Magnus Effect

The Magnus effect is the effect in which one can observe a ball or cylinder curving from its initial path of motion through the air. Contents

   1 The Magnus Effect
       1.1 A Mathematical Model
       1.2 A Computational Model
   2 Examples
       2.1 Simple
       2.2 Middling
       2.3 Difficult
   3 Connectedness
   4 History
   5 See also
       5.1 Further reading
       5.2 External links
   6 References

The Magnus Effect

The Magnus Effect is the lift force created on a rotating spherical or cylindrical object about an axis as it moves through a fluid. The force is perpendicular to the forward motion and causes the object to deviate from its standard flight path.

A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example dp⃗ dtsystem=F⃗ net where p is the momentum of the system and F is the net force from the surroundings.

The Magnus effect is an application of Bernoulli's theorem. This theorem states that if a fluid has velocity v, the pressure p of that fluid is equal to 1rv^2, with r being the constant fluid density. Since the pressure is normal to the surface of an object, the upward component is -sin(q)p(q). If we integrate the pressure times the surface area of a cylinder with radius r, we get the lift: F_p = -\frac{\rho}{2} int\limits_{0}^{2pi} \sin\theta \left [ \frac{\sin\theta}{2} \left (1+\frac{1}{r^2} \right ) + \frac{\Gamma}{2\pi r} \right ] r, d\theta = -\frac{\rho \Gamma}{4} \left (1+\frac{1}{r^2} \right )

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript Examples

Be sure to show all steps in your solution and include diagrams whenever possible Simple Middling Difficult Connectedness

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History

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Books, Articles or other print media on this topic External links

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References

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