Design a single stage rocket for Mars orbital insertion (liftoff from Mars). Required DeltaVee=3.5 km/sec using monopropellant hydrazine. The key to this problem is that higher chamber pressures lead to higher Isp, but they make the propellant tank heavier. Higher pressures also make the rocket engine easier to design. To make it easier for calculations, you should use Isp=250, pc=50 psi (or .35 Mpa) as a starting point. Determine mass ratio, chamber pressure and area ratio (Use above estimates at first, then check for consistency later), use tank mass for spherical composite or titanium tanks. (You can figure the tank mass or use a hydrazine tank from (https://www.psi-pci.com/) Assume structural mass 10% of tank mass. Engine mass=2% of thrust on Earth. (i.e. 100 lbf engine weight 2 lb) What is the exhaust pressure? (Answer: Mars Ambient=700 Pa, source https://mars.jpl.nasa.gov/MPF/science/atmospheric.html ) Determine chamber pressure to be significantly higher than exhaust ambient pressure on Mars, and pick an expansion ratio. Use these numbers to figure Isp from equation discussed in class. Some typical real numbers for pressure and Isp can be found at (https://cs.space.eads.net/sp/SpacecraftPropulsion/MonopropellantThrusters.html#ModelCHT400 Your number should be close (~20%)
For this case, assume that the pressure losses in the injector etc. are neglected. Determine required mass ratio given hydrazine Isp, make sure that the numbers add up. Neglect the weight of the pressurization system. Determine the max pressure that will still achieve orbit.