EXTROVERT ADVANCED CONCEPT EXPLORATION ADL P- 201112121 August Bradley, Chris Duffy Georgia Institute of Technology School of Aerospace Engineering Missile Interceptor December 12, 2011
EXTROVERT ADVANCED CONCEPT EXPLORATION 2 Publishing Information We gratefully acknowledges support under the NASA Innovation in Aerospace Instruction Initiative, NASA Grant No. NNX09AF67G, to develop the techniques that allowed such work to be done in core courses, and the resources used to publish this. Tony Springer is the Technical Monitor. Copyright except where indicated, is held by the authors indicted on the content. Please contact the indicated authors komerath@gatech.edu for information and permission to copy. Disclaimer Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Aeronautics and Space Administration.
August Bradley and Chris Duffy Stage 8 12/12/2011
Table of Contents Table of Contents... i List of Figures... i List of Tables... ii Introduction... 1 Understanding the Issues... 1 Requirements... 1 Transonic Carrier... 1 Supersonic UCAV... 1 Hypersonic Weapon... 1 Initial Proposal... 2 Conceptual Design... 2 Aerodynamic Assessment... 5 Stage 5... 9 Stage 4... 9 Stage 3... 12 Stage 2... 15 Stage 1... 19 System Configuration... 20 Stage 3... 20 Stage 2... 20 Timeline... 21 Stage 6... 21 THAAD Comparison... 22 Appendix A... 24 References... 36 List of Figures Figure 1: Weight Regression... 2 Figure 2: Lift Coefficient vs. Angle of Attack... 6 Figure 3: UCAV Pitching Moment... 7 Figure 4 : UCAV Subsonic Compressible and Supersonic Pitching Moment Coefficient. 8 Figure 5: Lift cofficient for Subsonic Flow... 8 Figure 6 :UCAV preliminary Design... 10 Figure 7 :UCAV Lift Curve Slope... 10 Figure 8 : Max Lift Coefficient... 11 Figure 9: UCAV Drag Polar... 11 Figure 10 Wave Drag with varying mach number... 13 Figure 11 Skin Friction Coefficient Subsonic... 14 Figure 12 Skin Friction coefficient supersonic... 14 Figure 13 Turning Radius... 15 Figure 14 Ramjet Thrust Curve... 16 Figure 15 Rate of climb curves... 17 i
Figure 16 : TPC Drag Polar... 19 Figure 17 : TPC Flight Enevelope... 20 Figure 18: Enemy Missile Mission Profile... 22 Figure 19 : THAAD Weigh Comparison... 23 List of Tables Table 1 :Fuel Fractions... 3 Table 2 UCAV Weight Distribution... 3 Table 3 UCAV Geometric Relations... 12 ii
Introduction This assignment is designed to develop and analyze a missile interceptor system capable of quickly eliminate enemy ICBMs. The missile interceptor will be particularly designed to intercept the incoming ICBMs just before, during, and right after re-entry. The system will consist of 3 separate bodies. The launch vehicle is a subsonic cruiser that will loiter during heightened alert situations. It will carry four Unmanned Combat Air Vehicles that will pursue the target and launch a hypersonic weapon. Understanding the Issues This Missile Interceptor is to be designed for the purpose of discouraging irrational nations from launching ICBMs by proving the futility in the attempt. Requirements Transonic Carrier The large transonic carrier must be capable of long and fuel-efficient loitering, carrying extensive electronic communication and countermeasures systems, plenty of fuel, and four uninhabited combat air vehicles that can be launched on warning. It will operate at a cruise altitude of 40,000 feet. Supersonic UCAV Three Unmanned Combat Aerial Vehicles (UCAV) will be carried in the transonic patrol carrier. Small enough too fit into the fuselage of the aircraft, they are capable of accelerating and climbing to over 150,000 feet rapidly. Each UCAV must be capable of safely landing on a surface. The UCAV must be able to accelerate to supersonic speeds while carrying its hypersonic weapons. The weapons weight and length will be a defining characteristic that must be met by the UCAV Hypersonic Weapon These weapons must be capable of destroying ICBMs by kinetic kill, or by explosion in proximity. Hypersonic engines are air breathing. The air is compressed by the shock at the nozzle, though a serious problem that is encountered is the length. The air is moving so fast through then engine, that if it is to short the fuel will combust after it exit the engine reducing thrust significantly. In order to get a better sense of some of the available hypersonic weapons, the following weight regression of hypersonic weapons was created. 1
