How to measure Bow Speed without a Chronograph! (ft. Average Jack Archery)

[@TheBudgetSportsman]

The number one question I have received about my method is why the phone needs to go in the middle and why I don't calculate for the speed of sound. I am no scientist or mathematician, but from my testing, it really does matter where you place the phone. To the best of my understanding, placing the phone in the middle eliminates the need to calculate for the speed of sound. Here is the best that I can explain it...and I could be wrong. Feel free to comment. Imagine putting the phone at the shooter end by the bow. The phone will pick up the sound of the shot immediately but the sound of the arrow hitting the target has to travel back to the phone AFTER the shot is over. As a result, when you measure the time between the two sounds you will get a LONGER time and a slower bow speed. Now imagine that you put the phone at the target end. The sound of the bow going off has to travel to the phone meaning the sound gets to your phone DURING the arrow flight when it has already traveled part of the way to the target. The sound of the arrow hitting the target gets to the phone immediately. This creates a SHORTER amount of time and results in a much faster bow speed result. Finally, by putting the phone in the middle you are canceling out the delays. The sound of the bow going off takes time to get to the phone DURING the arrow flight and shortens the time. The sound of the arrow impact takes time to reach the phone AFTER the arrow flight and lengthens the time. If the phone is an equal distance from each source of sound they will cancel each other out. This has been the only way I have been able to achieve accurate results. You can also scroll through the comments and you will find another thread where a gentleman asked a similar question and I tried to answer including some math. The primary thing to realize is that the depending on which end you place the phone it will either create a longer or shorter time.

[@williambilse]

Awesome explanation for a knuckle dragging mouth breather like myself. 😆👍🏻👍🏻

[@ethanceretaen5519]

Great video! thanks guys! I do not need a chronograph, but I do had the curriocity to check my bows to see how they fit on the context of various videos I see on the internet. Not willing to pay money for that curiocity. This really helped.

[@TheBudgetSportsman]

Awesome. Should be perfect for what you’re trying to do.

[@kenwallace4203]

Hi many thanks for that I'm of to try it and measure my arrow speeds. I'm a retired engineer and maths was my special subject, so if you or anyone else is interested I set out below the math proving you are right when you eliminated the speed of sound by placed the phone equidistant from the bow top the target, Let the distance from the bow to target be Dt, the distance to the phone be D2, the distance from the target to the phone be D3. Now At time 0 the arrow is release. Time for arrow flight to target is (Tt), time for sound of release to reach phone is (Ts) and finally, time for impact sound back to phone is (Tb). And Now for the math, Tt is given by the distance Dt divided by the arrow speed (Va), Tt = Dt/Va (1). Time for sound of release to phone is : Ts = D2/Vs (2) where Vs is speed of sound, Time the target impact back to phone is heard is : Tb = D3/Vs + Dt/Va So we measure the time of flight by subtracting Ts from Tb, Tb - Ts = Tt ( arrow flight time ) subt. 1 & 2 D3/Vs + Dt/Va - D2/Vs = Tt Lets tidy this up : Tt = Dt/Va + (D3-D2)/Vs ........ (3) So here's the beauty of putting the phone in the middle ( equal distance from bow to target) is that D3 equals D2 hence D3-D2 is zero and we have an equation independent of the speed of sound!!, Tt = Dt / Va so arrow speed is then obtained by Va = Dt/Tt This exactly what was guys found, Also we can use the general equation (3) to calculate the arrow speed if the phone isn't equidistant and we know the speed of sound Vs Va = Dt/( Tt - {D3-D2}/Vs) ........ (4). Hope this clears it up, keep up the good work......

[@TheBudgetSportsman]

Hey, Ken. I would love to hear about your experience using this method. Also, thank you SO much for taking the time to work out the math. Math is certainly not my strong point, but I was pretty sure that logically I was correct. I appreciate you confirming it for me!

[@scottbrammer8275]

Awesome! And I literally was just getting ready to spend $100 for a chronograph I would only need one time. Thanks!

[@TheBudgetSportsman]

Great. Would love to hear how it goes!

[@olmostgudinaf8100]

Same here. You have just literally saved me £40 ($50) on a chrony (on eBay). The only drawback is that the results are not immediate, but I can live with that ;-)

[@kovona]

I used this technique and compared it to my shooting chrony. Within 5 fps difference, and I don't have mess around with light and diffusers. 👍 A light sensing chrony might also give you bad results since any off angle pass by the arrow might mean one sensor detects the arrow tip, while the other might miss it but pick up the fletching instead, giving you a higher reading.

