Measure your arrow speed with sound

[gfugal]

So here's an Idea I got from a guys science paper I found on the web: https://arxiv.org/ftp/arxiv/papers/1511/1511.02250.pdf (starting pg 19). As long as you have access to some recording device and a computer you should be able to calculate the speed of your arrows. The idea is that if you know certain distances between you and your target and the microphone and the speed of sound you can figure out its velocity by the time difference from the twang of the string and the impact of the arrow. The simplification of the equation he gave is shown in figure 1. where V = velocity in feet per second, Z = distance from string at brace to target in feet, t = time difference from twang to impact in seconds, A = distance of mic to bow subtracted from distance of mic to target in feet, and c = speed of sound in feet per second (FYI 1125 fps).

One thing to keep in mind is that the further away you are from your target the slower the velocity will measure due to air drag. So if you want it comparable to a chronograph you have to do it relatively close, (I've successfully done it at 20 ft) or calculate the drag factor and determine what it would be at release. The later method is complicated and the guy explains it in his article bu I won't go into it.

In order to measure the time between twang and impact, you need a recording device (i used my phone) and a precision sound editing program. You can download one called audacity for free on the internet. It's what I used and also what the guy who wrote the article used.  My phone recorded it in a weird video format so I had to convert it to mp3 in iTunes before audacity could open it. Once you open it in audacity you can zoom in and select the frames of the two sounds like shown in the picture he included in his paper. 

[EdwardS]

Sounds good.

(pun was too easy)

So measuring arrow speed with the Doppler effect essentially?  I need this app...

[DC]

There's a free app for that. TA Arrow Speed App. I've never used it.

[Jim Davis]

I've been guesstimating by sound for some time. I say, hm, that  took between a third and a half second to go 60 feet, so it would go 120 to 180 feet in a whole second. Yep, probably going 150 feet per second or so...

Jim Davis

[StumblyRhino]

That's a very useful article, and Audacity has been a favorite of mine for years.

[Pat B]

Why bother. Once you've shot a few bows you can tell the difference in a shooter and a good shooter just by shooting them.

[mikekeswick]

Why bother. Once you've shot a few bows you can tell the difference in a shooter and a good shooter just by shooting them.

A pluck of the string tells you a lot too
How much is an I spy phone compared to a chronograph?
Interesting stuff though thanks for sharing.

[gfugal]

Why bother. Once you've shot a few bows you can tell the difference in a shooter and a good shooter just by shooting them.

I don't disagree with you there Pat B. While your question of "why bother" is very likely rhetorical, I would like to answer it. As stated, you can definitely tell when one bow shoots faster than another. However, you can tell even easier when one bow is heavier than another yet people still regularly measure the draw weight of a bow. If I posted a bow on here without any stats, you guys would be left wanting. For example, imagine I posted a picture of a bow on a tillering tree and said it has a real heavy long draw and shoots really fast. Sure I have an idea of what it's like because I've handled it and can compare it to every other bow I handle, but no one else has handled it and thus can't compare it to anything. For all they know, a really heavy draw for me is 45 lbs. That's why you hardly ever see anyone post a bow without posting its draw weight. Yet I feel draw weight is a vastly less useful measurement than arrow speed. I would argue the success of a bow (other than looking pretty) is determined by its ability to launch a projectile efficiently. While bows of similar draw weight will shoot arrows at similar speeds if you really want to know how efficient your bow is you must know the arrow's speed. Therefore I think it's definitely worth the bother. However, that "bother" doesn't have to cost $100 dollars or more for a chronograph if you happen to already have a phone and computer. If you don't have a cell phone or computer than I would agree that this isn't that helpful for you (I forget that this is "primitive" archer and that many of you delight distancing yourself from technology wich is perfectly fine).

[bubbles]

Interesting.  I've been wanting to check the speed of some of my bows. I'm going try this out.

[bubbles]

I'm a little confused at the Value for A, and adding it to (t).  Since the speed of sound would be considered 'lag' time in the measurement, I would expect to subtract the value of A from (t).  Or perhaps i'm not understanding correctly.  Maybe I should be getting a negative value for A?   

If you set up the mic right beside the bow at 20 feet, the sound of the twang would be almost instant, but the sound of the impact would have to travel back to the microphone 20 feet, therefore, your arrow would impact .017 seconds (20/125) before the microphone hears it actually impact.

[Badger]

  The sound pattern it makes right after release is also interesting. I wonder how much it will vary from bow to bow.

[gfugal]

I'm a little confused at the Value for A, and adding it to (t).  Since the speed of sound would be considered 'lag' time in the measurement, I would expect to subtract the value of A from (t).  Or perhaps i'm not understanding correctly.  Maybe I should be getting a negative value for A?   

If you set up the mic right beside the bow at 20 feet, the sound of the twang would be almost instant, but the sound of the impact would have to travel back to the microphone 20 feet, therefore, your arrow would impact .017 seconds (20/125) before the microphone hears it actually impact.

So it is confusing to add the A/c (the adjustment for sound to travel) to t. Like you said intuition would have you subtract A/c. Truth is, it depends on where you place your mic. If you're imagining it like you are, where the mic is next yo you, then A computes to be a negative number. As we should know, adding a negative is in fact subtracting. However, If you placed your mic near the target it would be the opposite and you would be adding it to t.

For example, when I did it, I was 21 feet away from the target. However, my mic was 3 feet behind me and thus 24 feet away from the target. A was then 3-24 or -21 feet. In the pictures you can see this with a 30 lb recurve I measured. You can't tell the time in the default view it pops up as (in image 1), but if you zoom in on the spot (the two peaks to the right) then you get what you see in image 2. If you highlight the release and impact and hit the length button on the bottom it will tell you the time it took to the millisecond. As you can see in the bottom of image 2 it took 0.207 seconds.

Now I have all the information I need to compute the speed: Z = 21 feet, t = 0.2 seconds, A = -21 feet, and c = 1125 feet/second. Therefore V = 21/(0.207 + (-21/1125)). This comes out to be 112 fps.

  The sound pattern it makes right after release is also interesting. I wonder how much it will vary from bow to bow.

I tend to do about 4-6 shots in one recording and get the average time it takes. I noticed that in some of them it was clear enough to distinguish the string swoosh from when the arrow leaves and other times the whole twang was one blur so I just measured it from the beginning. I would suggest putting the mic close to you vs close to the target since the twang is a more precise sound.

[bubbles]

It would be very interesting to see somebody try the sound calculation vs. a real chrono and try to find the margin for error.  Or perhaps the writer of the article already did this?

At first I was very dissapointed with my numbers.  I was getting 130's for a 450 grain arrow on a 55lb bow.  But I was Adding the distance of mic to target instead of subtracting (or adding a negative number) 
I re-did it - cutting the shooting distance down from 30 ft to 15 feet.  Doing the correct calculation (subtracting the distance from mic to target and adding a small distance from mic to bow)  I'm now getting 184 fps for a 520 grain arrow from the same bow.  That seems a bit too good, although I'd love to believe it.  

Here are my numbers.
15 feet from string to target.
-15 feet from mic to target
+3 feet from mic to bow (mic on ground at the 15 feet line)
Time from arrow to target .09 sec - Did 3 shots.  All were .09 sec

I'm right to not count the string swoosh?

[bubbles]

I'm wondering if one should account for the fact that when the arrow first impacts the face of the target, the nock of the arrow is still a few feet in front of the target, therefore reducing the distance its actually traveled? 

If I take that into account, with a 2.5 foot arrow, my distances reduce to 12.5 feet, and my new fps is 153, which is more believable. 

[Badger]

  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.