Library / Aerospace / AER-02

Aerospace

Induced drag coefficient

Drag penalty from producing lift on a wing of finite span.

Ref: AER-02
Rev: v1
Field: Aerospace
Result: C_D,i

C_{D,i} = \frac{{C_{L}}^{2}}{π e AR}, AR = \frac{b^{2}}{S}

C_D,i is the induced-drag coefficient, C_L the lift coefficient, e an efficiency factor (about 0.7–0.95), b the wing span and S the planform area. AR = b²/S is the aspect ratio. Total drag follows the parabolic polar C_D = C_D0 + C_D,i.

Every wing producing lift leaves a trail of swirling air behind, which costs drag. Long, narrow wings waste less energy this way, and the loss grows with the square of the lift being produced.

Calculator

Solve for

C_D,iInduced drag coefficientComputed

C_LLift coefficient

0.11.6

bWing span

260

SWing area

m²

1100

eEfficiency factor

0.61

Aspect ratio AR = b²/S9
Induced drag ÷ lift at the same q0.02497

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Induced drag coefficient () current value 0.01498

bWing spanKey driver

5.99e-40.539

C_LLift coefficient

4.16e-40.107

SWing area

9.36e-40.0936

eEfficiency factor

0.01270.0212

Gliders have very long, narrow wings (AR above 30) because induced drag dominates at low speed.
Induced drag is highest when the aircraft is slow and heavy, and fades at high speed, where parasitic drag takes over.
High-speed missiles and fighters use low-aspect-ratio wings to cut wave drag, accepting a large induced drag.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing ()	Local step	Change in result
b Wing span	2 to 60 m	5.992e-4	0.5393	0.5387	+10%	−17.4 %
C_L Lift coefficient	0.1 to 1.6	4.161e-4	0.1065	0.1061	+undefined%	—
S Wing area	1 to 100 m²	9.362e-4	0.09362	0.09268	+10%	+10 %
e Efficiency factor	0.6 to 1	0.01273	0.02122	0.008488	+undefined%	—

Sweep of Lift coefficient

Lift coefficient	Induced drag coefficient
0.1	4.161e-4
0.2875	0.003439
0.475	0.009388
0.6625	0.01826
0.85	0.03006
1.038	0.04479
1.225	0.06244
1.413	0.08302
1.6	0.1065

Sweep one variable

Vary

Induced drag coefficient ()Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

C_D,i

Induced drag coefficient

Result ·

What the equation gives you. Everything else feeds it.

C_L

Lift coefficient

· typical 0.1 to 1.6

Lift coefficient at the flight condition. The dominant driver: induced drag scales as C_L², so doubling lift quadruples it.

Wing span

m · typical 2 to 60

Tip-to-tip span. Raises aspect ratio at fixed area; induced drag falls with b².

Wing area

m² · typical 1 to 100

Planform area. A larger area at the same span lowers the aspect ratio and increases drag.

Efficiency factor

· typical 0.6 to 1

1.0 is an ideal elliptical lift distribution; real wings are lower. Inversely proportional.

Worked example with the values above

Aspect ratio: AR = b²/S = 12² / 16 = 9.
Denominator: π e AR = π × 0.85 × 9 = 24.03.
C_D,i = 0.6² / 24.03 = 0.01498.

Assumptions and limits

Subsonic, attached flow.
Parabolic drag polar over a limited lift range.
Planform and e representative of the actual wing.

Common mistakes

Using total drag in place of the induced part.
Entering the semispan rather than the full span.
Using this near stall or in transonic flight.

Statistics and uncertainty

The efficiency factor is estimated, not measured, and its ±5–10% range feeds directly into the answer. The C_L² dependence means a 5% error in lift coefficient produces about a 10% error in induced drag.

Where it is used

Estimating range and endurance of UAVs and aircraft.
Choosing wing aspect ratio.
Predicting climb and glide performance.

Maths you need

Lift coefficient: dimensionless lift
Ratios: AR is span squared over area

Related formulas

Practise this formula