Problem 1: Merlin 1D engine produces a thrust of 850 kN at sea level and specific impulse of 311 seconds. Calculate the total mass flow rate from Falcon 9 rocket’s propellant tanks.

Useful data:  g = 9.81 m/s

A: 278 kg/s
B: 2507 kg/s
C: 380 kg/s
D: 3800 kg/s

Solution:

F = ISP x g x (mass flow rate)

Use the above formula to get mass flow rate for one engine = 278.6 kg/s

For 9 engines of Falcon 9: 278.6kg/s x 9 = 2507 kg/s

Problem 2:

Falcon 9 rocket’s dry mass is 50,000 kg and the engine’s effective exhaust velocity is 2500 m/s. How much propellant (in kg) you must carry if you need to produce a total Delta-v of 500 m/s.

Useful data: e^(0.2) = 1.221 ; e^5 = 148.41

A: 61050 kg
B: 11050 kg
C: 38950 kg
D: 25080 kg

Solution: Delta v = V_exhaust x ln (Initial Mass/final mass)

Final Mass = 50,000 kg, V_exhaust = 2500 m/s, Delta-v = 500 m/s

Substituting the values in above equation, we get, Initial Mass = 61050 kg

Amount of propellant = Initial mass – final mass = 11050 kg

Problem 3: Velocity of Falcon 9 after one minute

Falcon 9’s initial mass is 500,000 kg. Each of the Merlin engines starts to eject mass at a rate of 40 kg/s with an effective exhaust velocity of 2000 m/s. What’s the velocity of Falcon 9 after one minute.

Useful data: ln(0.9568) = -0.044, ln(1.045) = 0.044, ln(1.0048) = 0.0048

A: 88.3 m/s
B: 9.6 m/s
C: 108.3 m/s
D: None of the above.

Solution:

Delta v = V_exhaust x ln (Initial Mass/final mass)

Final mass = Initial mass – mass flow rate of one engine x number of engines x time

Initial mass = 500000 kg

Time = 60 seconds

Exhaust velocity = 2000 m/s

Final mass = 500000 – 40x9x60 = 478400 kg

Substituting in above equation we get

Delta v = 88.3 m/s