Thirty-Three Feet of Margin
Runway 18 at a mountain airport: 3,000 ft usable, dry grass surface, no obstacles off the departure end. Field elevation 5,900 ft, altimeter 29.92, OAT 30°C, wind 180 at 10 kt. Your POH shows, for 6,000 ft pressure altitude and 30°C, a ground roll of 1,180 ft and a total distance over a 50-ft obstacle of 2,150 ft. The POH notes state: for operation on dry grass, increase both figures by 15 percent; for tailwind, increase both figures by 10 percent for each 5 kt of tailwind component. The same chart at 20°C gives 990 ft and 1,800 ft.
1. Compute the ground roll and the 50-ft total distance at 30°C and at 20°C, and state the remaining runway margin in each case.
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Pressure altitude = 5,900 ft with the altimeter at 29.92, which rounds to the 6,000 ft chart column. Wind 180 at 10 on runway 18 is a direct 10 kt tailwind, which is two 5 kt increments, so a 20 percent increase.
At 30°C:
- Ground roll: 1,180 × 1.15 = 1,357; × 1.20 = 1,628 ft
- Over 50 ft: 2,150 × 1.15 = 2,473; × 1.20 = 2,967 ft
- Margin over 3,000 ft usable: 33 ft, about 1 percent.
At 20°C:
- Ground roll: 990 × 1.15 = 1,139; × 1.20 = 1,366 ft
- Over 50 ft: 1,800 × 1.15 = 2,070; × 1.20 = 2,484 ft
- Margin: 516 ft, about 17 percent.
The multipliers are applied to the chart value, not added to each other: 1.15 × 1.20 = 1.38, not 1.35. A student who adds the percentages will under-predict by about 130 ft on the 50-ft distance.
2. The 30°C case technically fits. List the reasons you would still cancel, and quantify the most fragile assumption.
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Fitting on paper is not the same as fitting in the airplane:
- 33 ft is smaller than the accuracy of the chart and of a grass surface in unknown condition. The 15 percent grass correction is a note, not a measurement; wet or long grass is worse than dry grass.
- The tailwind is reported at the surface. At 50 ft the tailwind is typically stronger, and the POH correction was derived from sea-level calm-air flight test; the gradient is not modeled.
- No abort margin. Ground roll of 1,628 ft leaves 1,372 ft to stop in, which is acceptable, but a pilot who floats or lands long has nothing left.
- The chart assumes a new engine, correct tire pressure, a pilot rotating at exactly the right speed, and maximum braking. A 40-year-old airplane on grass gets none of these for free.
- A gust or a 2.5 kt increase in tailwind costs 5 percent of 2,967 ft, about 148 ft - more than four times the entire margin.
The most fragile assumption is the tailwind increment. A single 5 kt change wipes out the flight, and 5 kt is within the reported wind's own variability.
3. A student asks why the POH gives a distance over a 50-ft obstacle when this runway has nothing to hit. How do you answer, and what exercise do you assign?
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The 50-ft figure is not about the obstacle you can see; it is a standardized benchmark that includes a climb segment rather than just an acceleration segment. Ground roll tells you whether the airplane can get off the surface. The 50-ft distance tells you whether it can then climb - which is the question that matters at 6,000 ft pressure altitude and 30°C, where the climb gradient is a fraction of sea-level standard. On this runway, the relevant "obstacle" is the terrain and the rising ground beyond the departure end, plus your own ability to turn or climb away from it. A ground roll that fits with no climb performance behind it is a runway overrun waiting to happen.
Assign: have the student solve for the tailwind at which the total distance exactly equals 3,000 ft, and solve for the temperature at which it does, holding everything else constant. Then have them state, in one sentence, the conditions under which they will not depart this runway. Making them find the break-even point themselves teaches the arithmetic and the judgment in the same exercise.