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What is the relative contribution to braking forces in a typical large commercial aircraft from the three different devices contributing to braking after touchdown:

  1. Wheel brakes
  2. Speed brakes / Spoilers
  3. Reverse Thrusters

The relative contribution should change with velocity so even nicer if we have the velocity depended thrust contributions. e.g. Reverse Thrusters provide more braking at the initial high velocity part of the roll out.

I'm posting a illustrative (but totally made-up) graph to clarify for what I was looking for:

enter image description here

I am looking for either empirical data or theoretical predictions for the thrust. Qualitatively I'd expect the spoiler contribution to fall off with a square law dependence on velocity. I'd think the reverse thrust offers a somewhat constant component but perhaps higher initially due to parasitic drag by the clamshells? Not sure, and this is what I'm trying to get: A quantitative relationship.

In case the answer will vary hugely depending on aircraft, I'm open to any specific case being illustrated.

Let's use the limiting case of full brakes with anti skid on.

PS. Since spoilers directly add to drag as well as indirectly help braking by dumping lift teasing out their braking thrust contribution might be harder?

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    $\begingroup$ Good pilot braking technique should result in somewhat of a bell curve, though I can't speak for auto brake. The reverse thrust should as well. As you suggest, spoilers drag braking should vary according to the airspeed, and your post script is insightful. Can't add much more than that. $\endgroup$ – J Walters Jan 24 '16 at 14:47
  • $\begingroup$ @JonathanWalters Thanks. Any idea about relative strengths? e.g. I've used something like 40-40-20 at touchdown. Is that reasonable? $\endgroup$ – curious_cat Jan 24 '16 at 15:21
  • $\begingroup$ I really don't know. I do know that thrust reverse will not start immediately at touchdown, and I would think the same would be true with braking. $\endgroup$ – J Walters Jan 24 '16 at 20:02
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    $\begingroup$ At touchdown you have negligible weight on wheels. Allow the aircraft to de-rotate first, so you have maybe 60% weight on wheels. Add spoilers, and the weight on wheels goes to maybe 80% after de-rotation. $\endgroup$ – Peter Kämpf Jan 25 '16 at 2:34
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Your question shows that you understand the issue already very well, and more detailed fractions of the single components depend on the particular airframe and engine, so my answer will not add much insight.

The only detail I can add is a plot of tire friction coefficient over speed. Unfortunately, I do not know the source of it; I collected it sometime in the past and never found a reason to doubt its validity. tire friction coefficient

Also, this document might be helpful. Below I copied Figure 3 from it, because it comes closest to answering your question. But keep in mind that the details depend on the particular aircraft and its systems, as well as runway condition, wind speed, tire and brake condition.

Typical deceleration forces during landing roll

Typical deceleration forces during landing roll, from this document. Note that the aerodynamic drag with spoilers plus reverse thrust at high speed produce already more deceleration than what is desired at low auto brake setting.

In order to find the overall contribution of each braking component, compare the areas under their respective plot lines.

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  • $\begingroup$ Thanks Peter! Very helpful information (as always)! One question: How about this thought experiment: Bring a landing aircraft to a dead stop under three different conditions: Autobrakes only. Reversers only. And spoilers only. Any idea how the stopping distances would vary? A dead stop might be an unfairly stringent requirement for the reversers / spoilers so how about 20 knots. $\endgroup$ – curious_cat Jan 25 '16 at 2:57
  • $\begingroup$ Would the answer to my follow up question i.e. stopping distance ratios under different braking devices used individually be essentially the ratio of the three areas under the curves in your figure? If so, eyeballing the graphs, would you say it is a fair assumption that all three contribute roughly equal braking contributions? $\endgroup$ – curious_cat Jan 25 '16 at 2:59
  • $\begingroup$ Perhaps this deserves a separate question? $\endgroup$ – curious_cat Jan 25 '16 at 3:04
  • $\begingroup$ @curious_cat: No, the wheel brakes will dominate the picture. Note that the "Low Mode" setting allows for 3 kt/s deceleration, while there is a Medium Mode with 6 kt/s and a maximum deceleration with full brakes and 8 to 10 kt/s. Thrust reversers are retracted between 80 and 70 kts; if they were deployed to the standstill they would also contribute more. An experiment without drag will be hard to pull off, and spoilers alone will result in the longest stopping distance. There is a clear rank: 1. Wheel brakes, 2. Thrust reversers, 3. Spoilers. $\endgroup$ – Peter Kämpf Jan 25 '16 at 7:24

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