# I have a question about the physics an arrow

1. Dec 16, 2012

### southshorerat

Hello I am new here an the only thing I know about physics is how to spell it. So if you folks would be so kind I have a question.

It is about archery and arrows. Years ago when bows were slower you could shoot about any arrow with little difficulty. Today as bows are becoming much more efficient there is a need to build better and better arrows.

In doing so it appears there is a need to understand some of the physics behind the way an arrow reacts when shot from a bow.

I have done some research and found that the anatomy of an arrow has three specific points along the length of the arrow.

1 is the FOC balance point. This point is determined by taking a finished arrows adding a point on the end and balancing it to find its FOC or Front Of Center point

2 is the front Node also known as the centre of mass, this point lies somewhere between the FOC balance point and the front tip of the arrow

3 is the back Node of the centre of drag, this point lies somewhere between the FOC balance point and the rear tip of the arrow.

There are those in archery who feel you can go through a series of steps to bounce the arrow off the corner of a table to identify the front Node. Their thought is you can place the arrow on the edge of the counter or table and lay the back of the arrow in your hand or on another table and pull down on the arrow and let it go to watch the bounce. Then move the arrow forward of that point and back from that point and repeat until you find a dead spot. They believe this is the node!

My question is this, if they are correct in finding the front node in this way would the node be in the same place when the arrow is shot from a bow. You have an arrow that you are bouncing by hand sideways and the only energy placed on the arrow if from the process of pulling the arrow down and letting it go to make it bounce. compared to an arrow that is being launched in a horizontal plane after the energy of the bow is placed on it.

2. Dec 17, 2012

### sophiecentaur

Hi and welcome.
This could be an interesting topic but I have a query. I don;t understand your description of how you find (and the relevance of) the FOC balance point. How is this different from the centre of mass of the arrow? It should only balance in one place along its length, surely.

3. Dec 17, 2012

### A.T.

Finding the center of mass is quite easy:

4. Dec 17, 2012

### sophiecentaur

5. Dec 17, 2012

### A.T.

Sounds like the same as C.O.M.:
http://scientificarchery.com/foc.html [Broken]

Last edited by a moderator: May 6, 2017
6. Dec 17, 2012

### southshorerat

One additional comment, the Centre Of Gravity or Balance Point is the Front Of Center Location

7. Dec 17, 2012

### southshorerat

Correct! For the sake of this discussion the FOC point will only come into play if it is needed to construct a formula to identify the Centre Of Mass location.

Here is another point about why I am interested in this, When an arrow is shot from the bow it begins to flex as soon as the string is released. During the first milliseconds of flight the arrow is in contact with the arrow rest. Because the arrow is in contact with the rest some archers feel if you identify the Centre Of Mass and place it on the arrow rest on this location you will have a more consistent shot. Most target archers use a fixed blade arrow rest and most hunters use a drop away arrow rest where the launcher is pulled down instantly when the string is released. This action removes all influence of the bow and archery from the arrow instantly. So if the arrow can sit on the Centre Of Mass there is a valid argument that it will improve the shot consistency.

Last edited by a moderator: May 6, 2017
8. Dec 17, 2012

### A.T.

What is the difference between point 1 and 2 then?

9. Dec 17, 2012

### Staff: Mentor

Just based on your description, I think it can make it worse, too, depending on the forces and their direction.

Looks like a method to find the center of mass. Just shifting the arrow over the edge of the table until it falls down would be possible, too.

10. Dec 17, 2012

### southshorerat

The FOC balance point is where the arrow shaft balances at rest after it is built. It is determined by the weight of the nock, vanes point and Grains Per Inch of the shaft. An arrow with a very heavy point will have the FOC balance point closer to the front than an arrow with a light point. This determines the amount of lever arm the vanes have to steer the arrow. The Centre of Mass and the Centre Of Drag are axis points that sit still or try to sit still during the flight of the arrow as the front, middle and rear of the shaft oscillate.

I hope I am explaining this properly

11. Dec 17, 2012

### southshorerat

Here is a drawing of the anatomy of an arrow.

if you were to push the arrow across the edge of a table it would fall but this would show you the FOC balance point not the Centre of Mass.

Last edited: Dec 17, 2012
12. Dec 17, 2012

### Staff: Mentor

Your explanation of the FOC balance point matches exactly the properties of the center of mass.

13. Dec 17, 2012

### A.T.

Can you give an example of an arrow design, where FOC and Centre of Mass are at different positions?

14. Dec 17, 2012

### AlephZero

OK, that's what I guessed from your OP. The problem is that your terminology here is completely different from how the words are used in Physics.

Center of Mass in physics is what you called the FOC.
Center of Drag in physics has nothing to do with what you are describing (though it is relevant to the aerodynamics of arrows!)

The points you are describing as "center of mass" and center of drag" seem to be the two nodal points of the first transverse bending mode of the arrow.

This thread probably isn't going anwhere useful unless we all agree on what we are talking about!

I think the criterion that they are the same is that the arrow is stiff enough in bending so that it won't buckle elastically, when the bowstring applies a force at one end and the arrow acclerates. But none of the criteria you have described seem very relevant to whether or not that is true.

15. Dec 17, 2012

### southshorerat

We can use any terminology that will work. If we need to call the Centre of Drag and the Centre of Mass the two nodal points of the first transverse bending mode of the arrow I am fine with that. I thought there may be a difference in terminology when I began the thread. Is there a formula that a guy with no physics background can use to identify the front nodal point of the first transverse bending mode.

16. Dec 17, 2012

### sophiecentaur

I find myself asking - if have no physics, what would you do with that info?

