in order toensure that the body will always be inside of the shock wave generated by it. Figure 5.1shows

a typical WaveRider body shape. In this configuration, the center area will be used to store thepayload as well as fuel.

Figure 5.1: Conically Derived WaveRider Body Shape Courtesy of A. Filippone [9]

The ramjet/scramjet combination engine will be placed near the center of the body. The body infront of the engine will act as a dynamic compressor and the aft body will act as an expansionnozzle. Similar to the figure, this concept will utilize delta wings as the primary source ofaerodynamic lift. The body wings will be similar to a Caret wing with an anhedral to thebody. This generates a shock between the leading edges trapped horizontally spanwise andvertically as well. This traps a large volume of air between the shock and the fuselage. Thiscauses a pressure differential creating extra lift. The Caret wing also reduces thermal loads onthe fuselage since the shock is held away from the body. While anhedral wings typically are

unstable, this effect can be negated by increasing leading edge sweep angle. Every five degreesof sweep has the same stabilizing effect as one degree of dihedral, so with a significant sweep,the anhedral instability can be overcome. With a max scramjet operating range up to Mach15, the minimum sweep angle to ensure the body is within the Mach cone is 86.1 degrees. Inorder to ensure the aircraft has enough lift at low velocities, heavy lift devices such as flapsand leading edge slats will be added if necessary. The airfoil shape itself will be biconvex foroptimal performance in the super to hypersonic regime.

In section 5.4, the required wing areas under different wing loadings with different take offmasses can be seen. Assuming maximum takeoff weight of 304,111 kg using a 25

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5.3 Design Sizing

In order to calculate the total initial takeoff mass, Equation 5.1 the rocket equation wasused.

v= ve ln(m0m1

) (5.1)

In this equation, v is the total velocity change, ve is the effective exhaust velocity (equal tothe specific impulse multiplied by Earths standard gravity), m0 is the initial mass, and m1 isthe final mass.

It was assumed that the rocket engines used would have a specific impulse similar to that of thespace shuttle engines which have a specific impulse of 452.3 seconds. The orbital velocity in lowearth orbit at an altitude of 400 km is 7.67 km/s. The Earths rotation velocity is approximately0.47 km/s at the equator. The vehicle will utilize the ramjet/scramjet engine to reach Mach 15

before firing the rocket engines which gives the vehicle an initial velocity of 4.75 km/s. Utilizingthe initial velocity and Earths rotational velocity results in a required delta V of 2.45 km/sto reach LEO. This information was used to find the required initial mass to utilize the rocketbased on the initial conditions.

A contingency from 10% to 40% was added to account for the ramjet/scramjet fuel. Sincethe specific fuel consumption of a ramjet or scramjet is not known, especially when using aLACE system, it is difficult to estimate an exact number. This contingency range was chosento represent the high and low ends of the spectrum. A preliminary estimation was performedto verify this range. Using a thrust to weight ratio of 1, a specific impulse of 1550 which wasfound to be typical of a ramjet/scramjet [10], and a lift to drag ratio of 7 which is similar tothat of a Concorde. Using the 100,000 kg payload with 10% structural contingency gives a total

thrust available of 2,678,428 N for a net thrust of 2,295,796 N. Using a fuel flow rate of 176kg/s results in a total fuel mass of approximately 40% of the total initial mass. This verifiesthe initial contingency range.

The total mass estimates with contingencies can be found in Table 5.1.

Table 5.1: Total Mass Sizing (kg)

Payload Mass Mass Percentage Structural Mass Initial MassMass with Contingency

10% 40%

50,000 10% 55,000 95,578 105,136 133,809

50,000 20% 60,000 104,267 114,693 145,97450,000 25% 62,500 108,611 119,472 152,05675,000 10% 82,500 143,367 157,704 200,71475,000 20% 90,000 156,400 172,040 218,96075,000 25% 93,750 162,917 179,209 228,084

100,000 10% 110,000 191,156 210,271 267,618100,000 20% 120,000 208,534 229,387 291,947100,000 25% 125,000 217,222 238,945 304,111

Under a worst case scenario, the ramjet/scramjet engine will act like a rocket. Under standardconditions, the ramjet/scramjet is much more fuel efficient than a rocket due to its airbreathing

nature. The rocket equation, Equation 5.1 was used to simulate a worst case scenario interms of fuel consumption. Using an Isp of 1550, an initial takeoff mass of 304,111, and a final

