Arthur P

I really don't know what you could call a minimum for momentum, Sylvan.

Back in the day, 45 pound recurves were favored as a deer hunting bows by a great many people. Myself included. In those days, they wanted just enough penetration to get both lungs and leave the broadhead inside the chest cavity so the animal's running motion would whip that sharp broadhead around and do more damage for a quick kill. Even though they often got complete passthroughs, the idea of actually wanting a complete passthrough is a relatively new concept. If we figured they were shooting a 460 gn arrow around 160 fps, they were getting some 26 ft lbs of energy and .3263 lb-secs of momentum. Maybe something around that might be reasonable for deer hunting. It worked back then, but I just don't know.

And yes, that would be about the equivalent of driving a 350 gn arrow at 210-211 fps and 34 ft/lbs. But wouldn't driving a 400 gn arrow at 200 fps, 35 ft lbs and .3547 lb-secs be even better, maximizing energy and momentum with hardly any difference in midrange trajectory (about 1/10th of an inch)?

Sylvan

Arthur P,
What you say makes sense and I appreciate that you recognize that whatever momemtum spec you put on it you can come up with a spec in KE that basically accomplishes the same thing. That is not to say 1 is better than the other, I also appreciate the momentum agument.

Here's why this whole thing gets a little silly for me. Let's say we don't have a spec with numbers. No talk of pounds or momentum or KE. Lets just say the state has some standard material for a target and they say to be legal you must be able to drive your arrow 9 inches into this target at 30 yards. The guys shooting 80 or 90 ft/lbs are chuckling as they bury their arrows 15 to 20 inches. But along comes the borderline guy and his arrow only goes in 8 1/2 inches. What does he do? Regardless of whether you talk in terms of KE or momentum the actual advice you give him will be the same. He needs more punch right? So either store more energy in the bow and/or put on a heavier arrow and/or reduce the virtual mass(this one won't take him far) but all of the advice you give him will be intended to increase both the KE and the momentum together. The guy isn't going to care about a physics lesson or care if its KE or momentum working for him he just wants 9 inches. LOL

manboy

sylvan, u didn't listen to my reply![:@]
on your post the guy with only 8 1/2 inches of penetration needs not to up his k.e. or his momentum. he needs to up his p.s.i= pounds square inch.
all he needs to do is sharpen his broadheads, or use a smaller diameter shaft, not a lighter shaft. or he could use a slimmer field tip, not lighter.
it is a fact that u can gain penetration without increasing the k.e. or momentum!

zak123

I used to shoot a light setup, about 37 ke. I went hunting with it only because I had sharp cut on contact heads. I used the Magnus Stingers. I couldn't get them to group well so I tried the Muzzy's. They grouped much better. I worked on my draw weight and got it up a to 60 pounds. I could then safely use the Muzzy heads. If you have a low KE then use cut on contact heads. Those Magnus Stingers are mighty sharp. I could throw one at a deer and get a pass through.

Arthur P

Yes, it's possible to do that. However, momentum is a heckuva lot easier to come by than KE. The example I talked about above, for example, where a 350 grain arrow has to be driven at 300 fps and 70 ft/lbs of energy just to equal the momentum of a 700 grain arrow at 150 fps and only 35 ft/lbs. For those people who simply cannot increase their KE, due to physical or equipment limitations, increasing their momentum might mean the difference between a short blood trail and a lost, wounded animal. That is the main point I'm trying to get across.

Someone shooting a light draw weight bow is not going to be trying to reach out to 40-50 yards with a shot. They're going to be limiting their shots to well under 30 yards. Light arrows are not going to improve trajectory at all at those distances. Distances, by the way, where the vast majority of bow kills are made anyway. Unless one routinely shoots at animals beyond 30 yards, trajectory is pretty much a moot point.

Even higher up the speed and energy scale, if one limits his shots to 30 yards and under, he can use a heavier arrow and get more KE and momentum without a serious increase in trajectory. The difference in midrange trajectory at 30 yards between an arrow at 250 fps and 300 fps is only about an inch. Plus having a bow that's even quieter and easier to tune with broadheads. Understanding how little trajectory truly means over typical hunting shot distances, doesn't it make sense to use the bow's power to add even more penetration potential to the arrow, just in case? Pulling a shot too far forward and getting into the shoulder blade, for example. Or a shot at a severe downward angle, like a deer that's real close to your treestand. There's a lot more body depth than there is width and you need extra penetration to get through it. And if you hit that spine without having enough punch to bust through it...

That's why I favor a 400 grain minimum arrow weight. It's not so heavy someone shooting a 40-45 pound bow will be lobbing them in at 30 yards, but heavy enough to reliably do the job. And it's not so heavy as to really cause anyone any problems with a high speed, high energy bow at extended yardages either. After all, most guys who stretch 'em out use a rangefinder before they shoot. And it doesn't matter if we're talking KE or momentum, a 400 grainer beats a 350 grainer on both counts... especially downrange where penetration takes place.

Just look at all the critters Chuck Adams has taken at 50 yards and more with those logs he shoots.

