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What landing distance

Something to ponder on a rainy day…

Many POHs only have landing performance figures — threshold speed and landing distance — for maximum mass. If you land with a lower mass, you can of course compute the proper threshold speed from the speed for maximum mass or even from first principles (1.3 * Vs0).

But suppose you don’t and fly using the speed for maximum mass. Will the actual landing distance be shorter or longer than that for maximum mass?

On the one hand, you will have more excess energy so you will float longer and touch down further from the threshold.
On the other hand, the ground roll will be shorter since the inertia is less.

Which one of these effects will dominate? How is the answer affected by wind, density altitude, runway surface conditions, runway slope etc.

The practical value of the answer is probably low, but it is an interesting puzzle.

ESKC (Uppsala/Sundbro), Sweden
Last Edited by loco at 01 Aug 20:09
EPPO, EPPK

It will be shorter due to some (less) mass * velocity magic (err I mean physics).

Even shorter if less mass * less velocity.

I’ll leave it to the geniuses here to explain further ;)

EASA CB IR Training
Europe/Austria

Runway length required (after touch down) is independent of aeroplane mass, density altitude and wind, except insofar as these affect ground speed (which we can read directly from a GPS display).

The GO/NO-GO formula (for conventional undercarriage) is simple: µ = (((V2)/(2*g))-H)/L

Where µ is tyre friction required, V is ground speed at touch-down, H is height of runway end above touch-down point, L is runway length from TDP, and g is acceleration due to gravity (constant on planet earth).

Typical values for available tyre friction are: Grass/gravel 0.3-0.5, Sand 0.2-0.3, Wet grass 0.1-0.2, Snow/ice 0.05.

As long as tyre friction required is comfortably less than available tyre friction, the runway is long enough – if the pilot takes his hands out of his pockets.

Additional notes/assumptions:
Assumes zero aerodynamic drag after touch-down.
Assumes zero tyre rolling resistance.
Assumes constant braking with full weight on main wheels after touch-down (i.e. a moderately competent pilot).
Usable tyre friction is limited by net overturning moment at end of ground roll.

There’s an Excel sheet at https://www.dropbox.com/s/mu7o9mahq4xclwq/Back-country-landing-calc.xlsx?dl=0

Glenswinton, SW Scotland, United Kingdom

It is clear that the ground roll will be shorter with lower mass, as touchdown speed will be lower (both as TAS and GS). (Yes, I was incorrect talking about inertia. I really should have known better.)

But will that be offset by the later touchdown point or not?

Last Edited by Airborne_Again at 02 Aug 07:27
ESKC (Uppsala/Sundbro), Sweden

Assuming lower mass (eg 900kg, 70KIAS) but touchdown speed that of a higher mass (eg 1000kg, 70KIAS) the stopping distance should be the same, no? Brakes will be hotter though.

EASA CB IR Training
Europe/Austria

@Jacko great formula, would it be a form of apostasy to get the tyre friction on tarmac?

For us flying on 6.00 tyres instead of meat and potatoes 8.50 or 31 inch, does the formula still work?

Finally is it m/s2 for the V and g values?

I did solve L for a Warrior on grass, no gradient (at the TDP 45 knots), and got 104 metres – which seems optimistic? This was using 0.3, 0.5 would be around 65 metres.

Last Edited by RobertL18C at 02 Aug 08:02
Oxford (EGTK)

I think your assumption that the touchdown point is extended is flawed.

There is no reason for the flare to be extended as far a physics is concerned, it is mainly a function of the pilot being able to safely arrest the descent and bring it to acceptable rate, and most importantly bring it to that rate in a reasonably fault tolerate way. i.e. something the average pilot can do safely.

There might be edge case where you can’t actually get the mains on safely first, but that should not be in the speed range in POH.

It is still a good thought experiment.

Last Edited by Ted at 02 Aug 08:18

Ted wrote:

I think your assumption that the touchdown point is extended is flawed.

There is no reason for the flare to be extended as far a physics is concerned, it is mainly a function of the pilot being able to safely arrest the descent and bring it to acceptable rate, and most importantly bring it to that rate in a reasonably fault tolerate way. i.e. something the average pilot can do safely.

There might be edge case where you can’t actually get the mains on safely first, but that should not be in the speed range in POH.

If you fly it on then, as you say, the pilot should be able to touch down at the same spot regardless of speed, as long as (s)he can get the main wheels on the ground first.

But if you fly it on with higher speed, then you will have more residual lift which will further reduce the weight on wheels and thus friction, extending the ground run. You will also have to wait unloading the nose wheel to avoid ballooning, further reducing friction as only the main wheels have brakes.

But actually I was considering the case of a fully stalled landning. In that case certainly the touchdown point will be extended.

ESKC (Uppsala/Sundbro), Sweden

Airborne_Again wrote:

fully stalled landning

In many types a full stall does not happen, you just run out of elevator authority, and/or the amount of residual lift left is very low. e.g. on C-172 the skid will hit first before the mains with a full stall. I let that happen at least once by mistake.

The plane should also decelerate quicker because it has less momentum but a very similar amount of drag. I think it a good thought experiment as it get you thinking how speed affects your handling, and handling is the dominate effect in the stage up to touchdown.

However we do have strong mental model of what a fully held off landing is for a given type, or the “correct” attitude that we aim for.

Last Edited by Ted at 02 Aug 09:51
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