๐ Performance
Performance is about one question asked again and again: with this mass, on this runway, in this air, can the aeroplane do what is needed โ and can it still do it if an engine fails? The first six chapters explain the physics of take-off, climb, descent, cruise and landing. The rest apply the operating rules, first for small propeller aeroplanes (Class B), then for airliners (Class A).
๐งฐ Quick tools & cheat sheet play with the numbers
Ten small calculators for the sums performance asks for again and again, and a one-screen list of the factors and gradients worth knowing by heart.
๐ Gradient and rate of climb
๐ฌ๏ธ Wind and the ground gradient
โฐ๏ธ Obstacle clearance
โ Gross to net gradient
๐ซ Class B take-off distance
๐ฌ Landing distance required
๐ง Hydroplaning speed
๐ช Glide or drift-down range
๐ Mach number
๐ Load factor in a turn
๐ Cheat sheet โ numbers worth knowing
| Idea | Class B | Class A |
|---|---|---|
| ๐ซ Take-off screen | 50 ft | 35 ft (15 ft wet / contaminated, engine out) |
| ๐ Field length factors | TORA ร1.25 alone ยท or ร1.0 TORA, ร1.3 ASDA, ร1.15 TODA | all-engines distances ร1.15 |
| ๐ฑ Take-off surface | dry grass 1.2 ยท wet grass 1.3 ยท upslope +5% per 1% | โ |
| ๐ฌ๏ธ Wind | โค 50% headwind ยท โฅ 150% tailwind (both classes, take-off and landing) | |
| ๐ Climb | AEO 4% ยท OEI positive at 400 ft ยท 0.75% at 1 500 ft | 2nd segment 2.4 / 2.7 / 3.0% ยท final 1.2 / 1.5 / 1.7% |
| โฐ๏ธ Obstacle margin | 50 ft ยท net = gross ร 0.77 | 35 ft (50 ft if turn > 15ยฐ) ยท net โ0.8 / 0.9 / 1.0% |
| โ๏ธ Lateral margin | 90 m + 0.125 D ยท (span < 60 m: 60 m + ยฝ span + 0.125 D) | |
| ๐ En route | net ยฑ0.5% ยท not above 300 ft/min ceiling | net โ1.1 / 1.4 / 1.6% ยท 1 000 ft or 2 000 ft clearance |
| ๐ฌ Landing | within 70% LDA (ร1.43) ยท grass ร1.15 ยท wet ร1.15 ยท downslope +5% per 1% | jet 60% (ร1.67) ยท turboprop 70% (ร1.43) ยท wet ร1.15 |
| ๐ฏ VREF | โฅ 1.3 VS0 | โฅ 1.23 VSR0 and โฅ VMCL |
| ๐ Landing climb | AEO 2.5% ยท OEI 0.75% at 1 500 ft | AEO 3.2% ยท approach 2.1 / 2.4 / 2.7% ยท CAT II/III 2.5% |
| ๐ง Hydroplaning | 9 โP rotating ยท 7.7 โP non-rotating (P in psi) | |
| ๐ Rate of climb | ROC (ft/min) โ gradient % ร TAS (kt) ร 1.013 | |
1 Performance Introduction Chapter 1
The vocabulary of the subject: ceilings and altitudes, the declared runway distances, runway surfaces, the V-speeds, gross and net performance, and the performance classes.
Net performance = gross performance made worse on purpose. Gross is the fleet average; net is set about five standard deviations lower, so the chance of not achieving it is less than one in a million. Obstacles are always cleared on net figures.
Declared distances
Worked example โ too much clearway
TORA 2 400 m with a 1 500 m clearway. Only half the TORA (1 200 m) can be counted, so TODA = 2 400 + 1 200 = 3 600 m, not 3 900 m.
Runway surfaces
Dry
Neither wet nor contaminated; includes grooved or porous runways kept effectively dry.
Damp / wet
Damp: moisture but not shiny. Wet: reflective, but no significant standing water.
Contaminated
More than 25% of the area used covered by water over 3 mm deep, or slush or loose snow equivalent to more than 3 mm of water.
Ceilings and altitudes
- โฌ๏ธ Absolute ceiling: rate of climb zero. Service ceiling: a small specified rate is still available.