Empty Weight (lbs) ( ) Missile Interceptor Missile Length Weight AiM-9L/M 9.5 210 Shafrir 1 8.2 209 Python 3 9.6 288 Derby 11.8 310 Fim 92A-Stinger 4.9 41 Hyper-45A 12 338.86 W e i g h t 350 300 250 200 150 Missile Regression y = 39.77x - 138.38 R² = 0.9107 Missile Regression Linear (Missile Regression) l b 100 50 0 0 5 10 15 Length (ft) Initial Proposal Conceptual Design For the subsonic carrier the conceptual design is based on the design book from Jan Roskam. The initial design is based on using a weight regression of similar aircraft weights. This provides the means to make an estimation of the weight. The aircraft chosen for the estimation include the following: the KC-135, the B-52H, the Boeing 787, the A350-900, the B747-100B, and the A380-800. 400000 350000 300000 250000 200000 150000 100000 50000 0 Weight Regression y = 0.1615x + 131622 R² = 0.355 0 500000 1000000 1500000 Takeoff Weight (lbs) FIGURE 1: WEIGHT REGRESSION The amount of fuel can be determined by the mission profile. The mission profile provides fuel fractions for specific engine performance requirements. The mission profile consists of start, taxi, takeoff, climb, cruise/loiter, descent, and landing. 2
TABLE 1 :FUEL FRACTIONS Segment Column1 Fuel Fraction 1 Start 0.99 2 Taxi 0.995 3 Take-off 0.995 4 Climb 0.9868 5 Cruise 0.71 6 Descent 0.985 7 Land 0.992 Mff 0.66851195 The UCAV s conceptual design is based on the ability to carry its payload, and the highspeed characteristics necessary to reach supersonic speeds of about Mach 4. It is equipped with a scramjet engine that burns hydrogen fuel. The advantage to hydrogen fuel to jet fuel is compressed liquid hydrogen has about 123 mega joules of energy per kg, where Jet Fuel only has about 43 Mega joules of energy per kg. This allows for greater endurance, and higher performance of the scramjet engine. Due to the size of the Hypersonic missile the UCAV is designed with a scramjet engine, and a turbojet engine. The Turbojet engine will provide thrust for the initial acceleration to Mach 1.3. Once above mach 1.3 the ramjet will be used for all performance characteristics. TABLE 2 UCAV WEIGHT DISTRIBUTION Empty Weight Fuel Weight Missile Weight 3000 [lb] 1200 [lb] 1355.44 [lb] The weight distribution of the UCAV can be found above in table 2. Each UCAV will carry a payload of around 1,000 lb. The Empty weight of the UCAV is around 3,000 lb. The max takeoff weight of the UCAV is about 5,500 lb. If the aircraft can sustain a lift to drag ratio of around 8, the ramjet can produce around 1,200 lb of thrust at high altitudes, at high mach. The drag of the aircraft was a major concern. The ballistic kinetic kill missile will produce and extraordinarily large amount of lift, and turbulence if it is attached on the outside of the hull. The solution to this problem is to enclose the aircrafts weapon system in the hull, eliminating a large amount of drag. Using Fluid-Dynamic Drag, by S. Hoerner we were able to come this conclusion. The Hypersonic missile is an extraordinary piece of technology. Capable of traveling in excess of Mach 6, the missile does not require many explosives. When launched the missile will be traveling at supersonic speed, allowing it to accelerate to hypersonic speeds without the need of a rocket. The conceptual design was based off of data from the X-51 missile being developed by Boeing. This allows for a significant weight reduction, because there would be no need in a two-stage fuel system. The rocket has a thrust to weight ration of approximately 100:1. Once the missile has left, the aircraft accuracy may not be as important. If the missile is detonated in a 30 km region of the weapon, a shrapnel blast will be able to destroy the missile. This gives an extremely large 3
