Post by michihunter on Jul 12, 2007 6:32:33 GMT -5
Not quite sure what you are referring to BT. Momentum is:
Momentum = Weight X Velocity / Acceleration of Gravity (or a scientific equation in mathematical terms).
Always has been and always will be. It describes the amount of TIME it takes to slow a body in motion. KE however describes that very motion(but it also describes the total energy which includes more than speed and mass!!).
Here's an excerpt from a link provided by Hunters Friend.
In the terms of physics, all broadheads are classes as a "simple machine". As such, all broadheads are no more than a series of inclined planes. The mechanical advantage (M.A.) of a "simple machine" is the ratio of the resistance to the effort. The mechanical advantage of an inclined plane is equal to the length of the plane divided by the height of the plane. A single blade broadhead, with a straight taper, 1" wide by 3" long can be viewed as 2 inclined planes, each of which has a mechanical advantage of 6.0 (3" divided by 1/2"). The mechanical advantage of the two planes combined would be 3.0 because the height would be doubled while the length remains the same. What this means is that with an exerted force (effort) of 1 pound, a weight of 3 pounds can be lifted from the tip of the broadhead to the back edge of the broadhead. The higher the M.A. the more work a broadhead can do with the force available.
To determine the mechanical advantage of any broadhead with a straight taper to the cutting edge, divide the length of the one cutting blade by 1/2 the width of the broadhead (or, more precisely, the distance from the central axis of the arrow to the highest point on the plane) multiplied by the number of blades. In an equation this would be expressed as:
M.A. = Length of cutting edge / (1/2 width of head) X (number of blades)
Example #1
As stated above, a single blade broadhead 3" long by 1" wide has a mechanical advantage of 3.0. If that same head has three blades, the M.A. would be 2.0, ie: (3" length/.5" lift distance X 3 blades). If it had four blades, the M.A. would be 1.5, or one half that of the single blade.
Simple enough, right? Mechanical advantage tells us that the more blades on a broadhead (ie: the more surface area), the more resistance that head will meet upon impact with the target. This makes sense. As an example, which object would be easier to penetrate a wall – a screwdriver or a baseball bat?
We must also consider the energy that the arrow carries. Again, from Dr. Ashby’s paper:
KINETIC ENERGY vs MOMENTUM
As a base point for a discussion of momentum and kinetic energy, one must understand that the laws of physics dictate that energy can never be manufactured or destroyed but only transformed or directed in its flow. The equations for these two measurements are:
Kinetic Energy = Weight X Velocity Squared /2 X Acceleration of Gravity
Momentum = Weight X Velocity / Acceleration of Gravity
The kinetic energy (K.E.) of a moving body increases as the square of the velocity whereas the momentum increases directly as velocity increases.
With the advent of compound bows and overdraw setups, with their higher velocity capability, it has become common to see kinetic energy figures cited as a supposed measure of the penetration capability of a particular bow-arrow-broadhead combination. This use of kinetic energy reflects a misunderstanding of these basic principles of physics. By definition, kinetic energy is the capacity to do work. It is the TOTAL ENERGY of a body in motion. K.E. is scalar, or non-directional, in nature. As applied to an arrow in motion, K.E. includes such things as: radial energy due to arrow flexion, rotational energy due to arrow spin, sonic energy due to vibration, heat energy due to friction, and potential energy (all other remaining energy). (Simple use of K.E. alone, also fails to take into consideration the mechanical advantage of the broadhead.) The kinetic energy of an arrow, by definition, is not a direct indicator of the penetration capability of the bow-arrow-broadhead combination. Momentum is the measure used in physics to quantify the "impulse"; the force exerted over a period of time IN ONE SPECIFIC DIRECTION. Momentum is a unidirectional force vector. Another of those basic laws of physics states that "in cases of collision, whether the bodies are elastic or inelastic, the momentum before collision is equal to the momentum after impact". This means that momentum is the measure of how much energy, due solely to the weight and velocity of an arrow, must be transferred to whatever it impacts before the arrow comes to rest. (Again, momentum alone will not fully predict the penetration capability of an arrow, and the mechanical advantage of the broadhead must also be considered.)
