Magnus Effect: Difference between revisions
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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 | Contents | ||
1 The | 1 The Magnus Effect | ||
1.1 A Mathematical Model | 1.1 A Mathematical Model | ||
1.2 A Computational Model | 1.2 A Computational Model | ||
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6 References | 6 References | ||
The | 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. | |||
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What are the mathematical equations that allow us to model this topic. For example dp⃗ dtsystem=F⃗ net | 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. | 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 | A Computational Model | ||
Revision as of 23:00, 5 December 2015
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
How is this topic connected to something that you are interested in? How is it connected to your major? Is there an interesting industrial application?
History
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why. See also
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context? Further reading
Books, Articles or other print media on this topic External links
[1]
References
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