[@TheBudgetSportsman]

Awesome to hear your results!!

[@micahengum]

This is great, thanks for putting this video together. Been having fun with dissecting the sound waves and using it as one of the references for tuning my bow.

[@TheBudgetSportsman]

Glad you enjoyed it! Thats pretty cool. Sounds like you are digging way deeper than I have.

[@zekeshandles]

This worked great! 280 compound and 152 self bow! Thanks dudes!!!!

[@TheBudgetSportsman]

Glad it worked for you!!

[@stephencarter7495]

What a great idea! I was able to knock this out using a free voice recorder app and audacity audio editing program. Thank you, awesome stuff!!!

[@TheBudgetSportsman]

Your so very welcome. I’m glad you found it useful!

[@umbratherios5614]

Wavepad on android gives a time measurement down to 1/1000th of a second. can do it all on my tablet :)

[@TheBudgetSportsman]

That’s a great tip

[@nickotto4539]

COLAB! I love em! Great Work Gents!

[@TheBudgetSportsman]

Thanks Nick! Appreciate you watching!

[@averagejackarchery]

Thanks, Huntavore!

[@leafinitup1]

Excellent result. Great method guys

[@TheBudgetSportsman]

Thanks Andrew! Thanks for watching!

[@boomerrangerron]

Great job Nate and very creative! Just too complicated for me but the maths simple for sure! I need a chronograph!

[@TheBudgetSportsman]

I got the chrono for this test but eventually sold it because I didn’t use it that much.

[@compoundbowpro8175]

Thanks really helpful. Will share video with my friends.

[@TheBudgetSportsman]

Thank you! Really appreciate you sharing!

[@jander1781k]

Like someone else mentioned, the WavePad app for Android will show your selection to 1/1000 of a second IF you hold your phone in landscape mode. Only took me 20min to figure out. lol Anyhoo, thanks for saving me from buying a chrono!

[@TheBudgetSportsman]

Thanks for the tip and glad you found it useful.

[@danielww9022]

Slow motion video feature on every cell phone works fine. Just be sure the camera angle captures your entire shooting lane. How long does it take the arrow to reach the target? Distance divided by time equals speed.

[@TheBudgetSportsman]

I’ve tested this. The results are not accurate. Recording audio give me a time reading of .001 ( 1/1000th of a second) where as video will only give approximately .01. You can get an idea but not a very precise measurement.

[@swostillwateroutdoors]

That is awesome!! Great content!!

[@TheBudgetSportsman]

Thanks for watching!

[@TexasBowHunter]

Great collab, thinking I should give this a try.

[@TheBudgetSportsman]

Definitely give it a try! If you do I would LOVE to hear about your experience and results!

[@Mackahroney]

so i did this at 20 feet in my basement. my setup is at 70lbs on my bear authority shooting 456 grain arrows and got an average of 290 fps (20/0.069). not sure if that is accurate but i may try it another time outdoors at 20 yards (60 feet). this is a neat trick, i might bring my bow into a shop and compare when i have the time, thanks for the awesome video

[@TheBudgetSportsman]

That actually sounds like a reasonable speed for that weight and draw weight. I will say that I’ve had better results at 60 feet then at 20 feet.

[@cjeoutdoors405]

I'm digging this one allot man. It's so simple.

[@TheBudgetSportsman]

Glad you enjoyed it Chris! Nate and I have been brainstorming this for quite a while. It was a lot of fun working on it together!

[@kenwallace4203]

Yes I'd tried this out, and it works great. My distance was 7 metres as I've an indoor setup in my garage, using a recurve bow with 40lbs limbs and 335 grain arrows I averaged 191 ft/sec. What was remarkable was the consistency of the results, out of 10 shots the results varied only +/- 2ft/sec. And that was more likely my inconsistent form. Brilliant technique for speed measurement without using a chronograph, great call you guys. Now I wonder if I could write an android app to do it automatically on my phone ???. There's a real challange

[@TheBudgetSportsman]

I had wondered the same thing about the app but I’m far from being a developer. That would be awesome!

[@adurks4846]

This is a bit late but I did find "chrono connect Mobile." It's built for pellet guns but as long as your arrow actually hits something it seems to work fine. It won't' catch every shot but it'll give you a general idea. I just shot at a milk jug from 20 yards.

[@musikSkool]

I would have used the camera, but this is amazing. You have way more accuracy with sound than you could possibly get with a 60 fps camera.

[@TheBudgetSportsman]

Yes I tried the camera at first, but I just couldn’t get the level of accuracy that I wanted. Thanks for watching

[@musikSkool]

@@TheBudgetSportsman My calculations for 60 feet and 60 fps are 4 frames = 240 fps, 5 frames = 300 fps. With sound you could theoretically be within a couple inches.