Assuming there is no bending of broadhead or arrow shaft, how far into the target an arrow will go before all available energy is lost (the amount of penetration) depends on three MAIN factors: the resistance of the object impacted (target), the momentum of the arrow, and the efficiency with which the arrow (broadhead) utilizes the force available to it. The resistance of the target we have little control over. Arrow and broadhead selection we do have control over. Use of a broadhead with a high mechanical advantage and use of heavier arrows with high levels of arrow momentum maximizes the penetration of hunting arrows, regardless of what target resistance is encountered.
Note: the best arrow/broadhead combination tested provided a momentum of .57 lbs-sec.
TO ACHIEVE .57 POUND SECONDS OF MOMENTUM: (The momentum of the "Best" performing arrow/broadhead combinations in study, all of which had broadheads of 3.0 mechanical advantage):
A 740 Grain Arrow must reach a velocity of 161 Ft./Sec.
A 550 Grain Arrow must reach a velocity of 234 Ft./Sec.
A 450 Grain Arrow must reach a velocity of 285 Ft./Sec.
A 350 Grain Arrow must reach a velocity of 367 Ft./Sec.
Now that we have a better understanding of mechanical advantage, and kinetic energy vs. momentum, we can begin to understand their relationship towards a hunting arrow. I must stress again, at this point, that the “magic” number of .57 lb-seconds of momentum was established for large African game. Such a momentum is not necessary for the whitetail hunter, but the principles behind the calculation remain. The next logical question, for the whitetail hunter, becomes ‘what should my momentum be’, and ‘how to I relate mechanical advantage to momentum?’. Those questions will be answered shortly. There’s one more factor to discuss. Remember those three main factors determining arrow performance? Ability to do work, energy, and resistance? Well, its true that we can’t factor the resistance of the target. But we can factor the resistance of the arrow shaft as it passes through the animal.
To determine shaft drag through testing, Dr. Ashby used the same broadhead on arrow shafts that were
1) smaller diameter than the ferrule of the broadhead
2) same diameter than the ferrule of the broadhead
3) larger diameter than the ferrule of the broadhead
The results of his testing gave him the respective multipliers of 1.0, .9, and .6.
Dr. Ashby uses his own calculation, which throughout the data demonstrates a strong correlation to the arrow’s penetration ability. This is how he ties momentum to mechanical advantage, as well as shaft drag. He refers to the measurement as Tissue Penetration Index, or TPI.
Now, let’s finally take a look at a real world hunting setup, using Dr. Ashby’s TPI as a predictor of the penetrating ability of the arrow. We’ll also compare this to one of the many examples that Dr. Ashby cites in his paper. First off, to calculate your TPI, use the following:
(momentum*MA*shaft drag factor)
For our example, we’ll use my hunting rig, which is:
2004 Martin Prowler, Tru-arc hybrid cam system, 62 lb, 29” draw, with a 450 grain carbon arrow (Beman ICS shaft), tipped with a Magnus Stinger, 100 grain, 2 blade broadhead having a cutting surface of 2 1/8” and a cutting diameter of 1 1/16”.
First, lets calculate the momentum of my arrow:
momentum= (weight*speed)/(acceleration of gravity), with weight it pounds and speed in feet per second, therefore:
m=(450/7000)*(230) / 32 feet per second per second, which roughly equals 0.462 lbs-sec.
Now consider the mechanical advantage of my broadhead:
MA=2.125/((1.0625*.5)*2)= 2
Lastly, my arrow shaft is slightly smaller than the ferrule of my broadhead, so when considering shaft drag, I can use a multiplier of 1.0.
Based on this information, I can determine the TPI of my arrow to be:
(momentum*MA*shaft drag factor) or in my case:
.462*2*1 = 0.924 TPI
Great, you might say, but how does that relate to whitetails? Consider two examples from Dr. Ashby’s paper:
From longbow:
Consider a 60 pound longbow firing a 788 grain compressed cedar arrow, with a 190 grain Grizzly two blade broadhead, at 148 fps has only 38.34 ft. lbs of K.E., .52 lb.-sec. of momentum, but has a TPI of 1.50. T hat combination was used to repeatedly shoot through the scapula of a large zebra stallion and through the thorax to the off side, often breaking off-side ribs (never failing to penetrate the scapula and completely through the thorax).
