Home Made Bearpaw Spine Tester

dvd8n

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Ok, I said that I'd look at a centre of gravity / front of centre calculation at some time which, given that there are two gauges supporting the arrow, ought to be easy.

Intuitively, the centre of gravity position ought to be a simple calculation based on the ratio of the weights, but I couldn't justify to myself why, or exactly what the formula to use would be. So, I tried to work it out. My wife saw what I was doing, and pitched in to help. This led to a bit of colourful language as, being a civil engineer she insisted on thinking of the problem in terms of the reactions upwards at the supports whereas I, being a normal human being, wanted to think in terms of downward forces on the gauges. Once we sorted that out we figured out the sums:

IMG_20210613_221818.jpg

This sorted things out in my head plus gave a nice formula for plugging values into. Giving this:

IMG_20210613_221635.jpg

Yay! The centre of gravity is 455mm in front of support 1. That's good, isn't it?

Well no, not really. You can find the centre of gravity of an arrow by balancing it on a finger. What you really want to know is the front of centre position as a percentage of total arrow length, which is what all the recommendations for good arrow flight are in terms of.

FOC.jpg

This is in theory a simple calculation; in fact trivial for the microprocessor. However it involves knowing the arrow length plus its relative position on the supports. This is data that's not easy to enter on a device without a keyboard. And the data input can't be more trouble than it's worth.

This will need some thought...
 

dvd8n

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One idea that I had was to place a stop at one end to butt the end of the arrow against. That would mean that at least the overhang at one end would be constant and known.

However the Easton FOC calculation uses Easton's 'Correct Arrow Length' which goes from the base of the nock string groove to the end of the shaft. This makes the idea of an end stop impractical.

It also raises the question of why. The shape of the head will definitely affect the length of the arrow to the extent that it will affect the percentage calculation.
 

dvd8n

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I finished implementing the FOC calculation code.

I abandoned the idea of a stop for the arrow - the answer that I came up with was much simpler.

IMG_20210618_221408.jpg

The solution that I came up with was simply to require the arrow to be placed on the support such that the base of the nock groove is right over the support. There may be some designs of nocks where this isn't possible but so far all the ones that I have tried are ok. It's not even fiddly to do.

IMG_20210618_221530.jpg

My FOC is 12% which is within the recommended range of most advice. This was of course skillful arrow building and not a lucky choice of components at all :rolleyes:

The solution for total arrow length was to ask for a confirmation of arrow length the first time that weighing is carried out after a power up. The user can either confirm or tweak the length then confirm. The value is stored in EEPROM (alongside the gauge calibrations) so is not lost between uses of the tester. So, most of the time it costs the user one extra confirmation key press per session unless a different length of arrow is used.

IMG_20210618_221305.jpg

You may notice that I have changed the weight display to grains and the arrow length is in sixteenths of an inch. The tester has turned into a Frankenstein combination of metric and imperial units.

Internally all data is stored and calculations are performed in metric (of course it is I'm not nuts).

The mechanics of the tester are also metric apart from the spacing of the supports which is 28" and the depression of the central pillar which is half an inch. Of course this is down to the Easton spine calculation definition which is all imperial and uses these values.

The user interface is pretty much all imperial. Arrow spine display is imperial (eg '500' is actually 500 thousands of an inch which you may not realise until you think about it). I switched arrow weight display from grams to grains because, whereas I am fine with grams in everyday use, I have no idea whether a 32g arrow is good or bad, and on the other hand I do understand what a 498gn arrow means. In a similar vein, my arrows aren't 768.35mm long, they are 30 1/4 inches.

It's this sort of stuff that causes NASA to make $300 million craters on the surface of Mars...
 

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dvd8n

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While AIUK was out I wrote this up as an Instructable


and entered it in the Arduino build competition that they had running. I came second and won $150 :D
 
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