How can I accurately locate the front axis of an arrow for optimal flight?

[Jrat]

TL;DR Summary

I would like feedback on the anatomy of an arrow from a physics point of view

I have studied arrows and arrow flight the best I can for a number of years owning an archery shop

A number of years ago I began testing arrows in the shop which we refer to as a static test

We look at straightness, deflection matching and weight matching

We also test to find the stiffest point and index that point to the same orientation

It is believed that by finding the stiffest point the arrows will flex 90 degrees from that point during flight

Now we also believe arrows have two axis points, the front point is called the centre of mass, the rear the centre of drag

My question is how can I find the front axis

Some in archery feel you can pinch the arrow between two fingers then tap the arrow on a hard surface and then pay attention to the vibration in the shaft. Moving the pinch left and right a little at a time until you find the location of the longest vibration

So if anyone could help with this I'm all ears

 

[berkeman]

Welcome to the PF.

Now we also believe arrows have two axis points, the front point is called the centre of mass, the rear the centre of drag

My question is how can I find the front axis

To find the center of mass (CoM), you just balance the arrow on a fulcrum, no?

 

[kuruman]

Welcome to the PF.

To find the center of mass (CoM), you just balance the arrow on a fulcrum, no?

You are correct about finding the CM, but I think OP is looking for the center of percussion, a.k.a. sweet spot, which can be found by the method he describes.

 

[kuruman]

To @Jrat :
Have you seen this link? It contains some useful information about the physics of arrow flight. It appears that the arrow initially flexes about its center of mass as it flies but the oscillation is damped by the tail feathers. If you need to find the center about the arrow flexes, that should be the center of mass, but you should proceed as @berkeman suggested. Tapping the arrow will also work because I now realize that you are not looking for the center of percussion. You are looking for the maximum deflection, a physicist would say for the antinode of the standing wave, which occurs at the center of mass. Probably the easiest and most accurate way would be to make a loop at the end of a vertically hanging string, put the arrow through the loop and mark the spot on the arrow where it hangs pretty much balanced horizontally.

The video accompanying the link is quite interesting (at least to me) and here is another link of a more extended version. I hope your question has been answered.

 

[Jrat]

You are correct about finding the CM, but I think OP is looking for the center of percussion, a.k.a. sweet spot, which can be found by the method he describes.

I'm wanting to find out if

The centre of mass and the front node or axis are the same point

 

[kuruman]

I'm wanting to find out if

The centre of mass and the front node or axis are the same point

I am not familiar with your terminology. How do you define the front node or axis? Is it the point on the arrow that flexes the most relative to the ends? If so, yes, they are the same point.

 

[Jrat]

Could there be a node that you can find by pinching the arrow between your finger and thumb then tapping the arrow on a hard surface and feeling for the point where you get the longest harmonic resonance

Many archers feel this point is the location of the centre of mass

I need to note in archery perception wins most scientific arguments not facts

I believe the centre of mass is the balance point that denotes the FOC balance point

And I also believe it one of two axis points that are the hinge for lack of a better way to explain where the flex is a shaft originates from

I believe in flight the front of the arrow the middle of the arrow and the rear of the arrow flex

At the sam time the centre of mass and the centre of drag do not flex

 

[Jrat]

Here is an image

 

[kuruman]

Here is an image

So if you rest the arrow on your finger at what you call the center of mass in the image will the arrow balance on your finger? It's a yes or no answer.

I believe in flight the front of the arrow the middle of the arrow and the rear of the arrow flex
At the sam time the centre of mass and the centre of drag do not flex

You can see for yourself what flexes and what doesn't in the two video links that I provided in post #4. Perhaps you didn't notice that they were highlighted as links, so here they are spelled out.

https://www.real-world-physics-problems.com/physics-of-archery.html

I need to note in archery perception wins most scientific arguments not facts

In science it is the facts that rule.

 

[A.T.]

Here is some more slow motion footage:

 

[Lnewqban]

Could there be a node that you can find by pinching the arrow between your finger and thumb then tapping the arrow on a hard surface and feeling for the point where you get the longest harmonic resonance

Many archers feel this point is the location of the centre of mass

I need to note in archery perception wins most scientific arguments not facts

I believe the centre of mass is the balance point that denotes the FOC balance point

And I also believe it one of two axis points that are the hinge for lack of a better way to explain where the flex is a shaft originates from

I believe in flight the front of the arrow the middle of the arrow and the rear of the arrow flex

At the sam time the centre of mass and the centre of drag do not flex

I believe that the locations of the center of mass, the center of drag and the natural vibration nodes of the arrow are not related.

Stroking the arrow creates longitudinal vibrations in the rod, which are waves that travel along the length of the rod.
The waves travel to the ends of the rod and are reflected back and forth between both ends.

On their way back, they collide in a head on collision with other waves traveling in the opposite direction, cancelling each other and creating those nodes or points if minimum deflection that your fingers can detect.

Please, see this explanation about the vibration modes of a rod:
http://hyperphysics.phy-astr.gsu.edu/hbase/Music/barres.html#c3

The location of the center of mass does not move sideways during the flight, it must describe a more or less parabolic trajectory.
The arrow, however, can oscillate around that imaginary center as much as it has to; therefore, at some points on the flight trajectory, the center of mass may be located way out of the physical rod (think of the location of the center of mass of a donut).

The center of drag only exists when the arrow is flying and fighting the aerodynamic resistance of the air; hence, its location is purely geometrical and aerodynamical and has nothing to do with the location of the nodes of the vibrating frequencies of the arrow, other than some additional damping of the vibration.

Since the center of mass is always above the supporting edge, finding its location is not always easy by simply supporting the arrow.
For a fine location of the center of mass, you could built a rig more or less similar to this one:
https://www.rcuniverse.com/forum/tips-techniques-180/708060-vanessa-c-g-rig-how.html