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Author Topic: KE and MOMENTUM explained  (Read 3070 times)

Online Wudstix

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Re: KE and MOMENTUM explained
« Reply #20 on: January 26, 2022, 09:53:30 PM »
It helps to think of KE as potential and Momentum as motion.
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« Last Edit: March 02, 2022, 09:34:57 AM by Wudstix »
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Offline CIDCrazyJay

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Re: KE and MOMENTUM explained
« Reply #21 on: February 27, 2022, 05:31:18 PM »
I've compiled several charts that proved to be enlightening for myself, I thought y'all might like to see the info presented in this manner. I prefer graphs, as they often contain 10,000 words.

Data is a mix of about a dozen real world data points, two dozen reference points from other forum posts.
All data was approximated to 5lb increments, assuming 28" draw, filled in with more...math.

Your results will almost certainly vary, but these charts should prove useful for finding ballpark figures.

1: It's interesting to note, we can plot arrow velocity against grains per pound with somewhat reasonable precision.

2: Chart -2- shows additional data, which is presented here in simplified form. Momentum is read on the right hand side, Arrow Mass along the Bottom. And all other data is graphed together on the left. - (Note: If one were willing to shoot a really heavy arrow, sacrifice a significant amount of velocity, and therefore range, then a #20lb bow may very likely generate sufficient Momentum & Kinetic Energy for whitetail. As long as the yardage was sufficiently close, the arrow preferably traveling downward with gravity. Good info for a survival situation).

3: The Big Daddy Chart. Again, Momentum read on the Right, Arrow Mass along the Bottom, All other Data on the Left.

[Also Note: I chose to graph arrow velocities below 120 FPS for entertainment purposes only! I would consider 120FPS the baseline slowest usable arrow velocity, at that speed an arrow will only cover 20 Yds in a little over 0.5 seconds when accounting for drag. - This gives an equivalent arrow trajectory-drop to a Compound Bow shooting 50 Yds at 300 FPS].




Offline CIDCrazyJay

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Re: KE and MOMENTUM explained
« Reply #22 on: February 27, 2022, 11:44:24 PM »

Offline Terry Green

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Re: KE and MOMENTUM explained
« Reply #23 on: February 28, 2022, 08:40:54 AM »
Yeah Wud,

I couldn't care less about KE, but I ran those numbers years ago since I had the momentum data.  :campfire:
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Offline ALDO

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Re: KE and MOMENTUM explained
« Reply #24 on: February 28, 2022, 11:29:09 AM »
So what is the basic formula used to obtain the .411 result?
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Offline Terry Green

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Re: KE and MOMENTUM explained
« Reply #25 on: February 28, 2022, 12:05:48 PM »
ALDO, one formula is on the 1st post.

Now, what is the formula for the number 6? .... there's not just one....

1+5, 2+4, 3+3 all = 6.

 So you gotta run your numbers to find out where your at....  :campfire:
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Offline CIDCrazyJay

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Re: KE and MOMENTUM explained
« Reply #26 on: February 28, 2022, 04:19:29 PM »
So what is the basic formula used to obtain the .411 result?


Momentum Formula looks like this:

(Arrow Mass X Velocity) / (7000 X 32.17405)


Where Arrow Mass is in Grains
Velocity is in Feet per Second
- Because there are 7000 Grains in a Pound.
- Gravitational Constant is 32.17405.
Note: One Slug [Mass] = 32.17405 Pounds [Force].


Arrow Kinetic Energy Formula:

0.5 X (Arrow Mass X Velocity^2) / (7000 X 32.17405)


Hope this helps.

Offline ALDO

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Re: KE and MOMENTUM explained
« Reply #27 on: February 28, 2022, 04:29:44 PM »
Justin,  Thanks for the formula so my next question is what is a good Momentum result.  The example given in the first post puts the 50# bow at .411, is that good?  My set up produces a 570 gr arrow at 153 fps so a resulting Momentum of .387.  Is that good?  I know the arrow gets through most of the deer and hogs I have shot.  Just curious. 
Thanks
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Offline CIDCrazyJay

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Re: KE and MOMENTUM explained
« Reply #28 on: February 28, 2022, 09:05:22 PM »
Momentum is just a number. Arguably the most important one, yes. You can think of Momentum as a Budget. Some gets spent on air resistance, some on penetration of fur, hide, bone, etc. The more budget available the better.

Using the legal minimum in most states for deer as #40lb draw, and assuming 10 gpp arrow is 400gr traveling at say 180fps is just shy of 0.32 slugs.

If we take Fred Bear at his word that "#45 bow can take any animal in north america" with a well placed shot, assuming 10gpp again, 450gr at 180fps is 0.36 Slugs.

So, it would seem 0.32 is certainly adequate for whitetail. Around 0.36 for larger game such as Moose would probably be marginal at best. Round up to 0.4 slugs for Elk sized animals. Now Lets assume most people trad hunting brow bear are shooting at least #65Lb and 650gr, then we get a Momentum of 0.52 Slugs or more for tough or dangerous animals.

Taken to the extreme, One whole slug is a lot of force for anything that lives (on land). And it can be obtained with a heavy enough arrow based on the above charts.

Keep in mind, its only a momentum budget. A dull or damaged broadhead, additional blades, bone impacts, etc. are going to cost more than a super efficient arrow.

Also note that resistance to motion goes up at the square of speed. This includes air resistance and also flesh. Think about jumping into a lake from a boat, vs jumping into a lake from an airplane. They say water becomes like concrete at high velocities. This is resistance going up in a cubic relationship to speed. Animals and people are made up primarily of water, and arrows are traveling awfully fast. So, adding momentum and taking away speed helps on both ends of the penetration equasion.

