# Rollercoaster meets a bird. How to measure damage

Hypothetical question. I want to know how to calculate this. Rollercoaster car at high speed meets bird flying at it with high speed. Direct hit. What is the damage?

Rollercoaster car, full of people, 6 rows, 2 persons in each, 70kg average weight of one person. Empty car have a mass of 450-3000kg, so let's say this one have 1000kg, with people it will be 1850kg. Speed is 160 km/h.

Bird is flying 40km/h, mass of 2kg, size around 50m^2.

I would like to know how to calculate this, which conditions I need to have, to be able to calculate this, what units are necessary to define this damage.

• Two kilograms is a fairly heavy bird like an eagle. I'm not sure there are generally agreed units of "damage" - probably the best you can do is calculate the energy absorbed by the bird, which depends on how inelastic the collision is. – Suzu Hirose Oct 21 '16 at 1:08
• It's the 50 $m^2$ that's got me scared. That's a big bird. – M. Enns Oct 21 '16 at 1:21
• ... and a 160 kph roller-coaster... also rather scary. – sammy gerbil Oct 21 '16 at 4:19

Consider conservation of momentum.

$p = mv$

Deduce momentum before collision for the car and the bird.

Conservation of momentum says that the sum of momenta after the collision must be the same as before the collision.

If you can then figure out the momentum of the bird after the collision (god forbid the bird and car become one lumped mass), then you can figure out how much energy was transferred to the bird in the collision.

I'd reckon that a limit exists on how much energy can be transferred to the bird before it dies.

You may pick an arbitrary unit which scales with energy, and call it "damage" if you choose

"Damage" has no definition in physics. What damage will result depends not only on the momentum and KE of the colliding objects but also how fragile they are.

You could quantify the collision by the relative speed of approach, the combined momentum or the total kinetic energy.

This sort of problem can't be answered acceptablly by a "rigid body" model.

You need far more details on the structure of both bird and rollercoaster. You (or your computer) can then build a mathematical model of the structure calculate how the forces will propagate through both structures as they deform. However you need to be aware that such models are only an approximation of reality.

There is a reason why they test car safety by actually crashing cars.