KE and MOMENTUM explained

[Sam Spade]

Thought this might be of some help, Jo jo to start.

Hopefully this post will clear the waters...

These 3 bows were delivered to me back in 2004 to celebrate Tradgang's 1st Anniversary. I have been hunting with the 60 & 70#ers ever since, and Rob has been hunting with the 50#er since then till about 2 years ago when he sent it to me so I could use it in my golden years. (not there yet  )

So, all made at the same time, by the same bowyer, all the same model, all the same lengths, all the same materials, all the same draw lengths.  All also use the same arrow, weight was increased for the 60#er by adding aquarium tubing and head weight change, and the 70#er with weed eater line inside the aquarium tubing and different head weight. All arrow weights were right at 9.5 grains per #, and arrow speed was right at 185-187FPS with all 3 bows. Although the speed might be relevant to the hunter, it is irrelevant in the test as long as all 3 are very close to the same, as well as arrow speed.

Here are the numbers I ran on them back then..... Kinetic Energy and Momentum.


50# - KE = 37.99 - MO = .411
                                                 
60# - KE = 45.59 - MO = .493 

Difference in Percentages - KE = 27.795 % - MO = 19%

This is a very significant increase of power in the two bows.

*************************************************************

50# - KE = 37.99 - MO = .411
                                                 
70# - KE = 53.19 - MO = .575

Difference in Percentages  - KE = 55.804 % - MO - 39.903 %

This is a HUGE increase in the power of the two bows. 

Momentum is really the most important number, and its right at a 40% Increase.

So, if the OP old_goat2 went from 45# limbs to 65# limbs, he would expect very close to those same percentages in increase of power.

 

[Wudstix]

So is KE a better measure or MO?
 

[Sam Spade]

Momentum.   

[Wudstix]

Explain.  Kinetic Energy is the kind of energy an object has because it's in motion.  Momentum is the quantity of motion of a moving body, measured as a product of its mass and velocity.  Explain the difference.
 

[GCook]

Thirty years ago the accepted answer was just the opposite of what it is today. 
The math and physics has not changed.  Just the fad.

[string bean]

I must have missed something.  All I'm seeing is that the 70lb bow cast a 9.5gr/lb arrow just as fast as the 60lb can cast a 9.5gr/lb arrow.  Same with the 50lb bow.  Just seems pretty obvious which one will have the most power.

If you had two arrows of unequal mass and their momentum works out the same because of their speeds, which one has the better penetration?

[Flbowhunter]

In my physics class we learned that the change in momentum is equal to the net force, so a bigger net force over the same time period requires a larger change in momentum. What this means is that a larger external force is needed to slow the object with more momentum down. Since a given animal only has so much force to exert on the arrow, the object with more momentum should offer deeper penetration. Now you might be asking shouldn’t the arrow with a higher speed have a shorter period meaning less force would be exerted on the arrow? Well, yes theoretically it should, but at the speeds traditional bows operate I do not believe it has as big an impact as one might think. We are typically talking a difference of 20ish fps. I do not believe this would shorten the period dramatically enough for the arrow to have enough force exerted on it by the animal to cause the light arrow arrow to outperform the heavier one. Take this all with a grain of salt as it is coming as it comes from an understanding of physics based on a high school physics class, and I’m not ashamed to say I do not know everything. Just thought I’d add my 2 cents.

[Wudstix]

So the heavier arrow, that is going faster, penetrates better. 
 

[Flbowhunter]

It does not necessarily have to be faster wudstix, sorry if I made an error in my first post. In this case let’s say the lighter arrow is going 15 feet per second faster. That faster arrow will shorten the period during which the arrow is passing through the animal very slightly, which would lessen the amount of time the animal can exert force onto the arrow. But because the heavier arrow requires a larger force to slow it down the same amount, the heavier arrow should out penetrate the lighter one.

[Friend]

By definition, kinetic energy is the capacity to do work.  It is the TOTAL ENERGY of a body in motion.  By definition, kinetic energy is the capacity to do work.  It is the TOTAL ENERGY of a body in motion.  K.E. is nondirectional in nature. 
The kinetic energy of an arrow, by definition, is not a direct indicator of the penetration capability of the bow-arrow-broadhead combination.

 Momentum is a unidirectional force vector. Another of those basic laws of physics states that "in cases of collision, whether the bodies are elastic or inelastic, the momentum before collision is equal to the momentum after impact".  This means that momentum is the measure of how much energy, due solely to the weight and velocity of an arrow, must be transferred to whatever it impacts before the arrow comes to rest.  (Again, momentum alone will not fully predict the
. Arrow Mass- Greater mass increases bow efficiency, absorbing more of the bow’s energy when fired. That means more arrow force.
- Arrow’s tissue penetration is directly proportional to its momentum.

Momentum is a far better predictor and much more correct in its application to arrow penetration lethality.

For an extreme illustration of the differences in the effect of impact overwhelmingly due to  he vast differences in mass. Being struck by a ping pong ball traveling 100 mph vs. being struck by a train traveling 5 mph. Give me the ping pong ball.

[Terry Green]

Thanks Scott.... I would have explained but I've been busy. 

[Terry Green]

So the heavier arrow, that is going faster, penetrates better. 
 

Yes. And the heavier arrow at the same speed as a lighter arrow also.

That's not even all physics either; it's common sense as well. 

[Bamboozle]

Yeah, thanks Friend.  Maybe now some will actually get it.

[Wudstix]

TG and Scott;
Thanks, I always get lost in the physics explanation, and sometimes fall asleep.  I always think about a ping pong ball and a golf ball, both pretty much the same size.  I'll take a ping pong ball at 30 mph over a golf ball at the same speed.
 

[Bamboozle]

Yup, I figured as much, some people are just not going to accept reality. 

[GCook]

But that is the lie that makes all the smart math just a bunch of BS. 
The golf ball and ping pong ball will not be going the same speed if driven with an equal force. 
Real tests with real arrows out of real bows prove the difference in energy does not necessarily translate into better penetration or lethality.  Especially at longer ranges. 
What it also shows is that the small percentage increase in penetration potential is seldom worth the significant trajectory loss down range.
Now most of us the longer ranges won't matter.  But most of us will never really benefit from shooting more than 12gpp or over 20% foc.  With 10 to 12 gpp giving the best balance in trajectory and penetration.

[Terry Green]

In the numbers I posted you can take the bow weights out of the equation as they are really irrelevant... the other numbers have no clue what the bows weigh are.

[Jim Jackson]

I'll take a ping pong ball at 30 mph over a golf ball at the same speed.
 

HUH‽????

[Trenton G.]

Jim, what he's saying is that a ping pong ball moving at 30 mph is going to hurt a whole heck of a lot less than a golf ball moving at 30 mph as the golf ball has a much higher mass and will hit significantly harder than the ping pong ball.

Also just because I want to dive into these numbers a bit more, what unit is momentum given in in the first post?

[Terry Green]

Trent...

500, 600, and 700 grains.... all moving at 185 fps.