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Aerospace
Steady glide sink rate
Downward speed in a steady unpowered glide with total speed V along the flight path and lift-to-drag ratio L/D.
- Ref
- AER-30
- Rev
- v1
- Field
- Aerospace
- Result
- ws [m/s]
In a steady glide the flight path is inclined at γ below the horizontal with tan γ = 1/(L/D), so the vertical component of the speed V along the path is V sin γ = V/√(1 + (L/D)²). This is the exact result, and it reduces to V/(L/D) for small glide angles. The sink rate depends on the speed chosen, and it is least at the speed for minimum power.
Downward speed in a steady unpowered glide with total speed V along the flight path and lift-to-drag ratio L/D. This is the exact force-triangle result with no shallow-angle approximation. Still air.
Calculator
- Glide angle, atan(1/(L/D))4.764 °
- Horizontal speed, V(L/D)/√(1 + (L/D)²)34.88 m/s
- Time to descend 100 m34.4 s
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 sinks at 2.907 m/s and moves forward at 34.879 m/s, on a path 4.764° below the horizon.
- At this rate it loses 1000 m in 5.734 minutes.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| L/D Lift-to-drag ratio | 3 to 60 | 0.5833 | 11.07 | 10.48 | +10% | −9.04 % |
| V True airspeed along the path | 10 to 100 m/s | 0.8305 | 8.305 | 7.474 | +10% | +10 % |
Sweep of Lift-to-drag ratio
| Lift-to-drag ratio | Sink rate (m/s) |
|---|---|
| 3 | 11.07 |
| 10.13 | 3.44 |
| 17.25 | 2.026 |
| 24.38 | 1.435 |
| 31.5 | 1.111 |
| 38.63 | 0.9058 |
| 45.75 | 0.7648 |
| 52.88 | 0.6618 |
| 60 | 0.5833 |
Sweep one variable
Variables and how each one contributes
Sink rate
What the equation gives you. Everything else feeds it.
True airspeed along the path
The true airspeed along the flight path, in m/s. Raises the sink rate in direct proportion. Raising it by 10 % (to 38.5) moves the result by +10 %, from 2.907 to 3.197 m/s.
Lift-to-drag ratio
The lift-to-drag ratio at that speed. A higher L/D lowers the sink rate in inverse proportion. Raising it by 10 % (to 13.2) moves the result by −9.04 %, from 2.907 to 2.644 m/s.
Worked example with the values above
- Hypotenuse: √(1 + (L/D)²) = √(1 + 144) = 12.0416.
- Divide the speed: 35 / 12.0416.
- ws = 2.90659 m/s.
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