tag:blogger.com,1999:blog-3092603842974378319.post4280936021912790383..comments2024-01-24T11:36:17.328-08:00Comments on Explore: Beneath & Beyond: On Archery II: LongbowsJoe Nuttallhttp://www.blogger.com/profile/02395295081337987607noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-3092603842974378319.post-86502687595947695052015-08-30T02:23:37.876-07:002015-08-30T02:23:37.876-07:00Thanks Leland - sorry for the late reply - I was o...Thanks Leland - sorry for the late reply - I was on holiday with no internet access.<br />Your calculations work, assuming 100% efficiency (all potential energy is converted to kinetic energy). However they imply that the lighter you make the arrow the faster it will shoot, so (as you said) you have to make assumptions about the weight of the arrow for giants.<br /><br />When scaling up you assume 4* mass and 4* draw force; I went with 6* mass but also invoked the lever principle to mean the draw force only increased to be 3*. Plugged into your equations this gives the same result - a constant velocity.<br /><br />We'll always have to make assumptions about how much weight a giant can lift (unless you happen to know one) but if have a consistent set of principles then we're less likely to end up with nonsensical results.<br /><br />As an aside note that the difference between the effectiveness of the different size bows is due to the difference in kinetic energy, not the difference in momentum. During the impact, momentum is conserved (pushing the target backwards) but most of the energy is lost, which is what causes the damage. If you ever find someone's throwing rocks at you, remember to ask them to double the mass of the rock, but halve the velocity.<br />Joe Nuttallhttps://www.blogger.com/profile/02395295081337987607noreply@blogger.comtag:blogger.com,1999:blog-3092603842974378319.post-24229451950611991872015-08-22T08:33:09.956-07:002015-08-22T08:33:09.956-07:00I've found some of my notes, so let's see ...I've found some of my notes, so let's see if I can reconstruct the thinking. I started by looking for the "muzzle velocity" of an arrow fired from a bow with a given draw weight.<br /><br />I assumed an arrow of mass 50g, with an 0.7m (28") draw distance. Somewhere or other [citation needed] I read that the velocity of an arrow in m/s is approximately 8 * sqrt(bow draw weight in pounds). <br /><br />The work done on the arrow by the bow (the imparted KE) is 1/2 * Kx^2 where x is the draw distance in meters and K is the force applied by the bow at full draw (treating the bow as a spring, K is the spring constant). If we set this KE equal to the KE of the arrow in flight (= 1/2 * mv^2) we solve for v and get:<br /><br />v^2 = Kx^2/m<br /><br />But K = D / x (from the spring equation, F = Kx, F = D = draw force at full draw) so<br /><br />v^2 = Dx/m, v = sqrt (Dx/m)<br /><br />where D = draw force in Newtons, x = draw distance in meters, m = projectile mass in kg.<br /><br />For our arrow, v = sqrt (222.5 * 0.7 / 0.05) = 56 m/s. This appears generally consistent with your data above. [And it matches the V = 8 x sqrt (draw weight in pounds) equation I referenced earlier, for whatever that's worth.]<br /><br />Then I wondered about a large creature, a giant or ogre or something, twice as tall as a man. The draw distance is doubled. I assumed the projectile mass increases by 4x (we double the length, but only scale up the thickness some). I guesstimate that the draw force/weight of the bow is doubled as well. The arrow masses 0.2 kg with a 1.4m draw distance and a draw force of 445N; the initial velocity works out to be ... 56 m/s again.<br /><br />A small creature, half the size of a man, halves the draw force and length, and quarters the arrow mass, and once again we get the same initial velocity. I found this interesting initially, but it's not actually that surprising since it stems from my assumptions about how to scale the draw weight and arrow mass. Of course, there's a big difference in projectile momentum, and that would significantly impact (heh) effectiveness as a weapon. This also implies that there are more effective arrow weights for larger or smaller bows (which would have different initial velocities).<br /><br />Hmm, now I'm going to have to think about this some more...Leland J. Tankersleyhttps://www.blogger.com/profile/17257381741308085613noreply@blogger.comtag:blogger.com,1999:blog-3092603842974378319.post-73931827417933406932015-08-19T04:12:52.982-07:002015-08-19T04:12:52.982-07:00I'd be interested to hear what your methodolog...I'd be interested to hear what your methodology and conclusions were. For firing at long range dispersed targets my thoughts on this need some diagrams, and will probably have to require a simulation, so I'll put them into a separate post. In brief when at short range you can only hit the front rank, whereas at long range the arrows coming down at not as steep an angle as you might think so people are say half as big a target, but you can also now hit the back ranks. So what's of interest is the vertical arc for launching arrows between the foot of the front rank compared to the heads of the back rank, and what proportion in between is target. Joe Nuttallhttps://www.blogger.com/profile/02395295081337987607noreply@blogger.comtag:blogger.com,1999:blog-3092603842974378319.post-75235019041070316372015-08-18T08:48:00.728-07:002015-08-18T08:48:00.728-07:00This is interesting stuff (to me, at least). I di...This is interesting stuff (to me, at least). I did some math calculations about a year ago on this topic, and I think I came to similar conclusions but from a different methodology, which is encouraging. I'm on vacation and don't have my notes handy; maybe next week I'll review. I've been meaning to comment on your prior Archery post also but never had both the inclination and the time at the same moment. The gist was that I think that firing at long range at large, somewhat dispersed targets (such as firing at a large enemy formation) is maybe somewhat less likely to succeed than you calculate because of the effects of plunging fire and the different grazing angle. At close range with a flat trajectory, shooting at a mass target is like shooting at a really wide person - the target area is like a rectangle about 6' high and however many files wide. But at long range, the angle of the incoming projectile means that the target cross-section of each individual is reduced; I think that would be sufficient to reduce the effective target area enough to warrant an additional penalty.Leland J. Tankersleyhttps://www.blogger.com/profile/17257381741308085613noreply@blogger.com