SME
Propulsion
Nozzle performance
Use this for “A rocket chamber at 7 MPa feeds a 0.05 m² throat, with CF = 1.6 and c∗ = 1600 m/s. Find F, ṁ and Iₛₚ.”
Diagram
Shape
drawn
for
a
nominal
exit,
not
to
scale:
type
Aₑ
Aₜ
to
draw
it
to
scale.
This is an example. Type your own values to start a new problem.
F (kN)
=
CF
×
pc (MPa)
×
Aₜ (m²)
ṁ (kg/s)
=
pc (MPa)
×
Aₜ (m²)
÷
c∗ (m/s)
Iₛₚ (s)
=
CF
×
c∗ (m/s)
÷
g
Formulas
F
=
CF
×
pc
×
Aₜ
560,000 = 1.6 × 7,000,000 × 0.05
ṁ
=
pc
×
Aₜ
c
∗
218.8
=
7,000,000
×
0.05
1,600
Iₛₚ = CF × c∗ ÷ 9.81
261
=
1.6
×
1,600
9.81
Formulas are worked in Pa, N. The step-by-step shows the conversions.
Assumptions
•
The thrust coefficient CF holds the nozzle’s expansion and the ambient pressure.
•
The characteristic velocity c∗ holds the propellant and its combustion.
•
g = 9.81 m/s² defines the specific impulse Iₛₚ.
Step-by-step
WE KNOW
pc = 7 MPa, Aₜ = 0.05 m², CF = 1.6, c∗ = 1,600 m/s
FIND
thrust (F), mass flow (ṁ), specific impulse (Iₛₚ)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to Pa, N).
pc = 7 MPa = 7,000,000 Pa (1 MPa = 10⁶ Pa)
Step 2 · Find thrust (F)
Use F = CF × pc × Aₜ
The chamber pressure on the throat area, times the thrust coefficient.
F
=
1.6
×
7,000,000
×
0.05
F
=
(1.12
×
10
7
)
×
0.05
F
=
560,000
N
Step 3 · Find mass flow (ṁ)
Use ṁ = pc × Aₜ ÷ c∗
The chamber pressure on the throat area, over the characteristic velocity.
ṁ
=
7,000,000
×
0.05
1,600
ṁ
=
350,000
1,600
ṁ
=
218.8
kg/s
Step 4 · Find specific impulse (Iₛₚ)
Use Iₛₚ = CF × c∗ ÷ 9.81
CFc∗ is the effective exhaust speed; dividing by g gives seconds.
Iₛₚ
=
1.6
×
1,600
9.81
Iₛₚ
=
2,560
9.81
Iₛₚ = 261 s
Step 5 · Convert the answers
Change each answer back to the unit you chose.
F = 560,000 N = 560 kN (1 kN = 1000 N)
Check
Put the numbers back in. Both sides should match.
560,000 = 1.6 × 7,000,000 × 0.05 ✓
218.8
=
7,000,000
×
0.05
1,600
✓
261
=
1.6
×
1,600
9.81
✓
Topic check
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