arrow physics 2

[Richie Nell]

Sir Jim,

If a plastic golf ball and a real golf ball were propelled into a glass widow, why would the plastic ball require much more speed than the real golf ball to break the widow?


The original question was..which one has more force (momentum) downrange?  

And you are saying they have the same?  Not possible

[Richie Nell]

Another example is the Little League soft baseballs.  I new a 5-6 year old boy that was hit in the chest with a "soft" baseball and died.  It was soft but not light weight like a plastic whiffle ball.  The texture obviously has nothing to do with making the ball safe.  The weight behind the ball, the force that was exerted on impact even at slow speeds is the killer...unlike the light weight whiffle ball.  It would take an incredible increase in the speed of a whiffle ball to come anywhere close to serious danger.  

The force downrange (or across the diamond) is NOT the same for objects of different weights.

[Jim now in Kentucky]

Richie, force=mass X acceleration.

A plastic golf ball has far less mass than a real golf ball. But if the plastic one is going at a speed that gives it the same kinetic energy at impact, it too will break the glass. (Don't try this in the living room.) lol

Yes, the original question was, "which will have the most force when it hits the target?"

Some above have noted that variable of 20 yards of air that must be penetrated before reaching the target.

The heavier arrow would lose less velocity, but at that range, any difference in force at the target would probably be within a margin of error that could be attributed to the uncertainties of measuring the force.

At longer distances, the ratio of the drag area to the mass, and the higher drag on the faster arrow would begin to be obvious.

It all ends up that there is a wide range of values that will do what is needed. Success in our hot pursuit of the ultimate combination would only increase the percentage of kills per shot by a tiny, probably unnoticeable, amount.

[Jim now in Kentucky]

Zradix,

Those "tubes" are "Reparrows." They are hard wood footings that glue on the standard taper of a wood arrow to foot, extend or repair it.

[Zradix]

Really cool!! Thanks

[Jim now in Kentucky]

And now they are gone. Musta stept ona toe.

[Rob DiStefano]

Originally posted by Jim in Maine:
And now they are gone. Musta stept ona toe.

check yer email ....

[dbldroptyne]

Some food for thought. Would you want me to throw a ping pong ball at you, or would want a golf ball thrown at you. Which do you think would hurt more thrown at full speed.

[Rob DiStefano]

physics is physics, and for any specific hunting stick bow i'll prefer as heavy an arrow as i can handle.  

and i'll make sure to push as much of that arrow weight as far forward as possible.

why?  don't need to be a physicist to read and understand the empirical data results found in dr. ashby's reports.  ain't hurting me to use those results to help my hunting.

[Greg Skinner]

This has been an interesting discussion.  It's been awhile since I had physics, but I'm trying to follow along here.  Jim, could you explain the difference between force and momentum. They both seem to be a factor of mass and velocity. Also, I think your comment regarding arrows shot from the same bow is most appropos - which is why I like a little heavier arrow in order to gain as much efficiency from any given bow as possible. Obviously someone else can come along and shoot a lighter arrow faster than my heavy arrow and have more energy at the target, but it will be from a different bow.

[Richie Nell]

Sir Jim,
"But if the plastic one is going at a speed that gives it the same kinetic energy at impact, it too will break the glass."

Of course it would..but that is my point.  It will NOT be going at the speed necessary to have equal force at impact.  

It loses speed quicker downrange than the heavy golf ball thus NOT having equal force like you say it will.

"The difficulty in understanding this is that we never have a controlled situation and enough instances to see a clear picture of the results."

A clear picture of which has more force at impact is countless arrows penetrating better due to more force downrange at target impact.  That happens for a reason and that reason is more momentum downrange.

[Richie Nell]

Rob,
Not surprisingly, you are exactly right.  It is not rocket physics.

[Overspined]

this is all way over analyzed. just shoot arrows that fly good and with 10 gpp or more and you are good to kill. hunting dangerous or very large game is where a little more info may be necessary.