- ๐ชฆ Aerodynamic ceiling: low- and high-speed buffet meet at 1 g. The 1.3 g ceiling keeps a 0.3 g margin.
- ๐ Chart altitude is pressure altitude (1013 hPa set). Density altitude has the same density as the actual air. Aerodrome elevation is the highest point of the landing area.
- ๐ก๏ธ ISA: 15ยฐC, 1013.25 hPa, 1.225 kg/mยณ, lapse 1.98ยฐC per 1 000 ft to โ56.5ยฐC.
The speeds that come up most
| Speed | Meaning |
|---|---|
| VMCG | Ground control with the critical engine out โ primary controls only, no nose-wheel steering |
| VMCA | Air control with critical engine out; โค 5ยฐ bank towards the live engine; not above 1.13 VSR |
| VMCL | Control on the approach with an engine failing |
| VEF | Engine failure speed assumed for calculations; never below VMCG |
| V1 | Highest speed for the first action to stop ยท lowest speed to continue after a failure at VEF |
| VR ยท VLOF ยท VMU | Rotation ยท lift-off ยท minimum unstick |
| V2 | Take-off safety speed (Class A), reached by 35 ft |
| VMBE | Maximum brake energy speed |
| VX ยท VY | Steepest gradient ยท greatest rate of climb |
| VMD ยท VMP | Minimum drag ยท minimum power (VMP is slower) |
| VSR ยท VS0 ยท VS1 | Reference (1 g) stall ยท landing configuration ยท configuration in use |
| VREF ยท VFTO ยท VZF | Landing reference at 50 ft ยท final take-off ยท zero flap |
| VLO ยท VLE ยท VFE | Gear operating ยท gear extended ยท flap extended |
IAS โ (instrument and position error) CAS โ (compressibility) EAS โ (density) TAS. Mach = TAS รท local speed of sound.
Performance classes
Class A
All multi-engine jets, and multi-engine turboprops with more than 9 seats or MTOM above 5 700 kg. Large aeroplane code.
Class B
Propeller aeroplanes with 9 seats or less and MTOM 5 700 kg or less. Small aeroplane code.
Class C
Piston aeroplanes with more than 9 seats or MTOM above 5 700 kg.
Take-off thrust is limited to 5 minutes (10 minutes after an engine failure, if approved); maximum continuous thrust has no time limit. The en route phase is from 1 500 ft above departure to 1 000 ft (Class B) or 1 500 ft (Class A) above the destination. Gradient = height รท distance ร 100: 600 ft in 10 000 ft = 6%.
2 General Principles of Take-off Chapter 2
The take-off run is a race between thrust and drag to reach a speed. Anything that lowers the acceleration, or raises the speed that has to be reached, lengthens it.
Distance = Vยฒ รท 2a, with a = (thrust โ drag) รท mass. Distance grows with the square of the speed: 10% more speed means about 21% more distance.
Forces in the run
- ๐ฅ Jet net thrust falls slightly as speed rises (intake momentum drag); propeller thrust falls faster. A flat-rated engine holds a fixed maximum below its cut-off temperature to protect the compressor.
- ๐ Wheel drag = ฮผ ร (W โ L): it falls as lift builds and is zero at lift-off. Rotation raises induced drag, so total drag rises โ and acceleration falls through the run.
What lengthens the take-off
| Factor | Why | Effect |
|---|---|---|
| More mass | Less acceleration, more wheel drag, higher speeds | longer |
| High, hot, humid | Less thrust; more TAS for the same IAS | longer |
| Tailwind | More ground speed needed | longer (use โฅ 150%) |
| Headwind | Less ground speed needed | shorter (use โค 50%) |
| Upslope | W sin ฮธ acts backwards | longer |
| Slush, standing water | Displacement and spray drag | longer |
| Ice or snow on the airframe | More weight and drag, less lift | not allowed |
| More flap | Lower speeds but more drag | shorter up to an optimum |
Worked example โ factored winds
Reported tailwind 12 kt: plan with at least 1.5 ร 12 = 18 kt. Reported headwind 20 kt: plan with no more than 10 kt. Most charts build these factors in, so you enter the reported wind.
3 General Principles of Climb Chapter 3
Angle of climb depends on excess thrust; rate of climb depends on excess power. Everything in this chapter follows from those two lines.
Gradient % = (T โ D) รท W ร 100. Rate of climb = (power available โ power required) รท W. Wind changes neither โ only the gradient over the ground.