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mass of 217,222 when the vehicle is at Mach 15 in the stratosphere prior to firing the rocketengine yields a total v of 5.11 km/s. In the stratosphere, Mach 15 corresponds to 4.43 km/s.Since the vehicle takes off at around Mach 1 at sea level, there is an initial velocity of 341m/s which yields a total v to Mach 15 of 4.09 km/s. Again utilizing Equation 5.1indicatesthat the initial takeoff mass required to achieve Mach 15 is 284,308 kg. This is a margin of

19,804 kg of fuel. This margin should be even greater in reality due to the greater efficiency oframjets/scramjets.

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5.4 Wing Loading and Speed Variations

The wing loading can be considered since the range of possible masses has been found. Thefast that an aircraft travels, the more lift is produced by each unit of area on each wing. Thisallows a smaller wing to carry the same weight in operating with a high wing loading. Since

this aircraft will be mostly composed of a large blunt body creating compression lift, the wingscan be even smaller, further increasing wing loading. The aircraft is also being launched fromthe runway at Mach 1 which reduces the requirement of having the wings create a lot of lift atlow speed, further increasing wing loading.

Historically, the heavy lift vehicles tend to have very high wing loading parameters in the areaof approximately 500-800 kg/m2. The space shuttle had a wing loading value of 586 kg/m2. Forthis reason, this range of wing loadings will be considered. Table 5.2shows the range of wingareas in square meters under different wing loadings using the 10% mass contingency valuesfound in Table 5.1.

Table 5.2: Wing Area Variations (m2) with Different Wing Loads at 10% Mass Contingency

10% Mass Contingency (kg)Wing Loading (kg/m2)500 650 800

105,136 210.3 161.7 131.4114,693 229.4 176.5 143.4119,472 238.9 183.8 149.3157,704 315.4 242.6 197.1172,040 344.1 264.7 215.1179,209 358.4 275.7 224.0210,271 420.5 323.5 262.8

229,387 458.8 352.9 286.7238,945 477.9 367.6 298.7

Table 5.3shows the range of wing areas in square meters under different wing loadings usingthe 40% mass contingency values found in Tables 5.1.

Table 5.3: Wing Area Variations (m2) with Different Wing Loads at 40% Mass Contingency

40% Mass ContingencyWing Loading (kg/m2)500 650 800

133,809 267.6 205.9 167.3145,974 291.9 224.6 182.5152,056 304.1 233.9 190.1200,714 401.4 308.8 250.9218,960 437.9 336.9 273.7228,084 456.2 350.9 285.1267,618 535.2 411.7 334.5291,947 583.9 449.1 364.9304,111 608.2 467.9 380.1

As shown in Table 5.2and Table 5.3,the wing area can vary from 131 m2 to 608 m2 depending

on the wing loading and total takeoff mass. Since the wings are required to be rather smalldue to sweep angle restrictions, high wing loadings are more ideal. A wing loading value of 800kg/m2 is therefore reasonable, especially since mag-lev rails are accelerating the vehicle to Mach

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1 prior to takeoff. With large wing areas, most of the area will be composed of the length ratherthan wingspan, again due to the limitations on sweep angle. This is also rather convenient sincescramjets typically have to be very long in order to function properly.

5.5 Staging

This conceptual aircraft is essentially a single stage to orbit aircraft since none of the stagesare jettisoned and most rely on each other. The initial stage will be the mag-lev rail usedto accelerate the vehicle to Mach 1. At this point the vehicle ignites the ramjet engine andleaves the rail. In the ramjet configuration, the engine must compress the air to approximately140 atmospheres in order to liquidize the oxygen and cool it before entering the combustionchamber to ensure the components will not melt. The engine will utilize a precooler heatexchanger to perform this task. Excess LOX will be stored in oxidizing tanks for later use withthe rocket engine. When Mach 5 is achieved, the baffle and intake shape will change so thatthe air in the combustion chamber is supersonic and the scramjet can be used. The scramjet

will accelerate the vehicle to Mach 15 and an altitude of approximately 25 kilometers wherethe air becomes too thin and oxygen deprived to reliably use air breathing engines. At thispoint, the air intake will be completely closed to make the vehicle as aerodynamic as possible.The rocket engines will be fired, giving the vehicle a boost to 7.67 km/s needed to reach orbitalaltitude. The rocket engines will produce around 300 tonnes of thrust during this final stage inorder to ensure that the orbital altitude is achieved. These velocities and staging points werecalculated using the supersonic, hypersonic, and rocket equations to maximize efficiency andfuel consumption. These calculations can be found in the previous section (Wing Loading andSpeed Variations).

