# To what extent does pressurisation increase the rigidity of an airframe?

A vessel such as a balloon or the rubber air-cell of an inflatable boat will become more rigid when pressurised.

The same must happen to the fuselage of a pressurised aircraft - but to what extent?

Unlike balloons and inflatable boats, aircraft are not flaccid when unpressurised...

I imagine that the effect must be so tiny as to be not just utterly negligible, but literally impossible to measure; is it possible however to calculate theoretically (and if so, of what order is it likely to be)?

• It's linear, so you can do the calculation as if it were a long balloon and that's the added rigidity. Sep 28, 2017 at 21:26
• Balloons become more rigid because they have high plasticity. Airframes are already rigid, increasing the air pressure inside (as relative to external pressure) shouldn't increase it's rigidity at all, it narrows the gap between the material plasticity and it's yield point. The more times this happens, the worse it gets, like bending metal back and forth until it snaps. It's not impossible to measure, it's quite easy using strain gauges to measure surface deflection, I've done it on ice breaker ship hulls. Sep 28, 2017 at 21:44
• I flew with a C5 pilot who told me that they had to observe extra operational limitations when unpressurized (ramp down, doors open, or just inop) because the pressurization actually provided rigidity. Sep 29, 2017 at 2:20
• This is especially relevant for rockets. If they are not pressurised, they cannot be transported. Sep 29, 2017 at 9:53
• @PeterKämpf: Depends on the rocket. Mar 16 at 22:12

Disclaimer: I am not a pilot, nor do I have anything with planes. I am a mechanical engineering student, so I do know quite a bit about the strength of materials.

What you should know is that whenever something is filled with air, that air is trying to achieve a state in which it has the lowest pressure, meaning it is trying to increase in volume. This is the reason balloons are roughly round, because a sphere has the largest volume for the lowest surface area. The same pretty much applies to planes. What generally happens when you bend a tube (and a fuselage is in essence a big tube) is that two sides are getting closer, making it easier to bend because the second moment of area decreases. This does however mean that the hull becomes less round, thereby decreasing the volume. The air inside will try to prevent this volume change, which makes it harder to bend the tube, which means the stiffness increases. Note however that more stiffness does not necessarilly mean it is also stronger.

• This is a good explanation of why the aircraft is stiffer - but doesn't answer the question of how much. A quick back-of-the-envelope to give an order-of-magnitude estimate should be easy for a mechanical engineer :-) Sep 29, 2017 at 14:40

Pressurisation indeed increases rigidity of the structure. Air pressure expands the fuselage, and applies a tension stress uniformly throughout the fuselage skin.

When in the air, the aircraft is suspended by the wings and garvity attempts to bend the fuselage downwards. The failure mechanism of bending a tube is buckling: the top side has tension stress, the bottom side compression stress, and this is the side that buckles. Internal air pressure helps in two ways:

• The bottom side has pre-tension stress applied by the air pressure. The gravity bending is now resisted by a reduction in tension stress, instead of an increase in compression stress. This results in less deflection difference between upper and lower surface - higher stiffness.
• The fuselage expands as a result of the overpressure, increasing the distance between upper and lower surface and therefore reducing reaction stresses from bending.

We don't want to compress sheet metal, it buckles pretty quickly. However if air presses against it, that helps in preventing that particular failure mode.