Long Answer Problems (70 pts total)
1. (24 pts) Engineers are asked to analyze the potential to increase travel capacity on a flight
from Los Angeles, California to Tokyo, Japan (9,000 km) by improving propulsion system
performance. Some specifications of the aircraft are given: lift-to-drag ratio (L/D) = 15,
cruising Mach number ($M_0$) = 0.7, freestream conditions at cruise ($T_0$ = 220 K, $P_0$ = 10 kPa),
R = 287 J/kg-K, $\gamma$ = 1.4.
a) Calculate the total intake air mass flow rate ($\dot{m}_0$) if the aircraft has four engines, each
with a freestream intake capture area of $A_0$ = 5 m².
b) Calculate the thrust-specific fuel consumption if the fuel-to-air ratio (f) is 0.01 and the
exhaust velocity of the engine ($u_e$) is 1000 m/s. Assume the exhaust is optimally
expanded.
c) Calculate the increase in available mass capacity for payload (in kg) given a 10%
reduction in thrust-specific fuel consumption using results from (a) and (b). Assume the
structural mass is 300 metric tons (300,000 kg). Note: $M_{total} = M_{structure} + M_{payload} + M_{fuel}$
