August density altitude and a tailwind on runway 33
Situation. August, 15:30 local time. You are pilot-in-command of a four-seat, fixed-gear single with a fixed-pitch propeller. Maximum take-off mass 1,150 kg, empty mass 745 kg, maximum take-off power 180 hp.
Aerodrome: inland Kuwait, elevation 500 ft, QNH 1000 hPa, OAT 46 °C. Runway 33 is 1,300 m of dry asphalt with a 0.5% upslope in the take-off direction. The surface wind is 150°/12 kt. Runway 15 is the reciprocal, same length and the same slope, and is currently in use by nothing but a departing helicopter.
Load sheet: pilot 80 kg, passenger 78 kg, bags 25 kg, fuel 120 litres at 0.72 kg/litre. The club load sheet shows the centre of gravity inside both limits.
POH figures at 1,150 kg: take-off ground roll at sea level ISA 285 m; distance to 50 ft 520 m. The POH and the club notes give: add 8% per 1,000 ft of density altitude; add or subtract 10% per 2 kt of tailwind or headwind component; density altitude ≈ pressure altitude + 120 ft per °C above ISA.
The tower clears you to line up on runway 33 because it is the runway in use.
1. Calculate pressure altitude, ISA temperature deviation and density altitude, then the take-off distance to 50 ft on runway 33.
Read the worked answer
Work it step by step and show the units.
- Pressure altitude = 500 + 30 × (1013 − 1000) = 500 + 390 = 890 ft.
- ISA temperature at 890 ft = 15 − 1.98 × (890/1000) ≈ 15 − 1.76 ≈ 13.2 °C.
- ISA deviation = 46 − 13.2 = +32.8 °C.
- Density altitude ≈ 890 + 120 × 32.8 ≈ 890 + 3,936 ≈ 4,830 ft.
Take-off distance to 50 ft at 1,150 kg:
- Density altitude correction: 4.83 × 8% ≈ 39%. 520 × 1.386 ≈ 721 m.
- Wind: the wind is 150° against runway 33 (330°), so the component is essentially a 12 kt tailwind. 12 ÷ 2 = 6 increments × 10% = +60%. 721 × 1.60 ≈ 1,153 m.
- Add the 0.5% upslope and the fact that a POH distance assumes a new aeroplane, a test-standard technique and a smooth surface: the real figure is worse than 1,153 m on a 1,300 m runway, leaving about 11% margin.
- Say so explicitly: two chained rule-of-thumb corrections of this size are outside the range where they are accurate. The answer is not 'it fits'. The answer is 'this is far too marginal to accept on rules of thumb - go to the actual chart or change the plan'.
2. Is the aeroplane legally and operationally within its mass and balance limits, and does the fact it is below maximum take-off mass help you?
Read the worked answer
Check the arithmetic first, then be careful about taking credit.
- Mass: empty 745 + pilot 80 + passenger 78 + bags 25 + fuel (120 × 0.72 = 86.4) = 1,014.4 kg. That is 135.6 kg below the 1,150 kg maximum take-off mass, so the take-off is legal on mass.
- Centre of gravity is inside both limits according to the load sheet, so the loading is legal. Do not let that reassure you too far: an aft centre of gravity shortens the take-off run slightly but reduces pitch stability and can make rotation over-eager; a forward centre of gravity lengthens the ground roll.
- The POH figures you used are at 1,150 kg, so they are conservative for a 1,014 kg aeroplane - performance will be better. However, you may only claim that margin if you have the actual-weight column or chart. You cannot manufacture a 12% weight saving out of a full-weight chart and then apply it on top of a 60% rule-of-thumb penalty.
- The correct handling is the actual chart at 1,014 kg and 4,830 ft density altitude, with the tailwind line applied separately.
- Legality is not the question here. The question is whether the aeroplane clears 50 ft with a safe margin at the end of 1,300 m, and on the numbers above the answer is not comfortably yes.
3. What do you do with the clearance to line up on runway 33, and how do you justify the change to ATC?
Read the worked answer
Ask for runway 15, and be prepared to cancel the take-off if it is refused.
- Runway 15 gives a 12 kt headwind where runway 33 gives a 12 kt tailwind - a swing of roughly 120% in the rule-of-thumb correction, in the right direction. Using the club rule, 721 m reduced by 60% is about 288 m; the rule is not reliable at that size, but even the real chart at 1,014 kg will give a comfortable margin where runway 33 gives almost none.
- Runway 15 is also downhill: the 0.5% upslope in the 33 direction becomes a downslope, which further reduces the ground roll (a small effect, roughly 5–10 m over 1,300 m, but in your favour).
- The request is legitimate and safety-based, not convenience-based: 'Request runway 15 for performance - density altitude 4,800 ft, 12 kt tailwind on 33, distance available is marginal.' Controllers handle this routinely; a helicopter in the circuit does not commit you.
- If runway 15 is refused, hold at the holding point until the wind changes, reduce fuel or load, or wait for a cooler part of the day. Waiting is cheap.
- Before lining up, re-brief: V speeds for the actual mass, the abort point on the runway, the climb-out path and the engine-failure action after rotation at 46 °C.