Speed... Curiosity only

[bradsmith2010]

its nice when the practical experience and the science of it validate each other,,its nice to know the whys,,,I am not good at the math, and it really helps how clearly you guys explain it,,,and hope the discussion helps others with their hunting set ups,, the speed is just a small part of it,,Tim Baker said " Let the measured speed of your arrow weigh the merits of your conjecturing.The arrow ,by the speed it chooses to fly,displays wisdom beyond Solmon's."

[PlanB]

I like that, BradSmith.

[Del the cat]

I did a search of kinetic energy vs momentum and could't find a decent explanation of the difference in layman's terms. Then I found this which really addresses our issues and is funny!

A Thought Experiment:

Suppose that you were captured by an evil physicist who gave you the following choice:

You must either:

Stand in front of a 1000 kg truck moving at 1 m/s, or
Stand in front of a 1 kg meatball moving at 1000 m/s.
What's your choice?

Hopefully, you picked the truck! It's a big truck, but it is moving rather slowly (about walking speed), so assuming you don't fall down when it hits you (That would be bad...) the truck is just going to bump into you and move you out of the way.

On the other hand, you probably suspect intuitively that the meatball is a very dangerous object. It isn't that massive, but it is moving very fast (about 10 football fields per second) - and when it hits you it would do considerable damage to you, and keep going!

Consider the momentum and kinetic energy of the truck and the meatball:

Truck:

Truck's momentum = mv = (1000 kg)(1 m/s) = 1000 kg m/s
Truck's kinetic energy = 0.5 mv2 = (0.5)(1000 kg)(1 m/s)2 = 500 Joules

Meatball:

Meatball's momentum = mv = (1 kg)(1000 m/s) = 1000 kg m/s
Meatball's kinetic energy = 0.5 mv2 = (0.5)(1 kg)(1000 m/s)2 = 500 000 Joules

We know intuitively that the meatball is more dangerous than the truck, yet the momenta of the truck and the meatball are the same. On the other hand, the meatball has 1 000 times the kinetic energy of the truck! Clearly, momentum and kinetic energy tell different things about an object!

Del

[mikekeswick]

You can compare the energy using 1/2 m times v squared... don't worry about units as long as you are consistent.
So the 485gn at 162 fps gives 6364170 units of energy
The 770gn at 124fps gives 5919760 units of energy which is less, so I'd say you are going a bit too heavy at 770 gn as you are loosing speed and energy.
Del

Then divide by 450240 = Kinetic enrgy

[H Rhodes]

   Your optimum spot is easy to find. The heaviest arrow will always be the slowest yet carry the most energy. You need to find an acceptable arrow weight for the game you are killing that is fast enough to be accurate with. Your 475 arrow is plenty heavy enough for deer and gives you good speed, I don't think I would want to go below 150 fps so if I were in your shoes I would choose something about 500 to 550 grains.

Bingo!  I agree.  Especially the part about "for the game you are killing..."  I have put a fair share of venison in the freezer with arrows in the 475 -550 grain range, using bows from 45 to 55 pounds to know that they will do the job.  If I am hunting big hogs or elk -  600 -650 grains is what I am shooting.   I am no scientist, just a guy who spends way too much time building bows and arrows and then shooting those arrows into animals.  If you are wanting an arrow to perform right for hunting it just needs a few qualities.  It needs to fly straight and true.  It needs to be quiet (heavier is usually quieter).  It needs something  damned sharp on the end.  It needs to be fast enough to get there before the target runs off (too heavy and it is too slow).  It needs to punch a deep enough hole to kill.   This has been a fun thread and I appreciate all you learned folks that didn't shy away from higher math.

[steve b.]

Easy.  Do a simple penetration test to see which arrow is "better".  If the heavier arrow, and you can accurately shoot it at the range you want, then you are done.

Regarding the energy thing, if you keep increasing the weight of your arrow then at some point the bow can't handle it, and it becomes pointless to use it.  So the energy formula doesn't matter if the arrow only shoots 10 ft.  You absorb more energy from the limbs with the heavier arrow, to a point.  But it is "pointless" to to go beyond what ultimately results in an arrow that is not shootable at the ranges you want.  If you want to shoot a heavier arrow, then build a bow that can deal with it.

[Tracker0721]

Now do you mean a more effiecent limb design Steve or a higher weight bow? What would the design need to exert more energy to the arrow and exert less on the limbs? Just wondering cause this has been mostly in regards to arrows but if I wanted a bow that shot heavier arrows better, is that possible? Like if I shoot 160fps with 400 whatever and 120fps with 700 whatever, is there a bow design that can get those numbers closer? Think it require an air bow to test though...

[Tracker0721]

Example: a pellet gun with a short power stroke of the same power will launch a heavier pellet slower then a light one but if you put a longer power stroke in it will launch the heavier pellet not as slow.

[Badger]

  Tracker no bow will shoot different weight arrows the same speed, lighter arrows will always be faster. Poorly made bows tend to benefit more from a heavier arrow but still perform poorly. Any 50# bow with a straight design will carry enough power to hunt successfully if it doesn't have excessive string follow or massive outer limbs. Just tiller the bow out carefully as to not damage the wood and keep your excess mass down in the limbs and you will be fine. Lots of perfect examples of styles posted here everyday you can reference.

