Interesting but short read on KE vs Momentum

[ozyclint]

to add to the above- while i like high FOC arrows i believe there becomes a point where increasing FOC becomes a limiting factor for penetration in certain real world hunting situations, being namely conditions of moderate to heavy crosswinds. while a high FOC arrow will experience less wind drift off target, it does however experience greater tail end wind deflection. this negates it's high FOC penetration advantages because it's not hitting the target straight.

as is the general rule of life- all things in moderation

 

[moxford]

Would you prefer ...
a) that the head hit closer to your aim point but with the tail deflected, thus less penetration, or
b) the entire arrow pushed over

I'm going to usually take (a) because even as much as I love heavy high-FOC arrows ... accuracy > penetration.

All things in moderation. Including moderation. =)

-mox

 

[brocksw]

I believe the formulas for KE and momentum that have been listed in the thread are missing some things. First off gravitational constant needs to be taken into consideration for each equation. If you're using English units this Gc = 32.174 fp/s^2.

KE (ft/lbs) = ((.5*m)*(v^2))/Gc

Mom (slugs) = (m*v)/Gc

Don't forget to convert your grains to lbs....so arrow weight in grains divided by 7000 (total grains in 1 lb).

For instance my own arrows momentum.

505/7000 = .07124 lbs = mass
274 fps = velocity
32.174 = Gc

(.07124 * 274)/32.174 = .606 slugs

I think its interesting to note that 1 slug equals 32.174 lbs of force. Also these figures (KE and momentum) are not proportional. They cannot be, even though speed and mass are equally represented in the momentum equation, proportionate changes in one do not equal a proportionate change in our final outcome. Mass is a more important factor and changes to mass have a larger affect. An object deriving more of its momentum from mass will out penetrate a faster arrow that has equal momentum,or in other words derives more of its momentum from speed. This is physics and these are the laws of physics. There are not exceptions.

There are other factors that contribute to penetration and speed, such as arrow flight and impulse. If one wanted to truly dig deep into this you would have to analyze the effect impulse has on an arrow as this throws the dimension of time into the equation.


F.O.C. or extreme F.O.C usually helps in penetration for a couple reasons, but one is sort of on accident. Typically, to get high FOC, you have to increase the amount of weight up front. This increases your FOC but also increases your momentum. One would have to to fire 2 arrows of equal weights and speeds...with one having a high FOC and one having a lower FOC to really see if FOC affects penetration significantly.

However a high FOC and a perfect centershot can combine to give you some advantages in arrow flight. A higher FOC and perfect centershot (bare shaft bullet holes) will be more efficient traveling through the air. The fetchings will have to work less, leading to decreased drag, better accuracy, less wind drift, tighter rotation. Higher FOC, in theory, also leads to less oscillation and arrow flex at point of impact. Personally I've never had the desire to test thee things to this extent, as it would probably require some camera gear and software to really see what's going on at impact. Logically it does make sense.

In general, I know shooting a heavier arrow (500 grains or above is my choice) has a couple benefits. Less affected by wind, better penetration, and a quieter bow. If I do my part and make sure I shoot bare shaft bullet holes through paper at 0,5, and 10 yards, I've found that I can typically get nearly "perfect" arrow flight and shoot bare shafts with my fletched shafts out to about 45 yards. This tells me my fetching is working very little and my bow is efficiently throwing my arrow. I am a firm believer in arrow flight playing just as large a role in penetration as momentum.


I think it's important to note my stance on this and that in the world of compound Archery, in my opinion, it's logical to fall somewhere in the middle of all this. Having a 700 grain arrow may penetrate better, but there aren't many sight housings that would allow extended ranges and not to mention if distance is misjudged or miscalculated by a few yards it doesn't allow you much room for error due to the sweeping arch in arrow flight. So once again, in my opinion (emphasis on my opinion) having the best arrow flight you can possibly have out of your bow and having a weight somewhere in the 480-550 range, will kill anything in North America with good shot placement (with a little forgiveness) as well as allowing extended ranges. It will also allow you much better penetration than a "light arrow" without giving up too much in terms of trajectory.

Obviously, you long draw shooters have a speed advantage compared to us short draw guys (I'm 27.5 inches). My first pin is at 30 yards, my 7th pin is 90 and the top of my bubble on my spott hogg is just over 100. So I have found an arrow weight and speed that get me where I want to be in terms of distance and penetration. I shoot every one of my arrows, bare shaft, through paper and spine index around the nock to insure the best arrow flight I can have. However, if I had a 30 inch draw, I would probably shoot a heavier arrow yet and not keep the additional speed from the longer draw length.

I agree with someone earlier in this thread, many great hunters/archers pay little attention to some or all of these things. To a certain point, this all may be over analyzing or maybe it's just type A personalities that like to tinker and feel confident in their setups squeaking out every advantage they can. It could even be too many guys having to much time on their hands. Regardless, more power to ya either way. However you get it done in the field, as long as it works for you, keep at it.


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