So the arrow build thread went off track related to the effect of FOC on arrow trajectory. My fault, sorry. It is a good writeup on arrow building and worth a look. Very detailed.
Now, because I have this kind of time, and was bored this fine Saturday morning. And I just got a batch of goodies to build some arrows for an upcoming hunt, so I decided to test this. Here are the ingredients:
Beman ICS Hunter Pro 300 shaft cut to 26.75" carbon to carbon.
100 grain brass insert
25 grain aluminum insert
3 Bohning Blazer vanes in eye annoying yellow (actually 6 vanes, you'll see why below)
1 G size nock
125 grain field tip
Total arrow weight of 494 grains.
Fletching was right helical lovingly applied in an Arizona EZ-Fletch jig. Bow used was a PSE Carbon Air 32 at 70lbs 28.5" draw, Schaffer XV rest. I didn't measure velocity since it is constant given no change in the arrow weight. Probably in the 270-275fps area.
I assembled the arrow with the 100 grain insert in one end and the 25 grain insert in the other. The G nock has a long enough shank to screw into the inserts, so that is how the nock was attached and it could be moved from one end to the other. Only one arrow was used. I stripped the fletching to put the 100 grain brass insert end either on the point end or the nock end and re-installed the fletching. By doing this the arrow weight was identical, and the aerodynamics of the arrow were also identical. Only the FOC changes.
Setup 1: the 100 grain insert at the nock end yielded a FOC of 3.6%.
Setup 2: the 100 grain insert at the point end yielded a FOC of 16.2%
That should be a sufficient difference to see any effect.
I sighted dead on at 50 yards with setup 1, then moved back to 75 yards and measured the drop between 50 and 75 for 10 shots. I drew a line across the top target at the center and used that to measure down to the arrow on the bottom target it was stacked on. The 10 shot string should be enough to minimize my poor shooting and aiming errors. 30 per would be the statistics guru number, but I had to shoot between rain showers today. Thus my toes were wet and cold all morning.
No changes were made to the sight and I shot setup 2 at both 50 yards and 75 yards.
The FOC theory states that the higher FOC setup would "nose dive" and hit lower at both 50 and 75 yards. The idea being heavier weight at the front will pull the point end down faster.
Results:
First, this is about as good as I shoot right now (might be as good as I ever shoot), but a vertical spread of 5" at 75 yards makes me fairly happy. I wanted to go to 100, but there is too much traffic today. 100 yards is across the road for me. Is 75 yards far enough to show a difference? Pretty sure it is given the idea that the arrow is moving something like 100" vertically from bow to target. This is also beyond most normal max hunting ranges (awesome if you shoot farther at game, most folks don't).
At 50 yards, both setups shot to point of aim and grouped as well as I can shoot. So, no change.
The chart shows the difference between the two. I call it even. Setup 1, IMO, showed some slight stability issues at 75 yards. It could also have been shooter influence since it was up first. Setup 2 flew really well and I couldn't see any odd behavior in flight. Probably the straightest flying arrow, I've shot (hint, this is probably my new build minus the insert at the nock end). I felt I shot setup 2 better. But that is purely subjective. The data says the center of the groups was for all practical purposes the same.
What does this all mean? FOC has no bearing on arrow flight in this test. I'll conclude that it doesn't, ever. Why? Because weight doesn't change the rate at which objects free fall. That rate is a constant at 9.8 m/s/s due to gravity regardless of mass. This is why trajectory calculations have no weight or mass component in them. All projectiles are affected by gravity the same. All, regardless of weight, balance point, etc. fall in the vertical plane at 9.8 m/s/s. Remember that gravity pulls on the entire length of the arrow, not just the balance point, or center of gravity (a misnomer in this instance). All points on the arrow accelerate toward the ground at the same speed. Attitude, or direction of travel, is dictated by the arc of trajectory and steering of the fletching. The pointy end starts pointing up'ish, and ends pointing down'ish. Air resistance is the reason for almost all other projectile behavior other than Coriolis effect, and spin drift.
The javelin argument has come up. Here is the walk through of that. The original design was balanced near the center and had symmetrical ends. The thrower would launch it at an up angle and the javelin would maintain that attitude until it hit the earth. This meant the front would plane on the air and float it farther, but it would land flat, not sticking point down. The redesign did two things: increase air drag, and move the balance point forward. Increased air drag is easy to understand, it slows faster since the air pushes harder on it. The balance point change was to allow the tail of the javelin to steer the front. In the original design there is no steering beyond the initial launch angle. In the redesign, the tail now forces the tip to be in line with the direction of travel which eventually changes to nose down when the apex of the arc is passed. It doesn't go nose down due to weight, but due solely to steering force.
That's it. Bring on the discussion, flaming, discontent, and of course feel free to heap on praise. PM for monetary donations, or to say things that aren't appropriate on an open forum.
Jeremy
In case you are wondering, I am a metallurgical engineer with 20+ years of experience. I generally hate math and avoid it if possible, but understand it well. If put in a life or death situation, I could integrate or solve a differential equation. Thank goodness, that is unlikely.
