Gliding flight and glide range
Force balance in a steady glide, glide angle and range from L/D, best-glide and minimum-sink speeds, and the effects of weight, altitude and wind.
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Why it matters
Every powered aircraft becomes a glider when its engines fail, and the distance it can glide decides which fields it can reach. Sailplanes live entirely on gliding performance, and airliners plan descents as near-idle glides to save fuel. Gliding is also the cleanest demonstration of why (L/D)_max and minimum power are the two key points on the drag polar.
Key ideas
Equilibrium in a steady glide. With zero thrust and a steady descent at glide angle γ (measured below the horizontal), weight is the only "engine":
- along the path:
D = W·sin γ - normal to the path:
L = W·cos γDividing,tan γ = D/L = 1/(L/D). The glide angle depends only on the lift-to-drag ratio at the flight condition — not on weight or altitude.
Glide ratio and range. In still air the horizontal distance per unit height lost is R/h = 1/tan γ = L/D. The flattest glide and maximum range are therefore at (L/D)_max, i.e. at the minimum-drag lift coefficient C_L = √(C_D0/K):
R_max = h·(L/D)_max.
An airliner with (L/D)_max ≈ 17 can glide about 17 km for every kilometre of height; a high-performance sailplane exceeds 50.
Glide speed. From L = W cos γ, V = √(2W·cos γ/(ρ·S·C_L)). For shallow glides cos γ ≈ 1. The best-glide speed:
- rises as √(W/S): a heavier aircraft glides at the same angle but faster, so it covers the same distance in less time;
- rises as 1/√σ in TAS, but is constant in EAS at a given weight. This is why gliders carry water ballast on strong-lift days: they lose nothing in glide ratio and gain speed between thermals.
Sink rate. The vertical speed is V_v = V·sin γ. For small angles,
V_v = √(2W/(ρS)) · C_D/C_L^(3/2).
Minimum sink is therefore at maximum C_L^(3/2)/C_D — the minimum-power condition, C_L = √(3C_D0/K), at about 0.76 times the best-glide speed. Minimum sink gives the longest time aloft (endurance), not the longest distance. Sink rate at a given C_L rises as √(W/S) and as 1/√σ.
Hodograph (speed polar). Plotting sink rate against forward speed gives the glider's speed polar. The top of the curve is minimum sink; a line from the origin tangent to the curve gives the best glide angle. Shifting the origin by the wind (or by rising/sinking air) and redrawing the tangent gives the best speed to fly in those conditions: fly faster than best-glide speed into a headwind or in sinking air.
Wind. The glide angle relative to the air is unchanged by a steady wind, but the ground distance is: R_ground = R_air·(V ± V_w)/V for a tailwind (+) or headwind (−) along the track, using the time in the air t = h/V_v.
Assumptions. Steady, wings-level glide in still air; parabolic polar; density changes over the glide height ignored (for long glides, integrate with σ varying); propeller windmilling drag and lowered gear or flaps increase C_D0 and reduce the glide ratio.
Formulas
D = W·sin γ, L = W·cos γ
tan γ = 1 / (L/D)
R = h·(L/D) (still air), R_max = h·(L/D)_max
V = √(2·W·cos γ / (ρ·S·C_L))
V_v = V·sin γ ≈ √(2W/(ρS)) · C_D / C_L^(3/2) (sink rate)
C_L,best glide = √(C_D0/K), C_L,min sink = √(3·C_D0/K)
t ≈ h / V_v (time aloft, density taken constant)
Symbols: W weight, L lift, D drag (N); γ glide angle below horizontal (rad or °); h height lost (m); R horizontal distance (m); V true airspeed along the path (m/s); V_v sink rate (m/s); ρ density (kg/m³); S wing area (m²); C_L, C_D lift and drag coefficients; C_D0, K drag-polar constants; V_w wind speed (m/s); t time (s).
Worked examples
Example 1 (standard): engine-out glide. Given: a light aircraft with (L/D)_max = 16 loses its engine at 2000 m above flat terrain in still air.
- Best glide angle:
tan γ = 1/(L/D)_max= 1/16, so γ = 3.58°. - Maximum range:
R = h·(L/D)_max= 2000 × 16 = 32 000 m = 32 km. - If the pilot glides at a speed where L/D = 12 instead, R = 24 km — 8 km less.
Example 2 (GATE level): sailplane best glide and minimum sink. Given: W = 3500 N, S = 12 m², C_D = 0.012 + 0.022·C_L², ρ = 1.112 kg/m³ (take constant).
- Best glide: C_L = √(0.012/0.022) = 0.7385; (L/D)_max = 1/(2√(0.022 × 0.012)) = 30.8; γ = arctan(1/30.77) = 1.86°.
- Best-glide speed:
V = √(2W·cos γ/(ρ·S·C_L))= √(2 × 3500 × 0.99947/(1.112 × 12 × 0.7385)) = 26.6 m/s; its sink rate = 26.64 × sin 1.86° = 0.865 m/s. - Minimum sink: C_L = √(3 × 0.012/0.022) = 1.279; C_D = 0.048; L/D = 26.65; γ = 2.15°.