[PlanB]

Yes, that's true.

I'm not sure why the need for it, but maybe somebody has one so I'm trying to think of an analogy to tracker's pellet gun with a longer stroke for a heavier projectile. I guess if you consciously short drew a lighter arrow than a heavier one, the speeds could be similar. And maybe if you had a second set of limb nocks the inners could be used for the heavier arrow. I dunno -- that seems something approximating the pellet gun example.

[Tracker0721]

Oh I'd hunt with a bow shooting only 100fps. That's plenty to kill a deer with a sharp broadhead. What I'm wondering is the most efficient. I know lighter arrows will always be faster but the more efficient the bow is the less the difference in FPS should be right?

[steve b.]

There's an argument that heavier mass limbs cast heavier mass arrows more efficiently than they do lighter arrows or than light mass limbs cast heavier arrows.  I don't have a chronograph but I have similar weight bows that obviously cast heavy mass arrows better than others, way more than your 770's.  Take a short bow, and a long bow, and change the tip weight and use the chronograph to see which combination gives the best performance with the heavy arrows.

Whoever said earlier here that the true flying arrow that is well placed is most important is way ahead.  But not if the animal jumps out of its way.  At 100 fps you better have a bow that is perfectly silent or plan to do a lot of blood tracking.  Same with the ultra heavy arrows.  Energy yes, but also slow, maybe too slow at the range you want. 
You can't have everything from a 50 lbs. bow.  All these formulas and theory only go so far in reality.  They don't account for animal reaction, bow noise, or lethality--meaning, are you trying to kill a twitchy 150 lbs. whitetail deer or a 800 lbs. bull elk that is rutting hard?  You might want that fast little arrow on the deer but that same arrow will bounce off the rib off an elk. 
So in the end you have to know when you shoot your combo whether it will work.  Does it go fast enough, penetrate enough, keep the noise down?

[PlanB]

Seems like an organized way to go about creating a dual purpose bow is to specify the two conditions that you want to achieve, rather than to try to generalize about it.

So let's say you want to shoot

1.)  _________ weight arrow at _________ fps, and
2.) __________ weight arrow at ________ fps.

for a draw weight of ___________ and draw length of ________.

If you set those specs, then there may be a path to achieve that. Or a couple of different paths. Or maybe none if it truly is impractical.

But if we just talk about generalities, then the same things get repeated, and you really don't get a bow out of it. The most interesting thing is to work toward something real, and see what occurs as you approach that.

[bradsmith2010]

the heavier the bow,, the better cast you will get from a heavy arrow,, and it will shoot a light arrow even faster, ,so if you want a dual purpose bow, shoot something like 70# @ 28,, then any arrow made from wood will work on any game,,, very dual purpose,, the lighter your bow, the more considerations goes into arrow weight  and range of the shot,,, the heavy bow will do it all,, you just have to able to handle the weight,, and shoot it as accurately as needed for you application,,, this has not been mentioned I don't think, the heavy bows are not quite as efficient as the lighter bows,, a heavy arrow going 180 fps may take more draw weight than expected,, but its still going 180 fps,, so there is some trad off,,

[Newindian]

I did a search of kinetic energy vs momentum and could't find a decent explanation of the difference in layman's terms. Then I found this which really addresses our issues and is funny!

A Thought Experiment:

Suppose that you were captured by an evil physicist who gave you the following choice:

You must either:

Stand in front of a 1000 kg truck moving at 1 m/s, or
Stand in front of a 1 kg meatball moving at 1000 m/s.
What's your choice?

Hopefully, you picked the truck! It's a big truck, but it is moving rather slowly (about walking speed), so assuming you don't fall down when it hits you (That would be bad...) the truck is just going to bump into you and move you out of the way.

The question of how much an arrow  will penetrate begins where your thought experiment ends, and for accuracy the two objects should have the same dimensions. After the collision the massive object will push you a hundred feet or so,  but the less massive one is going to bounce off of your body (more so than the massive one).
 
Consider a .015kg projectile (about the mass of a soda can) moving at the speed of sound (340 m/s), and another identical projectile With the exception of its mass, which we will make .25kg ( less than 2/3 of the mass of a full can), moving at 83.3 m/s. both objects have the same kinetic energy (867 joules) but their momenta differ quite a lot (the more massive object has about 4x the momentum).

Now if we consider this as though we are actually shooting the cans, and you were hit with the lighter can you would get a nasty bruise and lacerations, as the can shatters against your body, and probably the air knocked out of you, but in the end you'd be pretty healthy.
 But if it were the more massive object, you would be lucky to get away with a few broken ribs after being knocked back several feet.
Or you can make these objects about the size of a .22 and fire them into a wood block, you would find the more massive object penetrated about 4x as deep (assuming it doesn't shatter, etc.)

As far as distance is concerned, a faster arrow will always go further
 
Remember that momentum is literally a measurement of the quantity of motion,  whereas kinetic energy is the capacity to do work.