Additionally, he tested a modern compound bow:
This combination was also compared to a high energy compound firing a 450 grain carbon arrow tipped with a three blade head, with cut width of 1 1/8" and a cutting blade length of 2", at a velocity of 259+ fps. This combination yields 76.56 ft. lbs. of K.E., .52 lb.-sec. of momentum, but a TPI of only 0.62. It was unable to penetrate the zebra scapula.
Note that in both examples, the momentum was the same – the only thing that changed were two constants – arrow weight, and mechanical advantage of the broadhead. Performance could be matched with the compound bow if only different arrows and broadheads were selected. Now, you don't need to be able to penetrate the scapula of a zebra to hunt whitetails - I'm not claiming that AT ALL. but notice the difference in my bow setup compared to the one tested, and the TPI difference of .924 compared to .62 .
Based on this information, I'm very comfortable with my setup. its one man's research, I know, but he is very educated, has done years of testing, and considering the lack of any other real testing data, what else do we have to go on?
I realize this was long winded, but hopefully its clear enough to allow some people to get a picture of the real dynamics involved in killing with a bow and arrow, not just the often quoted draw weight, kinetic energy, and speed that are quoted by the manufacturers. I’d recommend to anyone interested to read Dr. Ashby’s works – it’s the most extensive testing I’ve come across. I’ll conclude with Dr. Ashby’s summary recommendations for today’s bowhunters:
1) Maximize your bow’s efficiency: 12 to 14 grains of arrow mass per pound of draw weight is peak efficiency for most compound bows.
2) Use broadheads of high mechanical advantage.
3) Use broadheads with a cut on impact tip
4) Accept nothing less than perfect arrow flight. A tuned bow with proper arrow spine will ensure that minimal energy is lost due to flexing in flight.
5) Do not use mechanical broadheads. In Dr. Ashby’s testing, mechanicals were the most prone to breaking, which stops penetration cold. They have a poor mechanical advantage as well, and require additional energy to deploy.
6) Use an arrow shaft smaller in diameter than the ferrule of the broadhead.
7) Shaft finish – basically, the smoother, the better – there is less resistance.
Momentum = Weight X Velocity / Acceleration of Gravity (or a scientific equation in mathematical terms).
Always has been and always will be. It describes the amount of TIME it takes to slow a body in motion. KE however describes that very motion(but it also describes the total energy which includes more than speed and mass!!).
Here's an excerpt from a link provided by Hunters Friend.
In the terms of physics, all broadheads are classes as a "simple machine". As such, all broadheads are no more than a series of inclined planes. The mechanical advantage (M.A.) of a "simple machine" is the ratio of the resistance to the effort. The mechanical advantage of an inclined plane is equal to the length of the plane divided by the height of the plane. A single blade broadhead, with a straight taper, 1" wide by 3" long can be viewed as 2 inclined planes, each of which has a mechanical advantage of 6.0 (3" divided by 1/2"). The mechanical advantage of the two planes combined would be 3.0 because the height would be doubled while the length remains the same. What this means is that with an exerted force (effort) of 1 pound, a weight of 3 pounds can be lifted from the tip of the broadhead to the back edge of the broadhead. The higher the M.A. the more work a broadhead can do with the force available.
To determine the mechanical advantage of any broadhead with a straight taper to the cutting edge, divide the length of the one cutting blade by 1/2 the width of the broadhead (or, more precisely, the distance from the central axis of the arrow to the highest point on the plane) multiplied by the number of blades. In an equation this would be expressed as:
M.A. = Length of cutting edge / (1/2 width of head) X (number of blades)
Example #1
As stated above, a single blade broadhead 3" long by 1" wide has a mechanical advantage of 3.0. If that same head has three blades, the M.A. would be 2.0, ie: (3" length/.5" lift distance X 3 blades). If it had four blades, the M.A. would be 1.5, or one half that of the single blade.
Simple enough, right? Mechanical advantage tells us that the more blades on a broadhead (ie: the more surface area), the more resistance that head will meet upon impact with the target. This makes sense. As an example, which object would be easier to penetrate a wall – a screwdriver or a baseball bat?
