FOC and Arrow Trajectory Tested

[Beendare]

Agreed on the 9.8m/s2.

Id like to see this physics experiment with FOC repeated as it applies to hunting. This really is where the controversy is anyways. Obviously I’m bored.

Does the addition of FOC have any affect on a hunting arrow?

.....

Ashby disagrees with Sir Isaac Newton.... as illustrated in his dog and pony show video.

I think the answer to all of your questions relates to perfect arrow flight. Thats why the pros use what they do.......and thats what works good for hunting. Sure you can get that with FOC in a pretty wide range.

My arrows got pretty squirrely in the 30% FOC range [long draw, compound bow at 80#] YMMV.

Wapiti did a pretty good test here......

I think the whole point....don't focus on FOC....focus on good arrow flight. Its really only one guy singing the praises of very high FOC....and all of the other legit experts focuses on arrow flight. It really comes down to who you want to believe- grin

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[Wapiti1]

In the test I did, a broadhead probably wouldn't shoot worth a darn at 3.6%. I'd have to spend some time tuning that one, and may not be able to get it to shoot.

Broadheads will always shoot better at higher FOC since they require the larger steering arm that provides. As for drop, they would drop at 9.8 m/s/s, but their drag would be higher, so faster speed loss at distance. Yes, I think you can go too high. At some point you reach a buckling limit for the shaft at launch that a non-tapered shaft can't handle. I think you would have to go to a taper shaft to make it work. You put a lot of force in the section right behind the broadhead.

I know diddly about Olympic or target archers. Beendare is right, IMO. They would seek perfect flight and have their methods to get there.

Not sure on crosswind. My gut feeling is that it wouldn't matter. Crosswind would be a constant side force and arrow diameter, fletching size and broadhead diameter would probably dictate flight.

Jeremy

 

[live2huntelk]

https://www.researchgate.net/profile/Zulkifli_Ahmad5/publication/305321934_Development_and_analysis_of_arrow_for_archery/links/5788542008ae21394a0c7d0e.pdf

 

[Topo_trekker]

Don’t get me wrong I agree it was a good test. Thanks again for posting Wapiti.

I just had a problem with the statement “FOC has no bearing on arrow flight ever”. Should be FOC has no bearing on the pull of gravity. It certainly has an affect on arrow flight.


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[Wapiti1]

If I said it didn't affect flight, I meant it didn't affect trajectory. I agree it matters for good flight and tuning.

Jeremy

 

[Topo_trekker]

Doesn’t flight affect trajectory? If foc affects flight, then you could say it affects trajectory.

Gravity is not the only force. Thrust, lift, drag all affect the arrow. Changes in foc, change the flight. Bad flight equals drag, drag affects trajectory.

 

[SpineENGR]

This is on par with what Brian at Day Six recently spoke about in a podcast. I'm not a huge FOC fan by any means and have landed anywhere from 9% to 15% over the years. Hasn't really seemed to make a big difference in arrow flight as long as my bow was tuned.

 

[IdahoHntr]

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.

I appreciate this test and the efforts you went through to do it. I agree that it proves like most said in the other thread; at hunting distances FOC will not effect the trajectory of an arrow.

The physics question that I think more were wondering about (at least I was) is will it eventually have an effect on an arrow at distances where the linear velocity of the arrow drops below a certain point? At max arrow distances so to speak. It's more just an amusing thought that has absolutely no bearing on bow setup, but interesting to think about nonetheless. I was thinking it might eventually have an effect, and your javelin reasoning makes me think I might be right. If you have a higher FOC, similar to the javelin changes, wouldn't the steering force be greater, forcing the nose down sooner, and thus decreasing the distance? It wouldn't be weight and gravity pulling the arrow nose down, but a greater steering force due to the increased moment arm as you mentioned. It also would reason that if you built an arrow similar to the original javelin, it would also plane and fly further. So maybe FOC does have an effect eventually? Curious your thoughts on that. Everything you said about the javelin makes complete sense, so why wouldn't it apply to an arrow?

I'm still not sure I agree with your theory that gravity pulls on all points on the arrow equally. A "pull" is a force and F=ma. This leads me to believe mass effects the force of pull on the arrow. Why if a lawn dart is dropped from a horizontal position will it always land head down? By your theory shouldn't it land horizontal? Heavy FOC arrows do the same thing, though not as obvious. The point hits first, but the arrow doesn't turn vertical quite like a lawn dart. Just curious how you would explain that?

You can argue that mass doesn't have an effect on gravity and if I can resolve the aforementioned, I'd believe you, but you can't argue mass has no bearing on trajectory. Mass does have a bearing on trajectory. Why else would every ballistic calculator have a mass element (The Ballistic Coefficient), if it has no bearing on trajectory? By Newton's law a heavier object is harder to slow down. It may not be effecting the trajectory by virtue of gravity, but mass does matter in all real world trajectory equations.

For example two objects of the same size, shape, and coefficient of drag with different weights launched at the exact same speed would have different trajectories. You can make an exact replica of a bullet out of wood and plated metal to get identical drag coefficients, size, and shape, but the wood bullet just isn't going to fly as far. Mass does make a difference doesn't it?

I too can integrate or solve a differential equation if my life depended on it, but I haven't nearly the real world experience in the engineering field that you have and so very much value and respect your opinion. Thanks for sharing!

 

[Topo_trekker]

Idaho that’s what I was thinking too.

Flight trajectory is determined by thrust, lift, drag, weight, and the balance of all these. Changes to the balance(foc) changes trajectory.

A lighter rear ended arrow with weight more forward would be affected differently by the fletching drag/lift as well.


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[Wapiti1]

I appreciate this test and the efforts you went through to do it. I agree that it proves like most said in the other thread; at hunting distances FOC will not effect the trajectory of an arrow.

