Odd arrow physics

[Jackpine Boyz]

Hi,
Been messing with a chronograph and my R/D longbow.  I am shooting 750 gr arrow at 158-160fps.
My momentum with the archery calculator in 0.53 and kinetic energy is 42.6.

I swapped my 325 grain tip for a 125 grain tip.  Same arrow and bow.  I shoot at 178-180 fps with momentum of 0.43 and kinetic energy of 39.5.

I expected to drop momentum and increase speed.  However I don't understand the drop in kinetic energy.  Is there just more kinetic energy being pulled out of the bow with the heavier arrow?  I am not sure why the kinetic energy isn't increasing given that the KE= m x Velocity squared.  I really focus on momentum for hunting over speed.  This is my elk hunting bow, shooting 62# at 30" draw.

That arrow would be 12 grains per pound.
my 550 grain arrow is 8.9 grains per inch.
Both are sturdy arrow weights.

I used archerycalculator.com

Thanks for your thoughts.

[McDave]

750 grains = .0486 kilograms
550 grains = .0356 kilograms
159 fps = 48.5 meters/sec
179 fps = 54.6 meters/sec
1/2 (.0486 X 48.5*2) = 57.2 joules
1/2 (.0356 X 54.6*2) = 53.1 joules

The above shows the KE calc in joules.  The archery calculator may be using a different scale, but the relationship is the same.  The decrease in weight offsets the increase in speed, even though the speed was squared.

[Jackpine Boyz]

Mc Dave,
Thanks for the reply.  So my thought that there was untapped energy pulled from the bow with the heavier arrow isn't that far off.

I was surprised because i typically hear around 1 fps per 3 grain decrease.  I am seeing 1 fps per 10 grain decrease.  Is the 3 grain rule more for compound shooters that have a more efficient mechanism for transferring the stored energy?

Thank you

[McDave]

Your thought is why most traditional archers prefer to use momentum, MV, rather than kenetic energy to measure the effectiveness of a bow and arrow combination.   I don't know the answer to your question as to why there may be a greater pickup of speed as arrow weight is reduced in a compound vs a trad bow.

[Jackpine Boyz]

Hi,
Another thought I had last night is that I 've been suspicious that this particular bow is starting to Stack, that may be altering my results as well.  I will do some experimenting with a shorter draw to see what happens.

[McDave]

What brand of r/d longbow do you have, how long is it, and what is your draw length?

[Jackpine Boyz]

I have a Neew wood r/d long bow by Chris Hartwig in Merrill, wi.  Great bows, this one is a little short for me, designed for 54# at 26.5 "  I picked it up when I was still slouching as the original buyer backed out and I was drawing 28".  With form improvement I now draw 30".
I am 6'3" 195 #.  Chris does check all his bows 32" draw but this was meant for a shorter draw with 62" tip to tip.  I also like that he and I have similar builds so the bows really fit my frame when shooting at his place.

The bow shoots so nice I had a proper one fitted to me that is 64"-65" tip to tip and pulls 55# at 30".  I can feel the Stacking difference comparing the two.  I would highly recommend Chris, I knew the bow was a little short for me but worked well at the time.  

The 55# bow throws the 750 gr arrow at 149 fps, but I haven't shot the 550 with it yet.

Thanks for the feedback.

[McDave]

Yes, if it was designed for someone drawing 26.5", I can see where it might stack at 30", particularly if you can feel the difference when you pull your new bow.  Chris could probably pull the bow on his scale and tillering jig and tell you exactly how much it is stacking, if you're interested.

[Bladepeek]

Bows, guns, doesn't matter. A lot of us feel that lots of mass at a reasonable velocity = 1 hole in; one hole out.

I do believe that's part of the reason why we see these guys shooting 60# compounds only putting an arrow 1/3 of the way into a deer. Part of it is that a lot of them are shooting mechanical blades that are more like a machete than a broadhead, but I really believe part of it is they are shooting the lightest arrow they can get for more speed.

[forestdweller]

Bladepeek I agree with you. The majority of compound shooters use extremely light weight arrows with light tips and their arrows lose steam in a hurry. Their drop off and velocity down range drops off very quickly due to using such light weight arrows.

I bet if we took someone shooting a 60# trad bow shooting a 600 grain arrow vs a compounder shooting a 300 grain arrow then after the 40-50 yard mark the heavier arrow from the trad bow will be flying near the same speed as the 300 grain arrow from the compound and hitting a ton harder with much less of an effect from headwind and cross wind as well.

[McDave]

Originally posted by forestdweller:
I bet if we took someone shooting a 60# trad bow shooting a 600 grain arrow vs a compounder shooting a 300 grain arrow then after the 40-50 yard mark the heavier arrow from the trad bow will be flying near the same speed as the 300 grain arrow from the compound and hitting a ton harder with much less of an effect from headwind and cross wind as well.

I don't think so.  Trad flight shooters use lightweight arrows because they fly further, assuming the same initial force, than heavier arrows.  This is because wind resistance is minimized by using small fletches, so the higher momentum of a heavier arrow is not enough to offset the higher velocity of a lighter arrow.

When measuring penetration, higher momentum arrows have been found to penetrate further than lower momentum, higher velocity arrows.

We have to be careful of this, though.  When comparing two trad bows, one of which shoots a 500 grain arrow at 160 fps while the other shoots a 400 grain arrow at 180 fps, the slower arrow has a higher momentum, and thus should have better penetration.  In your example above, however, comparing a compound and a trad bow, a compound 300 grain arrow may have the same momentum as a trad 600 grain arrow if the compound arrow has a velocity of 300 fps and the trad arrow has a velocity of 150 fps.  We tend to generalize that higher arrow weights = higher momentum, but that only generally works when comparing arrows shot out of the same bow, and not if one is shot out of a trad bow and the other is shot from a compound.

[Jackpine Boyz]

Some follow up from my original question.
I had a chance to test the 55# bow that fits me well using the same two arrows again.  Before I didn't test this both with both arrows.  I found the same issue though.  I am seeing 149fps and 169 fps.  Both bows should exactly 20fps changes with 200 grain increase.  This also show increased KE and Momentum again with the heavier arrow.  I must have found a sweet spot with Chris's bows where I'm pulling more energy out of the bow than I am loosing with the heavier arrow.  I'm going to try increasing and decreasing the tip weights further and see if I fall back into a more expected ratio of weight to Fps.  I wonder if he has seen this with some of the other bows he's made.  I see he haunts this forum at times.

[Jackpine Boyz]

In regards to forestdweller's comment.
I found an article discussing how higher momentum arrows maintain KE further out than lower momentum arrows.  I am giving an example of what I recall but these are not the exact numbers.  I believe it was something like Heavy arrow with low KE had 15% loss at 40 yards while Light arrow had around 40% loss of KE at 40 yards.  In the example the lighter arrow was reduced pretty close to the KE of the heavy arrow but was lacking in momentum.  So there would be a point where the lines would gross.    I will try to find the specific article.  May have been in some of Dr Ashby's works I reviewed at Tuff Head.

[Jackpine Boyz]

Here is one of the articles describing what I mentioned above.  I did find one article that had similar conclusions but followed the arrow out to 40 yards.  

 http://archeryreport.com/2011/01/heavy-vs-light-arrows-speed-power/

For long bow vs wheelie bow the distances involved to see the lines converge may not be meaningful for hunting since the compound would have considerable more speed to start even if the arrow was lighter.