17. Dec 17, 2012

### southshorerat

A few years ago bows were slow compared to today. We are seeing compound bows shooting arrows in excess of 350 feet per second and some crossbows are shooting over 400 feet per second. The arrows of a few years ago dont do well with these very aggressive bows so the need to understand arrows and their design at a higher level is extremely important. I tell folks everyday that if you want to fly mach 1 you need a jet not a cesna. Gaining the ability to apply physics in a very small way to arrows and arrow design will help in to build better arrows. This is my reason for trying to get you folks to help with this issue. If I can find a formula and learn to use it may help me to help archers set their bows up better.

18. Dec 18, 2012

### jbriggs444

To me, the "front nodal point of the first transverse bending mode" of an arrow would refer to the following:

An arrow can bend in the middle. If you allow it to do so, it will resonate. This is a sort of standing wave. In a standing wave there are "nodes" where the amplitude of the wave is zero and "anti-nodes" where the amplitude of the wave is maximized.

An arrow that is bending resonantly around its middle, free from external supports, viewed from a frame of reference where its center of mass is at rest will have two nodes and three anti-nodes. One anti-node will be roughly centered, two more anti-nodes will be at the ends of the arrow. The two nodes will be between the anti-nodes.

The "front nodal point of the first transverse bending mode" would refer to the node that is nearer the arrow's tip.

In bending modes that correspond to higher harmonics there would be more nodal points, of course.

A quick trip to Google finds references in which similar terminology is used (in reference to glockenspiels and violins).

http://www.sarahtulga.com/Glock.htm
http://www.slac.stanford.edu/pubs/beamline/28/2/28-2-atwood.pdf

You can see similar behavior if you take a dangling rope and spin it. It is fairly easy to excite the first mode -- one node near your hand and one below. With practice you can get excite modes with additional nodes.

19. Dec 19, 2012

### TomTelford

Just joined but I'm hoping I can help here. I am a competitive traditional longbowman and P/T physics hack.

First, the FOC, in archery terms, isn't the balance point itself but the ratio between the distance between the arrow's centrepoint and the c of G to the overall length of the shaft. If it is zero then the the shaft balances in the middle. Typicially shafts are tip weighted to produce 10-25% FOC where 25% would mean the balance point would be 1/4 of the distance down the shaft.

Second, it sounds like the original post was about trying to tune the centres of mass and drag to the node points when the arrow begins flight and is oscilating. This oscilation is known as archer's paradox. When an arrow is fired from a traditional bow, the shaft bends slightly as it goes around the bow due to slightly offset forces. This creates the oscilation for the first 15-20 metres. The node points are NOT the same as the c of G or D points.

If the balance point was dead centre of the shaft, then the oscilation would be quite clean and shouldn't deflect the arrow at all but as the point moves forward with a heavier tip, the oscilation becomes unbalanced and the arrow will start to "kick". This is balanced by the type and size of fletching. However it is necessary for the c of G to be ahead of the c of D for stable flight. A final kicker is that most arrows use helical fletching that imparts spin to the arrow which also mitigates flexion of the shaft.

I think the poster is suggesting that if the c of G and c of D could be moved onto the front and rear resonant node points, that this would help the flight of the arrow. Probably at a FOC of about 18% and c of D back a little more, depending on shaft material, etc. An interesting thought though I cannot help with the math.

The hunting bows that I've seen use brush aperature rests so there should be virtually no archer's paradox and the shaft's are carbon fibre and are extremely light and stiff so I don't think internal resonance should enter into the flight characteristics. Internal vibrations of the bow probably have more impact.

As for crossbows the issue is shaft speed vs. length for stability. Whole 'nother ball of wax.

Lastly, you mention placing the c of G point on the rest? I shoot with about a 2" overhang on a 31" shaft, so the c of G is well back of the rest and I can't imagine increasing the length of the arrow to move 25% or more of the shaft in front of the bow. That said on hunting shafts the story may be different although, again, there shouldn't be much flex in them. But part of the stability of the shot is for the shaft to be on the rest as long as possible and for the nock point to move exactly along the shaft's long axis so putting the c of G on the rest would be counter-productive.

Hope this helps.

Last edited: Dec 19, 2012
20. Dec 26, 2012

### southshorerat

Tom, some archers feel that if you can locate the front node which we call the Centre of Mass also called the front nodal point of the first transverse bending mode and set it on an arrow rest that drops away at the beginning of the shot you can improve the shooter/bow consistency. The method these archers are using is to take a finished arrow and place it on the corner of a table at an estimated point of where they think the Centre of Mass or front nodal point of the first transverse bending mode is located. They then pull down on the shaft to bow it and let it go then watch the results. Then they move it and repeat the process until the arrow responds with little or not bounce. They feel this is where the Centre Of Mass or front nodal point of the first transverse bending mode is located. My reason for coming here is to see if a mathematical formula exists that I could use to identify the Centre of Mass also referred to by you folks as the front nodal point of the first transverse bending mode.

There are two types of arrow rests used in archery, a fixed type where the arrow is in contact with it though out the entire length of the arrow. The second is a drop away that falls as soon as the bow is shot. If we can apply a formula that will identify the front nodal point of the first transverse bending mode it is believed it will improve consistency of shooters using a drop away arrow rest.

One more point, the front nodal point of the first transverse bending mode will not be in the same location for each archer. We custom fit shafts to each archers setup. Draw length, draw weight, choice of component weights and arrow length are not always the same from archer to archer. Because of this I am assuming the front nodal point of the first transverse bending mode will not be in the same location from shooter to shooter, is this a correct assumption?