Who said that physics wasn't fun?
04-15-2007, 12:57 AM
#271
Join Date: Jan 2007
Location:
Posts: 83
RE: Who said that physics wasn't fun?
In the KE/Momentum discussion where you can shoot different weighted arrows out of the same bow and if you calculate the KE with actual results, there has to be a point at which the KE actually goes down. Think about it...theoretically, if I were to shoot an arrow so heavy that it left the bow and fell to the ground, there would not be enough Momentum/KE to penetrate a target let alone a deer. I have only a couple years of college physics classes under my belt (from which I am far removed...lol) and it is too late to work on an actual formula to back my theory but I'll state what I am thinking through plain ole logic:
If you take Bow A and shoot a 350, 400, 450, 500, etc grain arrow through a chrono and calculate the KE, yes, the KE will go up, but only to a point. The reason for this is because Bow A has a set amount of POTENTIAL energy at full draw (the area under the draw curve). The heavier the arrow, the more efficient the energy transfer, but the only way to transfer ALL of the bows potential energy into an arrow is for the string to come to a COMPLETE stop once the arrow is released....same must be true of the limbs, cams, and cables. This would mean that ZERO energy even makes it to the Riser (wouldnt need ANY dampening products).
So with that being said, the bow has a relative maximum effeciency as for as transfering PE to the arrow. The bow may become more efficient beyond that point but it may become irrelevant just as in the equation y= 1/x. As you increase x to infinity, the value of y gets closer and closer to zero, but never actually reaches zero.
My theory is that at some point in the test (as the arrow weights go up), the bow reaches it's maximum efficiency or energy transfer and once you go heavier than that, thevelocity begins to drop exponentially. This makes sense because we now have a fixed maximum KE....In the KE formula, Velocity is squared, therefore when KE is fixed and mass goes up, then Velocity decreases exponentially.
It is at this peak in the "curve" of speed vs. weight that KE is maximized. I am not sure that this is EXACTLY what is taking place, but I do know that as I tested my bow with different weighted arrows, there was a point at which KE plateau'd out and then began to drop. As soon as it plateaus, I suggest going with the lightest arrow/highest velocity for that KE.
If you take Bow A and shoot a 350, 400, 450, 500, etc grain arrow through a chrono and calculate the KE, yes, the KE will go up, but only to a point. The reason for this is because Bow A has a set amount of POTENTIAL energy at full draw (the area under the draw curve). The heavier the arrow, the more efficient the energy transfer, but the only way to transfer ALL of the bows potential energy into an arrow is for the string to come to a COMPLETE stop once the arrow is released....same must be true of the limbs, cams, and cables. This would mean that ZERO energy even makes it to the Riser (wouldnt need ANY dampening products).
So with that being said, the bow has a relative maximum effeciency as for as transfering PE to the arrow. The bow may become more efficient beyond that point but it may become irrelevant just as in the equation y= 1/x. As you increase x to infinity, the value of y gets closer and closer to zero, but never actually reaches zero.
My theory is that at some point in the test (as the arrow weights go up), the bow reaches it's maximum efficiency or energy transfer and once you go heavier than that, thevelocity begins to drop exponentially. This makes sense because we now have a fixed maximum KE....In the KE formula, Velocity is squared, therefore when KE is fixed and mass goes up, then Velocity decreases exponentially.
It is at this peak in the "curve" of speed vs. weight that KE is maximized. I am not sure that this is EXACTLY what is taking place, but I do know that as I tested my bow with different weighted arrows, there was a point at which KE plateau'd out and then began to drop. As soon as it plateaus, I suggest going with the lightest arrow/highest velocity for that KE.
04-15-2007, 05:17 AM
#272
Giant Nontypical
Join Date: Feb 2003
Posts: 9,175
RE: Who said that physics wasn't fun?
You raise very good points, doublelungingem. Finding the most efficientarrowfor your bow - while maintaininga decent level of'shootability' -does not equate to shooting the heaviest arrow you can find.