VX โ best angle
- Jet: VMD (thrust nearly constant)
- Propeller: below VMD, near VMP at low altitude
- Constant as an IAS with altitude
VY โ best rate
- Jet: above VMD (power available rises with speed)
- Propeller: above VMP
- Falls as an IAS with altitude; meets VX at the absolute ceiling
| Change | Angle / VX | Rate / VY |
|---|---|---|
| More weight | Less angle, VX faster | Less rate, VY faster |
| Flaps or gear (parasite drag) | Less angle, VX slower | Less rate, VY slower |
| Higher, hotter (lower density) | Less angle, VX same IAS | Less rate, VY lower IAS |
| Headwind | Steeper ground gradient | No change |
Worked example โ losing an engine
W = 400 000 N, L/D 10 so D = 40 000 N. Two engines give 100 000 N: (100 000 โ 40 000) รท 400 000 ร 100 = 15%.
One engine: (50 000 โ 40 000) รท 400 000 ร 100 = 2.5%. Half the thrust has cost five sixths of the gradient, because the drag is still there.
Air and ground gradients
Regulatory minimum gradients are air gradients. Wind is used only for obstacle clearance, factored 50% headwind / 150% tailwind. 8% at 120 kt TAS with a 24 kt reported headwind: use 12 kt, GS 108 kt โ 8 ร 120 รท 108 = 8.9%.
Obstacle heights are measured from reference zero, below the screen: remember to add the screen height (35 ft or 50 ft) to the height gained.
4 General Principles of Descent Chapter 4
The descent is the climb turned upside down: excess drag sets the angle, excess power required sets the rate.
Weight does not change the best glide angle โ L/D max is the same at any weight. A heavier aeroplane glides just as far, but faster, so it gets there sooner.
Flattest glide (range)
Zero thrust at VMD (L/D max). Raising the nose to "stretch" it slows below VMD and steepens the glide.
Fastest way down
Idle thrust, high speed (often VMO/MMO), speed brakes or gear โ the depressurisation descent to about 10 000 ft.
- ๐ฌ๏ธ A headwind shortens the range and steepens the ground angle; the time to descend is unchanged. Fly a little faster into wind, a little slower downwind.
- ๐ชถ Gear and flaps move VMD and VMP to lower speeds and steepen both the angle and the rate.
- ๐งญ A normal top of descent can be up to about 200 miles out.
5 General Principles of Cruise Chapter 5
In the cruise the questions are how long (endurance) and how far (range) the fuel will last, at which speed and which altitude.
Endurance follows fuel flow; range follows TAS รท fuel flow. Jet fuel flow follows thrust (drag); propeller fuel flow follows power.
| Jet | Propeller (incl. turboprop) | |
|---|---|---|
| Maximum endurance speed | VMD | VMP |
| Maximum range speed | โ 1.32 VMD | VMD (L/D max) |
| Best endurance altitude | at or above the tropopause | turboprop โ 10 000 ft or less ยท piston near sea level |
| Best range altitude | optimum altitude, rising as fuel burns | just above full throttle height (piston) |
Speeds and the CG
- โ๏ธ A forward CG needs more tail down load: more drag and effective weight, less range. Burning forward or centre fuel first moves the CG aft.
- ๐ Mach = TAS รท speed of sound (661 kt at sea level ISA, about 590 kt at 30 000 ft). Climbing at constant CAS, TAS and Mach rise; at constant Mach, TAS and CAS fall.
- ๐ Long range cruise is about 4% faster than maximum range cruise for about 1% less specific range.
- ๐ช Step climbs: about 2 000 ft above optimum, then 4 000 ft up; cost โ 1% fuel versus ideal (โ 10% if never stepping). Not worth it within about 200 NM of the top of descent.
- ๐ฌ๏ธ With a headwind fly a little faster; with a tailwind a little slower. A strong headwind can make a non-optimum level better.
6 General Principles of Landing Chapter 6
The landing distance runs from 50 ft over the threshold to a full stop. The rest of the chapter is about what slows the aeroplane down โ and what stops the brakes working.
Brakes need weight on the wheels. Spoilers dump the lift so the brakes bite early; below about 70% of the landing speed the brakes do most of the work.
