This document summarizes the solutions to several problems regarding rocket performance calculations for a rocket with a thrust of 8896 N, propellant consumption of 3.867 kg/s, and flight velocity of 400 m/s. It includes calculations of effective exhaust velocity, kinetic energy of the jet, internal efficiency, propulsive efficiency, overall efficiency, specific impulse, and specific propellant consumption. It also includes calculations of specific power assuming a dry mass of 80 kg and duration of 3 minutes. Finally, it describes plotting the variation of thrust and specific impulse against altitude using atmospheric pressure data and engine parameters from tables.

1. ‫الرحيم‬ ‫الرحمن‬ ‫هللا‬ ‫بسم‬
Sudan University of Science &Technology
College Of Post Graduates Studies
PhD Program in Mechanical Engineering by Courses and
Dissertation
GE 721 - Advanced Combustion
Homework No. (1)
Prepared by student:
Sabir Abushousha Ahmed Abushousha
Supervisor:
Dr. Mohammed Hassan Mohammed Abuuznien
February 2015

2. Question 2
A rocket has a thrust of 8896 N and propellant consumption of 3.867 kg/sec. The
vehicle flies at a velocity of 400 m/sec and the propellant specific energy content
(heat of combustion) is 16.911 megajoule/kg (from Sutton). Find the following:
a. Effective exhaust velocity
b. Kinetic energy of the jet for 1 kg of fuel
c. Internal efficiency (
d. Propulsive efficiency
e. Overall efficiency
f. Specific impulse )
g. Specific propellant consumption
Given the following from the problem statement:
F = 8896 N 𝑚̇ = 3.867
kg
sec
𝑢 = 400
m
sec
QR =6.911⋅106
J/ kg
a. Effective exhaust velocity:
𝐶 =
F
ṁ
=
8896
3.867
= 2300.5
m
sec
b. Specific kinetic energy of the jet:
𝐾𝐸𝑗𝑒𝑡 = 0.5 C2
= 0.5 ∗ (2300.5 )2
= 2.646130 ×106
J /kg
c. Internal efficiency
𝜂𝑖𝑛𝑡 =
𝐾𝐸 𝑗𝑒𝑡
QR
𝜂𝑖𝑛𝑡 =
2.646130 × 106
6.911∗106 = 0.38288 = 38.3
d. Propulsive efficiency
The speed ratio
𝑣 =
u
c
=
400
2300.5
= 0.1739

3. 𝜂 𝑝 =
2 . u
1 + u2
=
2 ∗ 400
1 + (2300.5)2
= 0.3375 = 33.75%
e. Overall efficiency:
𝜂 𝑝 =
F . u
m .̇ QR
=
8896 ∗ 400
3.867 ∗ 6.911 ∗ 106
= 0.1331 = 13.3%
f. Specific impulse:
𝐼𝑠𝑝 =
c
g
=
2300.5
9.81
= 234.6 s
g. Specific propellant consumption:
TSFCW =
1
𝐼𝑠𝑝
=
1
234.5848
= 0.0042629
1
S
Question 4
For the rocket in Problem 2, calculate the specific power, assuming a propulsion system dry
mass of 80 kg and a duration of 3 min.
ṁ =
80
3 ∗ 60
= 0.4444
𝑃𝑗𝑒𝑡 =
1
2
𝐹𝑔0 𝐼𝑠 =
1
2
𝐹𝑔0
𝐶
𝑔0
=
1
2
𝐹 𝐶
𝑃𝑗𝑒𝑡 =
1
2
∗ 𝐹𝑣2 =
1
2
∗ 8896 ∗ 2300.5 = 10232624 𝑤
∝=
𝑃 𝑗𝑒𝑡
𝑚0
=
10232624
80
=127907.8 w
Question 7
Plot the variation of the thrust and specific impulse against altitude,
using the atmospheric pressure information given in Appendix 2, and the
data for the Minuteman first-stage rocket thrust chamber in Table 11-3.
Assume that P2 = 8.66 psia.
Solution
CONVERT THE UNITS 8.66 psi = 59708.598158924 pascal
Assuming a ratio of specific heats to be 1.3 and gas constant to be 345.7 kJ/kg K,

4. FROM TABLE 11
EXIT VELOCITY
𝑣2 = √
2𝑘
𝑘 − 1
𝑅𝑇 [1 − (
𝑝2
𝑝1
)
(𝑘−1)/𝑘
]
Throat area (in 2 ) =164.2 =0.105935272 m2
• Expansion Area Ratio:
10 =
𝐴2
𝐴 𝑡
𝐴2 = 0.105935272 m2 ∗ 10 = 10.6𝑚2
Mass flow rate =A2*v2/V2
THURST 𝐹 = 𝑚̇ 𝑣2 + (𝑝2 − 𝑝3)𝐴2
Specific Impulse 𝐼𝑆 =
F
ṁ g0
All data are tabulated in excel sheet attached to the home work
0.1013 MPa
atmospheric pressure which has the value
*
A
A
A
A e
throat
exit
