Ballistics 101: Arrow Speeds with a Laptop and a Microphone

[DrRalph]

I wanted to measure the arrow speeds with Rodger's new UltraMag setup, only I don't have any specialised equipment, like a chronograph.

The New setup:
Hoyt UltrMag, 45lb, 27" 65% letoff Cam +1/2, 450+ 16 strands. 26" 256gr 670 ACE with blue spinnies. ABO Rating 305fps (70lb 30" draw, minimum weight arrows)

However I did have a 5m tape measure, a target and a laptop with a built in microphone. I reasoned that with the recording sampling at 44100Hz it should be possible to measure the sound of the arrow launch and the impact on the target very accurately.

I realised that at 50-100m/s the arrows are travelling between 16 and about 33 percent of the speed of sound, so the timing of the sounds would not be able to ignore the sound travel times to the microphone. If you put the microphone at the archer, you get the launch accurately, but the impact is delayed by the time it takes the sound to get back to the archer. *BUT* If you don't know the speed of sound precisely at the shoot location, how do you accurately get the timing, to say 1%.

The simple answer is to put the microphone exactly halfway between the archer and the target, then the sound delay reaching the microphone from the arrow launch is the same as the delay from the target. The interval between is then the flight time of the arrow, no matter what the sound speed is.

It is easy to measure the distance from the arrow tip at full draw (lined up over a line on the ground, to the target face at 10m to a few cm error, 10cm is 1% accuracy. So we set Rodger's tip arrow at 10m +/- couple cm. Then we placed the omnidirectional microphone (in the laptop lid) at the 5m line, and adjusted the recording levels in the software so the launch and the impact were recorded.

Figure shows a typical recording:

http://macnab.anu.edu.au/~ralph/archery/01halfway.gif

In the sound wave you can see the release itself and then the limbs/string making their noise, then a gap and the impact on the target.
The interval between the release and the impact is 0.133s +/- 0.001 depending on exactly where you put the mouse.

Now 10m in 0.133s is 75.188m/s or 246.7fps. The post launch speed is probably a bit more than this, and this time includes the acceleration itself, but it is probably a good eastimate as the blip due to the release is so short compared to the overall travel time.

I measured this 6 times to get a good average: 0.1328 +/- 0.0004 s. or 75.30 +/- 0.23m/s or 247.0 +/- 0.75 fps. This is about 0.3% error and smaller than the estimated 1% length errors, so finally I'd estimate 247 +/- 2.5 fps.

For comparison when I recorded the sound from next to Rodger I got:

http://macnab.anu.edu.au/~ralph/archery/00neararcher.gif

which shows a louder launch and quieter impact of course, but the big difference is the delay was 0.167s or (equiv to 59.9m/s or 196fps if interpreted naively)
The difference is about 0.034s or about 300m/s which is a measure of the speed of sound travelling over the 10m from the target to the microphone. There was no delay on the release, but a big delay from the target.

I'm going to test my recurve setup now. :)

If anyone has both a chronograph and sound editing software + digital recording capabilities to compare both methods I'd love to hear how they go.


PS the error on the sound speed is greater because 0.001s is a big error compared to 0.034, but reasonable compared to 0.133.

[Axilla]

Interesting reading, Ralph.

On a somewhat tangental note - Do you know of any slow-motion video or high-speed photos of an arrow being launched from compound bow?

[DrRalph]

Nope, they must exist though. There are high speed cameras in use by Australian coaches, I can't borrow the ACT one until I get a coaches level 1 qualification :(

If you find any let us know.

[Rodger]

http://www.newarchery.com/arrowrests/qt4.asp :-?

Rodg

[Eberbachl]

Nice Work DrRalph!

[2Dogs]

Well done Dr PArk!.....errrr Jim Ralph :lol:

[James Park]

Yes, excellent.

[Tony Pearce]

Ralph,

An idea. To remove the arrow acceleration error alluded to above......