VREF, Class A
Not less than 1.23 VSR0 and VMCL. VSR0 120 kt โ about 148 kt.
VREF, other classes
Not less than 1.3 VS0. VS0 60 kt โ 78 kt.
- โ๏ธ Airborne part from 50 ft to touchdown โ 1 000 ft; flying faster than VREF means the published distance will not be met.
- ๐ Jet reverse needs weight on wheels and spin-up, takes time to deploy and is cancelled around 50 kt (re-ingestion). Propeller reverse is just a blade angle change โ quicker and usable to a stop.
- โฐ๏ธ Upslope shortens the landing; downslope lengthens it, about 5% per 1%: 1 500 m with a 2% downslope โ 1 650 m.
- ๐ฑ Grass โ +15% for light aeroplanes; a wet runway can add up to 50% to the average dry distance. Dry ฮผ 0.8โ1.0, icy below 0.2.
- ๐ฌ๏ธ Wind factors as for take-off (50% / 150%); no crosswind factor โ there is a demonstrated crosswind limit instead.
Hydroplaning
| Type | When | Defence |
|---|---|---|
| Dynamic | Standing water; tyre lifted at VP โ 9 โP (7.7 โP non-rotating) | Grooved tyres and runway, camber, macro-texture |
| Viscous | Thin film on a smooth surface, lower speeds | Micro-texture |
| Reverted rubber | Long locked-wheel skid makes steam | Anti-skid (no lock-up) |
Worked example โ tyre pressure 196 psi
โ196 = 14. Rotating tyre 9 ร 14 = 126 kt; non-rotating 7.7 ร 14 โ 108 kt. So a tyre that spins down in water can keep hydroplaning to well below the speed at which it started.
On a slippery runway: firm touchdown in the zone, fly the nose wheel down, and without anti-skid brake only below the dynamic hydroplaning speed.
7 Single-engine Class B Take-off Chapter 7
For a single-engine Class B aeroplane the only take-off requirement is the field length โ but with factors for the runway set-up, the surface and the slope.
No stopway or clearway: TOD ร 1.25 โค TORA. With them: TOD โค TORA, TOD ร 1.3 โค ASDA and TOD ร 1.15 โค TODA.
- ๐ In commercial air transport: not at night, not in IMC except special VFR, and only where safe forced landing surfaces exist along the route.
- ๐ VR โฅ VS1; speed at 50 ft โฅ the greater of a safe speed and 1.2 VS1.
- ๐ The gross TOD accounts for mass, pressure altitude, temperature, surface, slope and factored wind.
| Correction | Factor |
|---|---|
| Dry grass | ร 1.2 |
| Wet grass | ร 1.3 |
| Wet paved runway | ร 1.0 |
| Upslope | ร 1.05 per 1% |
| Downslope | no credit |
Worked example โ dry grass and an upslope
Gross TOD 2 400 ft on dry grass with a 2% upslope: 2 400 ร 1.2 ร 1.10 = 3 168 ft.
No stopway or clearway: required TORA = 3 168 ร 1.25 = 3 960 ft.
Worked example โ which distance limits?
TORA 3 000, ASDA 3 600, TODA 3 300 ft. Maximum gross TOD: TORA 3 000; ASDA รท 1.3 = 2 769; TODA รท 1.15 = 2 870. The lowest, about 2 770 ft, is set by the ASDA.
Reading the chart: temperature and pressure altitude first (density), then mass, then wind (the slanted lines already apply the 50/150% factors), then the airborne carpet to 50 ft.
8 Single-engine Class B Climb Chapter 8
A single has no operational climb gradient or obstacle clearance rule โ the pilot keeps visual contact and avoids what can be seen. But the numbers are still worth knowing.
Time to climb depends only on rate of climb, which wind does not change. Ground distance and obstacle clearance use the ground gradient, which it does.
- ๐ The climb graph assumes full throttle, rich mixture, flaps and gear up, cowl flaps as required, at a stated IAS.
- ๐ก๏ธ The greatest mass for a required gradient depends on weight, altitude and temperature โ the WAT (or MAT) limit.
- ๐ Converting a rate of climb to a gradient needs TAS (or GS for a ground gradient), not IAS.
Worked example โ three quick sums
- 6 000 ft at 600 ft/min โ 10 min, whatever the wind.
