Range, Endurance and Gliding

Range is how far an aeroplane can fly on the fuel it carries; endurance is how long it can stay in the air on that fuel. The two are often confused, and they are flown at different speeds. A pilot who needs to reach a distant aerodrome wants the least fuel per nautical mile; a pilot holding while the weather clears wants the least fuel per hour.

Both are read from the same total drag curve, and so is the glide, the case in which there is no thrust at all. Which speed is best depends on whether the engines' fuel flow follows thrust, as in a jet, or power, as in a piston-propeller aeroplane. The curves themselves are developed in power curves and speed stability.

The drag curve and VMD

In level flight, thrust equals drag. The total drag curve is U-shaped: parasite drag rises with the square of the speed and induced drag falls with it. At the bottom of the curve the two are equal and the lift/drag ratio is at its maximum. This is the minimum drag speed, VMD.

Two other points on the curve matter here:

• The minimum power speed, VMP, lies on the back of the curve, at about 0.76 VMD for the idealised drag curve used in exams. Power required, drag times true airspeed, is least here.
• The point where a straight line from the origin touches the drag curve gives the least drag per unit of speed. It lies at about 1.32 VMD.

In that idealised curve, the drag at both 0.76 VMD and 1.32 VMD is about 15 per cent above the minimum, so the lift/drag ratio there is about 87 per cent of its maximum.

All three speeds are fixed indicated airspeeds for a given mass and configuration, and all rise with the square root of the mass: a 10 per cent lighter aeroplane flies them about 5 per cent slower. At altitude the same indicated airspeed is a higher true airspeed. On the Airbus A320, green dot speed shows the clean-configuration best lift/drag speed.

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Maximum range speed

Range depends on the specific range: distance flown per unit of fuel. Specific air range is true airspeed divided by fuel flow, in nautical air miles per kilogram or per litre. Specific ground range is groundspeed divided by fuel flow, and it is what decides whether the aeroplane reaches its destination. A light aeroplane offering 110 kt for 34 litres per hour or 95 kt for 25 litres per hour flies about 3.2 or 3.8 nautical miles per litre: the slower setting goes about 17 per cent further in still air.

The best speed depends on what fuel flow follows:

• Jet. Fuel flow is roughly proportional to thrust, so specific range is proportional to TAS ÷ drag. It is greatest where drag divided by speed is least, at the tangent point, about 1.32 VMD. This is maximum range cruise.
• Propeller aeroplane. Fuel flow is roughly proportional to power, drag times speed. The speed cancels out, so specific range is proportional to 1 ÷ drag, and it is greatest at VMD, the speed of the best lift/drag ratio.

Near the peak the specific range curve is flat, so jets usually cruise slightly faster. Long range cruise is the speed above maximum range cruise at which specific range has fallen to 99 per cent of its maximum. Airlines fly an economy speed set by the cost index (see cost index and cruise economics).

Three things move the best range speed:

• Wind. Into a headwind, fly somewhat faster than the still-air speed, cutting the time the wind acts; with a tailwind, somewhat slower. Slowing to endurance speed into a headwind is the classic error.
• Mass. A heavier aeroplane has a higher best range speed and a lower specific range. As fuel burns off, the speed for best range falls.
• Altitude. For a jet, climbing raises the true airspeed at the same indicated airspeed and lets the engines work in colder air, which improves specific fuel consumption. Range improves up to the optimum altitude. For a propeller aeroplane the true airspeed cancels out, so range depends little on altitude apart from engine effects.

Maximum endurance speed

Endurance depends on fuel flow alone: the lower the fuel burned per hour, the longer the flight. Wind has no effect on it.

• Jet. Fuel flow follows thrust, which equals drag, so maximum endurance is at VMD. On the A320, when no speed limit or constraint applies, the default holding speed is the maximum endurance speed, approximately green dot, which gives the lowest hourly fuel consumption.
• Propeller aeroplane. Fuel flow follows power, so maximum endurance is at VMP, about 0.76 VMD. The power required at a given indicated airspeed rises with altitude, because the true airspeed is higher, so a propeller aeroplane achieves its best endurance low down.

