If I took an arrow and shot it into a 3/4" piece of plywood and then careully measured the depth of penetration. I know the speed of the arrow, the weight of the arrow and the KE it carries as well as the momentum. How could I convert that information into a psi type rating. Suppose I was going to use a hydraulic jack to press the tip of the arrow into the plywood to the same specific depth that I achieved when I shot the arrow. How could I estimate the amount of PSI needed to do this. I already know that I have to convert the area of the point in relation to a sqaure inch. Assume the point had a 45 degree angle
I meant to put this into general questions
Thread relocated from IMHO to GQ.
Don’t know the equations off hand. But you might want to simplify the shaft portion. The energy of the shaft to the psi of it’s area of connection to the head. The energy of the head calculated separately and added to the shaft.
Pushing the head in with a jack would not include the kinetic energy of the head. The head may be more mass than the shaft or at least a good portion of it.
Heads come in a wide variety of types. Knowing what kinetic energy the complete arrow has, is only a very rough idea of how a head will penetrate. Then there is the varying type and amount of damage each head can do.
Clearly, the amount of energy required would build up as the arrow head penetrated the wood. Could you take an average from the point to the full width of the hole?
The arrow I am using actually has what they call a field point. Designed to reduce penetration for target practice. It has a hollow grind at the short point.
One of our common arguments is less mass more speed or more mass less speed. The momentum goes up more with mass while the KE seems to go up more with the speed. Tests actually favor more mass less speed as penetrating better on live game.
I have no real useful reason for wanting to make the conversion to PSI beyond curiosity.
I found this page.
https://www.quora.com/What-is-the-difference-between-kinetic-energy-and-momentum
Which seems to back up the idea of momentum delivering more penetration in most cases than kinetic energy. So mass over speed in the right balance.
The field point would be an easier calculation to use for penetration given a particular energy, due to it being a simpler model. Blunter. Disipating energy quickly. I put a two edged broad head partway through 3/4 inch plywood, with a relatively weak, cheap compound bow. So cutting ability really complicates the calculations.
It would be fun to go to a range with a speed trap and test out various weighted arrows with the same point and find a sweet spot for that bow. Same everything. Just add weight to the arrow in some way. Inside the shaft? So as not to affect aerodynamics? I haven’t been into archery for some time now. Maybe you can get shafts that are weighted differently.
As you add or subtract arrow weight speed goes up or down at a very predictable rate. heavier arrows tend to suck more energy out of the bow so are more efficient besides besides having more momentum and KE. There is a lower limit for speed that most hunters don’t like to dip below which is about 150 fps. This pretty much limits how heavy your arrows can be., The majority of hunters actually prefer slightly lighter faster arrows as long as they carry sufficient energy to get the job done. They have a flatter trajectory and are easier to aim accurately.
Yes a faster arrow is more forgiving of range miscalculation. And one that has enough mass to properly react with your bow dynamics makes for a nicer fire. I noticed way back when, that the heavier broad heads seemed to “work” better with that cheap bow. The field points were more likely to let the string slap me and were noisy. Though the slap could likely be avoided with better form than mine. It seemed the bow had more than enough power for the light points, and dissipated the power badly. I am considering getting back into archery. Just target shooting. My brief previous experience, shows I need to take more care in matching my equipment up.
I don’t think you will find a simple equation to do this. Due to the complex nature of plywood, the shearing and bending forces of the various layers and glue joints, the friction of the arrow as the wood tightens around it, etc. This is finite element territory.
Or, take the direct route and set up a press with a load measuring device. It could be an arbor press with pressure gauge to indicate the cylinder pressure, or a scale under the plywood to reads pounds of force.
Nobody calculates metal hardness, for instance. They use a very simple device that pushes a point using a specific weight into the metal and measures how far , then they consult a chart to get the hardness of the metal.
Dennis