SME
Aircraft Design
Mission profile and takeoff-weight sizing
Use this for “Crew 2 kN, payload 18 kN, fuel fraction 0.22, empty fraction 0.55. Estimate the takeoff weight.”
Chart
Crew: 2 kN
Payload: 18 kN
Fuel: 19.13 kN
Empty: 47.83 kN
This is an example. Type your own values to start a new problem.
W₀ (kN)
=
Wcrew (kN)
+
Wpayload (kN)
1
−
−
Wₗ
Fixed load
calculated
Wf
Fuel weight
calculated
Wₑ
Empty weight
calculated
Formulas
Wₗ = Wcrew + Wpayload
20 = 2 + 18
W₀
=
Wₗ
1 − (Wf/
W₀
) − (Wₑ/
W₀
)
86.96
=
20
1 − 0.22 − 0.55
Wf
=
(Wf/
W₀
)
×
W₀
19.13 = 0.22 × 86.96
Wₑ
=
(Wₑ/
W₀
)
×
W₀
47.83 = 0.55 × 86.96
Assumptions
•
The fuel fraction comes from the mission; the empty fraction from similar airplanes.
•
Takeoff weight W₀ = Wcrew + Wpayload + Wf + Wₑ.
•
So 1 − Wf/W₀ − Wₑ/W₀ is the share of W₀ left for crew and payload.
Step-by-step
WE KNOW
Wcrew = 2 kN, Wpayload = 18 kN, Wf/W₀ = 0.22, Wₑ/W₀ = 0.55
FIND
fixed load (Wₗ), takeoff weight (W₀), fuel weight (Wf), empty weight (Wₑ)
Step 1 · Find fixed load (Wₗ)
Use Wₗ = Wcrew + Wpayload
The
fixed
load:
crew
and
payload,
the
weight
that
does
not
grow
with
W₀
.
Wₗ = 2 + 18
Wₗ = 20 kN
Step 2 · Find takeoff weight (W₀)
Use W₀ = Wₗ ÷ (1 − (Wf/W₀) − (Wₑ/W₀))
Fuel
and
empty
weight
grow
with
W₀
,
so
the
fixed
load
is
the
share
1
−
Wf/
W₀
−
Wₑ/
W₀
of
it.
W₀
=
20
1 − 0.22 − 0.55
W₀
=
20
0.23
W₀
=
86.96
kN
Step 3 · Find fuel weight (Wf)
Use Wf = (Wf/W₀) × W₀
The fuel weight is its fraction of the takeoff weight.
Wf = 0.22 × 86.96
Wf = 19.13 kN
Step 4 · Find empty weight (Wₑ)
Use Wₑ = (Wₑ/W₀) × W₀
The empty weight is its fraction of the takeoff weight.
Wₑ = 0.55 × 86.96
Wₑ = 47.83 kN
Check
Put the numbers back in. Both sides should match.
20 = 2 + 18 ✓
86.96
=
20
1 − 0.22 − 0.55
✓
19.13 = 0.22 × 86.96 ✓
47.83 = 0.55 × 86.96 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
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