advantage to the aircraft based missile systems. The subsonic carrier cuts the necessary time for the supersonic UCAV to reach its target, then the hypersonic missile launched from the UCAV has a wide range of accuracy which is capable of destroying the missile quicker than a land based rocket launch. FIGURE 2: MISSILE SIZE ESTIMATE To validate this intial estimate we used a CAD drawings to make sure the size and shape were correct. Below are initial drawings using mainly boxes to make sure the missiles will fit into the UCAV. The UCAV will be a total of 24 ft long, taking up about 690 ft 3 in the transonice carrier. 4
FIGURE 3: CAD VOLUME ESTIMATE Aerodynamic Assessment Stage 7 Using Homer s Fluid Dynamic Lift publication, we found the supersonic lifting surface equation for the UCAV. The curve can be seen below. As you can see at higher speeds the aircraft C L performance is greatly increased due to the swept angle of the wings. This makes sense because the design characteristics of the UCAV favor supersonic speeds. 5
The estimate for C L is only valid for angle of attacks up to 25 degrees. After around 35 degrees, the wing is likely to stall due to vortex bursting along the wings. Analytically the way to predict these occurrences is using a CFD code and wind tunnel testing. FIGURE 2: LIFT COEFFICIENT VS. ANGLE OF ATTACK Using Homer s Fluid Dynamic Lift, we calculated the correct lifting surface theory for the aircraft. The Computation is below in Equation 1. EQUATION 1 SUPERSONIC LIFT CALCULATIONS Using The Theoretical Lift and Pitching Moment of Highly-Swept Delta Wing on a Body of Elliptic Cross-section, by T. Nonweiler, we calculated the pitching moment of the aircraft. The Incompressible downward pitching moment can be found below. 6
FIGURE 3: UCAV PITCHING MOMENT The Equations used to find the pitching moment were: EQUATION 2 INCOMPRESSIBLE PITCHING MOMENT Using Prandlt Glauert s Subsonic Compressibility factors, the moment coefficient was found. EQUATION 3 PRANDLT & GLAUERTS COMPRESSIBILITY FACTOR C p C p o 7
FIGURE 4 : UCAV SUBSONIC COMPRESSIBLE AND SUPERSONIC PITCHING MOMENT COEFFICIENT Also Updated the lift coefficient for incompressible flow. FIGURE 5: LIFT COFFICIENT FOR SUBSONIC FLOW Using Hoerners method for the compressibility effects on a delta wing flying in subsonic compressible regime. The computational equations can be found below. 8
EQUATION 4 SUBSONIC COMPRESSIBLE LIFT COEFFICIENT EQUATIONS AR sub AR 1 M 2 K p.7 K V.64 K Psub.comp. f m K p 1 M 2 1 Tan( ) 1 M 2 Tan( ) K VSubComp K V f m C LSub K psub Sin( )Cos 2 ( ) K Vsub Cos( )Sin 2 ( ) Stage 5 The hypersonic weapon is designed to have a slender waverider shape. In the first stage of drag calculations the hypersonic weapon drag coefficient was calculated using the tangent-cone method, based on a conical waverider design. It was determined to be C D =0.3899 assuming a cone-section semivertex angle of 20 degrees. For designing purposes, the weapon drag will also be estimated based on a wedge waverider shape. Assume the weapon shape to be a 2-D wedge, with a round nose, and traveling at Mach 8. The top of the weapon is assumed to be flat, so the upper surface Cp=0. The weapon will be approximately 11.5 feet long and 15 feet wide. The weapon will be flying at an altitude of approximately 80,000 ft, density is 0.000084 slugs/ft 3, temperature is T=221K. Based on Newtonian aerodynamics: Lower Surface Pressure, Lift, and Drag Coefficient At ɵ=10 C p =2*sin 2 ɵ=0.060 C L =C p *Cos ɵ=0.059 C D =C p *Sin ɵ=0.010 At ɵ=20 Cp=2*sin 2 ɵ=0.234 C L =C p *Cos ɵ=0.220 C D =C p *Sin ɵ=0.080 Stage 4 To find the Supersonic Lift and Drag Coefficients on the UCAV, we must first calculate the lift and drag in subsonic incompressible flow. A sketch of the Planform Area of the UCAV can be found in figure 1. As you can see the UCAV has a delta wing. In order to calculate the Lift and Drag Coefficients for the aircraft we needed to use a lifting surface 9