5.6 Preliminary Aerodynamics

Since the vehicle exits the transonic regime into the supersonic regime while still on the mag-levtrack, subsonic aerodynamics are not of primary concern. Supersonic lift is generated strictlyas a function on angle of attack and freestream Mach number. Just after takeoff at a 12 degreeangle of attack and a Mach number of 1.05 yields a lift coefficient of 2.6. As the Mach numberincreases, the lift coefficient decreases. At Mach 5 with 12 degrees angle of attack, the liftcoefficient drops to just 0.17. The drag coefficient can similarly be modeled and will be highnear the transonic regime which a value of 0.383 at Mach 1.05 dropping to just 0.036 at Mach5. Equation 5.2and Equation 5.3were the approximations used to find the supersonic lift and

drag coefficients respectively.

cl= 4M21

(5.2)

cd = 42M21

(5.3)

It is difficult to estimate exactly what the lift and drag coefficients will be in the hypersonicregime since these will primarily be a function of the body shape and the efficiency at which itproduces compression lift. Ideally, for a maximum coefficient of lift, the vehicle will be at an

extremely high angle of attack of 54.7 degrees which will be maintained until the 25 kilometeraltitude. This is similar to a flat plate estimation which is the best approximation available with

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the given information. At this angle of attack, the normal coefficient is 1.33, the lift coefficient is0.77, and the drag coefficient is 1.085. The angle of attack can be altered to change the lift anddrag coefficients to suit the needs of the mission. Equation 5.4, Equation 5.5, and Equation5.6were used to find the normal coefficient, lift coefficient, and drag coefficient approximationsin the hypersonic regime. Figure 5.2 shows the Newtonian flow field over a flat plate which

was used to calculate the lift, drag and normal forces.

cN= 2 sin2 (5.4)

cl = cNcos (5.5)

cd = cNsin (5.6)

Figure 5.2: Newtonian Flow Field over a Flat Plate Courtesy of Anderson [ 12]

Though this yields a maximum lift coefficient, the drag coefficient is also extremely high. If

a much more moderate angle of attack of 20 degrees is chosen, the result is a lift coefficientof 0.22 and a drag coefficient of 0.075. At lower angles of attack, there is a much better liftto drag ratio which is ideal for this aircraft. This tradeoff between lift and drag derived fromNewtonian theory can be found in Figure 5.3

Figure 5.3: Lift and Drag Predictions Derived from Newtonian Theory Courtesy of Anderson[12]

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The thrust to weight ratio will initially be approximately 0.667 initially after takeoff. Thisequates to approximately 200 tonnes of thrust. As the mass decreases as fuel is burned, thethrust to weight ratio will gradually increase. When the vehicle is converted from a airbreatherto a rocket engine, the thrust will increase to approximately 300 tonnes (1,350 kN) which willhave a thrust to weight ratio of approximately 1.5 which will increase to 2.4 at engine burnout.

This amount of thrust should be capable of inserting the vehicle into orbit.

In comparison, the Skylon has an atmospheric thrust to weight ratio of 0.768 and an exoat-mospheric thrust to weight ratio ranging from 1.2 to 3. Its takeoff weight is 345,000 kg so thethrust characteristics of this vehicle are very similar to that of the Skylon.

5.7 Advanced Aerodynamics

This vehicle will take advantage of a diamond shaped airfoil and body in order to maximizelift in both the supersonic and hypersonic regime. The diamond wedge airfoil has a leading

and trailing edge half angle of 10 degrees. With the total length requirement of 52.8 metersdetermined in the Body and Wing Shape section, this half angle yields a maximum mid chordheight of 9.31 meters. If the payload section is cylindrical is oriented horizontally across the23.87 meter span of the vehicle with added diameter design tolerances (yielding a 9 meterdiameter total), the total payload bay section volume would be 1,341.7 m3. In comparison, thespace shuttle payload bay had a diameter or 4.57 meters and a length of 18.3 meters for a totalvolume of 300 m3. If constrained by fuel volume, this payload volume can be reduced to fulfillthese needs. Figure 5.4 gives a visualization of the payload section located inside the mainbody of the vehicle.

