Catapult math

[pfreivald]

Originally Posted by Ether

It's not about "theory" really. It's about how to build a good simulation. If you have adequate empirical data to establish real-world parameter values for a simulation model, the model can be very useful.

True enough!

[Michael Hill]

Here's one of the fun oddities of this year's game.

Let's assume the ball is a sphere (it's close enough for this purpose)

Drag on a sphere is based on the Reynolds Number as seen here: http://www.grc.nasa.gov/WWW/k-12/air...ragsphere.html

To calculate the Reynolds Number, the formula is:

Re = ρvc/μ

Where:
Re = Reynolds Number
ρ = Fluid Density
v = Velocity
c = Characteristic Length
μ = Dynamic Viscosity

For air (We're assuming 20deg C):
ρ = 1.2041 kg/m^3
μ = 1.983*10^-5 kg/(m-s)

For the ball:
c = 25 inches = 0.635 m

So our formula for Re is now

Re = (1.2041 kg/m^3)*v*(0.635 m)/(1.983*10^-5 kg/(m-s))

Re = 3.8558 * 10^4 * v

Where v = velocity in m/s

I would say our ball is a fairly rough ball given the wrinkles and the material, so look more toward the rough line on the chart.

From v = 1 m/s to 5 m/s, we have Reynolds Number values between 3.8558 * 10^4 and 1.9279 * 10^5.

We pass straight through the transition between laminar and turbulent flow. So what does this mean? For some of the "hard" shooters, they're going to experience a transition from turbulent to laminar flow as the ball slows down causing potentially unpredictable results.

That's one of the reasons I like this game.

[Ether]

Originally Posted by Michael Hill

Here's one of the fun oddities of this year's game...

Thanks for posting this calculation Michael. The NASA page you linked was quite interesting too.