theory. After much debate we decided on using a cross between the Polhamus Leading Edge Suction Analogy, and the Multhopp lifting-surface theory. The leading Edge Suction Analogy called for separating the lift of a delta wing of small aspect ratio into two parts the lift due to potential flow, and the lift due to the vortex lift. FIGURE 6 :UCAV PRELIMINARY DESIGN To be brief the equation given below is the result of the paper: C L K P sin( )cos 2 ( ) K v cos( )sin 2 ( ) The results for the UCAV for incompressible, subsonic flight: K P.57 K V.81 The Lift Curve Slope is: FIGURE 7 :UCAV LIFT CURVE SLOPE 10
The C L max is around 1.3, to 1.4. Wind tunnel testing would be needed to find the place where the vortex burst. Below is the L/D Curve. It is maximum at 5 degrees angle of attack and has a maximum of 16.0347. The Drag Polar for the UCAV is: FIGURE 8 : MAX LIFT COEFFICIENT FIGURE 9: UCAV DRAG POLAR The Drag Polar was found by estimating the parasite drag to be.0017. 11
The TPC skin friction drag can be accurately calculated by using the Boeing correlation for reference temperature. This equation is applicable assuming the wall of the aircraft is adiabatic. This calculation is made assuming the TPC is flying in cruise conditions at Mach 0.6 and an altitude of 40,000 ft. At those conditions the Reynolds number is approximately 3.448e6, which is considered to be turbulent flow. Assuming the viscosity coefficient ratio can be related by the following equation: The skin friction equation is given below: The skin friction drag for the TPC can then be calculated from the following equation: Stage 3 TABLE 3 UCAV GEOMETRIC RELATIONS UCAV Geometric Relations S 115 ft B 8 ft L 23 ft AR.55 AR/L.025 (Sweep Angle) 50 Degrees E (Oswald Efficiency.9 Factor) The UCAV has an aspect ratio of.55. For Subsonic, incompressible flow we cannot use Prandtl s classical lifting line theory, that theory only applies towards to moderate and high aspect ratios. The UCAV has a semi delta wing shape, which means the circulation 12
around the wing changes with respect to the length of the aircraft. The flight characteristic of the aircraft, we are looking at a stall angle of about thirty five degrees. The lift-to-drag ratio is a critical to evaluating performance of any aerodynamic vehicle. The lift-to-drag is initially assumed to be 8 in level supersonic flight. If we assume the UCAV is launched at an altitude of 60,000 ft. The dynamic pressure at that altitude can be determined to be 1679 lbf/ft2. The UCAV is assumed to be traveling at Mach 4, so the velocity is approximately 3872 ft/s. The lift coefficient can be calculated by using the following equation found in Jan Roskam s aircraft design. If the total drag is assumed to be approximately equal to the wave drag, the drag coefficient can be determined based on the following equation. The UCAV is estimated to have a length of 25 feet based. FIGURE 10 WAVE DRAG WITH VARYING MACH NUMBER 13
The skin friction drag coefficient was found on the UCAV using the Boeing correlation method. Using the same formula used to calculate the skin friction on the transonic patrol carrier. Since skin friction is a function of Mach number, and density, below is a graph of two particular regimes. FIGURE 11 SKIN FRICTION COEFFICIENT SUBSONIC FIGURE 12 SKIN FRICTION COEFFICIENT SUPERSONIC If you would like to see a more in-depth look at the calculations please see the UCAV vehicle performance pdf in the resources section. To find the drag coefficient for the subsonic compressible regime, the drag polar was added with the skin friction drag resulting in the equation below. 14
