Library / Aerospace / AER-29
Aerospace
Still-air horizontal glide distance
Ground distance covered in a steady unpowered glide in still air, from the altitude lost Δh and the constant lift-to-drag ratio L/D.
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- AER-29
- Rev
- v1
- Field
- Aerospace
- Result
- x [m]
In a steady glide the lift and drag balance the weight, so the glide path angle satisfies tan γ = D/L = 1/(L/D). The horizontal distance covered for each metre of height lost is therefore L/D, giving x = Δh(L/D) in still air. A glider with L/D of 40 covers 40 km from 1000 m. Wind, turns and the final flare change the real distance.
Ground distance covered in a steady unpowered glide in still air, from the altitude lost Δh and the constant lift-to-drag ratio L/D. It follows from the force triangle of the glide. The final flare and any turns need separate treatment.
Calculator
- Glide angle, atan(1/(L/D))3.814 °
- Altitude lost per kilometre of distance, 1000/(L/D)66.67 m
- Distance in kilometres18 km
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.
- The aircraft glides 18 km from 1,200 m of altitude, at a glide angle of 3.814°.
- Each 1 % of L/D gained adds 180 m of distance, so clean aerodynamics pays directly in range.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Δh Altitude lost | 50 to 10,000 m | 750 | 150,000 | 149,300 | +10% | +10 % |
| L/D Lift-to-drag ratio | 3 to 60 | 3,600 | 72,000 | 68,400 | +10% | +10 % |
Sweep of Lift-to-drag ratio
| Lift-to-drag ratio | Glide distance (m) |
|---|---|
| 3 | 3,600 |
| 10.13 | 12,150 |
| 17.25 | 20,700 |
| 24.38 | 29,250 |
| 31.5 | 37,800 |
| 38.63 | 46,350 |
| 45.75 | 54,900 |
| 52.88 | 63,450 |
| 60 | 72,000 |
Sweep one variable
Variables and how each one contributes
Glide distance
What the equation gives you. Everything else feeds it.
Altitude lost
The altitude lost, in m. Raises the distance in direct proportion. Raising it by 10 % (to 1,320) moves the result by +10 %, from 18,000 to 19,800 m.
Lift-to-drag ratio
The lift-to-drag ratio in the glide. Raises the distance in direct proportion. Raising it by 10 % (to 16.5) moves the result by +10 %, from 18,000 to 19,800 m.
Worked example with the values above
- Height lost: Δh = 1,200 m.
- Lift-to-drag ratio: L/D = 15.
- x = 1,200 × 15 = 18,000 m.
Assumptions and limits
- Steady flight along a straight path at constant speed, with L/D and specific fuel consumption held constant.
- Still air, and weights taken at the start and end of the cruise segment.
Common mistakes
- Using mass-based fuel consumption directly in a weight-flow equation, which needs g₀.
- Using range formulas for a changing L/D without averaging.
- Treating a still-air glide ratio as the ratio over the ground in a headwind or tailwind.
Statistics and uncertainty
Climb, glide and Breguet results are quasi-steady estimates. Range from the Breguet equation is typically good to 5 % to 10 % for long cruise legs, and worse for short missions where climb and descent are large, or in wind, which the formulas ignore.
Where it is used
- Planning range, fuel, and glide-back or engine-out decisions.
- Comparing the efficiency of aircraft designs.
Maths you need
- Lift-to-drag ratio: L/D, the glide ratio
- Specific fuel consumption: fuel flow per unit thrust or power
- Weight fraction: the ratio of final to initial weight