SME
Aerodynamics · Problem type
Lift slope of a finite wing
Use this for “An airfoil with a₀ = 2π per radian makes a wing of aspect ratio 8 and e = 0.9. Find the wing’s lift slope a.”
Diagram
Drawn
rectangular
with
span
chord
=
AR
=
8.
This is an example. Type your own values to start a new problem.
a
=
a₀
1
+
a₀
π
×
×
adeg
Wing slope (per degree)
calculated
Formulas
a
=
a₀
/{1
+
a₀
/{π
×
e
×
AR}}
4.917 = 6.2832/{1 + 6.2832/{π × 0.9 × 8}}
adeg
=
a
×
π
180
0.08582
=
4.917
×
π
180
Assumptions
•
Lifting-line theory: downwash tilts the wind, so the wing needs more α than its airfoil for the same lift.
•
Thin airfoils have a₀ = 2π per radian (0.1097 per degree); e near 1 for a near-elliptic lift distribution.
•
Slopes are per radian; per degree is × π ÷ 180.
Step-by-step
WE KNOW
a₀ = 6.2832, AR = 8, e = 0.9
FIND
wing slope (per rad) (a), wing slope (per degree) (adeg)
Step 1 · Find wing slope (per rad): a
Use a = a₀/{1 + a₀/{π × e × AR}}
Divide
a₀
by
πeAR,
add
1,
then
divide
a₀
by
the
sum:
a
<
a₀
.
a
=
a₀
1 +
a₀
÷ (π ×
e
× AR)
a
=
6.2832
1 + 6.2832 ÷ (π × 0.9 × 8)
a
=
6.2832
1 + 6.2832 ÷ (7.2 × π)
a
=
6.2832
1 + 6.2832 ÷ 22.62
a
=
6.2832
1 + 0.2778
a
=
6.2832
1.2778
a
=
4.917
Step 2 · Find wing slope (per degree): adeg
Use adeg = a × π ÷ 180
Per
degree:
multiply
by
π
180
.
adeg
=
4.917
×
π
180
adeg = 0.08582
Check
Put the numbers back in. Both sides should match.
4.917 = 6.2832/{1 + 6.2832/{π × 0.9 × 8}} ✓
0.08582
=
4.917
×
π
180
✓
Topic check
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