Hi everybody, congrats on this great forum, it was completely new to me.(adsbygoogle = window.adsbygoogle || []).push({});

I am working on this project to measure the physics parameters of crossbows. My father is a member of this guild that uses crossbows for shooting contests. The goal is to shoot small discs from 12 meter high poles with arrows that consist of wooden cilinders (20 cm x 2 cm). The crossbows are often handcrafted and differ quite a lot in shooting speeds.

Last year I built a speed tester and I think that I can use arrow velocity to calculate some crossbow characteristics which would allow some sort of comparison between these handbuild crossbows.

The following parameters would be interesting to calculate and I would really appreciate if you guys would have a look at the calculations.

The following data are available:

Velocity of the arrow (m/s), constant v.

Mass of the arrow is 100 grams, constant m

Tension distance 0.192 m, constant d.

1) Spring constant, k (N/m)

The potential energy of the spring is Up = 1/2 * k * d^2

This is converted to kinetic energy when the spring discharges Uk = 1/2 * m * v^2

The spring constant can be calculated from Up = Uk or

k = m * v^2 / d^2

2) The tension force F (Newton)

Hooke's law states, F = k * d

With k known and d as well, the tension force can be calculated..

3) The Power of the crossbow (this value is more relatable than a constant k)

The amount of energy that is transferred can be derived from the amount of kinetic energy devided by the time the spring needs to transfer this energy to the arrow.

The Uk = 1/2 * m * v^2 corresponds with the kinetic energy of the arrow.

The time can also be derived but I am a bit stuck.

The acceleration is dependent on the tension distance in time.

Could you help me here?

Thanks in advance for your thoughts!

Regards,

Peter

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# Crossbow physics

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