Concept

Glide ratio — where it appears

The distance an aircraft travels per unit height lost, equal to its lift-to-drag ratio in a steady glide. It is a property of the aerodynamics alone — weight and altitude change the speed at which it is achieved and not its value.

Named by 7 essays across 3 fields — each of them below, with the objects they name alongside it.

A wing's two drags, and the lift at which they are equal. Friction drag and induced drag plotted against lift coefficient, with their sum above them. Friction is flat, because a surface costs the same whatever the wing is doing; induced drag rises as the square of the lift. The total is least where the two are equal, and that is also the point of best glide.

The two drags a wing pays

A wing pays for having a surface, and it pays for making lift with a finite span. One of those bills falls as it flies faster and the other rises, so there is a speed at which the total is least — and the condition for it turns out to be that the two are equal.

viscous · Drag budget

The cheapest way to stay up

There is a speed at which an aircraft's drag is least, and a different, slower speed at which its power is least. The ratio between them is the fourth root of a third — a number that does not depend on the aircraft, the altitude, or anything else about the flight.

viscous · Drag budget

Three times the wind, on a reach. The polar diagram: boat speed in every direction, as a multiple of the true wind speed, for drag angles of 14 and 6 degrees. The shaded wedge at the top is the no-go zone, whose half-angle is exactly the sum of the two drag angles. Everywhere outside about twice that angle the boat is faster than the wind, and the maximum is 2.92 times the wind at 110 degrees — which is 1/sin λ at 90° + λ, both checked.

Faster than the wind that drives it

An ice yacht in a fifteen-knot breeze does forty. That is not a trick and it does not need a special sail — it follows from two drag angles and a triangle, and the best speed a boat can reach is one over the sine of their sum.

applied · Sailing

The fastest way is not the straight one

A boat racing to a mark dead upwind sails seventy per cent further than the distance to it, and arrives first. The best angle is forty-five degrees plus half the apparent wind angle, it comes out of one line of trigonometry, and the same argument says to gybe downwind rather than run.

applied · Sailing $Induced drag against aspect ratio, all at C_L = 0.6. Induced drag for wings of different aspect ratio, each flown at whatever incidence makes it carry the same lift coefficient. The drag falls as one over the aspect ratio, so the longest wing here pays a fraction of what the shortest does for exactly the same load.$

The span is the whole story

Induced drag is the price of having ends, and the only thing that lowers it at a given lift is putting those ends further apart. Not more area, not a better section, not a cleverer planform — span, and everything else is a correction of a few per cent to it.

circulation · Finite wing $Lift takes the launch angle down far faster than drag does. The best launch angle against β for a ball whose lift is a fixed fraction ℓ of its drag, from ℓ = 0 — the drag-only curve — to ℓ = 1. At β = 10 drag alone puts the best angle at 32.6°; a lift-to-drag ratio of 0.4 takes it to 15.9° and 0.8 makes a level launch best. Once the curve reaches zero it stays there: the lift lifts the ball, and any angle given at launch is height the lift would have bought for less drag.$

A spinning ball should leave low

Drag alone takes a ball's best launch angle from 45° to the high thirties at the speeds sport is played at. Backspin takes it into the teens, because a ball with lift is a glider and a glider buys its height with lift rather than with angle. Every tenth of lift-to-drag ratio takes a fixed slice off the angle, and above a line that depends on the launch speed the best flight leaves the ground level.

applied · Sport ball

Losing the leading-edge suction doubles a slender wing's drag due to lift and multiplies a long wing's by about half its aspect ratio. The drag due to lift with no leading-edge suction, Cₗ²/Cₗα, over the induced drag a full suction leaves, Cₗ²/(πAe), against aspect ratio, from a vortex lattice for rectangular, delta and elliptic flat wings; with the closed form 1 + √(1 + A²/4) that Helmbold's lift slope gives an elliptic wing. Rectangular: 2.15 at A = 1, 3.46 at 4, 5.33 at 8, 7.11 at 12; delta: 2.22 at 0.5 and 2.83 at 2. The slender limit is 2.

A wing that cannot hold its suction gains little from its span

The leading-edge suction is a small force concentrated at one edge, and on a finite wing it decides what the aspect ratio is worth. With it, the drag due to lift is the induced drag, which falls as the span grows. Without it, the drag due to lift is the lift tilted back by the incidence, and that falls only as fast as the lift slope rises — which stops at the section's 2π. A slender delta that loses its suction pays exactly twice its induced drag; a wing of aspect ratio eight pays more than five times it. Without the suction no span can lift a wing's best lift-to-drag ratio past a ceiling set by the section alone.

circulation · Leading edge suction

Named alongside it

The objects these essays reach for when they reach for this one.

Drag polar Induced drag Drag Lift coefficient Model limit Apparent wind Aspect ratio Dimensionless Efficiency Lifting line Minimum-drag speed Optimisation

All concepts