I need to know if my method will work for calculating how stiff an arrow would have to be for a giant bow project I am working on. With regular archery bows we have basic formulas and rules of thumb we use to calculate the right spine for an arrow and then we use a 2# weight hung from the center of the arrow spaced at 26" to get our deflection which converts to a spine number.
The head of the arrow will vary greatly in weight so several arrows of different designs need to be made. The arrows will vary in weight from 100# to 10#. The point weight will vary from 10# to 0 Testing in advance is not possible so I need to get them in the ball park just based on calculations.
My thoughts are which might be wrong are that I need to find the center of dynamic mass to start my calculation, I can’t figure out the point I need to start this from, I am thinking 25% rear of center might be a good place but if it is or isn’t I am not sure why.
Some of the arrows will be using tapers of different types and all will have very different spine requirements.
I may not even be asking the right questions but basically I am looking for a way to calculate spine. I will know the acceleration rates and length of acceleration as well as the force being applied.
I’m not really sure what you are asking, but I will point out that for the arrow to fly true, the center of gravity must be in front the center of pressure.
You can change the center of gravity by increasing the weight of the head, or increase the center of pressure by increasing the size of the flights.
As for how stiff the spine needs to be, for a huge arrow, it seems to me that you would want to use something strong and hollow, like an aluminum tube.
Arrow tuning is actually fairly precise. The arrow has to flex just the right amount for proper flight so it isn't one of those things you do off the seat of your pants and expect decent results. Just trying to figure out how to approach it. The acceleration for the giant bow will be quite a bit slower than it is for a small bow, maybe as much as twenty times slower so comparatively I know I will need much softer spines. I think I have it right there?? Twenty times less spine scaled up might get me pretty close.
That would go along with the tuning once I figure out how much spine will affect flex at that scale. For example. a 50# archery bow would use an arrow with about .5 deflection in it with a 2# weight placed in the center supported at 26". Now the 50# figure is based on known acceleration rates for 50# bows and the tuning is based on length of arrow, point weight and how far it needs to flex around the bow. So the spine can vary by as much as .2 deflection based on all the factors.
So I am basically looking more for a method on how to approach it than I am an exact answer because I will have so many variables at work. In my case the arrow won’t need to flex around anything but they still have to have some flex, Maybe I will just have to figure out how to scale up spine requirements.
Very roughly (Euler’s approximation), the deflection will be inversely proportional to the Young’s modulus (ie stiffer materials flex less) and to the moment of inertia of the cross-section (thicker arrows flex less).