Why Is This Tyre Square On The BA A380?

One thing I saw on the news recently was the following image:

How has this happened?

Some details:

• British Airways A380-800.
• Flight BA-32 from Hong Kong to Heathrow.
• While climbing out of Hong Kong crew received a tyre pressure notification, but continued on as the A380 can land with 1 of it's 18 tyres flat.
• Landed safely, but had to request a tug to the gate.
• The photo above is after landing.

I can't seem to find a clear explanation to why the tyre has gone this square shape. Generally when a tyre is flat it's round with the bottom being straight. The explanations seem to vary between tyre pressure, to the way it lands, to the way it is stored.

What's the real reason it's square?

http://avherald.com/h?article=498050d8

• I think maybe we've found the answer to this question: What causes an airplane to rhythmically bounce during taxiing? – TomMcW May 12 '16 at 1:50
• My guess would be the thermal relief plug (or whatever the A380 uses to relieve the pressure of a tire nearing it's thermal limit) deflated it, and then it spent 10+ hours in a wheel well that got rather cold eventually. – Terry May 12 '16 at 1:53
• Looks like maybe it lost pressure at altitude and during descent the pressure caused it to collapse – TomMcW May 12 '16 at 1:54
• Reading again the question, I think I've been excessive, as the question is only about the shape. I apologize, and will revert my vote. You are right, it could have been a triangle or anything else rather than a square. Sorry again. The image is going to be famous! – mins May 12 '16 at 9:29
• @FreeMan Agreed! Superb answer. And I have retracted my vote. – CGCampbell May 12 '16 at 15:13

According to this document about the landing gear system, the wheel dimension of the main lading gears is 1400x530 R23. This is not the standard notation known from car tires, but it says that the diameter is 1400mm and the width is 530mm, so the tread has a surface of about 2,3m².

The same document further states:

Depending on the flight phase, a warning will be triggered if a tyre pressure is detected below a given percentage of the nominal tyre pressure (for 5 seconds continuously).
Likewise, a warning will be triggered if a differential pressure above a given percentage is detected across tyres on the same axle (measured from the tyre with the higher pressure).

though no concrete threshold is given.

The nominal pressure of the tires is 15Bar (atm) and will quickly fall, even when there's just a tiny leak. So no wonder there was a warning during climb.

During the 13h flight at up to 40.000ft, the pressure could easily fall to the environmental pressure of about 0.2Bar at that altitude. And from that altitude, it takes only 30min to landing (taken from flightaware for a BA32 flight), which may not be enough to equalize tire pressure to ambient pressure through a tiny leak. Also, ambient pressure will rise slowly in the beginning and reach 1Bar at ground quite late.

Considering the pressure in the tire was still 0.2Bar when landing, the pressure difference to the ambient caused a force of 176kN on the tread, which equals a weight of 18t or 39700lbs! (one could also say: 4.5t or 5000lbs on each of the sides of this square shaped tire.)

So it's no wonder that the tire was compressed, though this doesn't explain why the tire choose the square shape.

In general, the tire tries to minimize its volume while the surface is constant, but it can't change to any shape. Its stiffness and the rim only allow the tread to bulge inwards. From math, we know that the more sides a symmetric polygon has, the more surface it has w.r.t its circumference. So the less sides, the better. A triangular shape seems not to be possible due to the rim and the needed large force to bend side walls. A pentagon doesn't provide enough reduction of volume, so a square is the best choice.

So though the picture looks really crazy, the square shape is not that surprising.

However, a tire does not think about how to collapse best to minimize volume. It starts an one or more points and evolves. If it starts with three bulges, it could have stayed with it, and the A380 had landed with a triangular tire. May be, a fourth bulge has developed at some point. Maybe, the shape in air was different, and some punched during landing pushed the tire into that shape.

Finally, one can only say that it's clear that the tire collapses to something like this due to the ambient pressure working against the low pressure inside, but one can not really predict the resulting shape. But the rectangular shape seems to be the best to minimize volume.

• why the tire choose the square shape - I can almost see the thought bubble above the tire as it cruises along at 40000ft, shivering, thinking "I'm not under any pressure to make this decision, but I've got to pick something...". :) Excellent answer! – FreeMan May 12 '16 at 12:40
• @FreeMan "not under any pressure" groan – David Richerby May 12 '16 at 16:09
• @DavidRicherby I'm so glad somebody got that!! – FreeMan May 12 '16 at 16:11