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The New Shepard is a spacecraft designed by Blue Origin to just reach the edge of space, which isdefined as a maximum (apogee) altitude of ha = 100 km. It then descends and the rocket isrecovered. We will analyze both the launch and descent phases. In all parts, assume the nozzleexhaust is purely in the axial direction. (43 pts)a) During launch, the LH2/LO2 rocket provides a thrust of T1 = 490 kN at a specific impulse of Isp =450 s for a burn time of thi = 110 s. Consider a purely vertical flight under the influence ofgravity, but assume the force of gravity does not change significantly between the surface of theEarth at a height of 100 km (g(h) = ge = 9.8 m/s?). Ignore drag and assume perfect expansionin the nozzle throughout flight.Recalling the maximum height achieved by a single stage vertical flight rocket as a result of aburn is:hmax =(ueqInR1 )?R12ge- ueqtbi (Ri = ]InRi – 1show that the initial mass of the complete New Shepard spacecraft (Mo1) should be 32,300 kg inorder to just reach hmax = ha = 100 km. (8 pts)b) What is the flight speed at the end of the launch burn? (3 pts)c) What are the payload ratio and structural coefficient for the launch phase? (4 pts)d) In reality, the nozzle has a fixed expansion ratio of Ae/ A* = 15, so there will not be perfectexpansion throughout flight. During launch, the combustion chamber pressure is 3 MPa. Duringthe descent phase, the combustion chamber pressure is reduced to 0.3 MPa. In both cases,use y = 1.25. Assume that the combustion chamber temperature and gas composition do notzle the nozzle is isentropic, and the Mach number

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