Shoot an arrow through 2 sheets of paper exactly 10 metres apart. The 1st sheet of paper positioned immediately after the arrow leaves the string and the mic, once again, positioned exactly between the 2 sheets of paper. I am assuming that the velocity loss at the first sheet is negligible.

Tony

[DrRalph]

That could work, but it would be a lot of extra work setting up the sheets for the shots. At that level I think I'll borrow a chronograph.

Another idea I've wanted to try involves shooting arrows with magnetised tips though large wire loops, and record the amplified pulses as the arrow passes through a couple of loops (see the papers mentioned in some od Jim's other threads), but needs a bunch of custom op-amp circuitry and you might as well get a chronograph again.

What I liked about this method here is that is lets the archer shoot normally at a target, has no consumables, and used existing equipment.
You could probably use a digital camera or modern mobile phone to do the recording and analyse the sounds later - the laptop was all I had at the time. Most sound digitisers can do 44.1kHz and are great timers.

[mike]

Shoot an arrow through 2 sheets of paper exactly 10 metres apart. The 1st sheet of paper positioned immediately after the arrow leaves the string and the mic, once again, positioned exactly between the 2 sheets of paper. I am assuming that the velocity loss at the first sheet is negligible.

Tony

Interesting, now I am seeing an experiment (the scientist comes out...indulge me...)

It is actually not hard to do this, because even at 70m for a compound we are only talking 3 - 4 degrees of elevation at most, so it would not be hard to set up paper frames (of say 2m height) for every say 5 or 10 meters. Now, assuming you used say tissue paper, the drag effects of the paper woul be negligable and so you woud be able to then place a microphone next to each sheet and record the time of pass through of each sheet.

Shoot the shot, record the times. In fact you would would only have to work out where the archer would aim on the first sheet to ensure a hit 70m later and you've done it.

Having used geophone arrays for geophyisics studies I can say that these sorts of measurements can be very accurate indeed...

[mike]

Have discussed this further with Zoe (and must acknowledge...)

She isn't keen on the use of paper as a detection device. Whilst I think it could work, it has to be said that it is not ideal. I suppose the previously mentioned magnetic tip with coil arrays would be better. I would challenge someone to come up with the money to fund such a study though!!

OK, we need to be clever then. Arrows move at <<sonic speeds. Arrows are noisey, particularly the ones with spin wings. So, perhaps (and you might like this Ralph) we could set up a series of say 10 pairs of microphones (one towards archer, one towards target) and measure the dopler (sp.?) shift at each pair so as to determine when the arrow passed that pair. This might then give us a distance-speed profile.

I imagine that good position (b/w archer and target) and speed data would be VERY useful for the testing of some of the calculations that Jim uses in Accurate sights.

I think we might have a very cool experiment to carry out here (allowing for further forum development).
:D

[mike]

At the very least it would be fun and would involve lots of cool sensitive equipment and we could all stand around looking really cleaver-like saying that we are "Archery Physicists" and that results will be on a need-to-know basis-only-so-we-cannot-discuss-it-further-maam. I reckon people might actually take us seriously....

[Axilla]

http://www.newarchery.com/arrowrests/qt4.asp

Thanks for that Rodg, now I want a Quicktune 4000 to replace my 3000. :-?

[James Park]

Many years ago I tried taking pictures of the arrow part of the way out of the recurve bow (as it happens I was investigating how arrows flexed).
To do this I shot at night, tied a piece of cotton to the string with the other end to a micro switch which operated a camera flash. I got very sharp pictures showing the arrow flexing nicely, but it was a little difficult controlling exactly at which position of the arrow in the bow the flash operated. I will try to find them.

[DrRalph]

I reckon people might actually take us seriously....

I wouldn't go that far. :o

In another (incomplete) experiment I have made up a 2315 arrow with an electronic circuit (and small battery) inside it that flashes a large 10mm led, which Rodger and I turned down to make a tip. The idea was to try out different fletching options, and shoot it at nighttime into a straw bale. We planned to photograph it with a long exposure, giving the flight path of the tip on the exposure. The flashes are known frequency, so the lines of light will be dashed lines in the photograph - giving the speed and path of the arrow.

