Physics/Geometry behind string nock height?

[KodaChuck]

I know 1/2" to 5/8" nock height on my bowstring works and arrows fly well. That's not the question. What is the underlying logic, physics, geometry, principle etc. involved that causes arrows to fly well when we do this?

[McDave]

While the laws of physics certainly apply to shooting an arrow, the science of determining nock height is more empirical than theoretical.  We want to locate the nock such that a bare shaft shot from the bow will fly straight toward the target, not nock high or nock low.  When the bare shaft flies straight, less error is introduced into the flight path of the arrow from oscillations, and the force vector of the shot is aligned with the arrow, rather than having both a vertical and horizontal component, meaning better penetration on an animal.  The reason for the determination being empirical rather than calculated is that nock heights can vary from dead level to an inch over square, with many in the range of 1/2” to 5/8”, as you note, because of many variables from bow to bow and shooter to shooter.  Rather than trying to isolate all of these variables and devise a formula for them, it is simpler to just shoot a bare shaft and try different nock heights until you find one that results in level flight.

[KodaChuck]

McDave.....agreed.....I have throughout my life worked empirically like you describe....and generally, most bows fall into that 1/2" - 5/8" up nock height.....and I'm with you on the benefits of bare shaft straight flight.....and while not looking for a formula, I wonder what dynamics are at play behind the nock height. When nock set is done properly, good arrow flight is the observational result.....but what are the actual forces, dynamics or geometry that cause that?  That's what I was wondering about.

[onemississipp]

Where a arrow is nocked at rest is not the same as it is as it is drawn, in a geometry. Of course the location at full draw is the actual placement we are after but adjusting that location at rest is much easier. I’m sure a formula could be conceived and calculations carried out to find the optimal placement but math in public is not near as fun as shooting bare shafts and going through the arrow tuning process.

Maybe your answer lies here:

https://arxiv.org/pdf/1511.02250.pdf



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[McDave]

Two of the most important are where the shooter holds the string, e.g. 3 under or split, and relative strength of bottom and top limbs, i.e. tiller. In addition to where the shooter holds the string, how he holds it affects nock height, i.e. what pressure is exerted by the top finger and what pressure by the bottom finger.  For a split finger shooter, error, and nock height adjustments, will be introduced if downward pressure by the index finger on the nock is excessive. Spine and nock height are not as mutually exclusive as we would like to believe; I find it to be a process where successive steps are needed to get the optimal balance of both. Brace height may have a subtle influence on nock height. Probably there are other factors as well.

[McDave]

Maybe your answer lies here:

https://arxiv.org/pdf/1511.02250.pdf

Wow!

[the rifleman]

I have been running the nock height upwards of 3/4" to combine w longer arrows and head position to get a closer point on.  This shows very nock high on bareshaft, but works great w field points for 3d.

That said, i will retune my rig for level bareshaft flight and use a crawl for hunting.  I believe this will give me more penetration, and from a 40# bow, that's not a bad thing.

[Huntschool]

Maybe your answer lies here:

https://arxiv.org/pdf/1511.02250.pdf

WOW again.....  I had to have the wife, she is better at math then I, explain some of those operations......  I am old..... but now I can pull out my TI 35X and have at it..... LOL

Thanks for posting that, really.

[McDave]

This is what I was using back when I was figuring those things out:

[onemississipp]

McDave,
       No batteries needed.


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[onemississipp]

Maybe your answer lies here:

https://arxiv.org/pdf/1511.02250.pdf

WOW again.....  I had to have the wife, she is better at math then I, explain some of those operations......  I am old..... but now I can pull out my TI 35X and have at it..... LOL

Thanks for posting that, really.

No problem, that is not my cup of tea anyway.. I’m more of a rock scientist not a rocket.

So one day a friend had somehow stuck a huge cooler in the trunk of his wife’s car, there were two guys attempting to get it out. No idea how long they had been at it but the guy that stuck it in there saw me and said, “I bet Dustin can get it out he is a rock scientist”. Of course it was a matter to positioning the cooler.

As an environmental science major I was never so proud to be a rock scientist.




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