- 500 ft/min at 100 kt TAS (โ 10 130 ft/min) โ 500 รท 10 130 ร 100 โ 4.9%.
- Height after 2 NM at 5%: 12 160 ร 0.05 = 608 ft + 50 ft screen โ 660 ft.
9 Single-engine Class B En Route and Descent Chapter 9
If the only engine stops, the aeroplane must be able to glide to somewhere it can make a safe forced landing โ at every point on the route.
Net descent gradient = gross + 0.5%. The steeper assumed glide gives a shorter, safer range; the planned track must stay inside circles of that radius around forced landing areas.
Worked example โ gross 6%, height 8 000 ft
Net gradient 6.5%: 8 000 รท 6.5 ร 100 = 123 077 ft โ 20.2 NM. The gross 6% would give 21.9 NM โ not allowed for planning.
- โฌ๏ธ Planning may not use height above the altitude where the rate of climb at maximum continuous power is 300 ft/min. The aeroplane may fly higher; it just gets no credit.
- โฝ Range and endurance graphs assume the manual's technique (correct leaning) and often show figures with and without the 45 min reserve: 7.0 h โ 0.75 h = 6.25 h.
- ๐งญ En route for Class B: from 1 500 ft above departure to 1 000 ft above destination.
10 Single-engine Class B Landing Chapter 10
The landing must fit into 70% of the landing distance available, after corrections for grass, wet and slope โ and the despatch rules decide which runway and wind to plan for.
Gross landing distance ร corrections ร 1.43 โค LDA. The landing graph already gives the gross figure at VREF = 1.3 VS0.
| Correction | Factor |
|---|---|
| Grass (firm) | ร 1.15 |
| Wet runway (unless the manual gives wet data) | ร 1.15 |
| Downslope | ร 1.05 per 1% |
| Upslope | no credit |
| Regulatory (70% of LDA) | ร 1.43 |
Worked example โ grass and a 1% downslope
Gross 1 200 ft: 1 200 ร 1.15 ร 1.05 โ 1 449 ft; ร 1.43 โ 2 070 ft LDA required.
Despatch rules
- Plan to land on the most favourable runway in still air.
- Plan to land on the runway most likely to be assigned in the forecast wind.
- Use the lower of the two masses. If the forecast-wind case cannot be met, designate an alternate where everything can.
Normally still air is the lower; the exception is a one-direction runway with a forecast tailwind. A pure crosswind gives the still-air mass.
11 Multi-engine Class B Take-off Chapter 11
A light twin has the single's field length rules, plus three climb gradients and an obstacle clearance requirement up to 1 500 ft.
Net all-engines gradient = gross ร 0.77, and the net flight path must clear obstacles by 50 ft from 50 ft up to 1 500 ft.
| Requirement | Configuration | Gradient |
|---|---|---|
| All engines | Take-off power and flap; gear down unless it retracts in โค 7 s; speed โฅ 1.1 VMC and 1.2 VS1 | 4% |
| One engine out, 400 ft | Prop feathered, gear up, take-off flap, 50 ft speed | measurably positive |
| One engine out, 1 500 ft | Live engine โค MCP, gear and flaps up, โฅ 1.2 VS1 | 0.75% |
No accelerate-stop requirement (other than commuter category), though the manual may give the data.
Obstacle clearance
- ๐ซ The path starts at 50 ft at the end of the TODR and ends at 1 500 ft. No bank before 50 ft, then at most 15ยฐ.
- โ๏ธ The engine is assumed to fail where visual reference is lost (for example the cloud base): all-engines net gradient up to there, one-engine gross gradient after.
- โ๏ธ Lateral margin 90 m + 0.125 D (span < 60 m: 60 m + ยฝ span + 0.125 D). Ignore obstacles beyond 300 m (VMC) or 600 m with track changes up to 15ยฐ; 600 m / 900 m beyond 15ยฐ.
Worked example โ clearing a 600 ft obstacle
Gross all-engines gradient 10% โ net 7.7%. Obstacle 600 ft high, 8 000 ft from the end of the TODR.
Height = 8 000 ร 0.077 + 50 = 616 + 50 = 666 ft โ clearance 66 ft, more than the 50 ft needed.
12 Multi-engine Class B En Route and Descent Chapter 12
After an engine failure a twin does not need a field โ it must be able to reach an aerodrome. The plan uses net gradients and the drift down.