We must also consider the energy that the arrow carries. Again, from Dr. Ashby’s paper:
KINETIC ENERGY vs MOMENTUM
As a base point for a discussion of momentum and kinetic energy, one must understand that the laws of physics dictate that energy can never be manufactured or destroyed but only transformed or directed in its flow. The equations for these two measurements are:
Kinetic Energy = Weight X Velocity Squared /2 X Acceleration of Gravity
Momentum = Weight X Velocity / Acceleration of Gravity
The kinetic energy (K.E.) of a moving body increases as the square of the velocity whereas the momentum increases directly as velocity increases.
With the advent of compound bows and overdraw setups, with their higher velocity capability, it has become common to see kinetic energy figures cited as a supposed measure of the penetration capability of a particular bow-arrow-broadhead combination. This use of kinetic energy reflects a misunderstanding of these basic principles of physics. By definition, kinetic energy is the capacity to do work. It is the TOTAL ENERGY of a body in motion. K.E. is scalar, or non-directional, in nature. As applied to an arrow in motion, K.E. includes such things as: radial energy due to arrow flexion, rotational energy due to arrow spin, sonic energy due to vibration, heat energy due to friction, and potential energy (all other remaining energy). (Simple use of K.E. alone, also fails to take into consideration the mechanical advantage of the broadhead.) The kinetic energy of an arrow, by definition, is not a direct indicator of the penetration capability of the bow-arrow-broadhead combination. Momentum is the measure used in physics to quantify the "impulse"; the force exerted over a period of time IN ONE SPECIFIC DIRECTION. Momentum is a unidirectional force vector. Another of those basic laws of physics states that "in cases of collision, whether the bodies are elastic or inelastic, the momentum before collision is equal to the momentum after impact". This means that momentum is the measure of how much energy, due solely to the weight and velocity of an arrow, must be transferred to whatever it impacts before the arrow comes to rest. (Again, momentum alone will not fully predict the penetration capability of an arrow, and the mechanical advantage of the broadhead must also be considered.)
Assuming there is no bending of broadhead or arrow shaft, how far into the target an arrow will go before all available energy is lost (the amount of penetration) depends on three MAIN factors: the resistance of the object impacted (target), the momentum of the arrow, and the efficiency with which the arrow (broadhead) utilizes the force available to it. The resistance of the target we have little control over. Arrow and broadhead selection we do have control over. Use of a broadhead with a high mechanical advantage and use of heavier arrows with high levels of arrow momentum maximizes the penetration of hunting arrows, regardless of what target resistance is encountered.
Note: the best arrow/broadhead combination tested provided a momentum of .57 lbs-sec.
TO ACHIEVE .57 POUND SECONDS OF MOMENTUM: (The momentum of the "Best" performing arrow/broadhead combinations in study, all of which had broadheads of 3.0 mechanical advantage):
A 740 Grain Arrow must reach a velocity of 161 Ft./Sec.
A 550 Grain Arrow must reach a velocity of 234 Ft./Sec.
A 450 Grain Arrow must reach a velocity of 285 Ft./Sec.
A 350 Grain Arrow must reach a velocity of 367 Ft./Sec.
Now that we have a better understanding of mechanical advantage, and kinetic energy vs. momentum, we can begin to understand their relationship towards a hunting arrow. I must stress again, at this point, that the “magic” number of .57 lb-seconds of momentum was established for large African game. Such a momentum is not necessary for the whitetail hunter, but the principles behind the calculation remain. The next logical question, for the whitetail hunter, becomes ‘what should my momentum be’, and ‘how to I relate mechanical advantage to momentum?’. Those questions will be answered shortly. There’s one more factor to discuss. Remember those three main factors determining arrow performance? Ability to do work, energy, and resistance? Well, its true that we can’t factor the resistance of the target. But we can factor the resistance of the arrow shaft as it passes through the animal.
To determine shaft drag through testing, Dr. Ashby used the same broadhead on arrow shafts that were
1) smaller diameter than the ferrule of the broadhead
2) same diameter than the ferrule of the broadhead
3) larger diameter than the ferrule of the broadhead
The results of his testing gave him the respective multipliers of 1.0, .9, and .6.