EQUATION 5 SUBSONIC COMPRESSIBLE DRAG The drag coefficient in the supersonic regime was the addition of wave drag, with dealing with the supersonic compression of the lift coefficient as well EQUATION 6 SUPERSONIC DRAG COEFFICIENT Calculating the maximum turning radius for the UCAV, a load factor of 15 was used. The equation for it is: R 32.2 n 2 1 Therefore assuming a approximate temperature for the range of altitudes the UCAV operates in the following curve was found. V 2 FIGURE 13 TURNING RADIUS Calculating the Rate of Climb engine performance must be addressed. Using simple thermodynamic relations an ideal ramjet curve was used for the thrust. We assumed the mass air flow remained constant to simplify the calculations. The Equation used is: 15
EQUATION 7 RAMJET THRUST EQUATION The thrust curve shows that the engine operates best in the regime around Mach 4,5. FIGURE 14 RAMJET THRUST CURVE Once the thrust was found, the rate of climb was easily found. Using the simplification that rate of climb is equal to excess power over weight the following equations were found. As you can see it is a function of Mach, and Altitude. Therefore shown below is just a few representative curves. The graphs, are from the density at 150,000 ft to the density at 40,000 ft. Which as you can see that the initial rate of climb starts off slow, but eventually the rate of climb increases with altitude due to the ramjet engine. 16
FIGURE 15 RATE OF CLIMB CURVES Using Historical Data, the weight regression for the hypersonic missile can be found below: 17
Stage 2 The transonic patrol aircraft has a drag polar of C D =.015+.045C L 2. Through iteration, it also has an Aspect Ratio of 11.05, weight of 536500 lb. The payload capacity for the aircraft will be around 300,000 lb. It will be carrying the UCAVS, as well as extra fuel reserves to increase the endurance of the aircraft in order to complete its mission. The drag coefficient and equivalent skin friction for the TPC is given below. 18
Lift Coefficient C L 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.01 0.02 0.03 0.04 0.05 Drag Polar C D FIGURE 16 : TPC DRAG POLAR Stage 1 The transonic patrol aircraft has a drag polar of C D =.017+.036 C L 2. This is an initial estimate. Through iteration, it also has an Aspect Ratio of 11.05, weight of 536500 lb. The payload capacity for the aircraft will be around 100,000 lb. It will be carrying the UCAVS, as well as extra fuel reserves to increase the endurance of the aircraft in order to complete its mission. To find the time it takes for missile detection to the transonic aircraft to complete at 180 degree turn and head toward the target is in direct correlation to the minimum turning radius. Taking the velocity of the of the turn we get V Rmin = 438.609 ft/s Therefore, the minimum time to turn is around 15 seconds. This time to turn shows the value of the aircraft based missile defense. The grounds to air missiles are just beginning to be prepped for launch when the transonic patrol aircraft is enroot to possible targets. A rough estimate for the steady flight envelope of the aircraft is: 19
FIGURE 17 : TPC FLIGHT ENEVELOPE The hypersonic weapon shape is based on similar aircraft such as the Falcon HTV. The Falcon HTV is approximately 11.5 in length, and weighs about 1,800 lbs. This hypersonic design is about half the weight of the previous design considered on the X-51 Waverider. The weapon must be capable of quick assent which means high lift. The initial assumption is that the hypersonic weapon with L/D of 4, a bluntness ratio of 0.2, and a cone-section semivertex angle of 20 degrees. The hypersonic drag is estimated based on the Tangent-Cone method. ( ) =0.3899 System Configuration Stage 3 To land the UCAV safely we are exploring the option of putting two