What units are used in spin factor and coefficient of lift formulas?

[FGD]

I am trying to add the magnus effect to a golf simulator program but am getting stuck on the coefficient of lift. What are the units I should be using in these calculations? The rest of my program I use SI units. But I seam to get weird results when using them with these equations.

Spin factor = Angular Velocity * radius / velocity

Coefficient of lift = -0.05 + sqrt(0.0025 + 0.36 * radius * abs[angular velocity/velocity])

I've seen angular velocity in rpm or rad/s or...
I've seen velocity in mph or m/s or...
I've seen radius in inches or meters or...

The Coefficient of lift formula is taken from this paper.
The Spin factor from this paper.

If I get the proper units it should provide a graph with similar results to these. Left coefficient of lift, bottom spin factor.

If you know of better research papers or source code, I would love a link.
An example problem would also be very helpful.

Thanks

 

[A.T.]

What are the units I should be using in these calculations?

The spin factor looks dimensionless to me.

 

[FGD]

Yeah, both are supposed to be dimensionless. I was getting all kinds of weird results last night. (Maybe too tired) I tried again with SI units and calculations work now...
Angular Velocity = rad/s
Velocity = meters/s
radius = meters
Thanks for the reply.

 

[cjl]

Any units should work as long as you're consistent, so angular velocity is in units of 1/time (radians are kinda dimensionless), velocity is length over time, and radius is length. As long as your velocity and radius both use the same units of length, and similarly, your angular velocity and velocity both use the same units of time, you should be good.

So, you could do radius in miles, velocity in mi/hr, and angular velocity in rad/hr and it should work fine too.