one arrow weighs 688grns and is traveling 135 ft/sec and has 27.85 ft-lbs of force at release . Another arrow weighs 547grains and is traveling 150 ft/sec and has 27.34 ft-lbs of force at release.
The arrows are identical in cross section. Which arrow will have more force when it hits a target 20yds away?  

These are the actual measurements out of my bow. I just got a chrono yesterday and I'm trying to figure out which arrow to shoot. One arrow is 13.36 grns/lb the other is 10.62 grn/lb. I was really surprised my bow imparted basically the same amount of energy to both arrows.

The force, energy, momentum etc in your arrow is composed of mass times velocity. When you hit the target the velocity will bleed off. The mass will not. Invest the energy in mass. In other words shoot the heavy arrow. Dr Ashby reports are a long read but more than worth the time. Check 'em out.

JW

Too many real world factors to calculate and consider to render the exact correct answer from me. Need to know the actual velocity at impact. Jim

All things being equal, the heavier arrow will arrive with more whump at 20 yards.  The heavier arrows carries momentum farther and is probably more important than KE as far as hunting is concerned.  Hope this helps.
Jack

I don't know how to figure momentum exactly ,but I know that when you multiply the ft/sec X grns the lighter arrow has 82,050 units and the heavier arrow has 92,880 units. That's about 13% "units" more in the heavy arrow.

So from my other post it was decided the heavy arrow will lose speed slower than the light one. So the farther these two arrows travel the more power the heavy arrow will have when compared to the light arrow. Am I getting this right?

Zradix, if you shoot two arrows out of the same bow, the heavier will absorb the most energy.

engery = mass x velocity^2.  At the release from bow the heavier arrow has about 1.8% more energy.

I agree with Zradix.  The drag is proportional to the square of speed.  The lighter arrow would slow down in faster rate because of more drag from speed and less mass to counter the force.  I don't think the arrows will reach "terminal velocity" when reaching at 20 yards.  Just need to find a formula to simulate the flight.

The 688gr arrow will pinatrate more. The 547gr arrow will shoot flatter. How much penatration do you need? How flat do need the arrow to shoot?
Steve

The very bottom line is the heavier of the two is the BEST option for several reasons.
Based on quality research, there is no comparison in a 688 gr. arrow and a 547 gr. arrow when it comes to penetration and bone contact.

Zradix,  You really want to calculate "Hit Poundage" and forget the Kenetic stuff.  With your exact figures above the 688 gr. arrow hits with 41# of force and the 547 gr. arrow hits with 37#.  It's the old thing of would you want a 250# guy to run into you running 10 mph or a 100# guy.

The heavy arrow momentum is .412 and the light .364.

What would concern me is at 135 fps the heavy arrow will have a good deal more arc.

For close shots at 15 yds and under it won't matter and the heavy will pound em.  But at 25yds, you may be under the target.

Mike

no contest - heavy arras are yer best huntin' buddy.

the question might be a compromise for trajectory.  heavy arrows have more arc and that might shorten yer effective shooting distance.

10gpp is my minimum, and there is no maximum unless trajectory becomes an issue for consistent accuracy.

ymmv!

Penetration is most important. Momentum ( mass times speed) is a better indicator of penetration than than kinetic energy (mass times speed squared). A formula that squares the speed is biased toward speed but that doesn't translate into penetration. Bottom line, the heavier arrow will penetrate better. However your "light " arrow is still 10gr per lb. of bow weight which is plenty heavy for whitetails. Sorry to be so long winded.

Thanks for all the help guys. Yeah I have to admit I'm a little worried about overkill. Don't need to use an elephant gun on a mouse. I'm wondering if the 10gn/# will pass thru just like the 13 on whitetails.

It may not be that simple.      Depending on your bow, the efficiency of the bow may change with the arrow weight, which puts another factor into the equation. Longbows tend to increase in efficiency with increasing arrow weight, but a recurve may not.

I'm shooting a 1957 or 58 Bear Kodiak recurve 60" 52lbs at 28" heavy arrow is ash, light arrow is cedar. I'm shooting a Abowyer brown bear broadhead (175grn+15grn lead)

I would think that a 10 gr setup should pass through rib cage hits on whitetails most of the time,if you are tuned for good arrow flight.Wind can change things just like an untuned arrow.

I'm not sure there is such a thing as overkill,though.It is part of the choice to be satisfied with the trajectory though.

I have been shooting 13 gr per pound arrows out of several bows and don't have to think about trajectory out to 20 yds.I would rarely shoot at game past that range but if I want to shoot farther,I verify with my tip.At 25 yds,4" under and 30 is point on.

I shoot all recurves and every one penetrates deeper with heavier arrows.They also shoot quieter.

Both your setups are good ones.You can't make a bad choice there.Just juggle a few elements to help you decide but forget the kinetic energy formula.

Dumptruck & Hugo both traveling at 40 MPH. Which is easier to stop? Why?