How big before a fall will kill an animal?

Katie Haylor put this perilous pondering to physicist Stuart Higgins from Imperial College London...

Stuart - There is no clear answer on size threshold of animal before a fall will kill it. There are so many different physical and biological factors that can affect what happens during a fall that it's no one number that gives us the answer. However, physics can tell us more generally about why smaller animals such as cats are more likely to survive the same high fall as a human.

Katie - It’s all to do with momentum. Momentum is your mass times your velocity – how fast you’re going in a particular direction. The bigger your mass, the bigger your momentum at a given speed. Back to Stuart, and the hypothetical animal that’s just fallen out of a building...

When you stop, there’s a change in momentum, and that means you’re experiencing a force. The size of that force depends on how quickly you stop. If you can increase how long it takes you to slow down, the force is less. This is how seatbelts, airbags, and the crash mats used by stunt performers work.

Stuart - Cats and squirrels have smaller masses, so even if they’re falling at a similar speed, they won’t experience as large a force as a human would. Cats are also particularly smart, because they can twist their body mid-air, to allow them to rotate and land on their feet. They can then use their legs like shock-absorbers to again increase the amount of time it takes for them to slow down, and reduce the amount of force on their bodies.

Katie - As well as cats, Matt’s question mentions squirrels. But take a flying squirrel for instance. Its blanket-like body shape when all stretched out gives it an edge when it comes to surviving a fall. After-all, they are able to glide through the air, as their shape results in increased drag, or air resistance. So where does air resistance come in to our question?

The bigger an animal, the higher its mass, and also the larger its surface area. ( It’s surface area that affects air resistance, like with our flying squirrel.)
But as you get bigger and bigger, the mass increases at a much higher rate than the surface area, and so it's the ratio of surface area to mass that means that smaller animals have a lower terminal velocity (the fastest speed they can possibly fall at) than larger ones. So a flat, light animal would fall slower than a narrow heavy animal. So how fast an animal will fall could be affected by its surface area, but how much of an impact this has depends on how heavy it is.

So whilst its difficult to say how big an animal would have to be before a fall would kill it, mass and body shape can influence how you’ll fare in a fall. Of course, animals that spend their life jumping or gliding around may be better at falling safely than most, and if you’ve got wings, well, that’s just cheating. Thanks Stuart!

Next time, we’ll be battling the elements with this cold conundrum from Mike:

Mike - When I cycle my bike in cold weather my nose runs, it doesn't happen in warm weather. Why is this? And is their anything I can do to help with it?