A good explanation of momentum

[snag]

"Once an arrow leaves the string, the mass of the arrow continues to have a significant effect beyond the initial velocity. As good ol’ Sir Isaac Newton taught us, F=ma (Force=mass*acceleration). In archery terms, this simple equation states that the force slowing the arrow down (mainly air resistance) is proportional to the mass of the arrow and how quickly it decelerates. The greater the mass, the more force it takes to slow the arrow down. Considering two arrows of equal outside dimensions, including the point and vanes, but of different masses, the arrow with greater mass will take more force to slow it down. Because the two arrows have the same frontal profile, the air resistance will be the same and thus the lighter arrow will be subject to a greater deceleration. Of course the lighter arrow will begin at a higher velocity, but the heavier arrow will lose less of its initial energy downrange. Knowing that a heavier arrow will always have a higher kinetic energy and momentum to begin with, and knowing that it will also decelerate at a slower rate downrange, it becomes obvious that a heavier arrow will not only begin with more energy and momentum, but will retain a higher percentage of its energy and momentum downrange."

Here's where I found this along with some momentum and kinetic energy calculators------
 http://archeryreport.com/2009/11/arrow-kinetic-energy-momentum-archer/

[ChrisM]

Yep thats why for long range rifle shots you want a heavier bullet to retain velocity and energy.  I think its called balistic coeficient.  Compound guys like to use KE because you square the velocity and an increase of speed greatly effects the results in the formula.  But KE does not tell you how much energy it will retain when it meets resistance,  which is how you get a 330 fps arrow that only penetrates about 6 inches and a 170 fps arrow that sticks in the tree past the animal.    

[McDave]

I know that tests have shown that momentum is more important than kinetic energy in determining the penetration of an arrow.  Thus we are told that a heavier broadhead makes for a better hunting arrow, as long as velocity is not decreased below the point where we can make an accurate shot.

Are there situations where kinetic energy is more important than momentum, for example, in determining the flatness of trajectory in target shooting?

[Nathan Killen]

Great explination snag !  

[Ragnarok Forge]

Nicely done snag.  KE is a single point in time snapshot.   Trajectory is calculated using a different equation as well.

[Red Tailed Hawk]

Well put

[Keefer]

If it makes a hole going in and a bigger one coming out and the animal is graveyard dead within a few yards from where I shot it then I'm happy! That's my redneck Logic so to speak    :D

[Plumber]

Iam with ya keefer.I was not all that great at science but I can kill a deer!

[Sharpster]

Very cool post Snag,

I constantly have to try to inform (re-educate)wheelie bow guys who live and die by speed and KE that without including mass into the equation, speed and KE are virtually useless! Thanks for the great explanation. I'll be keeping a copy of that one for future reference,

Ron

[Keefer]

PLUMBER,
  We know Hot's on the left, cold is on the right and you know what don't run up hill...I never understood science to much but I do appreciate Snag trying to explain it to us...

[JimB]

If you like this stuff,check out this article from Tuffhead's site.Also at the bottom of that page are links to 3 more articles.The one from African Bowhunter is particularly interesting.He shows a chart for some KE numbers recommended for various African game and gives his own momentum number recommendations for the same animals.
 http://tuffhead.com/education/formulas_momentum.html

[snag]

Thanks JimB, I'll check it out.

[smokin feathers]

(I constantly have to try to inform (re-educate)wheelie bow guys who live and die by speed and KE that without including mass into the equation, speed and KE are virtually useless! Thanks for the great explanation)

not exactly true, i beilieve in momentum and heavy arrows especially in low poundage bows. But speed also plays a part as any time you can get more speed with the same weight arrow you are doing even better. I have  a 61 lb d style bow that shoots a 656gr arrow at 156fps, and my morrison shawnee 50lb bow shoots that same arrow 168fps so velocity helps for sure. As any extra speed you give the same weight arrow the harder it will hit. Also i have set up one bow here in my shop that shot 600gr arrows at 314fps at 70lbs. Speed and KE play a part for sure in this instance, cape buff was no match for it

