Birdbird Virtual Lab · Performance

Performance: take-off, climb, cruise and landing

A jet transport is certified to survive an engine failure at the worst moment of the take-off and to stop within the runway on landing with a margin. Here you can see where V1 comes from, what limits the take-off mass, how a jet climbs and cruises efficiently, and how much runway a landing really needs. Reference aircraft: Airbus A320 with illustrative values.

1 · Interactive

Take-off speeds and the engine-failure decision

Below V1 an engine failure means stop; at or above V1 it means go. V1 is chosen so that both outcomes fit on the runway. Choose a V1, let an engine fail at any speed and see whether the aircraft stops within the accelerate-stop distance available (ASDA) or reaches 35 ft within the take-off distance available (TODA).

Aircraft and runway
Engine failure
VEF · engine failure speed

The speed at which the critical engine is assumed to fail. It may not be lower than VMCG.

V1 · decision speed

The highest speed at which the first action to stop must be taken, and the lowest speed from which the take-off can be continued after a failure at VEF. The pilot recognises the failure about one second after VEF.

VMCG · ground control

The lowest speed at which the aircraft can be kept within 30 ft of the centreline with rudder only, no nosewheel steering, after a sudden engine failure at take-off thrust. V1 must be at least VMCG.

VR · rotation

Not less than V1 and not less than 1.05 VMCA. Chosen so that V2 is reached by 35 ft with one engine out, even with a normal rotation rate.

VMU and VLOF · lift-off

VMU is the lowest speed at which the aircraft can safely lift off. Lift-off speed VLOF must keep a margin above it, typically 1.10 VMU with all engines and 1.05 VMU with one engine out.

V2 · take-off safety speed

Reached by 35 ft with one engine out. At least 1.13 VSR and 1.10 VMCA. It is the speed flown in the second segment.

Two curves, one crossing. A higher V1 means more runway to stop but less to go. The V1 where the two distances are equal is the balanced V1, and that distance is the balanced field length.
The certified distances. Take-off distance (dry) is the longer of the one-engine-out distance to 35 ft and 115 % of the all-engines distance to 35 ft. Accelerate-stop includes two seconds at V1 and no reverse thrust credit on a dry runway.
Wind factoring. The calculations may use only 50 % of a reported headwind and must use 150 % of a reported tailwind. The models on this page do this: the readouts show the wind actually used.
After V1, go. A stop started above V1 is outside what was calculated, and the aircraft may not stop on the runway. Most high-speed rejected take-off accidents are stops started after V1.
2 · Interactive

What limits the take-off mass

The maximum take-off mass on a given day is the lowest of several limits. Heat and altitude (the WAT effect: weight, altitude, temperature) reduce engine thrust and raise the true airspeed for the same indicated speed, so every limit drops on a hot day at a high aerodrome. For why thin air hurts, see density altitude.

Aerodrome
Obstacle after the runway
Today's take-off
Field length

There must be a V1 that makes both the accelerate-stop and the accelerate-go distance fit, and 115 % of the all-engines distance must also fit. Longer runway, headwind, downhill slope and cooler air all raise this limit.

Climb

With one engine out a twin must have a gross gradient of at least 2.4 % in the second segment (gear up, take-off flaps, V2). This limit does not depend on the runway at all, only on mass, temperature and pressure altitude.

Obstacle

The net flight path, the gross path reduced by 0.8 % for a twin, must clear every obstacle in the take-off funnel by at least 35 ft. A close, tall obstacle needs a steep path and limits the mass.

Tyre speed and brake energy

The ground speed at lift-off may not exceed the tyre rating (typically 195 kt). V1 may not exceed VMBE, the speed above which the brakes cannot absorb the energy of a stop. Both bite at high, hot aerodromes and with tailwind.

Structural MTOW

The certified maximum take-off mass, independent of the day. For this teaching aircraft 78 t. The planned mass may also be limited by the landing mass at destination.