Figure 5.4: CAD Model of the Body of the Vehicle Including the Payload Section

Analysis of this airfoil was performed at Mach 2.5 at a 15 degree angle of attack. Figure 5.5shows how the airfoil was analyzed. Using Prandtl-Meyer expansion fan analysis on the top ofthe airfoil and a compression shock followed by an expansion fan on the lower surface yielded alift coefficient per unit span of 0.651 and a drag coefficient per unit span of 0.217. In comparison,using Equation 5.2and Equation 5.3yielding values of 0.457 and 0.120 respectively. As shown,the actual lift an drag coefficients from shock analysis are higher than the approximationsindicated. The actual L/D from the shock analysis resulted in a value of 3.

This body and wing shape can be utilized as a wave rider as well. As long as an angle ofattack of 10 degrees is maintained, the upper surface will always be in the shadow of the lowersurface. At Mach 15, using the Rankine-Hugoniot relations yields a cp,max value of 1.836. At10 degrees angle of attack, the leading underside edge is the only surface seen by the flow andthat surface is at a -20 degree inclination relative to the flow. With the upper surface parallel

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Figure 5.5: Diamond Airfoil Shock Analysis

to the freestream, this yields a cp value of 0.215. The corresponding lift and drag coefficientsare 0.202 and 0.073 respectively for a total L/D of 2.75.

Skin friction drag was estimated using the Boeing reference temperature approach. Equation5.7was used to find the reference temperature. Using this temperature, the dynamic viscositycould be found using Equation 5.8. With this information, the compressible skin frictioncoefficient could be found using Equation 5.9. The skin friction coefficient was then used in

the drag equation (Equation 5.10) to find the skin friction drag. This method was performedfor the length of 52.8 meters and planform area of 1260 m2 at Mach numbers of 1.2, 5, and 15with the approximate altitude locations where each respective Mach number will be reached.Table 5.4shows the breakdown of the skin friction drag data at each point.

T

T1= 1 + 0.1198M21 (5.7)

ref= (

T

Tref)0.75 (5.8)

Cf = 0.295 TT

[log(Re TT

)]2.45 (5.9)

D=1

2v2CfA (5.10)

The total lift produced by this vehicle during various flight conditions can be found in Table5.5. The lift coefficients found in the previous were used to help calculate total lift. Equation5.11 was used to calculate the total lift. The takeoff weight of the vehicle is 304,111 kg. Thisyields a downforce of 2,980 kN which can easily be overcome by the lift produced.

L=1

2v2ClA (5.11)

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Table 5.4: Skin Friction Drag Data

M Altitude (m) Density (kg/m3) Reynolds number Cf Drag (N)

1.2 0 1.225 1.4838E+09 1.140E-03 1475175 15,000 0.1936 1.0706E+08 4.570E-04 121707

15 25,000 0.0395 6.5022E+08 1.173E-04 58695

Table 5.5: Total Lift During Different Operating Conditions

M Altitude (m) Density (kg/m3) Cl Lift (kN)

1.2 0 1.225 0.1915 3,7182.5 15000 0.1936 0.651 6,52815 25000 0.0395 0.22 16,597

To ensure that the wing sizing is sufficient to allow the aircraft to liftoff from the mag lev rail,Equation 5.12the lift coefficient equation was used to solve for the planform area required. Theinitial takeoff weight was used as the lift required. The takeoff lift coefficient was calculated inthe same manner as above using shock analysis and was found to be 0.1915. The density andvelocity were taken from the standard atmosphere table at sea level at Mach 1.2.

Cl= L1

2V2S

= 304, 111kg 9.8m/s2

1

2(1.225kg/m3)(408.353m/s)2(S)

= 0.1915 (5.12)

Solving Equation 5.12 for the planform area and dividing by the length of 52.8 meters yieldsa required wingspan of 2.893 meters. With the chosen wing span of 3.6 meters, this yields

a margin of 0.7 meters. If desired, the wing sweep angle can be increased to 88.43 degrees,minimizing take off wing span which will further decrease drag. If Equation 5.2 is used, a liftcoefficient of 1.263 is found at Mach 1.2 with a 12 degree angle of attack. This yields a totalspan of 0.438 meters which seems like a gross underestimation.