Some people think new technology has changed archery and, in many ways, it has. However, one basicprecept remains. Archery is, has been and always will be, ablending of tradeoffs and balances. You can'tlevel up one area without a corresponding loss in another area.
You can't add arrow weight to gain energy and momentumwithout a loss in speed. You can't cut arrow weight to gain speedwithout a loss in energy and momentum.
You describe a bell chart. I would be more likely to make a double linegraph, speed and KE on one leg, arrow weight on the other. (I would even add a third line. Momentum. 
) We know as arrow weight increases, speed decreases and KE increases. So the speed line and KE line will intersect at some point. That intersection would mark the exactbalance point, the arrow weight where your bow delivers the very best arrow speed at the very best level of KE, within it's capability.
You can shoot that arrow at pretty much everything. Or, you can choose to go somewhat lighter or heavier, depending on what particular purposes you have in mind.
3D? Much lighter to maximize speed for the flattest trajectory and higher score. Thin skinned medium game with smaller broadheads with 2-3 blades? A good bit lighter. Thin skinned medium game with fairly largebroadheads and 4 or more blades? You don't want to go much lighter.Large, tough game at short range with a huge, nasty broadheads, like bear from a treestand? Since trajectory won't be an issue, you'll want to go heavier, maybe quite a bit heavier,to maximize KE.
Once you've got that chart in hand, you can do all kinds of things with arrow weight,and knowwhy.
Some people think new technology has changed archery and, in many ways, it has. However, one basicprecept remains. Archery is, has been and always will be, ablending of tradeoffs and balances. You can'tlevel up one area without a corresponding loss in another area.
You can't add arrow weight to gain energy and momentumwithout a loss in speed. You can't cut arrow weight to gain speedwithout a loss in energy and momentum.
It is at this peak in the "curve" of speed vs. weight that KE is maximized. I am not sure that this is EXACTLY what is taking place, but I do know that as I tested my bow with different weighted arrows, there was a point at which KE plateau'd out and then began to drop. As soon as it plateaus, I suggest going with the lightest arrow/highest velocity for that KE.
) We know as arrow weight increases, speed decreases and KE increases. So the speed line and KE line will intersect at some point. That intersection would mark the exactbalance point, the arrow weight where your bow delivers the very best arrow speed at the very best level of KE, within it's capability. You can shoot that arrow at pretty much everything. Or, you can choose to go somewhat lighter or heavier, depending on what particular purposes you have in mind.
3D? Much lighter to maximize speed for the flattest trajectory and higher score. Thin skinned medium game with smaller broadheads with 2-3 blades? A good bit lighter. Thin skinned medium game with fairly largebroadheads and 4 or more blades? You don't want to go much lighter.Large, tough game at short range with a huge, nasty broadheads, like bear from a treestand? Since trajectory won't be an issue, you'll want to go heavier, maybe quite a bit heavier,to maximize KE.
Once you've got that chart in hand, you can do all kinds of things with arrow weight,and knowwhy.
04-15-2007, 10:31 AM
#273
Fork Horn
Thread Starter
Join Date: Feb 2007
Location: Idaho
Posts: 384
RE: Who said that physics wasn't fun?
Very intriguing reading doublelunginum! A couple of thoughts....
I would be VERY interested to see where this point on the graph corresponds to other charactersitics,like momentum,of the system. As Arthur suggests (very astute man is Arthur!), perhaps a doublegraph on the same coordinate plane. Mass and velocity on the X and Y axis, then plot KE and momentum. The point you reference (where KE peaks and starts to go down) would be the vertex of the KE parabola. If the momentum line (y = mx + b, since momentum is a linear function) and the KE parabola were to intersect at the vertex of the KE parabola!!! hmmmmmmm..... If you think you smell wood burning, it is just me thinking!
Come to think of it, the momentum line would have to reach a maximum as well. One wonders where that point would be, and how that point would correspond to the KE parabola??
Who said that physics wasn't fun!!
Damn you doublelunginem! My poor little head will be slowly (slowly being the operative word!) grinding away on physics problems all day!! Oh man - I just had an idea for my physics class!!!! It will be, shall we say, challenging"! I take the "damn you doublelunginum back"!! Thanks man!!!