With one engine out and the other within MCP, the aeroplane must continue at or above the minimum safe altitudes to 1 000 ft above an aerodrome where it can land.
Net climb
Gross โ 0.5%: 1.2% โ 0.7%.
Net descent
Gross + 0.5%: 2.0% โ 2.5%.
Drift down: hold VMD; lower the nose so weight balances the excess drag; as the air thickens the live engine gives more thrust, the gradient flattens and the aeroplane levels off. The changing gradient is split into segments and the distances added, then the one-engine cruise range is added.
Worked example โ two segments
2 000 ft at 3% net, then 2 000 ft at 2% net: 66 667 + 100 000 = 166 667 ft โ 27.4 NM.
The 300 ft/min rule applies here too, using the all-engines rate of climb at MCP.
13 Multi-engine Class B Landing Chapter 13
The twin lands under the single's distance rules, but must also be able to climb away if it cannot land.
Landing climb limit mass = the greatest mass that still gives 2.5% all engines in the landing configuration and 0.75% one engine out at 1 500 ft.
| Case | Configuration | Gradient |
|---|---|---|
| All engines (baulked landing) | Power 8 s after levers to take-off, gear down, landing flap, VREF | 2.5% |
| One engine out | Feathered, live engine MCP, gear and flaps up, โฅ 1.2 VS1, at 1 500 ft | 0.75% |
These gradients apply to normal, utility and aerobatic aeroplanes over 2 722 kg. They are low because losing an engine costs about three quarters of the climb.
Worked example โ does it meet 2.5%?
250 ft/min at 100 kt (โ 10 133 ft/min): 250 รท 10 133 ร 100 โ 2.47% โ just below, so the mass must be reduced.
Distance: within 70% of the LDA (ร 1.43), with grass and wet factors of 1.15 each and +5% per 1% downslope. Despatch rules as for singles. The approach speed must also respect VMCL.
14 Class A Take-off Chapter 14
For an airliner an engine failure is planned for at every point of the take-off. V1 is the hinge: before it you stop, after it you go โ and both must fit on the runway.
VMCG โค V1 โค VR, and V1 โค VMBE. The maximum take-off mass is the lowest of field length, climb, obstacle, tyre speed, brake energy, runway strength and structural limits.
The three distances
| Required | Greatest of |
|---|---|
| TORR | All engines: (to VLOF + half of VLOFโ35 ft) ร 1.15 ยท one engine (dry): to the midpoint VLOFโ35 ft ยท one engine (wet): to 15 ft |
| TODR | All engines to 35 ft ร 1.15 ยท one engine to 35 ft (dry) ยท one engine to 15 ft (wet), V2 by 35 ft |
| ASDR | All engines to V1 then stop ยท engine failure at VEF then stop ยท on a wet runway also the dry case; the wet cases add 2 s at V1 |
VMCG-limited
V1 raised to VMCG: field needed is the ASDR at VMCG.
VMBE-limited
V1 lowered to VMBE: field needed is the TODR at VMBE; if V1 > VMBE, reduce mass.
VR-limited
V1 set equal to VR: field needed is the TODR at VR.
Spare runway
V1 can lie anywhere from VGO to VSTOP.
The speeds
- ๐ฆถ VMCG: rudder only (no ailerons near the ground). Highest in dense air โ low altitude, low temperature.
- โฑ๏ธ VEF is about one second before V1, the time to recognise the failure.
- โฌ๏ธ V1 rises with mass, temperature, altitude, upslope and headwind; falls with more flap, downslope and tailwind.
- ๐ VR โฅ V1, 1.05 VMCA, a speed giving V2 by 35 ft, and a safe VLOF over VMU. Early rotation by 5 kt must not increase the distance; reasonable variations โค 1%.
- ๐ซ VLOF โฅ 110% VMU all engines, 105% one engine (geometry-limited: 108% / 104%).
- ๐ฏ V2 โฅ V2MIN (1.13 VSR for twins and three-engine aeroplanes, 1.08 VSR for four-engine turboprops and jets with stall-reducing provision; and 1.1 VMCA), held to 400 ft.
- ๐ Tyre speed limit applies at VLOF (ground speed) โ a tailwind can make it bite. Brake energy โ ยฝMVยฒ with true ground speed; a downslope or hot brakes reduce VMBE (cooling times are in the manual).
