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Have you ever dreamed of making speed measurements of your crossbow, bow or airgun projectilze?
And didn't have any instrument to do that, I have a useful tip for you !

After the audio recording of your shoots, open your sound file with Audacity (you may also use audacity to record) :

http://audacity.sourceforge.net/?lang=en

The theory is simple : calculate the speed of your projectile by measuring the time between the shot and the sound produced by impact on target. When I tried the target was at 10 meters away from me.

On this picture, you can see my two shoots, let's make the measurement for the second (it seems to be faster) !

## Step 1: Highlight

First you have to highlight the two interesting moments (sound of the shot and the sound of the impact), you can do it by using the selection tool in the tollbar. Once the zone is selected, you can make zoom on it.

## Step 2: Measurement of Duration

Once the zoom is done, you can adjust the selected zone from the begining of the launch to the begining of the impact. Clic on duration in "begining of the selection" to have a value in seconds corresponding to the time of flight of the projectile.

## Step 3: Some Maths !

So, now we have the time and the distance. Let's calculate the speed !!!

The speed is just a distance by a time like kilometers per hour or miles per hour. Basicly the formula for the speed is :

V = D/T

With :

- V as speed in meters by second (m/s).
- D as distance in meters (m).
- T as time in seconds (s).

Remember, in my case I was at 10 meters from the target. We can read the time elapsed between the shot and the impact : 0.333 seconds then V = 10/0.333 = 30.03 m/s almost 108 km/h !

It could be funny to calculate kinetic energy ! Let's do it :

Ec = 0.5 * m * V²

With :

- Ec as kinetic energy in Joules (J)
- m as mass in kilograms (kg).
- V as speed in meters by second (m/s).

In my case the arrow's mass is 30 grams then : Ec = 0.5 * 0.030 * 30.02² = 13.52 J ! Not bad !

I am using units from international system, you are free to use others units to have your speed result in FPS for instance ...

Have a value is better than having nothing. This method allows you to calculate an average speed on X meters. The maximum speed reached by your projectile is highter than the value you may found.

## Step 4: How to Be More Accurate ?

For the aquisition, if you can use good quality microphone, do it for sharper variations. Personnaly I use my netbook's microphone, it works not bad. You can also increase the gain of your microphone in the parameters of your operating system.

The sampling is made at 44 kHz (Hi-Fi quality), it gives a precision around 22,7 µs ! It is probably possible to increase the sampling rate.

Make a good zoom allows you to make a good measurement. Be accurate in the selection and in your calcutions.

Another thing you can do is to subtract the time that sound makes for come from the target. In my case, I was at 10 meters from the target and my laptop too. The speed of sound is almost 340 m/s. v = d/t then t = d/v ...

So it takes 10/340 = 0,029 seconds for the sound to come from the target !

Here we can subtract this value to 0.333, we found 0.304 s

We can remake the calculation for the arrow's speed : V = 10/0.304 = 32,89 m/s almost 118 km/h !

And for kinetic energy : 16,23 J !

Don't hesitate to contact me to report some mistakes or for some questions !

Best regards.

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