# What is typical thrust to braking force ratio for a passenger airliner?

Is the ratio fairly constant across aircraft types, sizes and powerplants?

I'd like to ignore the reverse thrust component, since that's not available at the same time as forward thrust.

• Can you clarify what you mean by "thrust braking force ratio" if it's not the ratio of max forward thrust to max reverse thrust? – Penguin Aug 9 '17 at 12:24
• It depends a lot on the weight. Thrust is independent on weight, but break force is almost linear to weight. – user3528438 Aug 9 '17 at 15:50

## 1 Answer

If we assume that the braking system is designed to leave no unused braking capacity, the maximum braking deceleration is determined by the friction coefficient of the tyres. This NASA report gives a friction coefficient of around 0.5, for dry concrete with a functioning anti-skid system. This results in maximum braking deceleration of 0.5 g, around 5 $m/s^2$

A typical maximum thrust acceleration would occur for a typical airliner, at TO thrust, and medium range TO weight. Let's take typical numbers for an A320:

• A320: TO thrust = 2 * 120 = 240 kN, TO weight = 70,000 kg, a = F/m = 240/70 = 3.5 $m/s^2$
• B777: TO thrust = 2 * 500 = 1000 kN, weight = 300,000 kg, a = 1000/300 = 3.3 $m/s^2$
• Fokker 100: TO thrust = 2 * 67 = 134 kN, weight = 40,000 kg, a = 134/40 = 3.35 $m/s^2$

So across the board, the braking-to-thrust force ratio is around 5/3.3 = 1.5.

• That's consistent, but considerably lower than I expected. – Daniele Procida Aug 9 '17 at 15:02
• Yes, I remember learning a long time ago that hard braking was actually close to 1g but could not find a reference to it. – Koyovis Aug 9 '17 at 15:07
• Does it mean that at a dry concrete, a plane with TO thrust and full brakes won't ever move? – yo' Aug 9 '17 at 15:07
• @yo' It also needs to be at TO load. The ratio could easily reverse if the plane is not heavily loaded. – user3528438 Aug 9 '17 at 15:53
• @user3528438 Ah right! The max friction force is of course proportional to weight! Thanks for the hint! – yo' Aug 9 '17 at 15:59