The total drag was calculated during three conditions; right after takeoff, mid supersonic flight,and the upper regime of hypersonic flight. The drag coefficient for each condition was found inthe previous sections. Drag for each operating condition was found using Equation 5.10withCd instead of Cf. The SABRE engines used on the Reaction Engines Skylon have a capabilityof producing 1,960 kN at sea level and 2,940 kN in a vacuum. As shown in Table 5.6, thedrag on this vehicle far exceeds the thrust capabilities of the SABRE engines. At present time,there are no engines capable of overcoming this drag force. The thrust calculated in the DesignSizing section yielded 2.295 kN of thrust which also cannot overcome the drag produced. Untilan engine with a higher thrust output is produced, this design will remain unfeasible.

Table 5.6: Total Drag During Different Operating Conditions

M Altitude (m) Density (kg/m3) Cd Drag (kN)

1.2 0 1.225 0.383 7,4362.5 15000 0.1936 0.217 2,17615 25000 0.0395 0.075 5,658

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Chapter 6

Conclusion

Through aerodynamic analysis, it has been shown that this vehicle is capable of performing

as a single stage horizontal take off space access vehicle. This vehicle is capable of producingenough lift in the supersonic and hypersonic regime to easily counteract its own weight. At only52.8 meters long and 23.87 meters wide with a 3.6 meter wing span, this vehicle is smaller thanother similar proposed vehicles. The payload bay will have a volume 4.47 times the volume ofthe space shuttles payload pay.

The drag on the vehicle is its major downfall. Current engines may be capable of counteractingthrust in the supersonic regime, but closer to transonic and in the hypersonic regime, the dragovercomes the thrust produced. As engines improve and technology is pushed to new limits,this may no longer be an issue. With wind tunnel testing and further design iterations, thebody can be redesigned to more closely resemble a Sears-Haack body while still achieving thesame lift as the diamond shape. Aerospike nozzles used for the rocket engine may improve drag

as well.

Unmanned maglev rails have achieved speeds of approximately Mach 1.5. Some sources saythat manned trains will be able to achieve speeds of 1000 mph (Mach 1.3 at sea level) in thenear future[11]. While this is technically feasible, there have been no maglev rails built on thescale required for this vehicle. Extremely powerful magnets would also be required to ensurethat the vehicle will levitate. Additionally, liquid cooling in the vehicle to reduce temperaturewould be required unless a metal or alloy with an extremely high melting point was used suchas Tungsten (melting point of 3695 K).

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Bibliography

[1] Scaled Composites. SpaceShipOne. Digital image. HowStuffWorks. N.p., 20 June 2004. Web.5 Mar. 2013. .

[2] Virgin Galactic. SpaceShipTwo. Digital image. HowStuffWorks. N.p., 20 June 2004. Web. 5Mar. 2013. .

[3] Pegasus XL Launch Vehicle. Digital image. NASA. 10 Jan. 2012. Web. 5 Mar. 2013. .

[4] DARPA HTV-2 Falcon. Digital image. Aviation Week. N.p., 24 Apr.2010. Web. 6 Mar. 2013. .

[5] NASA X-43. Digital image. X-Planes Data Site. N.p., n.d. Web. 6 Mar. 2013. .

[6] Boeing X-51. Digital image. Business Insider. U.S. Airforce, 25

Oct. 2012. Web. 6 Mar. 2013. .

[7] Rockwell X-30 NASP. Digital image. Style of Speed. N.p., Feb. 2008. Web. 6 Mar. 2013..

[8] Skylon. Digital image. Reaction Engines, 2012. Web. 6 Mar. 2013. .

[9] Conically Derived WaveRider Body. Digital image. Advanced Topics in Aerodynamics. N.p.,2003. Web. 13 Mar. 2013. .

[10] Encyclopedia Astronautica. Encyclopedia Astronautica. N.p., 2012. Web. 29 Apr. 2013.

Encyclopedia Astronautica. Encyclopedia Astronautica. N.p., 2012. Web. 29 Apr. 2013..

[11] Murph, Darren. Chinas Maglev Trains to Hit 1,000km/h in ThreeYears, Doc Brown to Finally Get 1985 Squared Away. Engadget.Bloomberg, n.d. Web. 29 Apr. 2013. .

[12] Anderson, John David. Fundamentals of Aerodynamics. Boston: McGraw-Hill Higher Ed-ucation, 2007. Print.
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