[@TheBudgetSportsman]

@@musikSkool Actually I think your math is slightly wrong. If your arrow only took 4 frames to get to the target, then it would be able to travel that same distance 15 times in one second. 15x60ft is 900fps. 5 frames would be 720fps. My bow actually takes 14 frames to reach the target. That means the arrow can travel that same distance 4.2 times in one second. (60 frames in one second of video, divided by 14 frames = 4.2). Now 4.2x60ft = 257fps. So 15 frames = 240fps, 14 frames = 257 fps, 13 frames = 276 fps. Still not great accuracy.

[@musikSkool]

@@TheBudgetSportsman Oh. Yeah, having 19 fps increments isn't good enough. I sure hope I remember your approach if I ever need a chrono for anything.

[@HuntingFarmerOfficial]

Great way to do things on a budget 👍

[@TheBudgetSportsman]

Absolutely!

[@christopherbarker5016]

Brilliant. I wonder, are we getting that start-point measurement right? You're putting the arrow's point at the known distance from the target. Clearly, the second sound comes from the target. But where does the first, release, sound come from? Is it from the string as you release it, or from the point where the string rests and vibrates? If the former, the start point of the sound is a full arrow length behind the arrow head - 28" or so. If the latter, it's your brace height plus any arrow overhang behind the arrow head - perhaps just 10-12" or so. Either way, it seems to me the distance between where those two sounds are coming from is 1 to 3 feet greater than the distance you're measuring. You'll halve that error because your microphone is half way between the start and end points of the arrow's tip rather than of where the sounds are coming from. But that's still 0.5 to 1.5 feet error over 30 feet, which means overestimating arrow speed by ~1.5% to 5% speed. I'm suspecting that when you compared your figures against the chronograph and they agreed remarkably well, that was because the chronograph indicated the arrow's *initial* speed, your measurement calculated its *average* speed as it decelerated over 30 yards, and that overestimate happened to cancel out the arrow's deceleration. I *think* the solution would be to put the mike half way between the two sound sources - that's half way between the target point and wherever we reckon the release noise comes from instead of half way between arrow point and target - and still to use the arrow's tip-to-tip flight distance for the calculation. Right? - or am I missing something?

[@TheBudgetSportsman]

I am pretty sure I followed all of that. My thinking is that I am measuring the time that the arrow is in flight over a known distance so I believe I am still correct in the standing and positioning of the arrow. I could see your point however that the phone should likely be at the halfway point of the sound sources rather than half way from the arrow to the target. I fiddled a lot with the position of the shooter/arrow and this method is the way that I came up with that was consistently close to the chronograph. I did NOT play with slightly adjusting the positioning of the phone, so again you may very well be right that it could produce even more accurate results. If you decide to play with it, I would love to hear your results.

[@yoji0]

Wow, that might be even simpler than what I was thinking! I'm trying to figure out how fast some Nerf guns are shooting at, but I'm not ready to throw down the money on a chronograph. I'll definitely need to try this. And here I was about to go and make a Mythbusters-style speed chart and try my luck with a high-speed video app (which I still might try anyway)

[@TheBudgetSportsman]

Would love to hear about the high speed video app!!

[@steve8828]

Awesome. Going to try it.

[@TheBudgetSportsman]

Would love to hear how it goes

[@chrisdaniels1481]

I tried this in my workshop! It worked!

[@TheBudgetSportsman]

Awesome. Glad to hear that it worked for you!

[@rlemoyne007]

One source of error for the measurement is the time to accelerate the arrow. assuming a 30 pounds average force(134N), arrow weight 25grams, a=F/m, 5360m/s^2 speed of 279ft/s(=85m/s), t=v/a=85/5360=15.9msec. The bow took 16 millisec to accelerate the arrow.

[@TheBudgetSportsman]

Whoa, you might be going over my head now…but that would certainly be interesting to factor in those 16ms

[@MissConstable1]

Haha! The beginning was funny.

[@TheBudgetSportsman]

Glad you got a laugh. Thanks for loaning your husband for an evening!

[@MissConstable1]

@@TheBudgetSportsman Anytime :)

[@ronsarchery6378]

Interesting. Great explanation.

[@TheBudgetSportsman]

Thank you!

[@MarcRitzMD]

It would be really easy to write an app that monitors for peaks and calculates the speed in real-time for you. Just thrown it into a chat ai out of curiosity and that's already 80% of the work.

