Consider the design of an orbital transfer vehicle using LOX/LH2 propellants. a. Determine the ?V required to boost the payload from a 100 Nm circular orbit to GEO. b. Given the following: pc = 500 psi, ? = 60, ?o = 0.95, determine the optimal mixture ratio (to one decimal point), Isp, and c* of the liquid rocket engine propelling the vehicle. c. Given that the payload weight is 8000 lb, calculate the total weight of the propellant required to achieve the ?V value in part (a). Assume a propellant mass fraction of 0.85. d. To allow for boiloff, we must carry 5% more oxidizer and fuel than is necessary to complete the mission. In addition, the tanks must accommodate this boiloff volume as well as a 3% volume reserve for ullage. Calculate the total propellant required as in part c and the weight and volumes of fuel and oxidizer. e. Calculate tank lengths and diameter for cylindrical tanks arranged in a tandem fashion. Assume the L/D of the fuel tank is two. f. Given L* = 45 in and tb = 100 s, calculate the nozzle throat and exit radii and the flow rates of LH2 and LOX through the chamber. Determine the burning times required for each of the burns in the Hohmann transfer. g. Given: Ri = 0.5, R?tu = 1.0, R?td = 0.6, Ac/At = 2.5, ?i = 45o , ?d = 15o . conical nozzle, calculate the length of the chamber and nozzle dimensions, and draw the nozzle contour for this rocket engine. h. Assume the payload is a cylinder with 8 ft diameter and 6 ft length. Draw the payload, tankage, and chamber/nozzle of the rocket to scale. Allow 1 ft between tankage and payload for interstage and 2 ft between tankage and engine chamber for pumps. What is the gross weight of the OTV? i. Plot the vehicle velocity, mass, and acceleration (in g) as a function of time for each of the two burns assuming constant thrust. The payload has an acceleration limitation of 8g, will throttling be required? If so, how much (in %)?