Numerical Problem
1. Calculate the ideal density of a solid rocket
propellant consisting of 68% ammonium
perchlorate, 18% aluminum, and 14% HTPB by
mass.
Given: wAP = 0.68 wAl = 0.18 wHTPB = 0.14
From Properties of Rocket Propellants
we have, ρAP = 1.95 g/ml, ρAl = 2.70 g/ml, ρ HTPB =
≈0.93 g/ml
ρp = 1 / Σ i (w / ρ)i
ρp = 1 / [(0.68 / 1.95) + (0.18 / 2.70) + (0.14 / 0.93)]
ρp = 1.767
• A spacecraft's dry mass is 75,000 kg and the
effective exhaust gas velocity of its main
engine is 3,100 m/s. How much propellant
must be carried if the propulsion system is to
produce a total Delta V of 700 m/s?
3.A rocket having an initial mass of 3500 kg is
launched from the earth’s surface. If the
exhaust velocity of the jet from the rocket is 2
km/s,
• 1) The mass ratio necessary to boost the
vehicle velocity by 3 km/s is ____
• 2) The propellant mass carried by the rocket in
kg ____
4) A spacecraft’s engine ejects mass at a rate of
40 kg/s with an exhaust velocity of 2.8 km/s.
The initial mass of the spacecraft is 4000 kg,
and the entire propellant gets consumed in a
minute. Determine the velocity increment of
the spacecraft in km/s
5.The specifications of a Deepavali rocket are as below:
Propellant: Black powder Propellant density: 1700
kg/m3 , Propellant mass fraction = 0.14, Final mass of
the rocket = 18 grams, Jet exhaust velocity = 80 m/s
Initial acceleration of the rocket = 0.2g (g=9.81 m/s2 :
acceleration due to gravity) Dimensions of the
propellant chamber: 5 mm diameter; 40 mm length
• The velocity attained by the rocket in m/s at the end of
the burning period of its propellant?
• The burn rate (neglect the variations in burn rate) of
propellant in g/sec ?