Measure your arrow speed with sound

[gfugal]

So that's something I didn't realize would be as big an issue.  I'm guessing the closer you are to the target the more it messes with the result. I had two of my bows chornographed and did this method as well. One was a 40 lb compound bow and the other was the recurve I mentioned earlier. The compound measured 158 fps with the sound method but only 149 in the chronograph. Likewise the recurve was 112 fps with this method but chronographed at 103 fps. This was at 21 feet so I imagine the closer you get the greater the discrepancy, and likewise the further away you are the more accurate. There's probably a sweet spot where the slowing due to air drag compensates for the overestimating ther arrow length causes. Like you I also tried accounting for the arrow length but when I did that it underestimated it (98 fps for the recurve and 139 fps for the compound). You can see that it was about 10 fps faster if I don't account for the arrow length but 10 fps slower if I do. However, I found if you adjust for half the arrow length rather than the full amount, then you get pretty much the right speed. so instead of doing 21 or 18.5 feet from target to bow I did 19.25 and I got 149.2 fps for the compound and 104.8 for the recurve. I don't know why it wouldn't be the full length. Maybe the sound doesn't come from the tip on impact but rather when it comes to a stops when its embedded half way in the target.

Bubbles I bet you anything your bow is actually in the low 170 fps or high 160s. I got 173 fps when I calculated it with Z=13.75 instead of 15 or 12.5. If you have a bow you've already chronographed you should measure it this way and see if my adjustment also works for you.

[gfugal]

  In most cases when we are measuring arrow speed we are looking for some precision in accuracy. I wouldn't be too confident in the precision with a sound measurement.

Yeah getting it accurate is an issue. However, it is precise. I attached an image to illustrate the concept. Both Bubbles and I got very consistent results within a few milliseconds from each other. With the proper adjustment then accuracy should no longer be an issue.

[willie]

with a 2.5 foot arrow, my distances reduce to 12.5 feet

yes, but you still need to account for the fact that the sound travels a different distance.(from the front of the arrow)

also, if you wish to increase precision accuracy,  speed of sound for different air temperatures, needs to be adjusted

https://www.weather.gov/epz/wxcalc_speedofsound

[Greenriverwoodcraft]

thanks for this! I no longer need to save up for a chrono

[gfugal]

yes, but you still need to account for the fact that the sound travels a different distance.(from the front of the arrow)

also, if you wish to increase precision accuracy,  speed of sound for different air temperatures, needs to be adjusted

https://www.weather.gov/epz/wxcalc_speedofsound

Yes, temperature is the biggest factor that affects the speed of sound, humidity and air pressure do as well. You can check a weather station and figure all that out and plug it into a calculator like that. But I found that it is really negligible, even if the speed of sound was 100 fps faster or slower (which it won't be) it will still give a result that's within one fps or so, than if you did the normal value of 1125. for example, my recurve arrow speed would calculate as 105.9 fps if the speed of sound was 1025 fps rather than 104.8 fps calculated at 1125.

thanks for this! I no longer need to save up for a chrono

There's no doubt a Chronograph is better. I'll still probably end up getting one someday, but I find myself in your shoes and was thrilled to find out about this. Plus I love science and doing experiments like this (I know I'm a geek  ).

[bubbles]

I just think it's a cool tool to ballpark your bows speed.  You could use it as a comparison between different bows you have, as long as you keep the variables the same.