5,000 Feet, 30 Degrees, and a 3,500-Foot Runway
You are flying a four-seat, fixed-gear, normally aspirated airplane at maximum gross weight from a 3,500-ft dry asphalt runway at 5,000 ft MSL field elevation. The altimeter setting equals 29.92, and the outside air temperature is 30 °C. The POH, at 5,000 ft pressure altitude and ISA, lists a takeoff ground roll of 1,500 ft and a total distance over a 50-ft obstacle of 2,700 ft. The POH notes approximately a 10% increase in takeoff distance per 10 °C above ISA and about a 10% decrease per 10 kt of direct headwind. Wind is 210° at 10 kt; you are using runway 18. Trees 40 ft high stand just off the departure end.
1. Estimate density altitude and the corrected total distance over a 50-ft obstacle.
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Density altitude. ISA temperature at 5,000 ft is 15 − (2 × 5) = 5 °C. You are 25 °C above ISA. Using roughly 120 ft of density altitude per degree Celsius above standard:
5,000 + (25 × 120) = 8,000 ft density altitude
Distance correction for temperature. 25 °C above ISA at 10% per 10 °C = a 1.25 multiplier:
2,700 × 1.25 = 3,375 ft
Wind correction. Wind 210° on runway 180° is 30° off the nose. Headwind component = 10 × cos 30° ≈ 8.7 kt; crosswind = 10 × sin 30° = 5 kt. At roughly 10% per 10 kt of headwind, the reduction is about 9%:
3,375 × 0.91 ≈ 3,070 ft
That is the answer only if your technique matches the POH test pilot's. It does not include any margin for a slower-than-book rotation, a slightly lean mixture error, or a soft spot in the asphalt.
2. Given the obstacle and the runway length, is this departure acceptable? What margin standard should you apply?
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No - this departure should be refused as loaded.
- Corrected total distance is about 3,070 ft against a 3,500 ft runway: roughly 430 ft, or 12%, of unused surface. That is not a margin; it is measurement error, pilot technique variance, and a slightly high thermometer.
- The 12,000+ ft density altitude means the airplane will accelerate slowly, rotate at a higher true airspeed, and climb at a shallow angle. Once past the trees, the airplane must still out-climb the terrain and any rising ground beyond.
- The POH figure covers a 50-ft obstacle, so a 40-ft tree line is nominally covered - but only at the exact weights, temperatures, and techniques the manufacturer tested. If the actual temperature is 32 °C rather than 30 °C, or the wind goes calm, the margin is gone.
- A reasonable personal standard is at least 60% of the available runway for the planned total distance at gross weight on a hot day with obstacles. You would need about 2,100 ft of corrected distance to have that margin; you have 3,070.
Legal fixes: reduce weight (fuel or payload - 10% weight reduction buys roughly 20% distance reduction), wait for a cooler hour, or use a longer runway. Temperature is the highest-leverage variable and the one you can control by scheduling.
3. The pilot proposes departing at 0630 when the temperature is 12 °C. Evaluate that plan and identify the traps in the "cool morning" solution.
Read the worked answer
It is a real improvement, but verify it rather than assuming it.
At 12 °C you are 7 °C above ISA: density altitude ≈ 5,000 + (7 × 120) = 5,840 ft. The multiplier is about 1.07, giving 2,700 × 1.07 ≈ 2,890 ft - comfortably inside the 60% margin standard.
Traps to check:
- The wind credit disappears. Morning calm is common; that removes the 9% headwind reduction but also removes the crosswind. Recompute with zero wind rather than carrying the afternoon number forward.
- Use the actual altimeter setting, not field elevation. A 30.10 setting at a 5,000 ft field drops pressure altitude below 5,000 and helps; a 29.80 hurts. Pressure altitude is not elevation.
- Morning fog and dew point spread. A 2 °C spread at dawn often means radiation fog on a rural single-runway field with no approach - you may not be able to launch at 0630 at all.
- Engine and oil temperature. A cold start, an immediate full-power takeoff, and a leaned-for-altitude mixture is a recipe for rough running right at rotation. Allow a proper run-up and use the POH leaning procedure.
- Sunrise and obstruction lighting. Trees off the departure end are much harder to see in the low sun angle of early morning than at midday.