Tennis Net Tension: Calculating Deflection on Ball Impact

[jgpufc]

Hi

I'm wondering if you could help me with a problem I am having. I am currently mid process of designing a device used to measure tension in a tennis net, and I am stuck at trying to calculate the deflection in the net cord on ball impact.

I have calculated that the ball will impact the net with a force of around 6492.14676 N by using the extremes for a mens serve, ball dimensions and the weight. The recommended tension in the net cord is 500lbs, i have tried to model the system as a beam and work out deflection, but have had no joy, can you please help me!


Many Thanks

 

[Q_Goest]

The ball has some kinetic energy which must be absorbed by the net/wire rope. For a first cut at this, neglect the mass of the net and wire rope. It can be added in later.

Neglecting mass, the wire rope has an initial tension and 'stretch' determined by load, modulus and geometry. Stress equals strain times modulus. Now consider that if you deflected this wire dx, it has to stretch further, creating a force in the direction of deflection. Resolve the force per unit distance and you have a spring rate for the wire in the direction of this deflection.

Once you have a spring rate for the wire which is based on a deflection in the direction of the impacting ball, you can simply equate the energy of the ball to the energy of the wire rope as it deflects. The wire rope stretches, storing energy just like any spring.

~

The above neglects mass, so for a second cut, you might try adding mass back in. Make some assumptions about the mass of the wire rope and net which is being moved by the ball. When the ball hits the net, assume conservation of momentum and determine the velocity of the wire rope/net/ball right after impact. Assume the three parts stick together. This initial velocity is imposed on the system immediately after impact. Let's assume the rope/net/ball system now move together with some slightly higher mass. This higher mass now has an initial velocity which will stretch the rope as in the first cut. Equate the energy of the rope/net/ball to the energy of your wire rope spring and solve for deflection.

 

[oswaler]

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Hello [Name],

Thank you for reaching out. Calculating deflection on ball impact can be a complex problem, but I am happy to assist you with some suggestions. Firstly, it is important to note that the tension in the net cord can vary depending on factors such as temperature, humidity, and age of the net. Therefore, it may be helpful to take multiple measurements of the tension in the net cord to get a more accurate average value.

To calculate the deflection, you can use the formula for deflection in a beam under a concentrated load, which is:

δ = (FL^3)/(48EI)

Where δ is the deflection, F is the force of impact (in Newtons), L is the length of the beam (in meters), E is the modulus of elasticity of the material (in Pa), and I is the moment of inertia of the beam (in m^4).

In this case, the beam would be the net cord, and the length (L) would be the distance between the two points where the net cord is attached to the posts. The modulus of elasticity (E) can be found by researching the material of the net cord. The moment of inertia (I) can be calculated using the formula for a circular cross-section:

I = (π*d^4)/64

Where d is the diameter of the net cord.

Once you have all these values, you can plug them into the formula to calculate the deflection caused by the impact of the ball on the net cord.

I hope this helps, but if you have any further questions, please don't hesitate to ask. Good luck with your project!

Best,