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wintellect

How fast are my arrows?

For quite a while I've been curious to know how fast my arrows travel (in either "feet per second" or "meters per second").  Is there an equation that will allow me to roughly calculate this? Some basics I know are:

limb poundage:    36lbs
Draw length:       28.5 inches
Arrow weight:     need to weigh it (should this be grams?)

I'd really appreciate any help  
Mjollnir

The two equations I can imidiately think of tho help you solve this are

  • F=ma (F=Force in Newtons, m=mass in Grams, a=acceleration in metres per sec squared)

and

  • V=u+at (V = Velocity in Meters per second, u= initial velocity, a = acceleration, t = time in seconds)


so an arrow is at it's fastest just after it leaves the bow, there is no more acceleration forces being applied, only air resistance slowing it down. So....

From the above we can deduce a=F/m and V=at (because initial speed is 0) Therefore, V=(Ft)/m

So now all you need is the Force in Newtons (weight of the draw, will need to be converted from lbs), the mass of the arrow in grams, beware arrows are usually weighed in grains so and figures you find will be in this metric. and time in seconds of the loose. This is the most difficult to get, but not impossible.

That is the best I can think of quickly, I hope it helps.

of course you could always buy a device for messuring arrow speed
Ratfighter

got beat to it
Mjollnir

Oh and another point, the equations listed above assume constant acceleration, which of course a bow does not provide, the force behind the arrow decreases as the string returns to normal position.

but that is the thing with mechanics, everything has to be assumed lol
wintellect

Ok, so tell me if my math is right...

Here are my known facts:
1 pound-force = 4.4482216 newton (or so a website told me  )
limb poundage = 36lbs
Draw length = 28.5 inches
Arrow weight = 22g
loose = 0.5 seconds (is this too short?)

Seeing as this is not exact I'll assume I'm pulling 36lbs and that my loose is 0.5 seconds. Following the math you provided, the formula:

V=(Ft)/m

works out as:

V =  ( (36 * 4.4482216 ) * 0.5 ) / 22

therefore:

V = 3.63     <---  Ok, my math must be bad somewhere because 3m a second seems bad

Where am I going wrong?
Ruthy

wintellect wrote:
Ok, so tell me if my math is right...

Here are my known facts:
1 pound-force = 4.4482216 newton (or so a website told me  )
limb poundage = 36lbs
Draw length = 28.5 inches
Arrow weight = 22g
loose = 0.5 seconds (is this too short?)

Seeing as this is not exact I'll assume I'm pulling 36lbs and that my loose is 0.5 seconds. Following the math you provided, the formula:

V=(Ft)/m

works out as:

V =  ( (36 * 4.4482216 ) * 0.5 ) / 22

therefore:

V = 3.63     <---  Ok, my math must be bad somewhere because 3m a second seems bad

Where am I going wrong?


wintellect

Wouldn't it be easier just to get them through a chrono??
It's the only way to do it if you want it to be accurate (without the headache   )
wintellect

Yep, I'm sure it would.

Unfortunately I don't know how to get access to one, and I'm pretty sure nobody in my club has one.
Steve B

This may be of some assistance to you in calculating your arrow speed, best I can come up with for you

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