Wilson Departure: Weight, Density Altitude and the 50-ft Point
You are to fly a Cessna 172S from Wilson Airport (elevation 5,546 ft; runway 07, 1,524 m, asphalt, dry, 0.5% upslope) to Nanyuki, departing at 10:00. OAT is 26 C, QNH 1022 hPa, wind 090/05. On board: pilot 85 kg, three passengers of 85, 80 and 75 kg, baggage 25 kg and 151 L of fuel (109 kg). MTOW is 1,157 kg, basic empty mass 766 kg, maximum baggage 54 kg. Planned flight time is 1.5 h at 34 L/h, plus 45 minutes reserve and 5 L for taxi. The POH sea-level ISA figures at MTOW are 290 m ground roll and 500 m to 50 ft. Terrain rises beyond the departure end. The POH take-off chart is limited to 8,000 ft density altitude. One passenger must be in Nanyuki by 12:00.
1. Check the loading. Are you within mass and balance limits, and what are your options if not?
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Mass. Add it up: 766 + 109 (fuel) + 85 + 85 + 80 + 75 (people) + 25 (baggage) = 1,225 kg against an MTOW of 1,157 kg. You are 68 kg overweight. Baggage is inside its 54 kg limit, but that does not help with the all-up mass.
Balance. Four adults plus baggage in a 172 pushes the centre of gravity aft. You must plot the actual figures on the envelope, not assume it is fine; if the CG is behind the aft limit, the aircraft is unflyable at any mass and no amount of fuel reduction fixes it.
Can you fix it by taking less fuel? The minimum you can legally and sensibly carry is 1.5 h x 34 L = 51 L, plus 45 minutes reserve (25.5 L), plus 5 L taxi = about 82 L, which is 59 kg. Going from 109 kg to 59 kg saves 50 kg - but you are 68 kg over. You remain 18 kg over.
So the options are:
- Offload the 25 kg of baggage (still 43 kg over) and reduce fuel to 82 L (now legal, but with the minimum fuel and no baggage).
- Better: leave one passenger behind, or split the party into two flights. Offloading the 75 kg passenger brings you to 1,150 kg with full planned fuel and baggage - legal with a margin, and with fuel you can actually use for a diversion.
My choice would be option 2. Departing at exactly MTOW with the minimum fuel, on a hot high-altitude runway with rising terrain ahead, is legal arithmetic and poor airmanship.
2. Compute the density altitude and then explain how you would use the POH chart to judge the take-off against the 1,524 m runway.
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Density altitude.
- Pressure altitude = elevation + 30 x (1013 - QNH) = 5,546 + 30 x (1013 - 1022) = 5,546 - 270 = 5,276 ft.
- ISA temperature at 5,276 ft = 15 - 2 x 5.276 = 4.5 C. OAT 26 C, so ISA deviation = +21.5 C.
- Density altitude = PA + 119 x (OAT - ISA temp) = 5,276 + 119 x 21.5 = 5,276 + 2,559 = about 7,850 ft.
Using the chart. Enter the take-off distance chart at 7,850 ft density altitude and 26 C and read ground roll and distance to 50 ft at the actual weight, then apply the wind and slope corrections. As a sanity check on the sea-level ISA figures (290 m and 500 m), take-off distance roughly doubles by 8,000 ft density altitude - so expect something of the order of 1,000-1,100 m to 50 ft, possibly more at 26 C.
Judgement beyond the chart:
- On a 1,524 m runway that leaves only a few hundred metres - and the runway has a 0.5% upslope, which is charged against you on take-off.
- 7,850 ft is inside, but very close to, the 8,000 ft chart limit. Extrapolating beyond a chart limit is not permitted, so a hotter day, or a QNH drop, puts you off the end of the approved data.
- The 50-ft point is not the real obstacle. Terrain rising beyond the departure end is, and the chart does not tell you your climb gradient over it.
So: the runway length is marginal, the chart data is at its limit, and the obstacle situation has to be assessed with the climb gradient, not just the take-off distance.
3. What operating technique changes at this density altitude, and what is your final decision?
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Technique changes:
- Lean before take-off. Above roughly 3,000 ft density altitude, lean for maximum RPM at full throttle before rolling; an over-rich mixture costs power exactly when you have least of it.
- Check the static RPM against the POH limit at full throttle before brake release - low static RPM at high density altitude is an abnormal sign, not just hot weather.
- Use Vx to 50 ft, then Vy. Expect a climb of only 300-400 ft/min at this weight and temperature, so the departure path has to be planned, not improvised.
- No turns below 500 ft AGL. Brief the abort point and the engine-failure plan before you roll: at this climb performance there is no turn-back, you land ahead or in the best available clear area.
- Consider a cruise climb once clear of obstacles, for engine cooling and a better forward view.
Decision. I would not depart at 10:00 at 1,225 kg, and I would not depart at 1,157 kg with minimum fuel either. My plan:
- Offload one passenger and keep the baggage, giving about 1,150 kg.
- Depart at 07:00 instead. At an OAT of about 18 C the density altitude falls to roughly 6,900 ft, recovering nearly 1,000 ft - worth more than any technique.
- Recompute the chart with the actual figures, apply the 0.5% upslope, and confirm a positive margin to 50 ft and over the rising ground before starting the engine.
If the passenger cannot be offloaded and the early departure cannot be arranged, the correct answer is that the trip does not go in this aircraft.