MAE 5495: Launch Vehicle Analysis

MAE 5495: Launch Vehicle Analysis Homework #1 Due: 14 Feb 2008, 16:30 MST

1. (15%) A small ground to air missile has the following characteristics: Initial Mass 500 kg Final Mass (after thruster firing) 225 kg Payload Mass 120 kg Burn Duration 5.0 sec Propellant Specific Impulse 240 sec

Determine the inert mass fraction, the propellant mass fraction, the propellant mass flow rate, the thrust, the effective exhaust velocity, and the total impulse of the vehicle.

2. (15%) The following measurements were made during a sea level test of a solid propellant rocket motor: Burn Duration 50 sec Initial Mass 1250 kg Final Mass (after firing) 275 kg Average Thrust 63,321 N Combustion Chamber Pressure 7.0 MPa Nozzle Exit Pressure 0.07 MPa Nozzle Throat Diameter 0.09 m Nozzle Expansion Ratio 10

Determine the propellant mass flow rate, nozzle exit velocity, effective exhaust velocity and specific impulse at sea level.

Given the following information, determine the effective exhaust velocity and specific impulse at 1000 and 25,000 m altitude.

Ambient Pressure at 1000 m 0.0898 MPa Ambient Pressure at 25,000 m 0.00255 MPa

3. (25%) Calculate the total V produced by the Space Shuttle system with the following characteristics:  Stage Number: 0. 2 x Shuttle Solid Rocket B oosters Gross Mass (per SRB): 589,670 kg. Empty Mass(per SRB): 86,183 kg. Isp (average): 242 sec. Burn time: 124 sec. Diameter: 3.71 m. Span: 5.10 m. Length: 38.47 m. Propellants: Solid.

 Stage Number: 1. 1 x Shuttle Tank Gross Mass: 750,975 kg. Empty Mass: 29,930 kg. Isp: 455 sec. Burn time: 480 sec. Diameter: 8.70 m. Span: 8.70 m. Length: 46.88 m. Propellants: Lox/LH2  Stage Number: 2. 1 x Shuttle Orbiter Gross Mass: 99,318 kg. Empty Mass: 99,117 kg. Isp: 455 sec. Burn time: 480 sec. Diameter: 4.90 m. Span: 23.79 m. Length: 37.24 m. Propellants: Lox/LH2 No Engines: 3. Space Shuttle Main Engines.

4. (30%) The Air Force has contracted for the design of a new two stage launch vehicle that can provide low cost access to space. The winning contractor claims that their design can deliver 670 kg to a 200 km altitude, circular orbit with an inclination of 28.5 launched directly from Cape Canaveral. Their design has the following characteristics:

Staging Technique Serial staging Liftoff Mass 29,200 kg First Stage Thrust 383,125 N, average First Stage Propellants Lox/Kerosene (Isp = 285 sec, average) First Stage Burn Duration 169 sec First Stage Finert 0.06 Second Stage Thrust 31,137 N Second Stage Propellants Lox/Kerosene (Isp = 327 sec) Second Stage Burn Duration 378 sec Second Stage Finert 0.05

Determine whether this launch vehicle has enough V to perform the job

that the contractor has promised. Assume Vlosses = 1.3 km/sec.

5. (15%) Mission planners at the European Space Agency want to launch an Ariane

4 launch vehicle from French Guyana (Lo = 4) into a low Earth orbit with an inclination of 30 and a right ascension of the ascending node of 135. The local sidereal time at the launch site is 1430 hrs.

a. What is the launch window sidereal time for the ascending node opportunity? b. How long must you wait for the ascending node opportunity? c. What is the launch azimuth for the ascending node opportunity? d. What is the launch window sidereal time for the descending node opportunity? e. How long must you wait for the descending node opportunity? f. What is the launch azimuth for the descending node opportunity?

6. (Extra Credit) For the following single stage liquid propellant rocket, determine the maximum altitude the vehicle will achieve and the maximum acceleration on the vehicle. Assume that gravity is the only external force acting on the rocket that is launched from a ground based facility on the equator.

Initial vehicle mass 2000 kg Final vehicle mass 230 kg Burn Duration 56 sec Vehicle Thrust to Weight Ratio 5