rhustek

Texas,

First let me give you a link to PSE's website where they have all of these calculations done already for you.

http://www.pse-archery.com/ - scroll all the way to the bottom of the page, lower right, there are speed, Kinetic energy, and momentumtables

Now, let me give you a physics breakdown of how to calculate your kinetic energy(KE) and momentum(P) so that you can completely understand it. The problem with using these physics formulas is that your units have to match, meaning you cannot just simply put your arrow weight in grains and use your velocity in ft/s to come out with an answer. The units for kinetic energy are kg*m^2/s^2 = Joule = N*m from these you can convert to ft*lbs or whatever you like. Therefore you need to first start by converting your arrow weight to kg's and your ft/s to m/s. I found this the easiest when converting later to ft*lbs etc. You can convert them however you like as long as the units match. The key to finding a heavier arrow with more kinetic energy than a lighter arrow is to make sure that your bow can get the SPEED or VELOCITY required to get the extra energy, vice versa with the lighter arrow having to be at a much greater speed. The amount of KE you get out of your bow will be a % lower then the amount of potential energy it is capable of. This efficiency will be in the 90's for sure.

Here is a formulated breakdown of the above example:

KE = 1/2*m*v^2P = m*v(v=P/m, simply solved equation for v)KE = (P^2)/(2*m) (plugged momentum equation into KE)

KE = kinetic energy
P = momentum
m = mass (for my examples in kg)
v = velocity (for my examples in m/s)

Now a 350 grain arrow = 0.022679kg and a 550 grain arrow = 0.0356394kg
1ft/s = 0.3048m/s

First the compound bow and 350 grain arrow at 300 ft/s:

KE = .5*0.022679kg*(300*0.3048)^2 = 94.813 kg*m^2/s^2 = N*m = 69.930 ft*lb

Now the 550 grain arrow at 200 ft/s:

KE = .5*0.035639kg*(200*0.3048)^2 = 66.219 kg*m^2/s^2 = N*m = 48.841 ft*lb

If you simply convert your arrow weight from grains to lbs and then multiply it by your speed in ft/s you get your momentum in ft*lbs/s.

Again using the above example:

350grains = 0.0500 lbs
P = 0.05*300 = 15 ft*lbs/s

550 grains = 0.078571 lbs
P = 0.0786*200 = 15.72 ft*lbs/s

As stated the 550 grain arrow has a slightly higher momentum but much less kinetic energy. For arguments sake, without shooting them into a target and taking pictures I do NOT know which would penetrate the target further.

Now this topic is still a very highly debated subject all over the physics forums, the problem is which factor contributes the most to penetration and which is better, having your arrow stick in the deer and makeit stumble or just have your arrow pass right through it. In my opinion most deer are killed by bleeding out rather than just blunt force and knocking them down. With that said I would rather have an arrow combination that would send my arrow right through the deer as then their would be two holes to bleed out of instead of one, some will disagree.

Penetration requires work to be done in order to move the arrow into the target. That being said which of the two is a measurement of work? The answer is kinetic energy. This does not however state which of the two principles is more important when hunting. The two compliment each other, the truth is that you need to play with your setup to find the best balance and penetration.

I am one of those 3D CLOWNS and I do find the speed side of archery interesting, not because of hunting but because of accuracy and error in distance judgement. If I can get the same KE or close with a lighter arrow and higher speed then I am going to do it everytime, why? Because when I'm out hunting, a difference of 5 yds might mean the difference between a miss or a kill with a slower bow, that error is corrected with a faster one.

I can talk more about this subject but I believe the point has been made. What do you want when you are hunting? Would you rather try to knock the deer down because you have so much momentum or would you rather just have the arrow pass through it and let it bleed to death.

The last formula that I put in this post is the relationship that Momentum has to kenetic energy:

KE = (P^2)/(2*m) This is in fact where the truth lies, that kinetic energy is directly proportional to momentum(P) (as P increases so does KE) and inverstly proportional to mass(m) (as mass increases KE decreases).

The answer is somewhere in the middle and really comparing Momentum to Kinetic Energy is like comparing apples to oranges, they both taste good so take one of each!

