Arrow spine-making dials-warning contains tricky trig.

[stringnstik]

ok my math has never been good but please someone explain to me how this works.
Im sure there is a simple trap that I have fallen into as i dont believe there could be a mistake in a published and used dial.

In a nutshell.
Look at the colour dial.
The pointer rests on the arrow @ (X), 1" past the pivot point.
X is also the centre of the 2 arrow supports which are 26" apart.
The arrows centre is at X.
We apply 2lb weight at X.
If we had a weak spine(ie26) thus giving us 1" deflection we should see our needle at 90deg?
So why does the first segment(90-60deg) start at 30-35 spine??

ok read on.......

As mentioned on other posts I have built a spine tester. I have looked at 3 resources.
Jim's
http://www.jamesmhill.com/Spine_Tester.html
John's
http://marshal.ansteorra.org/archery/fi ... tester.pdf
Waterlogged's
https://www.primitivearcher.com/smf/ind ... 5#msg63485

Now I liked Waterlogged's cause it was colourful! No mainly cause it displayed in spine.
However after a few plays it proved to not have enough markings/divisions on it. I CAD a copy of his jpg and added my own deg dial 0-90 with every 2 deg and 5deg steps marked.
This was better but I wanted "more". So I grabbed John's dial, scaled it correctly and superimposed it onto Waterlogged's. This looked messy and Johns did not extend into the region I was mostly interested in.45-35. So I thought Ill just make my own from scratch..how hard can it be.
It was obvious that 1" from pivot gave a better mechanical advantage than 2", for the weaker spines I was interested in.
The CAD wanted degrees so I had to convert my deflections into degrees..Good old excel to the rescue. I deemed that a triangle was made from the points PP Z and right angle to the baseline(dotted red line). Knowing that PP to Z was always 1" and that Baseline to Z was the deflection (in this case .5") I could work out the angle at PP using trigonometry.

I created a chart of angles, deflection and spine.

I checked the angles v deflection using a rotate pointer in the CAD and it matched Johns grey dial. (see the pink and purple pointers)
(B) .5" deflection reads .500 on the dial and is 14.47751219 deg.
(C) 1" def reads 1000 on the dial and is 30deg.

I hate PINK!! cause at this point the wheels fell off..
See I knew that 1"=26 spine and .5=52spine.
and yet my pink pointer was reading 1" def on the 2" dial,(C) which correctly equated to .5" on the 1" dial(Z) BUT the 1" colour dial presented the spine as 55-60 (58ish).

I was in some deep doodoo without a calc to save me.
Where am I going wrong?

[GrahameA]

IMHO

Build the Jim Hill design. It is a little slower to load and operate but it gives better - ie more accurate - results.

To answer you original question - what happens if you have a shaft of say 20lb? Do not like some aspects of the design as the pointer motion is not linear. Then again you can change the mass to measure low spine values. If we are operating in a range that is valid for Hookes law.

[stringnstik]

sure the Jim hill is better no argument there, but I dont have a dial in my pocket and now this has become more of a challenge.
I found another reference of a degrees to spine chart(but no math to backit up and unfortunately it matches the colour dial. So I am indeed missing something.

[GrahameA]

Evening

My opinion. Just because things have been used many times does not make them correct.

I would work out the deflections/poundage from first principles - that way you are certain they are correct. Remember the sensing section of the pointer moves in an Arc and that whilst it may start underneath the centre of the shaft it will move laterally (as well as vertically) as the shaft is loaded.

Time for a Coffee, sheet of paper and a Scientific Calculator - or just use a spreadsheet.

p.s. Make the pointer long if you want to get "good" measurements.

[stringnstik]

ok First error.
I was aware of this one and although I still feel it has nothing to do with my current problem its worth mentioning for anyone building the dial types. AND expecting absolute spines. Most use them for relative measurements and thus because its a constant error its not a problem.
You must make sure with an arrow on the jig the pointer reads zero!

The thickness and exact placement of the pin that the arrow rests on.
In the picture below we have a blow up of point C.
The green line is our 2" arc.
The thick black is our arrowat 1" deflection.(horizontal dotted line)
2W is where the weight is hanging. Vertically inline with the 2" point.
The prple pointer has a 3mm(1/8) pin attached
The opaque pink unreal pointer is centerlined on the arrow.
You can see a diff already that the thickness of the resting pin makes.
the second picture shows the corresponding dial reading difference. Quite a bit!!

Also notice the horizontal dotted 1" line. @ the 2W point its resting on the arrow. Where the needle touches its just starting to come away and further Left of the picture there is a noticeable gap between the 1" down and the arrow shafts arc.At a point 1" left of the weight my emulated shaft was .01" up from the 1 "line. @ the pin the error was .002".
This is the error, I think Graeme was referring too. The "sensing" part of the pointer(pin) is not at centre and not at the weight.