[Margly]

Very good:)

[Sharpster]

Originally posted by smokin feathers:
(I constantly have to try to inform (re-educate)wheelie bow guys who live and die by speed and KE that without including mass into the equation, speed and KE are virtually useless! Thanks for the great explanation)

not exactly true, i beilieve in momentum and heavy arrows especially in low poundage bows. But speed also plays a part as any time you can get more speed with the same weight arrow you are doing even better. I have  a 61 lb d style bow that shoots a 656gr arrow at 156fps, and my morrison shawnee 50lb bow shoots that same arrow 168fps so velocity helps for sure. As any extra speed you give the same weight arrow the harder it will hit. Also i have set up one bow here in my shop that shot 600gr arrows at 314fps at 70lbs. Speed and KE play a part for sure in this instance, cape buff was no match for it

Agreed.    The point I was trying to make is that all 3 variables (speed, KE, and mass) have influential roles in the total equation/outcome. And all I hear mentioned is speed and KE, speed and KE. Have to think about mass too,

Ron

[snag]

Originally posted by Sharpster:
 

Originally posted by smokin feathers:
(I constantly have to try to inform (re-educate)wheelie bow guys who live and die by speed and KE that without including mass into the equation, speed and KE are virtually useless! Thanks for the great explanation)

not exactly true, i beilieve in momentum and heavy arrows especially in low poundage bows. But speed also plays a part as any time you can get more speed with the same weight arrow you are doing even better. I have  a 61 lb d style bow that shoots a 656gr arrow at 156fps, and my morrison shawnee 50lb bow shoots that same arrow 168fps so velocity helps for sure. As any extra speed you give the same weight arrow the harder it will hit. Also i have set up one bow here in my shop that shot 600gr arrows at 314fps at 70lbs. Speed and KE play a part for sure in this instance, cape buff was no match for it

Agreed.     The point I was trying to make is that all 3 variables (speed, KE, and mass) have influential roles in the total equation/outcome. And all I hear mentioned is speed and KE, speed and KE. Have to think about mass too,

Ron [/b]

Exactly Ron! There is an industry that is selling speed only.

[smokin feathers]

dead on the money there Ron!! you get all 3 and you have something to recon with.LOL!! just seems that some think speed is bad, but add speed to heavy arrow and you have a flatter shooting harder hitting rig.

i sell a lot of axis arrows by showing customers how a small diameter, heavier arrow will out penetrate a lighter bigger shaft and not loose that much speed in the process, 280 fps with a 450gr arrow trumps a 320fps 310gr arrow and the trajectory at average hunting distances are really no different but the penetration is!!

[Wary Buck]

Could an analogy to Snag's original post be as follows:

Take a couple of trains heading up by a couple Union Pacific locomotives with 100 coal cars behind that are moving 60mph.  One train is full of coal and the other is empty (lighter) but still has the same outside dimensions.  Have both apply the brakes or run into some resistance or just switch off the ignition, and tell me which one would take the longest to grind to a halt.

Kind of the same thinking I believe.

[BobCo 1965]

Originally posted by McDave:

Are there situations where kinetic energy is more important than momentum, for example, in determining the flatness of trajectory in target shooting?

I think it would depend on the distances and whether the distances are marked or not. For Olympic Style Recurve out to 90 meters (@100 yards) the best case scenario is to have the heaviest skinniest arrow that you can find that will reach the distance and still be within the site window of your riser (unfortunately these arrows are usually over $400 a dozen, if you use tungsten points add another $200-$250). This would mainly be to keep the arrow straight in wind. Fletching drag and potential parachuting also comes into play at those long distances. So in short for this style, yes, I believe momentum is more important then KE.

[7 Lakes]

The heaviest Pinewood Derby car wins, everything else being equal.  The lightest ones take the lead but just can't maintain it over the long run.