Performance Definitions and Variables - ATPL 032 — Performance

Performance speaks its own language, and the exam assumes you are fluent. This lesson collects the vocabulary in one place: the angles and gradients that describe going up and coming down, the declared distances that describe what a runway offers, the terms for how far and how long an aeroplane can fly, and the handful of curves that every later argument will be drawn on. Learn these shapes once, properly, and half the subject becomes recognition rather than derivation.

Angles and gradients

Climbing can be described two ways: as an angle in degrees, or as a gradient, the height gained per horizontal distance travelled, expressed as a percentage. The two carry the same information in different clothes:

The subtlety the syllabus insists on is which horizontal distance. The climb angle and climb gradient measure the aeroplane's path through the air: height gained against distance travelled through the air mass. The descent angle and descent gradient are the same definitions pointed downhill. The flight-path angle and flight-path gradient instead measure the path over the ground. In still air the two pairs coincide; the moment the air mass moves, they separate, and the difference between them is the wind.

A headwind steepens the path over the ground; a tailwind flattens it; the path through the air is untouched by either. This one picture decides many exam answers: obstacle-clearance questions live on the flight-path gradient, while questions about what the wing and engines can do live on the climb gradient.

The absolute ceiling

Climb performance shrinks with altitude, and the absolute ceiling is where it runs out: the pressure altitude at which the rate of climb falls to zero. There the aeroplane has no excess thrust or power left over what level flight consumes; climb angle, climb gradient and rate of climb are all zero at once. It is a theoretical roof (approached asymptotically, never operationally useful), and later lessons will hang the service ceiling and optimum altitudes below it.

The runway's declared distances

A runway offers more than its paved length, and the aerodrome declares exactly what may be used for what. Two areas beyond the runway end matter, both defined in CS-Definitions:

Stopway — a defined rectangular area beyond the end of the take-off run available, at least as wide as the runway and centred on its extended centreline, prepared so that an aeroplane can be stopped on it during an abandoned take-off without structural damage. It is ground you may stop on, not ground you may take off from.
Clearway — a defined rectangular area beyond the runway, under the control of the aerodrome authority, selected as suitable for an aeroplane to make a portion of its initial climb over, to screen height. It is at least 152 m (500 ft) wide, centred on the extended centreline, and nothing in it may project above a plane sloping up at 1.25 per cent (threshold lights excepted, if no higher than 0.66 m and set to each side of the runway). It can be grass, water or rough ground: the aeroplane never touches it.

From the runway and these two areas the aerodrome declares three distances, and every take-off calculation in this subject checks against them:

TORA — take-off run available: the length of runway declared available and suitable for the ground run of an aeroplane taking off.
TODA — take-off distance available: TORA plus any clearway, the distance available to accelerate, lift off and climb to screen height.
ASDA — accelerate-stop distance available: TORA plus any stopway, the distance available to accelerate and then brake to a halt after an abandoned take-off.

Reading these from an aerodrome chart is a syllabus skill of its own: the chart tabulates TORA, TODA and ASDA per runway direction, and the differences between the columns tell you what lies beyond each end. A TODA longer than TORA means a clearway; an ASDA longer than TORA means a stopway; and no declared distance ever includes both areas at once, because ASDA stops where the stopping surface stops and TODA measures flying distance, not stopping distance.

Screen height

Take-off and landing distances need a finishing line in the air, and the rulebooks use an imaginary screen standing at the end of the distance: the take-off distance ends when the aeroplane crosses the screen, and the landing distance begins as it crosses one on the way in. Its height depends on the rules in force: 35 ft for class A take-off on a dry runway, reduced to 15 ft on a wet or contaminated runway, and 50 ft for class B take-off and for landing generally. The lower wet-runway screen is a deliberate trade you will meet again in the class A module: it buys back some of the distance the wet surface costs.