Worked example โ the regulated take-off mass
Field limit 63 500, climb limit 61 200, obstacle limit 62 000, tyre 64 000, brake energy 63 000 kg; structural 62 800 kg.
Performance-limited = lowest = 61 200 kg (climb). It is below 62 800 kg, so the regulated TOM is 61 200 kg.
Class A charts usually give the maximum mass for the runway (Class B charts give a distance). The graph assumes TORA = TODA = ASDA; stopway or clearway is handled by V1 corrections. Speeds and % N1 come from tables; stabiliser trim from CG, mass and flap. Normal operation needs ACN โค PCN (newer systems: ACR โค PCR).
15 Class A Additional Take-off Procedures Chapter 15
Four procedures adjust the basic take-off: contaminated runways, the improved climb (increased V2), reduced or derated thrust, and an inoperative anti-skid.
Contamination reduces both the mass and V1 โ and if the adjusted V1 falls below VMCG, the take-off is not permitted.
Contaminated runways
- Find the dry-runway limiting mass (field, climb or obstacle).
- Apply the contaminant mass reduction and V1 reduction (deeper contaminant: bigger mass cut, smaller V1 cut).
- If in the shaded area, also find the TORA-limited mass with V1 = VMCG; use the lower mass.
- Check V1 โฅ VMCG. The take-off flight path starts at 15 ft.
Contaminant drag rises with speed until the aquaplaning speed, then falls.
Improved climb (increased V2)
When the climb limit is well below the field limit, use the spare runway to accelerate to a higher V2 โ closer to VX, so the gradient and climb-limited mass rise. The gain comes from (field โ climb) and (tyre โ climb) charts, the lower one wins, and VMBE is checked last.
Reduced thrust
Assumed temperature
- Thrust set as if the air were hotter
- Lowest of the maximum temperatures from each limit
- Max 25% reduction; within the max/min assumed temperatures
- Full thrust still available
Derate
- A fixed lower rating with its own data
- Lower VMCG/VMCA โ can help a short, VMCG-limited runway
- Do not add thrust near VMC
Anti-skid inoperative
The ASDR rises sharply. Reducing V1 shortens the stop but lengthens the go, so both V1 and the mass are reduced.
16 Class A Take-off Climb Chapter 16
From 35 ft to 1 500 ft with an engine failed at VEF, the take-off flight path is flown in four segments. Each must meet a gradient; the net path must clear obstacles.
The second segment is the hardest โ gear up but still at V2 with take-off flap. Meet it and the others follow. Its WAT limit is the climb limit on the take-off.
| Segment | From โ to | 2 eng | 3 eng | 4 eng |
|---|---|---|---|---|
| 1st | 35 ft at V2 โ gear up | positive | 0.3% | 0.5% |
| 2nd | gear up โ โฅ 400 ft, at V2, take-off flap | 2.4% | 2.7% | 3.0% |
| 3rd | accelerate V2 โ VZF โ VFTO, flaps in | โก 1.2% | โก 1.5% | โก 1.7% |
| 4th (final) | clean, VFTO, MCT โ 1 500 ft | 1.2% | 1.5% | 1.7% |
Obstacle clearance
Worked example โ 280 ft obstacle at 10 000 ft
Net gradient 3%: height = 35 + 10 000 ร 0.03 = 335 ft โ clearance 55 ft, more than 35 ft. Wind is applied (50/150%) because obstacles are fixed to the ground.
- โฉ๏ธ No turns below 50 ft or half the wingspan. Bank โค 15ยฐ to 400 ft, โค 25ยฐ above (special approved procedures: 20ยฐ from 200โ400 ft, 30ยฐ from 400โ1 500 ft).
- ๐ Bank costs gradient: 20ยฐ โ twice the decrement with V2 + 5 kt; 25ยฐ โ three times with V2 + 10 kt.
- ๐ A turn away from an obstacle can allow a heavier take-off if the lateral margin is met.
Noise abatement
NADP 1 โ close in
At โฅ 800 ft reduce thrust; hold V2 + 10โ20 kt with take-off flap to 3 000 ft; then accelerate and clean up.
NADP 2 โ further out
At โฅ 800 ft lower the nose, accelerate and retract flaps (thrust reduced with first retraction or when clean); VZF + 10โ20 kt to 3 000 ft.