However this .002 is not the "much bigger problem" Im seeing in the above posts.

more coffee

[little arrows]

Hi Mark,

Dare I ask what has prompted your little exercise,?
I haven't actually read the whole thread, but I do know that 500 on the guage equates to approx 51# spine arrow and 400 is close to 65#, so the figures on your guage aren't lining up (so to speak). We've had two dial guage spining jigs in the house, just to see what they were like, and they are a lot fiddlier than the other type.

sue

[GrahameA]

Good Afternoon

You must make sure with an arrow on the jig the pointer reads zero!

Yep, and you can adjust the arrow or adjust the scale or adjust the pointer.

Hi Sue

Dare I ask what has prompted your little exercise,?

I think he may have been a bit bored. The Maths, etc., are good for the soul.

My current Jig uses a dial gauge. It takes longer but I am happy to put up with that - for the moment. Although I may have to build myself another - with all the lessons I have learnt from the previous 3 or 4.

[stringnstik]

Good Afternoon
I think he may have been a bit bored. The Maths, etc., are good for the soul.

hhaahh youve found me out.. I was just going down with a bee in a china cup:)

Its all about understanding it now. Im convinced the colour dial is wrong, just finding away to prove or disprove. It might have something todo with the 1" from pivot as opposed to two. 1" may indeed give you mechanical advantage but Im assuming it also doubles "an" error and he has compensated for it.

[CraigMBeckett]

Hi stringnstik,

After reading your post and as I use a spine tester based on JJ's design I got intrigued with its accuracy and spent the last day playing with the maths involved.

Looking at JJ's dial all he has done is used simple trigonometry to calculate the deflection angle if the pointer arm moves by the amount obtained from the AMO equation deflection = spine/26, ergo an arrow with a spine or 26lb will deflect 1 inch under the applied 2lb load, and one with a spine of 52 lb will deflect 1/2 inch etc. The deflected angle for 1 inch deflection is the inverse tangent of deflection/arm length or ATAN(1/2) or 30 degrees.

JJ has ignored the fact that the 2 inch pointer arm moves away from the point of application of the load and the maximum deflection of the arrow is at the point of application of the load, ergo JJ's tester reads less than actual. However the error is relatively minor and is (if my calculations are correct) only of the order of 0.22 lb spine for an arrow indicated as being 100 lb and 0.08 lb spine for a 26 lb arrow.

It is to be noted that the above calculation assumed that the point of rotation of the indicator was placed exactly at the location instructed by JJ that is exactly 2 inches to the left of centre and 1/2 inch and level with the underside of the arrow. Any other location will introduce additional errors.

Therefore JJ's dial is fine.

Now if instead of 2 inches arm length you use 1 inch as instructed by Waterlogged in his post the angles of deflection change , for a 26 lb spine arrow the deflected angle would be 90 degrees, a 30 lb spine arrow the deflected angle would be approximately 60 degrees, and for a 52 lb spine arrow the deflected angle would be 30 degrees.

However when you look at the "dial" provided by Waterlogged, none of the above calculated angles agree with those shown and the error seems to be much more than could be explained by a correction for the type of problems I mention above.

Therefore I agree with you "dial" provided by Waterlogged appears to be wrong.

If you want to play around and do your own calculations the equations for deflection of a simply supported beam under the influence of a point load applied at its centre will be useful. (I don't seem to be able to use superscript on this page so I cannot put in the cube and square so will have to resort to multiple entries.)

Y = deflection, Y(max) is maximum deflection, Y(x) is deflection at some point x along the beam
L = length or span in this case 26 inches
E = modulus of elasticity of the wood,
I = moment of inertia of the arrow
* is the multiplication symbol as in 2*2 = 4
(you don't need to know E or I you can work out the value for EI or 48EI for each spine rating using the known maximum deflection.

Y(max) = (P*L*L*L)/(48*E*I)

(P*x(3*L*L-4*x*x)/(48*E*I)

Regards

Craig.

[stringnstik]

thankyou so much Craig. This is exactly what had me baffled it just seems wrong doesnt it. the 26 @ 1 inch @ 90deg is a dead giveaway.
I do now have a deflection dial as per james hill. I will build this, test some shafts and then use these to check/confirm, nail the coffin home the 2" and 1" dials:).
Just a tad busy getting ready for Dunolly and Hawkswood feast this week.
Ill also check my trig(on the work pc) with yours tomorrow.
Thanks.

[stringnstik]

For those interested in building Jims type jig I
found this in the junk mail today from gasweld.com.au
(530194) 1" dial indicators .001 res for $41
Not a bad price from what Ive heard.