# Surface roughness and Magnus force of a cylinder

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• devansh rathi
In summary, surface roughness can play a role in the Magnus force exerted by a rotating cylinder, but it does not directly affect the formula for calculating the force. However, it can affect the drag coefficient and the location of flow separation, which in turn can affect lift. More information on this topic can be found in Anderson's book "Fundamentals of Aerodynamics" or by reading about the Kutta-Joukowsky theorem.
devansh rathi
I know that the surface roughness plays an role in the Magnus force exerted of a rotating cylinder. But, i cannot find an equation that includes the surface roughness in the equation of the Magnus force. If someone could state the formula (and preferably a source to read up more on it) it would be very helpful.

$$L = \rho_\infty V_\infty \Gamma$$
Where ##\rho_\infty## and ##V_\infty## are the freestream density and velocity, respectively, and ##\Gamma## is the vortex strength over the cylinder: $$\Gamma = -\oint_C \textbf{V} \cdot \textbf{ds}$$See Anderson, Fundamentals of Aerodynamics, Sixth Edition, p. 269. Surface roughness does not have any influence on the Magnus effect.
Now, surface roughness does affect the drag coefficient; turbulent flow separates from a surface later compared to laminar flow, which is aerodynamically more desirable than a laminar boundary layer that separates more quickly.

Surface roughness absolutely does affect the lift due to the Magnus effect. It affects boundary-layer transition which affects separation location which affects lift. There isn't a simple equation to take that into account, though. I'm afraid you're out of luck there.

Boneh3ad is correct. The explanation I gave is actually only applicable for inviscid, incompressible flows, a fact that I overlooked when replying. When viscous effects are accounted for, surface roughness does indeed have an effect.

## 1. What is surface roughness and how does it affect the Magnus force of a cylinder?

Surface roughness refers to the irregularities or variations in the surface texture of an object. In the case of a cylinder, surface roughness can affect the flow of air around the cylinder, which in turn affects the Magnus force. Rough surfaces can create turbulence and disrupt the smooth flow of air, leading to changes in the Magnus force.

## 2. How does the shape of the cylinder impact the surface roughness?

The shape of the cylinder can impact the surface roughness by creating different flow patterns around the cylinder. For example, a cylinder with a smooth, streamlined shape will have less surface roughness compared to a cylinder with a jagged or irregular shape. This can result in different Magnus forces acting on the cylinder.

## 3. How is surface roughness measured and quantified?

Surface roughness can be measured using various techniques such as profilometry, laser scanning, and microscopy. These methods provide numerical values that represent the roughness of a surface, such as Ra and Rz. These values can then be used to compare the surface roughness of different objects.

## 4. What factors can influence the surface roughness of a cylinder?

The surface roughness of a cylinder can be influenced by the material it is made of, the manufacturing process, and any external factors such as exposure to weather or wear and tear. Additionally, the surface roughness can also be affected by the speed and direction of the air flow around the cylinder.

## 5. How can knowledge of surface roughness and Magnus force of a cylinder be applied in real-world situations?

Understanding surface roughness and Magnus force of a cylinder can be useful in various industries such as aerospace, automotive, and sports. In aerospace, it can help in designing more efficient and streamlined aircrafts. In automotive, it can aid in improving the aerodynamics of vehicles. In sports, it can be used to optimize the design of equipment such as golf balls and tennis rackets to enhance performance.

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