parachutes on either end of the aircraft. Upon landing the UCAV will deploy small floatation devices to provide for easy recovery at sea. Due to the relative small size of the aircraft, this may provide the simplest solution. The major concern is the space required to install the parachutes, and the explosives on the aircraft. The benefits of this system, is an easy and fast way of reusing the vehicles. Stage 2 The Transonic Patrol Craft (TPC) will carry four UCAVs inside its fuselage. Once the combat warning has been given to the operators, the UCAVs will be capable of being readied within 1 minute. The TPC will launch the UCAVs from the rear, or by release from below through bombay doors. The disadvantages to release through doors below are increased drag, potential sonic booms, and higher radar signatures. However, it would provide for quicker release. 20
Since the UCAV and hypersonic are held inside the fuselage, the takeoff and landing of the TPC shouldn t be limited by carrying this payload. The aircraft will be capable of takeoff with 9255 feet of runway, assuming sea level conditions, a wing loading of 120, a C Lmax of 2, and a thrust-to-weight of 0.127. The ground roll is determined by the following equation. ( ( )) Timeline Stage 6 Assuming the enemy has similar delivery capabilities, such as the Minotaur IV operated by the U.S., we can base the enemy s delivery system on the Minotaur s mission profile. In order for the missile defense system to be most effective, the hypersonic weapon must destroy the incoming ICBM just before reaching orbit or just after re-entry into the atmosphere. The Minotaur reaches an altitude of 404 miles within 14 minutes. If the missile stays at that orbit, it will travel at 7534 m/s. If the missile was traveling from Vladivostok, Russia to Los Angeles, the missile would travel 5513 miles. Assuming the missile travels 60% of that distance in orbit, the missile would reach re-entry approximately 25 minutes after ignition. Satellites can detect the launch within a minute of launch. After detection, the government must decide if the launch is an attack and if counter-measures must be taken it is assumed this is done within 2 minutes of ignition. The TPC cruises at Mach 0.6, and is capable of turning to face the target direction within 15 seconds. The next 105 seconds the TPC is flying at Mach 0.8, traveling 15.4 miles towards the incoming missile. 21
THAAD Comparison FIGURE 18: ENEMY MISSILE MISSION PROFILE Comparing the time for the transonic patrol aircraft to turn around, and head to the target. The thrust to weight ratio comparison was based on takeoff weight. These missiles all are designed for anti-ballistic defense. The heavier missiles are designed for intercepting earlier in the enemy missile s flight. The missiles considered include the MIM-104 Patriot, the Nike Ajax, the Nike Hercules, the Nike Zeus A, and the Spartan. The average thrust-to-weight of these missiles is 23. The Patriot had the lowest ratio at 15.6. 22
35000 30000 Takeoff Weight W TO 25000 20000 15000 10000 5000 0 0 100000 200000 300000 400000 500000 600000 Thrust-to-Weight T/W FIGURE 19 : THAAD WEIGH COMPARISON 23
Appendix A THAAD Missiles 1st stage thrust(lbf) 2nd stage thrust 3rd stage thrust W TO Range (mi) ISP (sec) Warhead (kg) T/W MIM-104 patriot 24052 1543 258 15.58782 Nike Ajax 59000 2600 0 2460 25 300 40 23.98374 Nike Hercules 222000 10000 0 10700 87 300 40 20.74766 Nike Zeus A 400000 0 11000 200 300 40 36.36364 Nike Zeus B 450000 23000 250 300 40 19.56522 Spartan 500000 29000 460 300 40 17.24138 35000 30000 Avg T/W 22.24824207 Takeoff Weight WTO 25000 20000 15000 10000 5000 0 0 100000 200000 300000 400000 500000 600000 Thrust-to-Weight T/W 24
Appendix B 25
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References [1] Roskam, Jan. Airplane Design, Preliminary Sizing Of Airplanes. Design Analysis & Research, 1997. Print. 36