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.
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).
The speed at which the critical engine is assumed to fail. It may not be lower than VMCG.
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.
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.
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 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
How the theory shows up in a typical A320 operation. Procedures differ by operator; your operations manual and the FCOM rule.
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.
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.
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.
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.
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.
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.
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.
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.
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.