ORIGINAL: doublelunginem
If you take Bow A and shoot a 350, 400, 450, 500, etc grain arrow through a chrono and calculate the KE, yes, the KE will go up, but only to a point. The reason for this is because Bow A has a set amount of POTENTIAL energy at full draw (the area under the draw curve). The heavier the arrow, the more efficient the energy transfer, but the only way to transfer ALL of the bows potential energy into an arrow is for the string to come to a COMPLETE stop once the arrow is released....same must be true of the limbs, cams, and cables. This would mean that ZERO energy even makes it to the Riser (wouldnt need ANY dampening products).
When you nail this idea down (100% efficiency = perpetual motion machine = wealth beyond your wildest dreams!), please keep your old friend bow_hunter44 in mind!! If I happen upon the solution, I will reciprocate, I promise!!
My theory is that at some point in the test (as the arrow weights go up), the bow reaches it's maximum efficiency or energy transfer and once you go heavier than that, thevelocity begins to drop exponentially. This makes sense because we now have a fixed maximum KE....In the KE formula, Velocity is squared, therefore when KE is fixed and mass goes up, then Velocity decreases exponentially.
Yup. At some point the mass of the arrow would be so great that its inertia would make it the proverbial "immovable object".
It is at this peak in the "curve" of speed vs. weight that KE is maximized. I am not sure that this is EXACTLY what is taking place, but I do know that as I tested my bow with different weighted arrows, there was a point at which KE plateau'd out and then began to drop. As soon as it plateaus, I suggest going with the lightest arrow/highest velocity for that KE.
If you take Bow A and shoot a 350, 400, 450, 500, etc grain arrow through a chrono and calculate the KE, yes, the KE will go up, but only to a point. The reason for this is because Bow A has a set amount of POTENTIAL energy at full draw (the area under the draw curve). The heavier the arrow, the more efficient the energy transfer, but the only way to transfer ALL of the bows potential energy into an arrow is for the string to come to a COMPLETE stop once the arrow is released....same must be true of the limbs, cams, and cables. This would mean that ZERO energy even makes it to the Riser (wouldnt need ANY dampening products).
When you nail this idea down (100% efficiency = perpetual motion machine = wealth beyond your wildest dreams!), please keep your old friend bow_hunter44 in mind!! If I happen upon the solution, I will reciprocate, I promise!!
My theory is that at some point in the test (as the arrow weights go up), the bow reaches it's maximum efficiency or energy transfer and once you go heavier than that, thevelocity begins to drop exponentially. This makes sense because we now have a fixed maximum KE....In the KE formula, Velocity is squared, therefore when KE is fixed and mass goes up, then Velocity decreases exponentially.
Yup. At some point the mass of the arrow would be so great that its inertia would make it the proverbial "immovable object".
It is at this peak in the "curve" of speed vs. weight that KE is maximized. I am not sure that this is EXACTLY what is taking place, but I do know that as I tested my bow with different weighted arrows, there was a point at which KE plateau'd out and then began to drop. As soon as it plateaus, I suggest going with the lightest arrow/highest velocity for that KE.
Come to think of it, the momentum line would have to reach a maximum as well. One wonders where that point would be, and how that point would correspond to the KE parabola??
Who said that physics wasn't fun!!
Damn you doublelunginem! My poor little head will be slowly (slowly being the operative word!) grinding away on physics problems all day!! Oh man - I just had an idea for my physics class!!!! It will be, shall we say, challenging"! I take the "damn you doublelunginum back"!! Thanks man!!!
04-15-2007, 03:58 PM
#274
Nontypical Buck
Join Date: Aug 2006
Location: Illinois
Posts: 3,076
RE: Who said that physics wasn't fun?
