[Morningstar]

Is there a generally accepted number for how many FPS you loose/gain for a certain amount of grains (say 25 grains)? I realize it is precisely dependant on the energy of the bow, but I'm just looking for a general answer for bows between 50 - 60lbs @ 28".

Also, what would be a general amount of FPS gained per pound of draw weight?

Nit picky in Iowa

 

[Wingman]

Assuming the bow efficiency doesn't change (which it will some...), the ratio of the velocities will be equal to the sqrt of (1/mass ratio). So for example:

If you have a bow shooting a 500g arrow 180 fps, the speed with 400g should be about 180*sqrt(500/400) = 200 fps

Ken

 

[Wingman]

Using ncsturkey's numbers for two bows (or sets of limbs) from the momentum thread (and shown below) here's a update to the above formula that accounts better for bow efficiency. Rather than just using the weight of the two arrows, the results work better if you add a fixed "virtual" mass to account for the mass of the bow that gets accelerated along with the arrow. Using ncsturkey's numbers, it looks like 200gr's is about right and easy to remember (you could calculate something more exact for a specific bow if you cared to and had measurements for two arrows). So for example using his first bow, if 640grs goes 179fps,

616gr, 179*sqrt((640+200)/(538+200))= 182fps estimated
538gr, = 191fps estimated
480gr, = 199fps estimated
366gr, = 218fpsestimated

2nd bow:
640 = 178 measured
575 = 185 estimated
403 = 210 estimated
338 = 222 estimated
(bow 2 would be better modeled with a higher virtual mass, about 275grs)

________________________________________________
ncsturkey's measured data:

limb# grains FPS KE# gr/# MO
Bow Number 1

54 DASX 640 179 45.5 11.9 0.51
54 DASX 616 181 44.8 11.4 0.50
54 DASX 538 190 43.1 10.0 0.45
54 DASX 480 200 42.6 8.9 0.43
54 DASX 366 222 40.0 6.8 0.36

Bow Number 2

57 DAS 640 178 45.0 11.2 0.51
57 DAS 575 182 42.3 10.1 0.46
57 DAS 403 207 38.3 7.1 0.37
57 DAS 338 215 34.7 5.9 0.32

 

[ncsturkey]

Looks as if the theoritical estimate was pretty accurate. There were actually two different bows and bow #2 has a higher mass weight than #1

I've never weighed to get the actual difference but #2 has added riser weight a heavier stabilizer and the actual riser might be a bit heavier Rod

 

[Quadrafletch]

One assumption these formulas seem to make is that the lighter and heavier arrows are both equal in their ability to store energy from the bow. Experience, however, shows that heavier arrows absorb more energy from the bow than lighter ones. Thus, the difference between the arrows may not be so great as estimated. Only one way to find out!

 

[Wingman]

One assumption these formulas seem to make is that the lighter and heavier arrows are both equal in their ability to store energy from the bow.

Quadrafletch--the updated formula with the "virtual mass" term tries to account for this effect. The virtual mass represents the energy absorbed by the string and the limbs that isn't available to the arrow. Because this term is independent of the arrow weight, it is proporationally more for a light arrow.

Its not going to be a perfect prediction, but it'll give you a good idea what to expect.

Ken