Recurve Bow Draw Force
As an archer, I was interested in the physics behind shooting my recurve bow, and therefore designed an experiment to examine the force involved with drawing my bow. My bow claims to be a 40lb bow, meaning that as the string snaps forward upon firing it, the arrow travels with 40lbs of force. Yet in my experience, drawing the bow seems much easier than lifting up a 40lb weight. I supposed that this was perhaps due to the construction of the limbs of the bow, and the transfer of the force from the large string to the thin arrow. So I designed a bow draw experiment as an attempt to see if the lbs of draw force were equal to the amount printed on the bow. I used the hooked attachment on the dual range force meter in place of my hand to draw the bow at an even pace to my full draw length. I repeated this several times to make sure my draw speed was even and that the force meter seemed to be correctly calibrated.
Description: Example of un-strung bow (for safety) and Dual Range force meter.
Figure 1. Raw Data From Dual-Range Force Meter
Figure 2. Approximation of force required to pull back bow a certain amount of distance
My results show that the force it takes to draw the bow the full 25in to firing position only actually takes 13.65lbs of force. As I pull the bow back, it gets exponentially harder to pull back until it is at its maximum extent, where it levels out for the duration of the test. This was always the same under repeated tests, and the graphs for pulling the bow back 5in, 10in, 15in, 20in, and 25in level off where I have indicated in figure 2. at 1.54lbs, 3.10lbs, 4.96lbs, 9.01lbs, and 13.65lbs, respectively.
This demonstrates that the bow is easier to pull back than the 40lbs it has printed on the limbs, and must be measuring some other statistic, even though it is called the draw weight. They seem to follow what I predicted based on feeling. Drawing a bow is not easy, but most people can do it, and you only use one hand to do so. In the same way, it seems to be much harder for most people to lift a 40lb weight, which is theoretically applying the same amount of stress to the arm, and takes the same amount of strength to lift. Observing this, it seems much more likely that it takes around 14lbs of force to pull back, which is much more doable.
My experiment taught me about using the Logger Pro software in conjunction with a force meter to examine force over time or distance. Both of these are concepts that could be used as part of the data necessary to calculate how fast the arrow it fires might travel, as well as how far the arrow will go. The science I used is directly related to energy, specifically the potential energy stored by the limbs in the bow. On top of this, my tests gave a more useful statistic on whether or not a person could actually pull back a bow or not, and while 40lbs of draw weight sounds like it would be quite difficult, 14lbs is more accurate to what actually goes on and gives people a more reasonable knowledge of whether they’ll be able to do it.
If I had to do this project again, I would possibly check with multiple force meters to make sure they were all calibrated correctly and that none of the data comes from a broken meter. I would also get some help to pull back the bow, as it would be easier to maintain a constant draw at any of the intervals shorter than maximum draw. I would also make sure my Logger Pro software was more cooperative with PC systems, as it took quite a lot of time to get it running.
If i could continue for another six weeks, I would measure the force transferred from the bow into the arrow, how much energy was lost to heat, and see if I could predict how far an arrow would go based on the weight of the draw. The speed of the arrow could then also be measured with a high speed camera and measuring equipment.