Speed vs Mass Considerations
May 2, 2010 14:45:23 GMT -5
Post by Harley on May 2, 2010 14:45:23 GMT -5
I have found that both the Carbon Maxx 2000 and Carbon Maxx 3000 will fly straight and group small from my 60# Mathews Z7 bow. My question is which arrow to choose for hunting whitetail deer.
If the question were which to choose for target shooting I’d choose the faster of the two (for the marginally flatter trajectory) and give it no more thought.
In hunting deer, though, time in flight (velocity) has to be balanced by a consideration of penetration; which is influenced by the mass of the arrow.
So, how much importance should I assign to the arrow’s velocity vs importance assigned to the arrow’s mass?
The most accepted comparison measure is Kinetic Energy, which is heavily influenced by velocity.
A rival measure, much less accepted by the archery community, is Momentum; it gives equal weight to arrow velocity and mass.
Until I did my own research this past week, I’d accepted unquestioningly that the correct reference formula was kinetic energy. I’d done so both because “everybody” said so, and because I come from a firearms background that rightly computes kinetic energy comparisons among projectiles.
I’ve come to believe, though, that this is just plain wrong when an arrow is the projectile; kinetic energy calculations are effective when we are describing tissue hydraulic shock comparisons, which are not applicable to arrow damage. An arrow normally kills by cutting its way through the target animal; it follows, then, that a measure of comparative penetration is more appropriate, and that is what the formula for momentum indicates.
I am omitting all formulas in this discussion; they are readily available elsewhere.
In summary, then, here are the comparative differences between the two arrows, shot from my bow:
Carbon Maxx 2000
MV = 291 fps
Mass = 335.3 gns
KE = 63 ft lbs
Momentum = .43 slug ft/s
Carbon Maxx 3000
MV = 284 fps
Mass = 354 gns
KE = 63 ft lbs
Momentum = .45 slug ft/s
Because the difference in mass is only ~5%, and the difference is MV is only ~2%, neither KE nor Momentum were significantly different.
I’d conclude, then, that my arrow choice – at, say, up to 30 yards – would depend only on how far I wanted my arrow to stick into the ground after it exited the deer; so, no problem here.
What I can’t figure, though, is the distance at which the heavier arrow, with its greater momentum, is the better choice for deep penetration. I could compute the Momentum formula to answer that question, but as far as I know it would require my shooting through the chrony at those greater distances in order to obtain the velocity portion of the equation. I’m not that bold.
I’d guess that these two arrows are so functionally close that no real advantage would be found for the heavier arrow at even the greatest distance. There are arrow comparisons, though, that would benefit from external ballistics analysis. I’m hoping someone can supply a Momentum formula that can be computed down range, not just at MV.
Harley
If the question were which to choose for target shooting I’d choose the faster of the two (for the marginally flatter trajectory) and give it no more thought.
In hunting deer, though, time in flight (velocity) has to be balanced by a consideration of penetration; which is influenced by the mass of the arrow.
So, how much importance should I assign to the arrow’s velocity vs importance assigned to the arrow’s mass?
The most accepted comparison measure is Kinetic Energy, which is heavily influenced by velocity.
A rival measure, much less accepted by the archery community, is Momentum; it gives equal weight to arrow velocity and mass.
Until I did my own research this past week, I’d accepted unquestioningly that the correct reference formula was kinetic energy. I’d done so both because “everybody” said so, and because I come from a firearms background that rightly computes kinetic energy comparisons among projectiles.
I’ve come to believe, though, that this is just plain wrong when an arrow is the projectile; kinetic energy calculations are effective when we are describing tissue hydraulic shock comparisons, which are not applicable to arrow damage. An arrow normally kills by cutting its way through the target animal; it follows, then, that a measure of comparative penetration is more appropriate, and that is what the formula for momentum indicates.
I am omitting all formulas in this discussion; they are readily available elsewhere.
In summary, then, here are the comparative differences between the two arrows, shot from my bow:
Carbon Maxx 2000
MV = 291 fps
Mass = 335.3 gns
KE = 63 ft lbs
Momentum = .43 slug ft/s
Carbon Maxx 3000
MV = 284 fps
Mass = 354 gns
KE = 63 ft lbs
Momentum = .45 slug ft/s
Because the difference in mass is only ~5%, and the difference is MV is only ~2%, neither KE nor Momentum were significantly different.
I’d conclude, then, that my arrow choice – at, say, up to 30 yards – would depend only on how far I wanted my arrow to stick into the ground after it exited the deer; so, no problem here.
What I can’t figure, though, is the distance at which the heavier arrow, with its greater momentum, is the better choice for deep penetration. I could compute the Momentum formula to answer that question, but as far as I know it would require my shooting through the chrony at those greater distances in order to obtain the velocity portion of the equation. I’m not that bold.
I’d guess that these two arrows are so functionally close that no real advantage would be found for the heavier arrow at even the greatest distance. There are arrow comparisons, though, that would benefit from external ballistics analysis. I’m hoping someone can supply a Momentum formula that can be computed down range, not just at MV.
Harley