I'll post some pictures of the arrow sometime.

We never completed the experiment, but we may try again this winter when we get really bored again.

The problems I see are:
1) we can only do this for large diameter arrows, mostly heavy Al, but possibly the CT HIPPO.
2) The circuit is light as possible (surface mount components - a real fiddle to solder by hand - embedded in hot melt and shrinkwrapped) but with the battery it adds even more weight to the arrow.
3) at 1000g takeoff I'm concerned the wiring will break.
4) perspective distortions in the lens geometry will make it hard to get a really accurate flight path - perhaps using simultaneous cameras from different angles would help?

plus a bunch more. :)

I was just hoping to show whether different fletches make a difference or not in a relative sense which seemed possible.

But you are right, it would be nice to measure the true flight path of arrows, not just the impact point. I'm still looking for a way that doesn't impact the arrow.

Are 3D high speed sonar systems high enough resolution? Jim?

R

[James Park]

Ralph,
I think that better understanding what is going on here is very usefull in knowing best how to optimise our gear and how we shoot it. So, the sorts of things you are thinking about are excellent.
I have been interested in how arrows flex from about the early 1970's and have always taken an interest in how best to actually measure these things rather than just think about the theory. However I have uniformly found them difficult to measure. For example, trying to directly measure the archers' paradox (the arrow flexing around the riser for a recurve) is non-trivial. Consequently, I have usually resorted to trying to predict the effects and then to measure the expected outcomes (although this is non-trivial as well). Perhaps with the rate computer power has advanced in recent years we could now tackle some of these measurements more directly than was possible in past years, as you are showing in your velocity measurements (when I was doing my higher degree work back in the early 1970's the fastest I could sample an electronic signal was 1 kHz)?

[Axilla]

I'd like to see how arrows flex on launch from a compound.

Found this, http://www.carbonexpressarrows.com/media_slow_motion_movies.shtml, not exactly what I'm looking for.

[coach]

Geeze you guys must be bored ! But your minds are amazing ! I couldn,t even contemplate how to do this! :D

[coach]

Oh by the way did you hit what you were aiming at?

[Rodger]

Oh by the way did you hit what you were aiming at?

In the sound test? Yes. Or are you talking about the paper one? :-?

Rodg

[coach]

Good on you! :D

[GrahameA]

Fluked this at the nationals

http://members.optushome.com.au/gamy/nationals/Img_2463.jpg

The archer is Cliff Freeman and you can observe the arrow about 10 metres downrange.

Note the amount of flex in the arrow.

I also have some video of an arrow in flight from a longbow which was taken with a Sony Video Camera. I then stretched the timeline in Premiere so that you can see the aroow porpoising in flight.

Using normal video gear is okay for taking clips of the archer but the frame is generally to slow to see the arrow being launced etc. Need a Redlake camera.[/img]

[James Park]

Excellent!!

[unclepete]

Excellent pic, Grahame. Another from the 300D?

Ralph,

Maybe I'm being a little naive here, but doesn't your test show average velocity over the entire flight, while a chrono fitted close to the bow would give a snapshot velocity at the (presumably) fastest arrow speed? How would you compare your results against manufacturers spec, which would be the chrono speed, presumably (again)?

Pete

[Jorge]

Interesting reading, Ralph.

On a somewhat tangental note - Do you know of any slow-motion video or high-speed photos of an arrow being launched from compound bow?

http://www.nacinc.com/image_gallery/archer.wmv

[Sandy Hancock]

5, 4, 3, 2, 1.... :snipersmile:

[dbjac]

i can't ban yet =( But i'll toast his post.

Thread necro and a spammer. Yeah, he was never going to last long.

[browning micro adrenaline]

yer look on youtube