[Richie Nell]

Overspined,
You are right, no doubt about it. But...it is fun to learn, tweek, read research, try to get it as good as you can sometimes.  It is just fun.

Like you said, at the same time we are having this overkill fun.  We all know that it doesn't take much momentum, force, weight, etc. to actually make a deer dead.

But did I mention overkill is alot of fun?

[Jim now in Kentucky]

OK guys, I think maybe some didn't read all of my last comment on drag etc.

First, this entire thread began with the calculations showing that the heavy arrow and the lighter faster arrow had, for practical purposes, the same energy.

You are all correct that that will not be true at some distance from the launching point. The lighter arrow will lose speed faster.

You are also correct in that, if I may paraphrase, the heaviest arrow your bow can give an acceptable trajectory will give the best penetration.

But that is only because the heavier arrow will retain more energy during its flight.

That probably was the intent of the first question. I just jumped in--a little rough shod I guess--when certain laws of physics were being presented incorrectly.

I tend to like the equations and principals a little too much, perhaps.

Greg,

A force is usually defined simply as a push or a pull. In the English system (nearly out of fashion now) the unit of force, foot-pound, is the amount of energy required to move a weight of one pound one foot against the pull of the earth's gravity.

This is also called the amount of work required...

Momentum is the  property of a moving body that it has because of its mass and motion and that is equal to the product of the body's mass and velocity.

An example in my old physics book may be interesting here. It states:

A 4-ton truck traveling east at 10 mph has momentum equal to that of a 2-ton truck traveling east at 20 miles per hour.

So, I think we can see that  a 1,000 grain arrow flying at 100 fps has the same momentum as a 500 grain arrow flying at 200 fps.

Of course, our arrows are not nearly as different as those two and there is drag to contend with.

Anybody who hasn't quit reading?

[Richie Nell]

"They would lose the same amount of energy in a substance of uniform consistency--and they would stop at the same point."

"But that is only because the heavier arrow will retain more energy during its flight."

Your two quotes above seem to be contradictory but the latter is correct.

That is precisely what I have said several times now.....  Which answers his original question of which has the most force at the target.

And I do like reading your information.

[Rob DiStefano]

just to keep this thread in perspective ...

interesting stuff, no doubt - the physics behind arrow mass/speed/penetration is all well and good.

but to put all of that gobble-dee-gook to the task of trad bowhunting, none of it matters squat at sane hunting distances with a well flying arrow that sports a sharp cut-on-contact broadhead that's put to the SPOT.  

don't care a fig about fps, gpp, foc, lmnop, or etc.   :D

[Jim now in Kentucky]

"You are all correct that that will not be true at some distance from the launching point. The lighter arrow will lose speed faster.

You are also correct in that, if I may paraphrase, the heaviest arrow your bow can give an acceptable trajectory will give the best penetration."

That's what I said. Boy, some of you seem to want to make it really hard to agree with you!

Richie,

You quoted me correctly:
"They would lose the same amount of energy in a substance of uniform consistency--and they would stop at the same point."

"But that is only because the heavier arrow will retain more energy during its flight."

But the two quoted passages are from entirely different contexts!!!

I shoot about 11 grains per pound of pull, if anybody cares. 8-)

[wingnut]

A long time ago in a place far far away, I was employeed to do some testing with a chronograph at 60 yds.

Yes it was a mechanical bow and at the time I was a pro shooter.

But that being said we did a study for the game dept on retained energy.

We shot arrows from 6 gpp to 12 gpp from a bow through a chrono that was 60 yds down range.

Not an easy task.

Anyway to make it short.  The difference in KE on the light arrow and the heavy arrow from the chrono at 3 ft and the chrono at 60 yds was 3%.

The heavier arrow retained 3% more energy then the light arrow over the distance.  Both arrows were flying perfectly.

Mike

[Jim now in Kentucky]

Thanks Mike, you made my day!