[@TheBudgetSportsman]

Man, I wish I was smart enough to do that.

[@SoloCamXTOutdoors]

That is pretty cool.. I'm going to get all over this one.. And I subbed ya.. Thanks.. Eric

[@TheBudgetSportsman]

Thanks for the sub! I would love to hear how it works out for you!

[@SoloCamXTOutdoors]

@@TheBudgetSportsman You are welcome! I think I will do a video on this to show my results and of course how I found out about it.. Thanks again!

[@TheBudgetSportsman]

Awesome. I’ll look forward to seeing the video. If you have any questions along the way feel free to ask.

[@averagejackarchery]

Awwww yeaaahhhhh

[@junglejim7664]

Very interesting. Try it outdoors and let us know how it works.

[@TheBudgetSportsman]

It works outdoors as well, however factors like wind and background noise can make it more difficult to get an accurate result. If you choose a calm quiet day and take the steps to do everything precisely, you should be pretty close.

[@aimeagle]

Nice video guys!!

[@TheBudgetSportsman]

Thank you!

[@AndreiAvramPlus]

to be more accurate, you can add the sound speed on those 20 yards ;)... actually delete the time that sound get's to the phone

[@TheBudgetSportsman]

That is possible but I wanted to keep the method as simple as possible. Also by putting the phone half way between the shooter and the target, the amount of time it takes for the sound to reach the phone after the shot should be very close to the same amount of time it takes for the sound to reach the phone after the arrow impacts the target...this basically cancels each other out.

[@AndreiAvramPlus]

@@TheBudgetSportsman nope :) actually is the same, let's say that sound get to the phone from the target in 2 sec with the phone placed beside the shooter, if you'll put the phone in the middle, between the shooter and the target you'll have 1 sec from the shooter and 1 sec from the impact delay, so will also be 2 seconds

[@TheBudgetSportsman]

Yes but the one second from the bow to phone would give you a shorter time, to impact. The one second from the arrow adds that second back on.

[@TheBudgetSportsman]

Andrei Avram Also consider this. The speed of sound is 1125 feet/second. So therefore it would take .053 seconds to travel 60 feet. Subtract that time from the arrow travel time in the video. .215 - .053 = .162 Let’s use that new time for our speed 60/.162 = 370 FPS Pretty sure that’s not right...why because we’ve already canceled out the speed of sound. Subtracting the speed of sound WOULD work if the phone was at one end or the other.

[@AndreiAvramPlus]

@@TheBudgetSportsman it's the distance from the source to receiver, you have to delete the delay of the sound according the distance between the shooter and the target

[@JimKimTheIdeaHunters]

Very cool method when a chrono is not handy!

[@TheBudgetSportsman]

Thanks for watching and commenting. I appreciate it!

[@IATowne]

Wouldn’t putting the phone in the middle be the same level of error as having the phone at one end as long as the phone is between the two points?

[@TheBudgetSportsman]

I am no scientist or mathematician, but from my testing, it is NOT the same results. Here is the best that I can explain it...and I could be wrong. Imagine putting the phone at the shooter end by the bow. The phone will pick up the sound of the shot immediately but the sound of the arrow hitting the target has to travel back to the phone AFTER the shot is over. As a result, when you measure the time between the two sounds you will get a LONGER time and a slower bow speed. Now imagine that you put the phone at the target end. The sound of the bow going off has to travel to the phone meaning the sound gets to your phone DURING the arrow flight when it has already traveled part of the way to the target. The sound of the arrow hitting the target gets to the phone immediately. This creates a SHORTER amount of time and results in a much faster bow speed result. Finally, by putting the phone in the middle you are canceling out the delays. The sound of the bow going off takes time to get to the phone DURING the arrow flight and shortens the time. The sound of the arrow impact takes time to reach the phone AFTER the arrow flight and lengthens the time. If the phone is an equal distance from each source of sound they will cancel each other out. This has been the only way I have been able to achieve accurate results. You can also scroll through the comments and you will find another thread where a gentleman asked a similar question and I tried to answer including some math. The primary thing to realize is that the depending on which end you place the phone it will either create a longer or shorter time.

[@IATowne]

The Budget Sportsman ha ya I see your point. Now that I think about it the closer you put the mic to the bow the longer the time delay, resulting in an underestimation of the true arrow speed and vice versa if the phone was closer to the target. There must be a sweet spot, which I guess is at about the middle. Great idea!

[@flushot6513]

I think knowing the draw weight and speed arrow weights all that is fun to know

[@TheBudgetSportsman]

I agree. That’s half the fun of archery.