Now, because I have this kind of time, and was bored this fine Saturday morning. And I just got a batch of goodies to build some arrows for an upcoming hunt, so I decided to test this. Here are the ingredients:
Beman ICS Hunter Pro 300 shaft cut to 26.75" carbon to carbon.
100 grain brass insert
25 grain aluminum insert
3 Bohning Blazer vanes in eye annoying yellow (actually 6 vanes, you'll see why below)
1 G size nock
125 grain field tip
Total arrow weight of 494 grains.
Fletching was right helical lovingly applied in an Arizona EZ-Fletch jig. Bow used was a PSE Carbon Air 32 at 70lbs 28.5" draw, Schaffer XV rest. I didn't measure velocity since it is constant given no change in the arrow weight. Probably in the 270-275fps area.
I assembled the arrow with the 100 grain insert in one end and the 25 grain insert in the other. The G nock has a long enough shank to screw into the inserts, so that is how the nock was attached and it could be moved from one end to the other. Only one arrow was used. I stripped the fletching to put the 100 grain brass insert end either on the point end or the nock end and re-installed the fletching. By doing this the arrow weight was identical, and the aerodynamics of the arrow were also identical. Only the FOC changes.
Setup 1: the 100 grain insert at the nock end yielded a FOC of 3.6%.
Setup 2: the 100 grain insert at the point end yielded a FOC of 16.2%
That should be a sufficient difference to see any effect.
I sighted dead on at 50 yards with setup 1, then moved back to 75 yards and measured the drop between 50 and 75 for 10 shots. I drew a line across the top target at the center and used that to measure down to the arrow on the bottom target it was stacked on. The 10 shot string should be enough to minimize my poor shooting and aiming errors. 30 per would be the statistics guru number, but I had to shoot between rain showers today. Thus my toes were wet and cold all morning.
No changes were made to the sight and I shot setup 2 at both 50 yards and 75 yards.
The FOC theory states that the higher FOC setup would "nose dive" and hit lower at both 50 and 75 yards. The idea being heavier weight at the front will pull the point end down faster.
Results:
First, this is about as good as I shoot right now (might be as good as I ever shoot), but a vertical spread of 5" at 75 yards makes me fairly happy. I wanted to go to 100, but there is too much traffic today. 100 yards is across the road for me. Is 75 yards far enough to show a difference? Pretty sure it is given the idea that the arrow is moving something like 100" vertically from bow to target. This is also beyond most normal max hunting ranges (awesome if you shoot farther at game, most folks don't).
At 50 yards, both setups shot to point of aim and grouped as well as I can shoot. So, no change.
The chart shows the difference between the two. I call it even. Setup 1, IMO, showed some slight stability issues at 75 yards. It could also have been shooter influence since it was up first. Setup 2 flew really well and I couldn't see any odd behavior in flight. Probably the straightest flying arrow, I've shot (hint, this is probably my new build minus the insert at the nock end). I felt I shot setup 2 better. But that is purely subjective. The data says the center of the groups was for all practical purposes the same.
What does this all mean? FOC has no bearing on arrow flight in this test. I'll conclude that it doesn't, ever. Why? Because weight doesn't change the rate at which objects free fall. That rate is a constant at 9.8 m/s/s due to gravity regardless of mass. This is why trajectory calculations have no weight or mass component in them. All projectiles are affected by gravity the same. All, regardless of weight, balance point, etc. fall in the vertical plane at 9.8 m/s/s. Remember that gravity pulls on the entire length of the arrow, not just the balance point, or center of gravity (a misnomer in this instance). All points on the arrow accelerate toward the ground at the same speed. Attitude, or direction of travel, is dictated by the arc of trajectory and steering of the fletching. The pointy end starts pointing up'ish, and ends pointing down'ish. Air resistance is the reason for almost all other projectile behavior other than Coriolis effect, and spin drift.
The javelin argument has come up. Here is the walk through of that. The original design was balanced near the center and had symmetrical ends. The thrower would launch it at an up angle and the javelin would maintain that attitude until it hit the earth. This meant the front would plane on the air and float it farther, but it would land flat, not sticking point down. The redesign did two things: increase air drag, and move the balance point forward. Increased air drag is easy to understand, it slows faster since the air pushes harder on it. The balance point change was to allow the tail of the javelin to steer the front. In the original design there is no steering beyond the initial launch angle. In the redesign, the tail now forces the tip to be in line with the direction of travel which eventually changes to nose down when the apex of the arc is passed. It doesn't go nose down due to weight, but due solely to steering force.
That's it. Bring on the discussion, flaming, discontent, and of course feel free to heap on praise. PM for monetary donations, or to say things that aren't appropriate on an open forum.
Jeremy
In case you are wondering, I am a metallurgical engineer with 20+ years of experience. I generally hate math and avoid it if possible, but understand it well. If put in a life or death situation, I could integrate or solve a differential equation. Thank goodness, that is unlikely.
Obviously I’m bored. 