Flex and derate

When the actual mass is below the limit, reduced thrust saves engine wear. Flex (assumed temperature): performance is calculated as if it were hotter, and TOGA is still available at any time. Derate: a certified lower thrust rating with its own, lower VMC; TOGA cannot simply be selected without losing those margins.

3 · Interactive

Climb, cruise and descent

A jet engine gives roughly constant thrust across the speed range, so the climb and cruise speeds of a jet sit in different places from those of a propeller aircraft. Change mass, altitude, wind and cost index and watch where the best speeds and altitudes move.

Aircraft
Gradient or rate

Climb gradient depends on excess thrust: (T − D) / W. Rate of climb depends on excess power: (T − D) × V / W. For a jet, thrust is nearly flat, so the best angle (Vx) is close to the minimum-drag speed and the best rate (Vy) is clearly faster.

Best range

Fuel flow follows drag, so the most distance per kilogram comes at the highest ratio of speed to drag, about 1.32 × the minimum-drag speed, until the drag rise near the critical Mach stops it. Long-range cruise gives up 1 % of the range for a few percent more speed.

Cost index

Time costs money too (crew, maintenance, connections). The cost index is the ratio of time cost to fuel cost. CI 0 gives the maximum range speed; a higher CI flies faster and burns more fuel to save time.

Optimum and maximum altitude

The optimum altitude gives the best range for the present mass and rises as fuel is burnt. The maximum altitude is the lowest of the certified ceiling, the altitude with a 0.3 g buffet margin, and the altitude where the residual climb rate drops to 300 ft/min. Step climbs follow the optimum upwards.

Wind

Range is distance over the ground. Into a headwind it pays to fly faster than the still-air best range speed, and with a tailwind slightly slower. A strong headwind can also make a lower level with less wind the better choice.

Descent

At idle, the descent gradient is about drag / weight, the inverse of L/D. Each aircraft flown at its own best-L/D speed (higher when heavier) has the same L/D, so the still-air glide distance is the same. The A320 descends at a fixed managed speed above that best-L/D speed; there the heavier aircraft is closer to its best L/D, so it descends more shallowly and its top of descent comes earlier. An early, idle, continuous descent is the most fuel-efficient.

4 · Interactive

Engine failure en route: drift-down

With one engine out at cruise level, the remaining engine at maximum continuous thrust (MCT) cannot hold the altitude. The aircraft drifts down until thrust equals drag again. Over high terrain the question is whether the net flight path stays clear of the ground all the way to an aerodrome, or whether a prepared escape route is needed.

Aircraft and day
Drift-down speed
Route
Track after the failure

Gross and net

The gross path is what an average aircraft would fly. The net path is the gross gradient reduced by 1.1 % for a twin (1.4 % and 1.6 % for three and four engines). It is a fictitious, deliberately pessimistic path, and the terrain rules are applied to it, not to the gross path.

Two ways to comply

Either the net path is still climbing (gradient positive) at least 1000 ft above all terrain within 5 NM either side of track, or the net path from cruise level to a suitable aerodrome clears all terrain in that corridor by at least 2000 ft. The corridor grows to 10 NM if the navigation accuracy does not meet the 95 % containment level.

Drift-down speed

Green dot (best L/D with one engine out) at MCT gives the shallowest descent and the highest level-off: the obstacle strategy. Where terrain is no problem, a faster standard strategy (M.78/300 kt on the A320) reaches lower levels sooner but gets to the diversion aerodrome faster.

Escape routes

Over the Alps, and on some routes over Scandinavian mountains, the planned track may not satisfy the rules at high mass on a warm day. Operators then publish escape routes: pre-computed tracks along valleys to an en-route aerodrome, with decision points that tell the crew which way to turn after a failure.

5 · Interactive

Landing distance

The actual landing distance is measured from 50 ft over the threshold to a full stop. Before departure the aircraft is dispatched against a factored distance; before landing the crew checks the distance for the actual conditions with a margin. Change the runway condition, braking, reversers and approach technique.