[@kastlekonfusion]

Can this method be modified to get the actual fps as the arrow leaves the bow before it is affected by drag deceleration? The drag should make the estimated fps lower as longer distances are used. The effect of drag is also interesting to investigate as it is likely very dependent on the arrow and the arrow slows at different rates as it flies since drag should be dependent on velocity. If possible, this could be superior to measuring with a chronograph at one distance. Any thoughts?

[@TheBudgetSportsman]

I’m far from a mathematician and my results were close enough to the chrono that I was happy with the results. However, I can see the desire to calculate drag. Here is what I know. 1. Precision matters. I had to work quite a while to make sure I had a working system and a lot of that had to do with making sure the arrow travelled 60 ft, not that I was standing at 60 ft. I say that because if you were going to take multiple measurements you would have to take extreme care to make sure each of them were done with precision. 2. I could see taking multiple measurements including longer distances to see the effect of drag over time. However I played around with measuring at 30 yards, and decided to go back to 20 yards. Depending on the sound environment and the microphone you are using, you may have a harder time picking up the sound. Doing in an enclosed range like in this video provides a better environment than outside where there may be background noise. 3. You could try it at several close range distances such as 5, 10, 15 and 20 yards and calculate the drag from the change in speed over time, however my suspicion is that for any modern compound, the effects of drag will be so small over that short distance that the tolerances of this method are not small enough to accurately calculate the drag. 4. I think you would have to calculate it by getting an average speed at 20 yards and an average at a much further distance like 60 yards. Again I already mentioned the limitations of records the sound at longer distances but maybe this method could be modified by using two wireless microphones connected to a common recorder to detect the sound at each end. Not sure if those thoughts are helpful or not.

[@smplatek]

This is awesome! Thanks! Once it stops working I am going to try it on a few self-bows, longbows, and recurve bows. Do you happen to know if there are any rate limiting, equation altering issues if I simply shorten the shot? I was thinking if I went 30 feet (i.e. 10 yards), which is way more doable in my yard (figuring outdoors noise would impact the sound recording) I would just change the formula to 30/n where n = the measured distance on Ocen. Does that sound legit or in your opinion will it not work?

[@TheBudgetSportsman]

I don’t see any reason why it shouldn’t work as long as you place your phone at the half way distance of the shot and modify the formula for the distance. That being said I did play around with different distances and compare them to the chronograph. It seems like I got the best results from 20 yards. However that was about a year ago and I can’t say I remember any logical reason 10 yards wouldn’t work. I should also mention again that the tip of the arrow being at the 30ft mark is also important. It’s surprising how much one or two feet off can impact your results. Good luck and let me know how it goes.

[@chrisnagy377]

Is there a reason you used a SUM function in the spreadhseet?

[@TheBudgetSportsman]

I am not a spreadsheet wizzard and thats just what I got to work for me. I guess in hind sight all I need was =60/CELL NUMBER

[@chrisnagy377]

No prob just wanted to make sure Thx for this whole method, will give it a try

[@VS-me7ff]

Don't you need to measure your 20 yd from where the tip of the arrow is when you're holding your bow up and it is at brace? Isn't that or the tip of the arrow would be when the sound of the bow firing occurs?

[@TheBudgetSportsman]

You can read through the other comments. There are some great explanations or at least food for thought. My best explanation is that if you figure that the arrow is going to travel 60ft you need to have the tip of the arrow at 60ft at full draw. This conclusion is verified by testing. HOWEVER, there are a lot of variables including where exactly the sound originates and when it originates in the shot cycle. My testing came consistently came within 5ft per second of the chrono but often closer. If I would change anything I would move the phone half way between the bow and target rather than half way between the top of the arrow and the target.

[@MrTyroneweaver]

Come to Utah Air Guns in "Provo" Utah. We'll sell ya a real hoodie.

[@TheBudgetSportsman]

Not sure what this comment means?

[@MrTyroneweaver]

@@TheBudgetSportsman Provo , Utah home of Brigham Young University

[@Endogamy]

You need to add the temperature factor also.

[@TheBudgetSportsman]

Can you elaborate??

[@olmostgudinaf8100]

@@TheBudgetSportsman the speed of sound depends on factors such as pressure, temperature and humidity. Though if you place the phone in the middle, inaccuracies caused by the speed of sound are eliminated anyway.

[@williambilse]

Now I know my recurve is shooting 146fps. Thanks a lot.

[@TheBudgetSportsman]

😂 your welcome

[@paulblackburn931]

Too much time.

[@TheBudgetSportsman]

The process takes too much time? The arrow takes too much time? Or the video takes too much time?