Takeoff & Landing Distance
Heat adds as much density altitude as the terrain does — and the linear 10%-per-1000ft rule beats the compounding version people reach for.
These show how the terms behave and why a number moves. Real distances come from the aircraft's own charts, at its actual weight, on the actual surface — and this model runs about 12% short of published C172 data at 8,000 ft, because it omits propeller efficiency loss, rolling friction and ordinary technique. Use the book, then add margin.
Which rule of thumb is right
Weight is the lever you control
Heat contributes as much altitude as the terrain does
Density altitude is pressure altitude plus 120 × (OAT − ISA), and ISA falls about 2 °C per thousand feet. So a 5,000 ft field on a 30 °C day sits at nearly 8,000 ft density altitude — a 25 °C excess adds about 3,000 ft on its own, the same order as the terrain underneath it. The aeroplane performs at the density altitude, not at the elevation on the chart.
I expected the "add 10% per 1,000 ft" rule to need compounding. It doesn't — the linear form is the better one. Against the physics, mean absolute error to 8,000 ft is 7.6% for the linear rule and 17.1% for the compounding version, which runs 28% high at 8,000 ft. The received rule is right as stated and wrong as "improved".
And the physics model itself is optimistic against real data, which is worth saying plainly. Roll scaling as 1/(σ·power) lands about 12% short of a published C172 chart at 8,000 ft. The linear rule's slight overestimate happens to compensate — so the rougher rule tracks reality better than the tidier model, and being conservative is the feature rather than a flaw.
The 50 ft obstacle multiplier grows with altitude: 1.78× the ground roll at sea level and 1.92× at 8,000 ft on a 172. Climb degrades faster than acceleration, so the obstacle case worsens faster than the runway case — exactly the wrong direction for a short strip with trees at the end. It's usually the obstacle figure that runs out first, not the ground roll.
- Roll goes as the square of weight, so 10% under gross is 19% less roll. It's the cheapest lever available and usually the only one you control on the day — the field elevation and the temperature are what they are.
- A tailwind costs more per knot than a headwind saves. The usual rule is 10% off per 9 kt of headwind against 10% on per 2 kt of tailwind — a factor of four and a half, which is why the downwind departure is so rarely worth it.
- Landing at altitude is a different problem. Roll scales with density but not power, so it degrades more slowly — but true airspeed at touchdown rises while indicated stays the same, so you arrive faster over the ground and brake from a higher speed.
- Published figures assume a new aeroplane and a professional pilot flying the technique exactly. The margin isn't decoration; it's covering the difference between the chart and the day.
How to use
- Work out density altitude before anything else — it is not field elevation.
- Check the 50 ft obstacle figure, not just the ground roll.
- Reduce weight if the numbers are tight; roll scales as weight squared.
- Take the real figures from the aircraft own charts, then add margin.
Frequently asked questions
What is density altitude and why does it matter?
The altitude at which the air has the density you are actually flying in, which is what the wing and the engine respond to. It is pressure altitude plus about 120 feet per degree Celsius above standard, and standard falls roughly 2 degrees per thousand feet. An aeroplane at a 5,000 foot field on a 30 degree day performs as if it were at nearly 8,000, which is why the elevation printed on the chart is the wrong number to plan with.
How much does temperature affect takeoff distance?
Enormously, and more than most people expect. A 25 degree Celsius excess over standard adds about 3,000 feet of density altitude on its own — the same order as the terrain underneath. At a 5,000 foot field that takes you from a 5,000 foot density altitude on a standard day to nearly 8,000 on a hot one, which is roughly a 40 per cent longer ground roll for no change in where you are parked.
Is the 10 per cent per thousand feet rule accurate?
Yes, as stated — but not if you compound it. Against the underlying physics, the linear form averages 7.6 per cent of error up to 8,000 feet while the compounding version averages 17.1 and runs 28 per cent high at 8,000. Adding ten per cent per thousand feet is the correct rule; multiplying by 1.1 per thousand feet is a well-meant improvement that makes it worse.
Why is the ground roll so much longer at altitude?
Two effects multiply. Lower density means the wing produces less lift at any given speed, so the aeroplane must reach a higher true airspeed to fly. At the same time a naturally aspirated engine produces less power, and rather less than the density ratio alone suggests. Roughly, roll scales as one over the density ratio times the power ratio, which is why the penalty compounds rather than being a single correction.
Does the 50 foot obstacle distance grow at the same rate as the ground roll?
No, faster. The multiplier between the two is about 1.78 at sea level for a light single and around 1.92 at 8,000 feet, because the climb segment depends on excess power and that is what altitude takes away first. So the obstacle case degrades faster than the runway case, which is exactly the wrong direction for a short strip with trees, and it is usually the obstacle figure that runs out before the ground roll does.
How much does weight affect takeoff roll?
It scales roughly as the square, because a heavier aeroplane has more mass to accelerate and must reach a higher speed before it will fly. Ten per cent under gross gives about nineteen per cent less ground roll. That makes weight the cheapest lever available and usually the only one you control on the day — the field elevation and the temperature are what they are.
How much does a headwind help and a tailwind hurt?
The usual figures are ten per cent shorter per nine knots of headwind and ten per cent longer per two knots of tailwind — a factor of about four and a half between them. That asymmetry is why a downwind departure is so rarely worth the taxi it saves, and why a light tailwind on a marginal strip is a much bigger problem than the same wind speed on the nose is a help.
Is landing distance affected by density altitude too?
Yes, but differently. The landing roll scales with density but not with engine power, so it degrades more slowly than the takeoff. The catch is that true airspeed at touchdown rises with density altitude while the indicated airspeed stays the same — so you arrive faster over the ground and brake from a higher speed. An aeroplane that just fits a runway at sea level does not at eight thousand feet.
Can I use these numbers for real flight planning?
No. They are planning figures for understanding how the terms behave, not performance data. The real numbers come from the aircraft own charts, for the actual aeroplane at its actual weight on the actual surface, and those already include effects a simple model omits. This one runs about twelve per cent short of published data at 8,000 feet, which is the wrong direction to be wrong in.
Why do published charts show longer distances than the physics suggests?
Because the physics model leaves things out: propeller efficiency falls at altitude, rolling friction is not free, and the technique flown on a certification day is better than an ordinary one. A simple density and power scaling lands about twelve per cent short of a published light-single chart at 8,000 feet, and that gap is the reason to treat any calculated figure as optimistic rather than authoritative.
What safety margin should I add to a calculated takeoff distance?
A common practice is fifty per cent over the book figure, and there are good reasons for it. Published numbers assume a new aeroplane, a professional pilot and a technique flown exactly, and none of those describes an ordinary day at an ordinary field. Some operators use a factor of 1.25 for the runway available and 1.43 for wet — the point is that the margin is covering the gap between the chart and reality rather than being decoration.
Does a grass runway make much difference?
Short dry grass adds roughly fifteen per cent to the ground roll and long or wet grass around thirty, from rolling resistance rather than anything aerodynamic — so it lengthens the takeoff without affecting the climb once airborne. Wet grass matters more for landing than for takeoff, because it removes most of the braking, and a genuinely soft field can prevent takeoff entirely rather than merely lengthening it.
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