- Minimum-sink speed: V = √(2 × 3500 × cos 2.15°/(1.112 × 12 × 1.279)) = 20.2 m/s; sink rate
V_v = V·sin γ= 0.759 m/s. - From 1000 m, time aloft at minimum sink ≈ 1000/0.759 = 1317 s (about 22 min), covering 26.7 km; at best glide it would cover 30.8 km but stay up only 1000/0.865 = 1156 s.
Common mistakes
- Saying a heavier aircraft glides less far. In still air the glide ratio, and hence range, is independent of weight; only the speed changes.
- Confusing best glide (max L/D, maximum distance) with minimum sink (max C_L^(3/2)/C_D, maximum time).
- Using
L = WandD = W·γwithout radians, or mixing sin and tan for steep glides. - Taking the stall speed or V = √(2W/(ρ·S·C_L,max)) as the best-glide speed.
- Forgetting that a headwind reduces ground range even though the air-mass glide angle is unchanged.
For GATE AE
Expect glide-range and glide-angle numericals from L/D and height, best-glide and minimum-sink speeds and sink rates from a given polar, and concepts such as the effect of weight, altitude and wind on glide performance. Practise the sink-rate expression in terms of C_D/C_L^(3/2) and the link with the minimum-power condition.
Quick check
- What is the glide angle of an aircraft with L/D = 20?
- Does adding ballast change a glider's maximum still-air range?
- Which lift coefficient gives minimum sink rate?
- From 1500 m with (L/D)_max = 12, what is the maximum still-air range?
Answers: 1. arctan(1/20) = 2.86°. 2. No; it increases the best-glide speed only. 3. C_L = √(3·C_D0/K). 4. 18 km.
Interview questions
All Aircraft Performance interview questionsTry answering each one aloud before you open it.
1.What is gliding flight in the context of aircraft performance?Concept
Gliding is steady flight with zero thrust, in which the aircraft descends along a path inclined at angle γ below the horizontal. The weight component along the path, W·sin γ, balances drag, and the component normal to the path, W·cos γ, balances lift. Dividing gives tan γ = 1/(L/D), so the glide angle depends only on the lift-to-drag ratio. Potential energy is traded for the work done against drag.
2.Explain the concept of glide range and its importance in aviation.Concept
Glide range is the horizontal distance an aircraft can cover while descending from a certain altitude without engine power. It is important because it determines how far an aircraft can travel in the event of an engine failure, allowing pilots to plan for emergency landings. The glide range depends on the glide ratio, which is the ratio of lift to drag, and the altitude from which the aircraft begins to glide.
3.How does the glide ratio affect the performance of an aircraft in gliding flight?Concept
The glide ratio is the ratio of the horizontal distance traveled to the vertical distance descended. A higher glide ratio means the aircraft can travel further horizontally for a given loss of altitude, which is desirable in gliding flight. It is influenced by the aerodynamic efficiency of the aircraft, including factors like wing design and surface smoothness.
4.Why is it important for pilots to understand the best glide speed of an aircraft?Application
The best glide speed is the speed at which an aircraft achieves the maximum glide range. Understanding this speed is crucial for pilots, especially in emergency situations, as it allows them to maximize the distance they can cover without engine power. Flying at this speed ensures the aircraft maintains the optimal lift-to-drag ratio.
5.What happens to the glide range if an aircraft is flying at a speed higher than the best glide speed?Application
If an aircraft flies at a speed higher than the best glide speed, the glide range decreases. This is because higher speeds increase drag, reducing the lift-to-drag ratio and causing the aircraft to descend more steeply. As a result, the aircraft covers less horizontal distance for the same loss of altitude.
6.How does altitude affect the glide range of an aircraft?Application
Altitude directly affects the glide range because the higher the altitude, the more potential energy the aircraft has, allowing it to cover a greater horizontal distance. The glide range is proportional to the altitude, assuming the aircraft maintains the best glide speed and optimal glide ratio.
7.Why might a pilot choose to glide at a speed lower than the best glide speed?Application
A pilot might choose to glide at a speed lower than the best glide speed to reduce the rate of descent, which can be useful when trying to extend the time aloft or when preparing for a landing in a confined area. However, this comes at the cost of reduced glide range, as the aircraft will not be operating at the optimal lift-to-drag ratio.
8.Calculate the glide range of an aircraft with a glide ratio of 15:1 descending from an altitude of 3000 meters.Numerical
To calculate the glide range, multiply the glide ratio by the altitude. Glide range = Glide ratio × Altitude = 15 × 3000 m = 45000 meters or 45 kilometers.
9.What factors affect the glide ratio of an aircraft?Application
The still-air glide ratio equals L/D, so it depends on the drag polar — C_D0 (cleanliness, surface finish, gear and flaps, a windmilling propeller) and the induced-drag factor K (aspect ratio, span efficiency) — and on flying at the right C_L. Weight and altitude do not change the best glide ratio; they change only the speed at which it is achieved. Wind does not change the glide angle relative to the air but does change the glide distance over the ground.
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