# ENAE 483

Principles of Space Systems Design

Fall, 2002

Question 6:

Use the regression values for delta and Isp from lecture 8,
page 7, and the costing equations for launch vehicles from lecture
9, page 7, to answer the following questions. Your goal is to
design a launch vehicle to carry 100,000 kg to low earth orbit
(delta-V=9200 m/sec). For each of the following questions, I want
to know vehicle gross mass, and inert mass, nonrecurring cost,
and delta-V for each stage.

**For both ENAE 483 and ENAE 788D:**

a) You are going to design a two-stage launch vehicle where
the first stage uses LOX/RP1 propellants, and the second stage
uses LOX/LH2. Design the vehicle for the case where vehicle gross
mass is minimized by selecting optimum delta-Vs for each stage.

b) Repeat (a) with the objective of maximizing payload fraction
(lambda)/inert mass fraction (delta).

c) Repeat (a) with the objective of minimizing total nonrecurring
costs.

d) You are going to build and fly 20 vehicles. The recurring
cost follows an 80% learning curve. Using your design from (c),
find the cost per kilogram of payload delivered to orbit, including
both nonrecurring and recurring costs.

**For ENAE 788D only:**

e) For the mission model discussed in (d), find the optimum
design for the launch vehicle which minimizes cost per kg of payload
to orbit.