Thought this might be of some help, Jo jo to start.
Quote from: Terry Green on October 24, 2021, 06:46:36 PM
Hopefully this post will clear the waters...
[attachment=1,msg2979842]
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 :laugh:)
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.
:campfire:
So is KE a better measure or MO?
:campfire: :coffee: :archer2:
Momentum. :campfire:
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.
:campfire: :coffee: :archer2:
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.
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?
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.
So the heavier arrow, that is going faster, penetrates better.
:campfire: :coffee: :archer2:
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.
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.
Thanks Scott.... I would have explained but I've been busy. :jumper: :jumper: :jumper:
Quote from: Wudstix on January 25, 2022, 10:35:52 PM
So the heavier arrow, that is going faster, penetrates better.
:campfire: :coffee: :archer2:
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. :archer:
Yeah, thanks Friend. Maybe now some will actually get it.
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.
:campfire: :coffee: :archer2:
Yup, I figured as much, some people are just not going to accept reality.
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.
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.
Quote from: Wudstix on January 26, 2022, 11:53:10 AM
I'll take a ping pong ball at 30 mph over a golf ball at the same speed.
:campfire: :coffee: :archer2:
HUH‽????
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?
Trent...
500, 600, and 700 grains.... all moving at 185 fps.
It helps to think of KE as potential and Momentum as motion.
:campfire: :coffee: :archer2:
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].
[attachment=1]
[attachment=2]
[attachment=3]
[attachment=1]
...And another Chart. :smileystooges:
Yeah Wud,
I couldn't care less about KE, but I ran those numbers years ago since I had the momentum data. :campfire:
So what is the basic formula used to obtain the .411 result?
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:
Quote from: ALDO on February 28, 2022, 11:29:09 AM
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.
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
ALDO
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.
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
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.
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.
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.
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.
:campfire: :coffee: :archer2:
Quote from: Terry Green 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.
I am not only posting, but hitting the 'LIKE' button also.
All I know is y'all make my head hurt.
Murray
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.
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.
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.
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'.
No argument from me there Terry.