# ENAE 483/788D Principles of Space Systems Design Fall, 2002

## Question 7:

Assume that the two-stage Saturn V augmented with four Space Shuttle Solid Rocket Boosters from Problem 5 could carry 200,000 kg to low Earth orbit. (I'm not saying that this is necessarily the right answer to Problem 5, just that you should assume it for this problem.) Your task is to design an upper stage for this launch vehicle which will maximize the payload injected into a Mars transfer orbit. The upper stage you are designing will use LOX/LH2 propellants with an Isp of 455 sec. The payload of the augmented Saturn V will consist of the upper stage and the Mars payload. Once in low Earth orbit, your upper stage will have to provide a delta-V of 3.644 km/sec to inject the Mars payload into the proper trans-Mars trajectory.

a) Assume the inert mass fraction for the upper stage is 0.08. Calculate the stage inert mass and propellant mass, and the mass of the Mars payload.

b) Using the mass estimating relations from Lecture 10, find the following system masses:

1. Oxidizer tank
2. Oxidizer tank insulation
3. Fuel tank
4. Fuel tank insulation
5. Forward fairing
6. Intertank fairing
7. Aft fairing
8. Avionics
9. Wiring
10. Rocket engine(s)
11. Thrust structure
12. Gimbals

Clearly list any and all design choices or assumptions you make. Some details you will need for the design process:

• The second stage to which you attach has a diameter of 10 meters. The payload has a diameter of 7 meters. You do not have to account for a payload fairing (the aerodynamic shell around the payload is taken care of by the payload), but you do have to have adapter sections so that the two ends of your stage are the same diameter as the components they connect to.
• Assume an initial T/W ratio of 0.5. The expansion ratio is 50:1. The chamber pressure is 2500 psi.

c) Tabulate your results, and incorporate a 30% margin for growth. Calculate the new payload mass, and calculate the actual value of inert mass fraction this represents.

d) Sketch the internal layout of your stage.