Hot-Day Takeoff at a Short Strip
You are planning a takeoff in a Cessna 172 with a maximum gross weight of 2,550 lb. The actual takeoff weight is 2,300 lb. The airport elevation is 3,200 ft MSL, the altimeter setting is 29.92 inHg, and the outside air temperature is 31°C. The runway is 2,300 ft long, level, and dry, but there are 50 ft trees 100 ft beyond the departure end. The POH chart for 3,200 ft pressure altitude and 30°C gives a total takeoff distance over a 50 ft obstacle of 2,350 ft at 2,300 lb, and 2,180 ft at 2,150 lb. There is no significant wind. The runway has no displaced threshold and no clearway.
1. Estimate the density altitude and explain why it matters even though the POH chart is entered with pressure altitude and temperature.
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Pressure altitude is 3,200 ft because the altimeter is 29.92 inHg. Standard temperature at 3,200 ft is about 15 - 2 × 3.2 = 8.6°C. The actual temperature is 31°C, which is about 22.4°C above standard. Using the common approximation of 120 ft per °C above standard, density altitude is about 3,200 + 120 × 22.4 ≈ 5,900 ft.
Density altitude matters because the POH chart already combines pressure altitude and temperature to represent air density. Entering at 3,200 ft and 30°C is effectively entering a high-density-altitude condition; you should not add another density-altitude correction on top of the chart. The practical result is that the chart’s 2,350 ft already reflects the thin, hot air, reduced engine power, and higher true airspeed at liftoff.
2. Using the chart values given, can you depart with the current load? What are your options?
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No. The required total distance over the 50 ft obstacle is 2,350 ft, but the runway is only 2,300 ft to the end, with trees immediately beyond. The aircraft would not clear the obstacle with the stated margin. Even a small deviation in speed, temperature, or weight would make the situation worse.
Options are to reduce weight by at least 150 lb, which the chart shows reduces total distance to about 2,180 ft, or to wait for a cooler time of day. Offloading baggage or fuel may be preferable to offloading a passenger, but you must recalculate weight and center of gravity and confirm enough fuel for the flight plus reserve. Do not plan to “rotate early” or “stay low” to clear the trees; those techniques reduce margin. If you cannot achieve a clear performance margin, cancel or depart from a longer runway.
3. If you reduce weight to 2,150 lb, what else must you verify before accepting the takeoff?
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You must verify more than the total distance. Recompute the center of gravity for the new loading, because removing weight from a forward or aft station can move the CG outside the envelope. Confirm the fuel load still meets the planned trip, alternate, and reserve requirements. Recheck the actual temperature and altimeter setting, since the chart margin is only about 120 ft and a few degrees warmer or a lower altimeter setting could erase it. Also confirm the runway surface and slope, since the chart assumes a dry, level runway, and consider a soft-field or short-field technique appropriate to the aircraft. Finally, brief a rejected-takeoff point: if the aircraft is not at expected speed by a chosen point, abort. A 120 ft obstacle margin is not enough to justify continuing with an unexplained slow acceleration.