Range versus endurance

Breguet range equation

The Breguet range equation shows what determines range for a jet cruising at constant speed and lift/drag ratio:

Range = (V ÷ c) × (L/D) × ln(W₁ ÷ W₂)

V is the true airspeed, c the thrust specific fuel consumption, L/D the lift/drag ratio, and W₁ and W₂ the weights at the start and end of the cruise. The equation separates three efficiencies:

• Engine efficiency, V ÷ c: faster flight on a lower fuel consumption per unit of thrust.
• Aerodynamic efficiency, L/D.
• Structural and fuel efficiency, the natural logarithm of the ratio of start to end weight. The more of the take-off weight that is fuel, the further the aeroplane flies, but with diminishing returns, because the extra fuel must itself be carried.

For a jet, range is greatest where the product V × L/D is greatest, which is again 1.32 VMD. For a propeller aeroplane, the V ÷ c term is replaced by propeller efficiency divided by power specific fuel consumption, so range depends directly on L/D and is greatest at VMD. As fuel burns the aeroplane becomes lighter and its specific range improves, which the logarithm captures: range cannot be found by dividing the fuel by an average fuel flow, and jet planning therefore uses integrated range tables.

Glide ratio and glide angle

In a steady glide there is no thrust. Lift balances the component of weight perpendicular to the path, W cos γ, and drag balances the component along it, W sin γ. Dividing one by the other:

tan γ = D ÷ L, so the glide ratio, distance flown per unit of height lost, equals L/D.

A lift/drag ratio of 10 gives a glide angle of about 5.7° and a gradient of 10 per cent: 1,000 ft of height buys 10,000 ft of distance, about 1.6 NM. EASA exam material puts typical single-engine piston aeroplanes at 9:1 to 12:1. Glide range is height multiplied by the glide ratio: at a 7 per cent gradient, 10,000 ft gives about 23.5 NM in still air, and 15,000 ft about 35 NM.

The glide ratio falls with anything that adds drag: gear, flaps and, above all, a windmilling propeller, which acts almost like a solid disc. A stopped propeller gives far less drag. Where the propeller can be feathered, feathering it improves the glide; on a single-engine aeroplane without feathering, selecting fully coarse pitch reduces the windmilling drag.

Best glide speed and glide range

The best glide speed is the speed of the maximum lift/drag ratio, VMD. It gives the flattest glide and the greatest distance from a given height. Flying either faster or slower steepens the glide. Flight manuals publish it for maximum mass.

• Mass does not change the best glide ratio or the still-air glide distance. It changes the speed: VMD varies with the square root of mass, so a lighter aeroplane should glide slightly slower than the published figure.
• Altitude does not change the best glide indicated airspeed either, but the true airspeed, and with it the rate of descent, is higher up.
• Wind changes the distance over the ground. Into a headwind, glide somewhat faster than the still-air speed, so that less of the descent is spent drifting back with the wind; with a tailwind, glide slightly slower.

Minimum sink and rate of descent

The rate of descent (ROD) in a glide is the true airspeed multiplied by sin γ, which for small angles is about TAS ÷ (L/D). An aeroplane gliding at 70 kt with an L/D of 10 descends at about 700 ft/min.

Put another way, the rate of descent equals the power required divided by the weight. It is therefore least at the minimum sink speed, which is VMP. In the idealised drag curve, gliding at VMP gives about 12 per cent less sink than at VMD but about 13 per cent less distance. Minimum sink gives the longest time in the air; best glide gives the greatest distance.

The choice depends on the situation. Close to a landing site, distance is what counts. Where time matters more, for example to complete restart drills, send a distress call or wait for help, minimum sink speed buys the most time. A heavier aeroplane at the same glide ratio descends faster and reaches the ground sooner, leaving less time for the drills.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.