Runway
Aircraft and technique
Autobrake
Reverse thrust
Runway condition codes (RWYCC)
At dispatch. Dry: the landing distance available must be at least the certified landing distance divided by 0.6, that is × 1.67. Wet: a further 15 %. Contaminated: the larger of the wet requirement and 115 % of the distance for the contaminant.
Before landing. The distance for the conditions at the time of arrival, with the planned braking and reverse, plus 15 %, must fit within the landing distance available.
Speed and flare. Energy grows with the square of speed. Ten knots too fast and a long flare can together add several hundred metres; a stabilised approach on speed with a firm touchdown in the touchdown zone is the best runway protection.
6 · Reading

In the aircraft

How the theory shows up in a typical A320 operation. Procedures differ by operator; your operations manual and the FCOM rule.

Take-off data

Speeds and thrust come from the performance application on the EFB, calculated for the runway or intersection, wind, temperature, QNH, runway state and configuration. Both pilots compute or cross-check independently and enter V1, VR, V2 and the flex temperature on the MCDU PERF TAKEOFF page. A gross error check against the expected values catches typing mistakes.

FLEX or TOGA

With a flex temperature entered, the thrust levers go to the FLX/MCT detent. If more thrust is needed, TOGA is always available by pushing the levers fully forward, because VMC is based on TOGA. TOGA is used when the runway is contaminated, when wind shear is expected, or when the margins are not there for flex.

The V1 call

A typical Airbus procedure: the captain keeps a hand on the thrust levers until V1. At low speed the take-off is rejected for any significant failure; at high speed only for major ones such as engine failure, fire or a sign that the aircraft is unsafe to fly. At V1 the hand comes off and the decision is go.

Runway condition

The runway condition report (in Europe via SNOWTAM and ATIS) gives an RWYCC for each third of the runway, for example 5/5/3, with contaminant type, depth and coverage. The crew enters the condition in the performance application. Flex is not used on a contaminated runway.

Landing distance check in flight

Before the descent the crew calculates the landing distance at the time of arrival with the expected runway condition, wind, autobrake and reverse, and checks it plus 15 % against the landing distance available. A failure such as a reverser or brake inoperative, or a change in runway condition, means a new calculation.

Cruise numbers

The cost index is entered on the INIT A page and the FMS flies the ECON speed and Mach. The PROG page shows the optimum flight level (OPT) and the recommended maximum (REC MAX). Green dot on the speed scale is the best lift-to-drag speed in clean configuration, used for an engine-out climb or drift-down.

Noise abatement departures: NADP 1 and NADP 2

NADP 1 (close-in): at or above 800 ft above the aerodrome, reduce to climb thrust and keep take-off flaps at V2 + 10 to 20 kt up to 3000 ft, then accelerate and retract. It protects neighbours close to the runway. NADP 2 (distant): from 800 ft or higher, lower the nose and accelerate, retracting flaps on schedule, with the thrust reduced during or after the retraction, then climb clean to 3000 ft. It reduces noise further out and saves fuel. Either way the noise procedure never overrides the obstacle and engine-failure requirements.

Why the A320 is Class A

The A320 is operated as a Class A aeroplane: an engine failure at any point of the take-off is covered by scheduled data, through V1, the accelerate-stop and accelerate-go distances, the net take-off flight path with obstacle clearance and the en-route drift-down rules on this page. Class B aeroplanes, by comparison, use simpler factored charts with no V1.

7 · Check your understanding

Test yourself

Teaching model. The aircraft is an A320-like twin jet with rounded, illustrative values (MTOW 78 t, MLW 64.5 t, simplified thrust, drag, braking and friction models, no compressibility in the take-off and landing calculations, TORA = TODA = ASDA with no clearway or stopway, sea level ISA in sections 1 and 4, pressure altitude equal to elevation in section 2). None of the numbers are FCOM or AFM data. Use them to understand relationships, not for operational decisions. Always follow the AFM, the FCOM, your operations manual and your instructor.