Range, endurance and specific range

How far and how long are different questions. Range is the distance an aeroplane can travel on its fuel; endurance is the time it can stay airborne on it. Maximising one does not maximise the other, and the speeds for each differ. To compare cruise efficiency the syllabus uses fuel-specific distances:

Specific range (SR) — nautical air miles (NAM) flown per unit of fuel: distance through the air per kilogram or tonne burned.
Specific range over the ground (SRG) — nautical ground miles (NGM) per unit of fuel: the same idea with the wind folded in. A headwind lowers SRG below SR, a tailwind raises it, and the fuel bill for a route is set by SRG, not SR.

Power available and power required

Thrust is a force; power is force times speed, and both versions of the engine-versus-airframe contest appear throughout this subject. Power available is what the powerplant can deliver at a given speed; power required is what level flight at that speed costs, which is the drag times the speed:

Excess thrust (thrust minus drag) buys climb angle; excess power (power available minus power required) buys rate of climb. That division of labour returns in the climb lesson; here it explains why the same aeroplane needs both a thrust picture and a power picture.

What moves the numbers

Before the curves, the cast list. The syllabus names eight factors that affect aeroplane performance, and every chart in the subject is entered with some subset of them:

Pressure altitude and temperature — together they set density altitude, the air the engines breathe and the wings work in.
Wind — headwind and tailwind components change every distance and every path over the ground.
Aeroplane weight — more weight means more lift, more drag and longer distances everywhere.
Configuration — flap and gear positions reshape the lift and drag the aeroplane flies with.
Anti-skid status — an inoperative anti-skid system lengthens every stopping calculation.
Centre of gravity — a forward CG adds tail download and trim drag, costing a little performance.
Runway surface — paved or grass, dry, wet or contaminated: friction on the way out and the way in.
Runway slope — uphill lengthens take-off and shortens landing rolls; downhill the reverse.

Thrust and power against speed

How the powerplant's offer varies with speed depends on what spins at the front. A turbojet's thrust is roughly constant with speed, so its power available (thrust times TAS) grows almost linearly from zero. A propeller delivers roughly constant power once the propeller is working efficiently, so its thrust is highest at low speed and falls as speed rises. Raising density altitude sinks both families: thinner air means less thrust and less power at every speed, for both types.

Drag against IAS and TAS

The airframe's bill is the drag curve, and its behaviour depends entirely on which speed scale you plot it against. Against IAS the drag curve is one curve for all altitudes: indicated airspeed is itself a measure of dynamic pressure, so the same IAS means the same aerodynamic forces whatever the air density. Against TAS the curve shifts to the right with altitude: the same IAS corresponds to an ever higher TAS in thinner air, so the whole bucket slides toward higher true airspeeds while its depth stays the same. Power required, drag times TAS, therefore shifts right and up with altitude: the same drag now acts at a higher speed and costs more power.

Weight and configuration move the curve rather than the scale. More weight raises the induced-drag side of the bucket, lifting the curve and moving the minimum-drag speed to a higher IAS. Extending flaps or gear raises the parasite-drag side instead, lifting the curve but moving the minimum-drag speed to a lower IAS. Power required copies whatever the drag curve does, times the speed, and on the TAS plot the same raised curves simply reappear at each altitude's shifted position. Keep the two directions straight; the exam checks them separately and together.

Define climb, descent and flight-path angles and gradients, and explain that wind is the difference between the air and ground references

Define the absolute ceiling

Describe clearway and stopway per CS-Definitions, and describe and determine TORA, TODA and ASDA from given data or aerodrome charts

Describe screen height and its values: 35 ft, 15 ft wet or contaminated, 50 ft class B and landing

Define range and endurance, and specific range in NAM per unit fuel and SRG in NGM per unit fuel

Define power available and power required

Name the eight factors that affect aeroplane performance

Describe how thrust and power available vary with speed and density altitude, for propeller-driven and turbojet aeroplanes

Describe how drag and power required vary with IAS and TAS for different density altitudes, weights and configurations