SME
Propulsion
Electric propulsion
Use this for “A 5 kW Hall thruster runs at 60% efficiency and Iₛₚ = 1800 s. Find its thrust and propellant flow.”
Chart
F(1,800) ≈ 339.8
This is an example. Type your own values to start a new problem.
vₑ (m/s)
=
Iₛₚ (s)
×
g
Pⱼₑₜ (kW)
=
η
×
P (kW)
=
½
×
F (mN)
×
vₑ (m/s)
ṁ (kg/s)
=
F (mN)
÷
vₑ (m/s)
Formulas
vₑ = Iₛₚ × 9.81
17,658 = 1,800 × 9.81
Pⱼₑₜ
=
η
×
P
3,000 = 0.6 × 5,000
Pⱼₑₜ
=
1
2
×
F
×
vₑ
3,000
=
1
2
×
0.3398
×
17,658
ṁ
=
F
vₑ
1.9243 ×
10
-5
=
0.3398
17,658
Formulas are worked in W, N. The step-by-step shows the conversions.
Assumptions
•
η is the share of electric power that reaches the jet as kinetic energy.
•
The jet power is ½ṁvₑ², which is ½Fvₑ since F = ṁvₑ.
•
g = 9.81 m/s² defines specific impulse, so vₑ = Iₛₚ × g.
•
The solar arrays limit the power, not the propellant: at fixed P, more Iₛₚ means less F.
Step-by-step
WE KNOW
P = 5 kW, η = 0.6, Iₛₚ = 1,800 s
FIND
exhaust speed (vₑ), jet power (Pⱼₑₜ), thrust (F), propellant flow (ṁ)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to W, N).
P = 5 kW = 5,000 W (1 kW = 1000 W)
Step 2 · Find exhaust speed (vₑ)
Use vₑ = Iₛₚ × 9.81
Specific
impulse
in
seconds
times
g
=
9.81
m/
s
2
is
the
exhaust
speed.
vₑ = 1,800 × 9.81
vₑ = 17,658 m/s
Step 3 · Find jet power (Pⱼₑₜ)
Use Pⱼₑₜ = η × P
Only
the
share
η
of
the
electric
power
ends
up
in
the
jet.
Pⱼₑₜ = 0.6 × 5,000
Pⱼₑₜ = 3,000 W
Step 4 · Find thrust (F)
Use Pⱼₑₜ = ½ × F × vₑ
Double the jet power and divide by vₑ.
F
=
2
×
Pⱼₑₜ
vₑ
F
=
2
×
3,000
17,658
F
=
6,000
17,658
F
=
0.3398
N
Step 5 · Find propellant flow (ṁ)
Use ṁ = F ÷ vₑ
Thrust is ṁvₑ, so the flow is the thrust over the exhaust speed.
ṁ
=
0.3398
17,658
ṁ
=
1.9243 ×
10
-5
kg/s
Step 6 · Convert the answers
Change each answer back to the unit you chose.
Pⱼₑₜ = 3,000 W = 3 kW (1 kW = 1000 W)
F = 0.3398 N = 339.7893 mN (1 N = 1000 mN)
Check
Put the numbers back in. Both sides should match.
17,658 = 1,800 × 9.81 ✓
3,000 = 0.6 × 5,000 ✓
3,000
=
1
2
×
0.3398
×
17,658
✓
1.9243 ×
10
-5
=
0.3398
17,658
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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