Dr. Ashby uses his own calculation, which throughout the data demonstrates a strong correlation to the arrow’s penetration ability. This is how he ties momentum to mechanical advantage, as well as shaft drag. He refers to the measurement as Tissue Penetration Index, or TPI.
Now, let’s finally take a look at a real world hunting setup, using Dr. Ashby’s TPI as a predictor of the penetrating ability of the arrow. We’ll also compare this to one of the many examples that Dr. Ashby cites in his paper. First off, to calculate your TPI, use the following:
(momentum*MA*shaft drag factor)
For our example, we’ll use my hunting rig, which is:
2004 Martin Prowler, Tru-arc hybrid cam system, 62 lb, 29” draw, with a 450 grain carbon arrow (Beman ICS shaft), tipped with a Magnus Stinger, 100 grain, 2 blade broadhead having a cutting surface of 2 1/8” and a cutting diameter of 1 1/16”.
First, lets calculate the momentum of my arrow:
momentum= (weight*speed)/(acceleration of gravity), with weight it pounds and speed in feet per second, therefore:
m=(450/7000)*(230) / 32 feet per second per second, which roughly equals 0.462 lbs-sec.
Now consider the mechanical advantage of my broadhead:
MA=2.125/((1.0625*.5)*2)= 2
Lastly, my arrow shaft is slightly smaller than the ferrule of my broadhead, so when considering shaft drag, I can use a multiplier of 1.0.
Based on this information, I can determine the TPI of my arrow to be:
(momentum*MA*shaft drag factor) or in my case:
.462*2*1 = 0.924 TPI
Great, you might say, but how does that relate to whitetails? Consider two examples from Dr. Ashby’s paper:
From longbow:
Consider a 60 pound longbow firing a 788 grain compressed cedar arrow, with a 190 grain Grizzly two blade broadhead, at 148 fps has only 38.34 ft. lbs of K.E., .52 lb.-sec. of momentum, but has a TPI of 1.50. T hat combination was used to repeatedly shoot through the scapula of a large zebra stallion and through the thorax to the off side, often breaking off-side ribs (never failing to penetrate the scapula and completely through the thorax).
Additionally, he tested a modern compound bow:
This combination was also compared to a high energy compound firing a 450 grain carbon arrow tipped with a three blade head, with cut width of 1 1/8" and a cutting blade length of 2", at a velocity of 259+ fps. This combination yields 76.56 ft. lbs. of K.E., .52 lb.-sec. of momentum, but a TPI of only 0.62. It was unable to penetrate the zebra scapula.
Note that in both examples, the momentum was the same – the only thing that changed were two constants – arrow weight, and mechanical advantage of the broadhead. Performance could be matched with the compound bow if only different arrows and broadheads were selected. Now, you don't need to be able to penetrate the scapula of a zebra to hunt whitetails - I'm not claiming that AT ALL. but notice the difference in my bow setup compared to the one tested, and the TPI difference of .924 compared to .62 .
Based on this information, I'm very comfortable with my setup. its one man's research, I know, but he is very educated, has done years of testing, and considering the lack of any other real testing data, what else do we have to go on?
I realize this was long winded, but hopefully its clear enough to allow some people to get a picture of the real dynamics involved in killing with a bow and arrow, not just the often quoted draw weight, kinetic energy, and speed that are quoted by the manufacturers. I’d recommend to anyone interested to read Dr. Ashby’s works – it’s the most extensive testing I’ve come across. I’ll conclude with Dr. Ashby’s summary recommendations for today’s bowhunters:
1) Maximize your bow’s efficiency: 12 to 14 grains of arrow mass per pound of draw weight is peak efficiency for most compound bows.
2) Use broadheads of high mechanical advantage.
3) Use broadheads with a cut on impact tip
4) Accept nothing less than perfect arrow flight. A tuned bow with proper arrow spine will ensure that minimal energy is lost due to flexing in flight.
5) Do not use mechanical broadheads. In Dr. Ashby’s testing, mechanicals were the most prone to breaking, which stops penetration cold. They have a poor mechanical advantage as well, and require additional energy to deploy.
6) Use an arrow shaft smaller in diameter than the ferrule of the broadhead.
7) Shaft finish – basically, the smoother, the better – there is less resistance.
....Let me be more to the point.