Aspect Ratio (AR)
The aspect ratio is an important geometric parameter of the wing.
Definition
AR = b² / S
with:
- b = wingspan (m)
- S = wing area (m²)
Alternatively for a rectangular wing: AR = b / c (chord).
Significance — induced drag reduction
CDi = CL² / (π · AR · e)
→ Higher AR = lower induced drag at the same CL.
Example:
- AR = 5 → CDi = CL² / (π × 5 × 0.85) ≈ 0.075 × CL².
- AR = 20 → CDi = CL² / (π × 20 × 0.85) ≈ 0.019 × CL² (= 4× less).
Typical values
| Aircraft type | AR | Remark |
|---|---|---|
| Cessna 172 | 7.4 | typical GA trainer |
| Piper PA-28 | 5.6 | shorter span |
| Cirrus SR22 | 10.1 | high for GA |
| Beechcraft King Air | 9.8 | turboprop |
| Boeing 747-400 | 7.9 | (surprisingly low due to thick wing) |
| Airbus A380 | 7.5 | |
| Boeing 787 Dreamliner | 11.1 | current generation |
| Glider Schleicher ASK 21 | 16.8 | standard training glider |
| Schleicher ASW 28 | 26.8 | high performance |
| U-2 spy plane | 10.6 | |
| Glider Eta | 51.3 | world record |
Pros and cons
High aspect ratio (AR > 10)
Pros:
- Low induced drag → better (L/D)_max.
- Better gliding performance.
- Better range (jet at (L/D)_max).
- Higher efficiency.
Cons:
- Structural problems: longer wings → larger bending moments → heavier structure.
- Roll inertia: less agile in roll.
- Lateral stability: more sensitive to crosswind / turbulence.
- Very long range benefit only if structural weight stays manageable.
Low aspect ratio (AR < 5)
Pros:
- Structurally light.
- Robust in manoeuvres (fighters).
- Low roll inertia → agile.
Cons:
- High induced drag.
- Lower (L/D)_max.
- High CL only at high α → earlier stall.
Winglets — alternative to more AR
Winglets are upward-pointing wing extensions that disturb the wingtip vortex. Effect: induced drag drops, without increasing wingspan.
- Effective AR rises by 20-30 %.
- Minimal structural weight increase.
- Examples: Airbus A320 Sharklets, Boeing 737 MAX winglets, Cessna Mustang.
Wing loading vs aspect ratio
Wing loading W/S and AR are independent parameters:
- High W/S (small S for given W): high Vs, good manoeuvrability.
- High AR: good efficiency.
- Glider: low W/S AND high AR.
- Fighter jet: high W/S, low AR.
Tapered wings — effective aspect ratio
For tapered wings the effective AR is higher than the geometric, because the lift distribution approximates the ideal elliptical form. Source: Anderson Ch. 5.