SME
Aerodynamics · Problem type
Aspect ratio and taper of a wing
Use this for “A wing spans 12 m with a 1.8 m root chord and a 0.9 m tip chord. Find λ, S and AR.”
Diagram
Drawn
to
scale:
AR
=
b
2
S
=
8.889.
This is an example. Type your own values to start a new problem.
λ
=
cₜ (m)
cᵣ (m)
S (m²)
=
b (m)
×
(
cᵣ (m)
+
cₜ (m)
)
2
AR
=
(
b (m)
)
2
S (m²)
cavg
Mean chord
worked out (not typed)
Formulas
λ
=
cₜ
cᵣ
0.5
=
0.9
1.8
S
=
b
×
cᵣ + cₜ
2
16.2
=
12
×
1.8 + 0.9
2
cavg
=
S
b
1.35
=
16.2
12
AR
=
b
2
S
8.889
=
12
2
16.2
Assumptions
•
Straight taper: the chord shrinks evenly from the root chord cᵣ to the tip chord cₜ.
•
The wing area S is the planform seen from above, including the part inside the fuselage.
•
The aspect ratio AR = b² ÷ S is the span over the mean chord.
Step-by-step
WE KNOW
b = 12 m, cᵣ = 1.8 m, cₜ = 0.9 m
FIND
taper ratio (λ), wing area (S), mean chord (cavg), aspect ratio (AR)
Step 1 · Find taper ratio (λ)
Use λ = cₜ ÷ cᵣ
Taper: the tip chord over the root chord.
λ
=
0.9
1.8
λ
=
0.5
Step 2 · Find wing area (S)
Use S = b × (cᵣ + cₜ) ÷ 2
A trapezoid: the span times the average of the two chords.
S
=
12
×
1.8 + 0.9
2
S
=
12
×
2.7
2
S
=
32.4
2
S
=
16.2
m²
Step 3 · Find mean chord (cavg)
Use cavg = S ÷ b
The mean chord: the area spread over the span.
cavg
=
16.2
12
cavg = 1.35 m
Step 4 · Find aspect ratio (AR)
Use AR = b² ÷ S
Square the span, then divide by the area.
AR
=
12
2
16.2
AR
=
144
16.2
AR = 8.889
Check
Put the numbers back in. Both sides should match.
0.5
=
0.9
1.8
✓
16.2
=
12
×
1.8 + 0.9
2
✓
1.35
=
16.2
12
✓
8.889
=
12
2
16.2
✓
Topic check
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