Can someone check my math???

warden415 · July 20, 2014, 11:58:00 PM

I just finished up building a new bow and am shooting and tuning it now. It is a 58" 48@25" which is what I draw or slightly under. I could tell it was a bit quicker than my other bows but just thought it was because of the extra few pounds draw over the other ones. I shot a 529 grain arrow at an average of 166 fps. That arrow worked out to be 11.02 gn/lb
I was trying to calculate a 10 gn/lb and a 9 gn/lb arrow
The way I calculated was 166 ÷ 11.02 which is 15.06 fps for each grain per pound?
So dropping to 10 gn/lb I should jump from 166 fps to 181
If I drop to 9 gn/lb I would add another 15 fps and be at 196 fps?
If I did this correct I am pleasantly surprised. Getting 196 fps at 9 gn/lb. And only a 25" draw.

Pheonixarcher · July 21, 2014, 12:03:00 AM

Unfortunately, I don't think it works that way. I could be wrong. Best thing to do is test it for yourself. Also, are you sure that your chrono is reading correctly. Try to shoot through a different one and see if you get the same results. If you do, you have a very fast bow for that draw weight/length.

AnAvidArcher · July 21, 2014, 01:40:00 AM

You're only partially correct. The issue is that while a lesser weight arrow takes less energy to propel forward at a faster speed, because of the reduced mass things like wind friction, shelf friction etc will have a greater effect on it because less mass=less inertia; Also, the arrow can only go as fast the limbs are traveling forwards, and the fastest possible limb travel would occur if you dry-fired your bow, which of course you do not want to do.

A similar, albeit not totally the same, example to think of would be that lets say a given arrow drops 1 inch at 10 yards, 2.5 inches at 20 yards, 6 inches at 30 yards, and 20 inches at 40 yards. If you were to plot these data points on a graph you would find the data is not linear but rather exponential, as the arrow is continuously slowing down due to air resistance at the same time it is being pulled towards to Earth due to gravity.

wingnut · July 21, 2014, 08:14:00 AM

By my calculation you could expect 184 fps @ 9 gpp.

Pretty dang quick for 26 inch draw.

Mike

2fletch · July 21, 2014, 08:49:00 AM

Sounds like everyone has a different angle, but then there are lots of factors. AnAvidArcher pointed out that the drop of an arrow is exponential rather than linear. That's because of the acceleration of gravity acting on the arrow. With air resistance slowing the arrow,it's surprising to see the graph showing the actual rate of fall. The forward motion of the arrow is decreasing while the downward speed is actually accelerating. The formula for the amount of drop (disregarding air resistance) is the time that the arrow is in the air squared x 32 feet divided by 2.

I'll take Wingnut's results. Those numbers look close.

Fletcher · July 21, 2014, 10:34:00 AM

When a bow is shot it is not moving just the arrow. You also have to figure in the weight of the limbs, string, etc. The arrow is just fraction of the total mass that must be accelerated.

warden415 · July 21, 2014, 11:11:00 AM

Thanks for everyone's input. No matter what it is I am happy with this bow. I will try and put up a new thread with a few pics. All bocote riser with glass and phenolic stripes. Bamboo cores with some great bocote limbs from Idaho curt

alex321 · July 21, 2014, 02:01:00 PM

QuoteOriginally posted by warden415:
I just finished up building a new bow and am shooting and tuning it now. It is a 58" 48@25" which is what I draw or slightly under. I could tell it was a bit quicker than my other bows but just thought it was because of the extra few pounds draw over the other ones. I shot a 529 grain arrow at an average of 166 fps. That arrow worked out to be 11.02 gn/lb
I was trying to calculate a 10 gn/lb and a 9 gn/lb arrow
The way I calculated was 166 ÷ 11.02 which is 15.06 fps for each grain per pound?
So dropping to 10 gn/lb I should jump from 166 fps to 181
If I drop to 9 gn/lb I would add another 15 fps and be at 196 fps?
If I did this correct I am pleasantly surprised. Getting 196 fps at 9 gn/lb. And only a 25" draw.

What are your units? gn/lb... If "gn" is a weight then you have a dimesionless quantity... It might still be useful, but I don't uderstand where it is coming from...How have you calculated it?
Cheers
Alex

July 21, 2014, 02:22:00 PM

As arrow weight drops, so does the limbs efficiency. However, that drop in limb efficiency is different for every bow.

lt-m-grow · July 21, 2014, 02:31:00 PM

Fun conversation...enjoyed reading this one.