Seeing all mammals are built with the same stuff, you don't actually need a very wide variation in momentum between an 80lb pig and an 800lb elk.




Offline Sam Spade

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Re: KE and MOMENTUM explained
« Reply #29 on: March 01, 2022, 07:04:27 AM »
How about non 80# hogs?  Check out the video and you will see what momentum is.  Momentum is way more than just a number, it's a very valuable measurement coefficient.  :campfire:

https://www.tradgang.com/tgsmf/index.php?topic=168282.msg2873449#msg2873449

Offline JamesD

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Re: KE and MOMENTUM explained
« Reply #30 on: March 01, 2022, 11:11:00 AM »
Upping the weight of your arrows above 10-12 GPP will also help lighter bows achieve penetration at a similar level as heavier bows that are shooting 10-12GPP.
Example. Fall of 2020 I hunted with 54# @ 30.5", shooting 615 - 635 grain (wood arrows) arrows with 125 grains up front. These arrows traveled about 165-170 FPS. Momentum for this setup was .46 - .47.
This past season I switched to a set of limbs that pulled 41# @ 30.5"
I kept the same spined wooden arrows and went to 290 - 295 grains up front vs. the 125 grains up front on the setup for the 54# limbs.
This put my arrow weights anywhere from 760 grains to 795 grains. These arrows, even though 35 grains apart in weight, only differ in speed by 2-4 FPS.
The momentum factor for this set up ranged from .466 - .478, roughly the same as the bow with 13# more draw weight.
I did lose 30 - 35 fps in arrow speed. It takes my arrow an extra .09 seconds longer to travel 20 yards than with the 54# setup.
My brain quickly adjusted to the new trajectory, and at distances under 25 yards, I shoot just as accurately with this setup as I did with the higher poundage and arrows at 10-12 GPP.
I took two whitetails with the new setup this past fall. The second was a doe at 15-17 yards, slightly quartering to me. The 765 grain arrow hit her humerus bone, an inch below the ball joint on impact. It shattered the bone, penetrated 20 more inches, and double lunged her in the process. She sprinted 35 - 40 yards to her death. I'm not certain that a 410 grain arrow would have made it past the humerus on impact. I'm not saying it would not have, but I have a lot more confidence with the heavier arrows. I also really enjoy shooting the lighter bow.
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Offline blacktailbob

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Re: KE and MOMENTUM explained
« Reply #31 on: March 01, 2022, 03:39:37 PM »
I came back to traditional because of the simplicity  :dunno:
Just give me a super sharp arrow that flies good at my hunting distances ( 25yds or less ) and screw all that physics stuff.
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Offline Terry Green

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Re: KE and MOMENTUM explained
« Reply #32 on: March 02, 2022, 09:21:49 AM »
I hear ya Bob.  I ran those numbers to prove a point with facts that no matter what people 'want to believe' that it don't make it true. And its not just a number....

It's a number, then another number.... showing proficiency that matters.

  A Bull Elk and an 80# pig are NOT the same either.
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Online Wudstix

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Re: KE and MOMENTUM explained
« Reply #33 on: March 02, 2022, 09:48:42 AM »
So one of my bows shooting 630 grain woodies at 190 fps is .532 (slugs?)  That'll do!!!  Recently put a 730 grain footed tapered arrow through and 20 yards past, a Javelina, to bad the through was not in the proper location.
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« Last Edit: March 02, 2022, 12:56:54 PM by Wudstix »
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Offline Mike Malvaini

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Re: KE and MOMENTUM explained
« Reply #34 on: March 02, 2022, 10:12:12 AM »
I hear ya Bob.  I ran those numbers to prove a point with facts that no matter what people 'want to believe' that it don't make it true. And its not just a number....

It's a number, then another number.... showing proficiency that matters.

  A Bull Elk and an 80# pig are NOT the same either.

I am not only posting, but hitting the 'LIKE' button also.

Offline mj seratt

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Re: KE and MOMENTUM explained
« Reply #35 on: March 03, 2022, 04:01:34 AM »
All I know is y'all make my head hurt.

Murray
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Offline charles m

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Re: KE and MOMENTUM explained
« Reply #36 on: March 03, 2022, 07:26:52 AM »
Mj, it's not really as complicated as some are making it out to be. The 1st post is pretty 1st grade and comes to the same exact conclusion as the overly complicated posts. 

A + B = C

A + B = C+

A is Arrow Weight and B is Speed.

Just fill in the A and B and you get your Cs.  1st grade.

Offline ozy clint

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Re: KE and MOMENTUM explained
« Reply #37 on: March 03, 2022, 08:05:08 PM »
It's important to remember that resistance increases with the square of the velocity. Double the velocity= quadruple the resistance.

Two arrows, identical in every way, of the same MO but different mass means one must be lighter and faster than the other. The slower arrow should penetrate more because it encounters less resistance.
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Offline JamesD

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Re: KE and MOMENTUM explained
« Reply #38 on: March 03, 2022, 08:40:56 PM »
Well Spoken Ozy and Charles. The concept is simple and it applies to every arrow, from every type of bow that you decide to launch an arrow from.
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Offline Terry Green

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Re: KE and MOMENTUM explained
« Reply #39 on: March 04, 2022, 07:39:56 AM »
Yes James, every arrow. 

My point was to those that claim a 40# bow is as efficient as a 50# bow. All things being equal, that statement is 100% 'make believe'.
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