My brain hurts after skimming throu 28 pages of math equations and disagreements[&o].....
the way i see it is a bow thats rated at say 315fps IBO if i can shoot a 550 grain arrow and still be around 230fps (example...only guessing) im gonna go with the heavier arrow....people act like 220 is slow when it is not by any means.
when things get below 200 fps(have to drawthe line somewhere)you start to notice trajectory but anything over 200 fps is still damn fast and plenty flat shooting out to 30 yards...
i guess what im getting at is,
why not take full advantage of the benifits new compounds offer....if i can shoot a 550+ grain arrow and still get 220 thats what im gonna shoot, instead of a 360 grain arrow at say 265+...its kind of like the difference between a .22 and a .45
I'm not saying that very quick arrows dont kill but i like the heaviest arrow i can get without sacrafising too much speed (i like around 220fps)...and thats the biggest advantage of todays super efficient compounds, they can shoot heavy arrows very fast rather than puney arrows at warp speed....somehow i think the industry got confused about why these new compounds are so great...
besides shooting an arrow out of you compound thats at least8 grains per pound will help keep your bow shooting trouble free, quiet and penty quick for a long time.
if you stood 25 yards downrange and i shot an arrow at you coming out of the bow at 220fps .......Ill bet your not gonna be thinking... man that arrow is coming at me slow, look at that rainbow trajectory,..... my bow is faster......SMAAAAACK BLOOD SQUIRTING EVERYWHERE, MOOOOOOOOOMMMMMMMMY, WAAAAA WAAAA WAAAAAAAAA, JESUS WHY WHY WHY OHNO LOOK AT ALL THAT BLOOD COMING OUT OF MY CHEST CAVITY WHYYYYY GOD WHYYYYYYY.... I DONT WANNA DIE PLEASE SOMEBODY HELP ME PLAESE HLEP MI MA I GONEEEE NITEY NIGHT CANT CONROL CRAPTING MEE DRAEWERS SLEEP AAAAAAAA.
[&o]
the way i see it is a bow thats rated at say 315fps IBO if i can shoot a 550 grain arrow and still be around 230fps (example...only guessing) im gonna go with the heavier arrow....people act like 220 is slow when it is not by any means.
when things get below 200 fps(have to drawthe line somewhere)you start to notice trajectory but anything over 200 fps is still damn fast and plenty flat shooting out to 30 yards...
i guess what im getting at is,
why not take full advantage of the benifits new compounds offer....if i can shoot a 550+ grain arrow and still get 220 thats what im gonna shoot, instead of a 360 grain arrow at say 265+...its kind of like the difference between a .22 and a .45
I'm not saying that very quick arrows dont kill but i like the heaviest arrow i can get without sacrafising too much speed (i like around 220fps)...and thats the biggest advantage of todays super efficient compounds, they can shoot heavy arrows very fast rather than puney arrows at warp speed....somehow i think the industry got confused about why these new compounds are so great...
besides shooting an arrow out of you compound thats at least8 grains per pound will help keep your bow shooting trouble free, quiet and penty quick for a long time.
if you stood 25 yards downrange and i shot an arrow at you coming out of the bow at 220fps .......Ill bet your not gonna be thinking... man that arrow is coming at me slow, look at that rainbow trajectory,..... my bow is faster......SMAAAAACK BLOOD SQUIRTING EVERYWHERE, MOOOOOOOOOMMMMMMMMY, WAAAAA WAAAA WAAAAAAAAA, JESUS WHY WHY WHY OHNO LOOK AT ALL THAT BLOOD COMING OUT OF MY CHEST CAVITY WHYYYYY GOD WHYYYYYYY.... I DONT WANNA DIE PLEASE SOMEBODY HELP ME PLAESE HLEP MI MA I GONEEEE NITEY NIGHT CANT CONROL CRAPTING MEE DRAEWERS SLEEP AAAAAAAA.
[&o]
04-15-2007, 05:49 PM
#275
Join Date: Feb 2003
Location:
Posts: 2,413
RE: Who said that physics wasn't fun?
Straightarrow,I just made an arrow that had an foc of 23.6% that was under 400 grains.
If they are spined correctly at 70 lbs, I'd love to try them. Unfortunately, I'd then have to find a shop that sold them. I wouldn't buy them without shooting a sample first.