SwampCollie

And if you will read mine... maybe you'll clue in about the SEARCH function.


For what its worth... the forumula for Momentum is simply mass x velocity. Its a big huge number... and its much easier to remember numbers between 0 and 100 as used with the KE formula that it is the results you'll have with momentum. The only use of it really is to see how mass and speed relate to each other, and how, generally, your arrows energy will change if you increase one or the other.

rhustek

Technically I gave him the technical formulas and examples so that Texas can compute his KE and P just like a Technician

Arthur P

KE is NOT directly proportional to momentum. KE does NOT decrease with an increase in mass.

If what you said were true, and KE is directly proportional to momentum, the 550 gn arrow in the example would have to have a very similar KE value as the 350 gn arrow because the P values are similar. But, in fact, it's KE value is significantly lower. 31% lower in fact.

It is also generally known that when shooting a light arrow and a relatively heavier arrow from the same bow at the same draw weight, the heavier arrow, even though traveling slower, carries slightly MORE KE because it absorbs more energy from the bow than the light one does - except in rare cases.

In my example, the two arrows are not shot from the same bow because the KE values are widely divergent. However, the heavier arrow is capable of doing a similar amount of work with a much lower KE value simply because it has a similar amount of momentum on it's side. Shoot both arrows from the same bow at the same draw weight and the heavier arrow will most likely have only 1-2 ft lbs more KE, but it's momentum figure will be substantially higher. Therefore it's penetration potential will be substantially better, all other things remaining equal.

It may not be technically correct to say, but the way I think it's easiest to understand it this way: KE is the capacity for doing work, but momentum is the deciding factor in determining how that capacity is used to do the work. They are complimentary values. Each has the thing the other needs to get the job done.

KE is the capacity for doing work. It's a quantitive value with no directional preference. Momentum is how that capacity is used over time, in a specific direction. It is your vector value. Those are the two things that work together to power that arrow through the air to the animal and then through the vitals. They are two sides of the same coin. It's how you choose your arrow weight that determines how much momentum you get. KE will remain relatively constant for a given bow.

The key thing to take from this is that if you have lower KE, like with a traditional bow, light draw weight, short power stroke, older and less efficient bow, and/or if you hunt larger, tougher animals and need more penetration, you can achieve the needed results by going to a heavier arrow and working up the momentum side. If you've got enough KE to blow a toilet plunger through an Abrams tank - many high performance 70 lb compounds these days are putting out more energy than bowhunters used to use for hunting elephants! - then you can fudge down on weight and momentum in interest of gaining speed and still get the job done. (How many times have I posted that before in these dead horse beatings? )

It's a trade-off. Add weight for more momentum and better penetration but lose some speed. Reduce weight for more speed and flatter trajectory but sacrifice momentum.

I take the momentum over speed for two reasons. I want all the penetration potential I can get and still retain a reasonable arrow speed and trajectory. No such thing as overkill on penetration, in my book. Second, when I misjudge yardage, I almost always go long. Flatter trajectory would just have me shooting higher over the critter's back.[&:]

Actually, I refuse to poke an arrow at game beyond 30 yards anyway, really prefer to get within 20. Getting close and not taking hero shots really cuts down on the error factor all by itself.

TexasBowHunter

Say Richard!!!!!! I did try the search and came up with nothing but thanks for your input....It is duly noted.

Arthur P

Search function here sucks. I never get any results at all when I've tried to use it. It's been that way for years.

TexasBowHunter

I agree 100%, I have tried it several times with zero luck.

JimPic

This is true but these measurements are calculated right off the rest.What will the lighter arrow do at say 30yds or 40yds? It'll lose more energy than the heavier shaft.That's plain physics and physics doesn't lie.

KE is a value for an object in motion hitting another object--that's all it is.Momentum is a value of an object hitting another object and remaining in motion after it hits

bowdaddy1964

Can't we all get along? Now who needs a hug? ? ? ? Anyone? Anyone? ..Crud...........

treboryerf

WOW! I never knew what I was getting into with all these equations,you guys are taking all the fun out of it.I'm going to work!