When a sphere moves through a fluid, its rotation and surface roughness affect the pressure distribution around the sphere, thereby affecting the sphere's coefficient of lift. This presentation explains a Matlab GUI mentioned, which is provided on Mathworks website, where the user can input a surface roughness and a non-dimensional parameter based off the angular velocity, sphere diameter and wind speed and outputs the coefficient of lift. Valid for a Reynold's number of 60,000 and the non-dimensional ((w*d)/(2U)) values of 1-4.

1. How Surface
Roughness and
Angular Velocity
Affect Cl
By Jon Kjar and Jeffrey Carruth

2. Introduction
A common study in fluids is that of lift and drag. For spheres, we learned that the
rotation of the sphere affects its lift and drag coefficients. This occurrence is
commonly known as the Magnus Effect. The following video explains what the
Magnus Effect is:

3. Magnus Effect

4. Research
After doing some research, we found out that surface roughness also plays a
part when determining the coefficient of lift, as described by our textbook:
“Although the drag coefficient is fairly independent of the rate of rotation, the lift
coefficient is strongly dependent on it. In addition, both Cl and Cd are dependent
on the roughness of the surface.”
-Munson, Fundamentals of Fluid Mechanics

5. Previous Research
The current research shown in the
graph is for a smooth sphere. This
correlates the coefficient of lift with a
non-dimensional number involving the
angular velocity.

6. The Question:
But what about for spheres of
different roughnesses?

7. CFD setup
We used a Star CCM+ model of a rotating sphere to get some answers.
Re = 60,000

8. Results
By varying the surface roughness and angular velocity of the sphere, we obtained
the following results:
As can be seen, there appears to be
only minor differences in the
coefficient of lift.

9. Matlab GUI
With the results, we made a Matlab
GUI that fitted a curve to the points
and allows the user to enter a
roughness and angular velocity to
find out the coefficient of lift!
You can find this calculator in
Matlab’s file exchange.
Search: Surface Roughness,
Angular Velocity, or Coefficient of
Lift.