Sniper151

Take a 25# shot bag and fill it with sand. Suspend the bag from a string that will allow it to swing freely. Now shoot the 357 or a 30:06 at the bag from 10 feet. Do the same with the arrow and lastly throw the baseball. The speed on the bullet dissipates less than 1 1/2" into the bag. It will not pass through and desindigrates. All the energy is expended abruptly after impact. The arrow will pass through the entire bag. Not just kinetic energy, but sustained inertia transferred from the limbs and the string into the shaft is transferred forward to the tip. Now the baseball. A large mass with the energy spread throughout the sphere that will hit the bag with no penetration and all the energy being expended on the outer cover and absorbed by the sand. Finding the balance between speed and weight isn't that difficult. Kinetic energy of 45 ft lbs. is considered the bottom scale for hunting with a broadhead. Anything above 45 ft. lbs. is icing on the cake.

Sylvan

That is absolutely correct. I was thinking totaly in terms of the bow and not the sharpness or other design criteria of the arrow other than mass. This actually is more reason to forget the momentum/KE argument. To exagerate to make a point again, if you had a bludgeon point on your shaft its unlikely that any arrow weight shot by the strongest man would penetrate adequately. When I used the example of the imaginary target material for the state I wasn't serious but maybe its not a dumb idea. After all I can't think of another critera that takes KE, momentum and the arrows role as far as sharpness etc into account all at the same time. This has been a very interesting discussion but still for all practical purposes I don't think it is much more than an acedemic exercise. In my previous post, if you add the advice to make sure your broadhead is as sharp as possible the total advice to the borderline guy still doesn't change at least with regard to the momentum/ke argument.

Sylvan

This is all true but I think all this is pointing out is that because arrows are much sharper than bullets they are able to penetrate the material you describe with less energy/momentum. But again, how about the cinder block? The arrow bounces off doning no damage and the bullets smash through destroying the cinder block. Again I don't think these comparisons are usefull.

Sylvan

I don't understand why you say momentum is a lot easier to come by then KE. You increase them both by doing precisely the same things. You can't separate them. Increasing the weight of the arrow for example has the same effect with regard to penetration whether you talk about it in terms of KE or momentum.

Anyway here is a physics problem. I have a projectile that weighs 300 grains and is traveling at 300 ft/sec therefore the KE=60 ft/lbs and momentum is 0.40 slug ft/sec. This projectile collides with a material that requires 40 pounds of force in order to push a projectile of this shape into it. Question: How long and for how far will this projectile be able to sustain the 40 pounds of push before it comes to a stop? The answer is 10 milliseconds and 18 inches.

Now 1 more physics problem. I have a projectile that weighs 500 grains and is traveling at 232.5 ft/sec therefore the KE = 60 ft/lbs and momentum is 0.52 slug ft/sec. This projectile collides with a material that requires 40 pounds of force in order to push a projetile of this shape into it. Question: How long and for how far will this projetile be able to sustain the 40 pounds of push before it comes to a stop? The answer is 12.9 milliseconds and 18 inches.

In these 2 examples the KE is the same but the momentum is larger in the 2nd case. The amount of penetration is the same. The difference is that the example with the higher momentum pushes for a longer period of time. That is what is meant when we say that KE is the integral of force over distance while momentum is the integral of force over time. If the time of the act of penetration is too short as is with high energy but low momentum projectiles the material that is to be penetrated can't get out of the way in time so the force goes up to a point where the projetile either shatters or bounces off. But if the time is long enough to allow penetration that is if its momentum is high enough to allow penetration it will be KE that determines how far it penetrates. This is why we say that KE determines how far a projectile penetrates and momentum determines whether or not it penetrates at all.

Again though this all comes down to an archer standing there with his bow trying to decide what to do to get more penetration. Whether you talk about KE or momentum it just doesn't make any difference with regard to the actual steps he takes. All other things being equal i.e broad head sharpess my advice is to put on a heavier arrow and if that isn't enough then go to the gym and build your muscles so you can shoot a bow that stores more energy.

Arthur P

Very easy. Run your program with a selection of arrows for your bow, running from very light to very heavy. Watch the changes in both KE and momentum. You get minimal increases in KE but much larger increases in momentum. Record your momentum value for the heaviest arrow. Then go back to the 330 grain arrow and run it again but, this time, begin increasing the speed and KE until the light arrow reaches the same momentum as the heavy arrow. How easy will it be to actually achieve that kind of speed and energy with your current bow?

Then, I'm sure, you'll understand why I said, "Momentum is a lot easier to come by than KE." You just increase arrow weight.

You physics problem left out a few things, if we're to correlate it to an arrow striking flesh and bone. Sectional density; drag (number of blades; blade sharpness; cutting angle; cut to tip/chisel tip/ cone tip); rate of spin. Your hypothetical material is homogenous and a deer is not. There are bone and lighter-denser muscles/organs and voids within the body cavity. What angle was the shot made from? Did the animal turn slightly after release and before impact? We're assuming the the arrow had not deflected in flight and was flying straight and stable. Of course, we also must assume the hunters are ethical and had their bows well tuned for the hunt; that they are knowledgeable and made the proper shot selection; and skillful enough to place the arrow at their intended points of impact.

Real life arrow penetration is way too complex to run a few formulas through the ol' calculator and come up with the magic arrow. It wasn't until guys started hunting with their 5 grains per pound arrows for their IBO 3D rigs that folks started all this mathemagical stuff, trying to 'prove' their light arrows were ethical. Certainly, when you're on the exreme light edge on arrow weight, you need to know precisely what kind of energy/momentum you're putting out. No matter what you're doing, any time you push to extremes you're walking on dangerous ground. The further you get away from the extremes, the less you have to worry about.

Go ahead on and walk on the edge of the dropoff along the shoulder of the highway if you want. I find things very comfortable over here in the middle of the road.