Obstacle Clearance After V1: A Hot-Day Engine Failure at Plaisance

Net gradient

For a two-engine aeroplane the net take-off flight path is the gross gradient reduced by 0.8 percentage points:

4.2% − 0.8% = 3.4% net.

Height at the obstacle

4.5 nm = 4.5 × 6,076 = 27,342 ft horizontal.

Height gain = 0.034 × 27,342 = 930 ft.

Starting at 35 ft at the end of the TODA, the net path is at 35 + 930 = 965 ft above the take-off surface at the obstacle.

Margin

Obstacle top = 700 ft; required clearance = 35 ft, so the minimum acceptable net path height is 735 ft. Margin = 965 − 735 = 230 ft.

The departure is compliant, but the margin is only 230 ft - about 0.8% of gradient. That is the key operational point: at this weight and temperature the take-off is legal only because the numbers were checked; any change (weight, temperature, QNH, a later rotation, a slower flap retraction) erodes a small margin quickly.

Find the limiting gradient

The net path may not fall below 700 + 35 = 735 ft, i.e. a gain of 700 ft over 27,342 ft:

700 / 27,342 = 2.56% net → gross = 2.56 + 0.8 = 3.36%.

Temperature margin

Available gross at 31 °C = 4.2%; limiting gross = 3.36%. Difference = 0.84 percentage points.

At 0.10 percentage points per °C: 0.84 / 0.10 = 8.4 °C.

So the departure becomes non-compliant at approximately 39 °C, all else equal. Note how little is left: a 39 °C afternoon at Plaisance with a light wind is not unusual in the pre-cyclic season, and a lower QNH would reduce the margin further because the engine and the wing both see a higher pressure altitude.

Options to restore margin

• Reduce take-off weight (offload payload or fuel) - the most effective lever, since gradient improves with lower weight.
• Use a different flap setting or an improved-climb procedure, if approved in the AFM.
• Reduce the assumed temperature (more thrust) - but check the resulting V1 and accelerate-stop distance on the 3,040 m runway.
• Change departure runway, if terrain and wind allow, or negotiate a departure procedure with an early turn away from the obstacle.

What must not happen is dispatching on a calculation made at 31 °C and then departing at 38 °C because the wind was light and 'the aeroplane always climbs better than the book'.

Flight path first

After the failure the priority is to fly the net flight path: hold V2 to the acceleration altitude, clean up, then either continue to the take-off alternate or enter the engine-out procedure. At 71.2 t and 31 °C the single-engine service ceiling is likely to be in the region of FL170–FL200, well above any terrain near Plaisance, so driftdown is not the constraint. The acceleration altitude must be chosen so as not to compromise obstacle clearance - it cannot simply be lowered to make the aeroplane clean up earlier.

Landing weight

Landing weight will be about 71,200 kg minus the fuel burnt in a short flight, perhaps 69,500–70,500 kg against an MLW of 66,300 kg. That is 3,000–4,000 kg overweight and the aircraft has no jettison system.

• Burning off 4,000 kg on one engine at low level would take roughly 2.5–3 hours. That is not a sensible trade against a contained engine failure on a serviceable airframe.
• The correct decision is to land overweight, with the following provisions: a long, stable approach with a low rate of descent at touchdown to limit the structural load; no autoland unless approved; minimum braking consistent with the runway length (3,040 m is ample, so brake energy can be kept low); fire and rescue services on standby; and an overweight-landing inspection entered in the technical log after the flight.

Weigh the risk: the flight risk is a damaged engine and a degraded climb capability on one engine; the landing risk is an overweight touchdown. A controlled overweight landing on a 3,040 m runway in good visibility is by far the smaller exposure.