04-15-2007, 06:03 PM
#276
Join Date: Feb 2003
Location:
Posts: 2,413
RE: Who said that physics wasn't fun?
My arrow is at 18%. I'm pretty sure 18% is close to 19%. Or, do you count numbers different than I do?
Just because he did not test arrows under 600 gr does not mean the same principle does not apply.
I'm not really sur why you keep stating it has to be that heavy to accomplish this?
04-15-2007, 06:09 PM
#277
Giant Nontypical
Join Date: Feb 2003
Location: HENDERSON KY USA
Posts: 6,634
RE: Who said that physics wasn't fun?
YES.I did actually make it.
The Traditional arrows spine only to 70#'s but I believe that is for a traditional bow and since I only shoot a 27" arrow at 58#,they tuned perfectly.They were shooting bullet holes at all but 2' and there it was real close.That is just showing a little paradox.Even there it was more of a wide hole than a tear.
http://www.nitro-stinger.com/Products.cfm#Traditional
For the record,the software isn't real accurate with the Stingers because of the taper.They are much heavier up front so it doesn't figure foc accurately.
I got lucky whenI ordered some Gold Stingers one time and they sent me a traditional light by mistake.I have had some fun playing with it and it ALWAYS yields better penetration,regardless of the weight.
From my experience with stingers,they do have a WIDE spine range.Ime the arrows tapered design will allow for this.
The Traditional arrows spine only to 70#'s but I believe that is for a traditional bow and since I only shoot a 27" arrow at 58#,they tuned perfectly.They were shooting bullet holes at all but 2' and there it was real close.That is just showing a little paradox.Even there it was more of a wide hole than a tear.
http://www.nitro-stinger.com/Products.cfm#Traditional
For the record,the software isn't real accurate with the Stingers because of the taper.They are much heavier up front so it doesn't figure foc accurately.
I got lucky whenI ordered some Gold Stingers one time and they sent me a traditional light by mistake.I have had some fun playing with it and it ALWAYS yields better penetration,regardless of the weight.
From my experience with stingers,they do have a WIDE spine range.Ime the arrows tapered design will allow for this.
04-15-2007, 10:53 PM
#278
Fork Horn
Thread Starter
Join Date: Feb 2007
Location: Idaho
Posts: 384
RE: Who said that physics wasn't fun?
ORIGINAL: Alpha Capo
i guess what im getting at is,
why not take full advantage of the benifits new compounds offer....if i can shoot a 550+ grain arrow and still get 220 thats what im gonna shoot, instead of a 360 grain arrow at say 265+...its kind of like the difference between a .22 and a .45
i guess what im getting at is,
why not take full advantage of the benifits new compounds offer....if i can shoot a 550+ grain arrow and still get 220 thats what im gonna shoot, instead of a 360 grain arrow at say 265+...its kind of like the difference between a .22 and a .45
Beside that, you are a funny guy!! I laughed out loud reading your post!!
04-15-2007, 11:26 PM
#279
Join Date: Jan 2007
Location:
Posts: 83
RE: Who said that physics wasn't fun?
Bowhunter44, Thanks for the terminology...it's all coming back to me...lol
So the KE would have to be a parabola since it is the integral of the draw force curve or the area under the curve. Just trying to refresh here, so how would the momentum graph reach a vertex (which we both agree that it must) since it is a linear function. I guess my thoughts are leading me to the fact that in this situation of dealing with bow performance, momentum would have to be graphed in relation to KE. As I stated before, when we get to the vertex of the KE graph, we are dealing with the maximum efficiency of the bow in the test. Once this is fixed, velocity decreases exponentially as weight goes up. So would this mean that the graph of the momentum be a " / " with half of an upside down parabola following it and connecting at the highest point? The 2nd half would resemble y= 1/x ?
What I am attepting to prove with out the math proplems or actual test results is that momentum and KE are so closely related that they would maximize at the same point. If infact, velocity is decreasing "exponetially" once the bow has maximized efficiency and KE is maximized, then momentum would have to decrease exponentially at that point as well.