Neither starts below 800 ft; initial climb speed โฅ V2 + 10 kt.
17 Class A En Route Chapter 17
The cruise of an airliner is shaped by speed schedules and cost, by how high it can go before the buffet margins close, and by what happens when an engine fails over high ground.
Net en route gradient = gross โ 1.1 / 1.4 / 1.6%. The net flight path must clear terrain by 1 000 ft (positive gradient all the way) or 2 000 ft (drifting down to an aerodrome).
Speeds and cost
- ๐ Climb at constant IAS until the planned Mach is reached at the crossover altitude, then constant Mach. A higher IAS gives a lower crossover. Usually 250 kt below 10 000 ft.
- ๐ฐ Cost index = cost of time รท cost of fuel. CI 0 โ maximum range cruise; very high CI โ towards VMO/MMO. ECON minimises total cost.
- ๐ Within 2 000 ft of optimum altitude keeps about 99% of the best range.
How high?
Thrust also limits: at the maximum altitude the thrust is at its maximum cruise value; hot air lowers it, sometimes almost to the optimum altitude.
Depressurisation
Masks on, idle, speed brakes, high-speed descent to about 10 000 ft or the minimum safe altitude if higher; Mach first, then IAS below the crossover.
Engine failure and drift down
- Hold level and slow to VMD (minimum excess drag), then lower the nose to keep VMD.
- Thrust rises as the aeroplane descends; the gross level-off has no margin, so planning uses the net level-off altitude.
- Heavier โ descends further and longer. Fuel jettison is allowed if the aerodrome is still reached with the required reserves.
Option (a) โ stay up
Net path positive at least 1 000 ft above terrain within 5 NM either side of track.
Option (b) โ drift down
Net path clears terrain in the corridor by 2 000 ft down to an aerodrome, and is positive at 1 500 ft above it.
Worked example โ high terrain
Highest terrain within 5 NM of track 12 400 ft. To stay up under option (a) the net path must level off at 13 400 ft or above. Gross 0.5% for a twin gives a net โ0.6%: still descending on the net path.
Distance from an aerodrome
Twins without special approval stay within 60 minutes at the one-engine cruise speed (TAS, still air) of an adequate aerodrome: 380 kt โ 380 NM. With approval (extended diversion time operations) longer times such as 120 minutes open direct ocean tracks, backed by data on critical fuel and net level-off altitudes.
18 Class A Landing Chapter 18
The maximum landing mass is the lowest of the landing climb limit, the field length limit and the structural limit โ and the despatch rules decide which runway and wind to use.
Jets stop within 60% of the LDA (ร 1.67), turboprops within 70% (ร 1.43), from 50 ft at VREF. A wet runway needs 15% more.
| Climb case | Configuration | Gradient |
|---|---|---|
| Landing climb (all engines) | Landing configuration, VREF, thrust 8 s after levers to take-off | 3.2% |
| Approach climb (one engine out) | Gear up, approach flap (VSR โค 110% of landing VSR), go-around thrust, โค 1.4 VSR | 2.1 / 2.4 / 2.7% |
| Low decision height (below 200 ft) | One engine out missed approach | 2.5% or published |
The more limiting climb case gives the landing WAT limit.
Worked example โ LDA needed
- Jet, dry landing distance 1 500 m โ 1 500 รท 0.6 = 2 500 m; wet โ 2 500 ร 1.15 = 2 875 m.
- Turboprop, 1 400 m โ 1 400 รท 0.7 = 2 000 m.
- LDA 2 400 m: a jet may need no more than 1 440 m.
- ๐ก๏ธ Based on pressure altitude and ISA temperature, factored wind, slope only if beyond ยฑ2%.
- ๐ฏ VREF โฅ 1.23 VSR0 and VMCL (โค 5ยฐ bank towards the live engine), with manoeuvring capability.
- ๐ฌ Approved steep approach or short landing: screen not below 35 ft.
Despatch rules
Check both
Best runway in still air and the likely runway in the forecast wind; use the lower mass. Still air 64 000, forecast wind 66 500, structure 65 000 โ 64 000 kg.
Forecast wind case fails
Despatch with one alternate where everything can be met.
Still-air case fails (single runway)
Despatch only with two such alternates.
Landing graphs work both ways: mass to distance, or distance available to maximum mass.