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

• FGD
In summary, when adding the magnus effect to a golf simulator program, the coefficient of lift should be calculated using the formula -0.05 + sqrt(0.0025 + 0.36 * radius * abs[angular velocity/velocity]). The spin factor should be calculated using Angular Velocity * radius / velocity. Both values should be dimensionless and can be calculated using any consistent unit system. It is recommended to use SI units, but other units such as mph or inches can also be used as long as they are consistent. The formula for the coefficient of lift is taken from a research paper, and the spin factor from another paper. It is also recommended to refer to other research papers or source code for better results, and an
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

FGD said:
What are the units I should be using in these calculations?
The spin factor looks dimensionless to me.

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...
Velocity = meters/s

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.

## What units are used in the spin factor formula?

The spin factor formula uses dimensionless units, meaning it does not have any specific units. It is a ratio of the angular velocity of a spinning object to the linear velocity of the airflow around it.

## What units are used in the coefficient of lift formula?

The coefficient of lift formula also uses dimensionless units. It is a ratio of the lift force generated by an object to the dynamic pressure of the airflow around it.

## Do the units in the spin factor and coefficient of lift formulas have any physical meaning?

While the units themselves do not have a physical meaning, the values obtained from these formulas can be used to analyze the aerodynamic properties of an object. For example, a higher spin factor indicates a higher rotational velocity, while a higher coefficient of lift indicates a greater lift force.

## Can the units in these formulas be converted to SI units?

Since the spin factor and coefficient of lift formulas use dimensionless units, they cannot be converted to SI units. However, the values obtained from these formulas can be used to calculate other aerodynamic parameters that do have SI units.

## Are there any variations in the units used for these formulas?

While the spin factor and coefficient of lift formulas use dimensionless units in general, there may be variations in the specific parameters used in the formulas. For example, some formulations may use the specific angular velocity of an object instead of the ratio of angular velocity to linear velocity in the spin factor formula.

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