Maybe you can actually come up with the proper formulas to prove or disprove this. You seem to have the technical math and physics on the front of your mind. I had 3 physics classes, Calculus I, II, III, and Differential Equations by my sophomore year in college which was 8 years ago. I remember bits and pieces....but maybe I just crammed it all in too short a period of time...lol
P.S...I had a physics and chemistry teacher simular to you in HS....he's the one that got me so interested in this stuff. We had a lab every week and it was all real life scenerios. We would spend Monday learning the physics and the rest of the week performing the physics that we learned...Lab report was due by end of class on Friday for a grade. He never taught from a book and never helped with the Labs...you had to listen on Monday very closely and figure it out on your own. He was the BEST DAMN TEACHER I ever had!!!!
So the KE would have to be a parabola since it is the integral of the draw force curve or the area under the curve. Just trying to refresh here, so how would the momentum graph reach a vertex (which we both agree that it must) since it is a linear function. I guess my thoughts are leading me to the fact that in this situation of dealing with bow performance, momentum would have to be graphed in relation to KE. As I stated before, when we get to the vertex of the KE graph, we are dealing with the maximum efficiency of the bow in the test. Once this is fixed, velocity decreases exponentially as weight goes up. So would this mean that the graph of the momentum be a " / " with half of an upside down parabola following it and connecting at the highest point? The 2nd half would resemble y= 1/x ?
What I am attepting to prove with out the math proplems or actual test results is that momentum and KE are so closely related that they would maximize at the same point. If infact, velocity is decreasing "exponetially" once the bow has maximized efficiency and KE is maximized, then momentum would have to decrease exponentially at that point as well.
Maybe you can actually come up with the proper formulas to prove or disprove this. You seem to have the technical math and physics on the front of your mind. I had 3 physics classes, Calculus I, II, III, and Differential Equations by my sophomore year in college which was 8 years ago. I remember bits and pieces....but maybe I just crammed it all in too short a period of time...lol
P.S...I had a physics and chemistry teacher simular to you in HS....he's the one that got me so interested in this stuff. We had a lab every week and it was all real life scenerios. We would spend Monday learning the physics and the rest of the week performing the physics that we learned...Lab report was due by end of class on Friday for a grade. He never taught from a book and never helped with the Labs...you had to listen on Monday very closely and figure it out on your own. He was the BEST DAMN TEACHER I ever had!!!!
04-16-2007, 01:18 AM
#280
Nontypical Buck
Join Date: Oct 2005
Location: Flushing Michigan
Posts: 2,355
RE: Who said that physics wasn't fun?
You brainiacs are right.A graph of kinetic energy on the y axis and arrow weight on the X axis looks like a parabola. There is an ideal arrow weight that maximizes the KE function. For my bow, thats around 12 grains per inch. If I go heavier than 12 gpi, kinetic energy starts to go down.
In addition, the momentum function also has a similar curve. However, it reaches its maximum value at a much heavier arrow weight than the KE curve does. For my bow, I thinkmaximum momentumwas around 16 grains per inch if I remember correctly. Beyond 16 gpi, the arrow velocity drops off very quickly so momentum actually starts to decrease with increasing arrow weight.
If you have On Target software, play around with different arrow weights going from 300 to 900 grains. Start a spreadsheet to calculate both KE and momentum for each arrow weight. Plot each function and notice that the optimum arrow weight for maximum KE is much lower than the optimal arrow weight for maximum momentum.
In addition, the momentum function also has a similar curve. However, it reaches its maximum value at a much heavier arrow weight than the KE curve does. For my bow, I thinkmaximum momentumwas around 16 grains per inch if I remember correctly. Beyond 16 gpi, the arrow velocity drops off very quickly so momentum actually starts to decrease with increasing arrow weight.
If you have On Target software, play around with different arrow weights going from 300 to 900 grains. Start a spreadsheet to calculate both KE and momentum for each arrow weight. Plot each function and notice that the optimum arrow weight for maximum KE is much lower than the optimal arrow weight for maximum momentum.