Glide Ratio⚠ unverified

Understanding the Parameters

• Glide ratio = distance ÷ height lost — the tangent of the glide-path angle's complement, or equivalently $1/\tan\gamma$ where $\gamma$ is the (shallow) glide angle below horizontal. A high glide ratio is a shallow descent; a low one is steep.

• Why it equals $L/D$ — in an engine-off glide the aircraft descends at a small angle $\gamma$, and the balance of forces along and across the flight path makes $\tan\gamma = D/L$ exactly (derived below). So the glide ratio $1/\tan\gamma = L/D$. Nothing about weight, size, or air density enters — only the ratio of the two aerodynamic forces.

• The maximum glide ratio — an aircraft glides farthest at the speed for maximum $L/D$ (the minimum-drag speed, $V_{md}$). Fly faster or slower and the glide ratio drops. This "best glide speed" is the single most important number after an engine failure — it maximises the reachable footprint.

• Representative values — modern sailplane: $40$–$70:1$; airliner (engines out): $\sim17:1$; light aircraft: $\sim10:1$; Space Shuttle on approach: $\sim4.5:1$ (a "flying brick"); Apollo capsule: essentially $0$ (ballistic). The number tells you at a glance how forgiving an engine-out situation is.

• Independent of weight — but not the speed to fly it — a heavy and a light glider of the same type have the same glide ratio, but the heavy one must fly faster to achieve it (its best-glide speed scales as $\sqrt{W}$, like Stall Speed). This is why sailplanes carry water ballast: same glide ratio, higher speed, better cross-country performance in strong conditions.

Derivation (Approaching a Proof)

Consider an aircraft in a steady, unpowered glide, descending along a straight path at a constant angle $\gamma$ below the horizontal, at constant speed (so no acceleration — forces balance). Three forces act: weight $W$ straight down, lift $L$ perpendicular to the flight path, and drag $D$ directly opposing the motion (back along the path). With no thrust, the aircraft's weight must supply everything.

Resolve the weight into components along and perpendicular to the flight path. Because the path is inclined at $\gamma$:

• Along the path (down-slope): $W\sin\gamma$ — this balances drag.
• Perpendicular to the path: $W\cos\gamma$ — this balances lift.

The two equilibrium equations are therefore

$$D = W\sin\gamma, \qquad L = W\cos\gamma.$$

Divide the first by the second — the weight cancels:

$$\frac{D}{L} = \frac{W\sin\gamma}{W\cos\gamma} = \tan\gamma.$$

The glide ratio is horizontal distance over height lost, which for a straight path at angle $\gamma$ is $\cos\gamma/\sin\gamma = 1/\tan\gamma$ (equivalently $\cot\gamma$). Therefore

$$\text{glide ratio} = \frac{1}{\tan\gamma} = \frac{L}{D}. \qquad\blacksquare$$

The identity is exact for any steady glide. (For the shallow angles of efficient aircraft, $\cos\gamma \approx 1$, so lift $\approx$ weight and the small-angle glide ratio is very nearly $1/\gamma$ in radians — but the $L/D$ identity holds exactly at any angle.) The beauty is that a purely geometric quantity — how far you go per unit drop — turns out to equal a purely aerodynamic one, the force ratio $L/D$, with the weight dropping out entirely.

Dimensional check. Both glide ratio (distance/height = m/m) and $L/D$ (force/force = N/N) are dimensionless ✓, so the identity is dimensionally consistent.

History and Development

• Lilienthal and the first glides. Otto Lilienthal's gliders of the 1890s made glide ratio a tangible, life-or-death quantity; his systematic measurements of lift and drag (however flawed the era's coefficients) were the first attempts to quantify what would become $L/D$.

• The soaring movement. After WWI, the Treaty of Versailles' restrictions on powered aircraft in Germany channelled energy into gliding; the Rhön soaring competitions (from 1920) drove relentless improvement in glide ratio through high-aspect-ratio wings and clean aerodynamics, laying groundwork for all efficient wing design.

• Engine-out as design case. Glide ratio became a headline safety number after dramatic powerless landings — the Gimli Glider (Air Canada 143, 1983, a 767 that ran out of fuel and glided ~17:1 to a landing) and the Azores Glider (Air Transat 236, 2001) — each a real-world demonstration that the engine-out $L/D$ sets the reachable footprint. Re-entry vehicles are designed around it at the other extreme: a low but nonzero glide ratio (Shuttle $\sim4.5:1$) buys crucial cross-range and a controlled runway landing that a ballistic capsule cannot achieve.

Related Concepts: Lift-to-Drag Ratio, Range Breguet, Drag Force, Lift Force, Best Climb Speed, Stall Speed, Induced Drag, Parasite Drag

Notes: Pure identity / pass-through — returns $L/D$ unchanged; the content is why glide ratio $=L/D$ (force balance along/across a steady glide path, weight cancels: $\tan\gamma=D/L$). Best glide at the max-$L/D$ speed. Independent of weight (but best-glide speed scales as $\sqrt W$ — hence sailplane water ballast). Sailplane $40$–$70:1$; airliner engines-out $\sim17:1$; Shuttle $\sim4.5:1$.