The physics question that I think more were wondering about (at least I was) is will it eventually have an effect on an arrow at distances where the linear velocity of the arrow drops below a certain point? At max arrow distances so to speak. It's more just an amusing thought that has absolutely no bearing on bow setup, but interesting to think about nonetheless. I was thinking it might eventually have an effect, and your javelin reasoning makes me think I might be right. If you have a higher FOC, similar to the javelin changes, wouldn't the steering force be greater, forcing the nose down sooner, and thus decreasing the distance? It wouldn't be weight and gravity pulling the arrow nose down, but a greater steering force due to the increased moment arm as you mentioned. It also would reason that if you built an arrow similar to the original javelin, it would also plane and fly further. So maybe FOC does have an effect eventually? Curious your thoughts on that. Everything you said about the javelin makes complete sense, so why wouldn't it apply to an arrow?

I'm still not sure I agree with your theory that gravity pulls on all points on the arrow equally. A "pull" is a force and F=ma. This leads me to believe mass effects the force of pull on the arrow. Why if a lawn dart is dropped from a horizontal position will it always land head down? By your theory shouldn't it land horizontal? Heavy FOC arrows do the same thing, though not as obvious. The point hits first, but the arrow doesn't turn vertical quite like a lawn dart. Just curious how you would explain that?

You can argue that mass doesn't have an effect on gravity and if I can resolve the aforementioned, I'd believe you, but you can't argue mass has no bearing on trajectory. Mass does have a bearing on trajectory. Why else would every ballistic calculator have a mass element (The Ballistic Coefficient), if it has no bearing on trajectory? By Newton's law a heavier object is harder to slow down. It may not be effecting the trajectory by virtue of gravity, but mass does matter in all real world trajectory equations.

For example two objects of the same size, shape, and coefficient of drag with different weights launched at the exact same speed would have different trajectories. You can make an exact replica of a bullet out of wood and plated metal to get identical drag coefficients, size, and shape, but the wood bullet just isn't going to fly as far. Mass does make a difference doesn't it?

I too can integrate or solve a differential equation if my life depended on it, but I haven't nearly the real world experience in the engineering field that you have and so very much value and respect your opinion. Thanks for sharing!

Gravity has a constant acceleration for a falling object regardless of mass. The object starts at zero, and accelerates as it falls. For the arrow, the zero spot is the apex of the trajectory, then all points on that arrow fall at the same rate. Weight or mass just change how hard it hits when it lands.

A lawn dart, if dropped horizontally, would land horizontally in a vacuum. Air resistance makes it land point down when you take away the vacuum. Gravity doesn't care about the mass.

Ballistic Coefficient isn't part of the trajectory equation. It is part of the drag function which is a separate calculation that adjusts the velocity only. It ratios the sectional density to the G model bullet. This applies to the aerodynamics, but doesn't affect the rate of drop. Drop is fixed at the acceleration due to gravity.

Actually two objects of the same size, shape and coefficient of drag, but different weights, would have the same trajectories if launched at the same speed. Why wouldn't the wood bullet fly as far? It's moving the same speed and losing velocity at the same rate. If the launch angle is the same, the trajectory is the same.

The steering force from FOC doesn't push the nose down, or pull it up. Fletching don't create lift. If they did, the arrow would nose dive immediately from the upward force at the tail of the arrow. Fletching create drag that keeps the point traveling through the trajectory. If you went to negative FOC, then the point would steer as in the javelin example. The fletching lose their effectiveness if they can't straighten the flight path.

I'm not sure how to explain it any better.

Jeremy

 

[IdahoHntr]

Actually two objects of the same size, shape and coefficient of drag, but different weights, would have the same trajectories if launched at the same speed. Why wouldn't the wood bullet fly as far? It's moving the same speed and losing velocity at the same rate. If the launch angle is the same, the trajectory is the same.

This defies Newton's law. Heavier objects require more force to be slowed down. If drag forces on a bullet are equal the heavier bullet will fly further, because it will require more drag force to bring it to the ground.

For reference I am assuming the coefficients of drag are equal, not ballistic coefficients. Ballistic coefficient is a function of mass and drag coefficient, so the BC would be different.

 

[Beendare]

Edit; I missed the heavier vs lighter bullet in Id's post too.

Trajectories are different. Sure the heavier object is harder to slow and as it relates to a bow, the heavier arrow absorbs more of the bows energy too. I dunno about the flying further part with an arrow.

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[Wapiti1]

This defies Newton's law. Heavier objects require more force to be slowed down. If drag forces on a bullet are equal the heavier bullet will fly further, because it will require more drag force to bring it to the ground.

For reference I am assuming the coefficients of drag are equal, not ballistic coefficients. Ballistic coefficient is a function of mass and drag coefficient, so the BC would be different.

Sorry, I read that as the ballistic coefficient was the same which would also mean the shape and size couldn't be the same. My mistake.

Yes, the trajectories differ since mass is part of the equation for deceleration.

Jeremy

 

[JBahr]

Of course FOC has an effect on flight, just like trailer loading has an effect on death wobble when weight is too far behind the axles. There is a reason we have always added weight to the front of arrows, since the beginning of time. All arrows should naturally have a balance point front of center. Do you need 20%, 9%? I don't think it matters...

Same goes for adding feathers to the back of the arrows. With a properly tuned bow you can shoot bare shafts at 60 yards and hit the target constantly within a foot of your fletched shafts. The feathers do not aid in loft of the arrow, they increase your consistency by providing drag and rotation. In fact my bare shafts hit high on average at 60 yards, less drag, more speed, less drop. The bare shaft is far less accurate and hits the target at inconsistent angles, despite shooting bullet holes at 6 feet and 5 yards.

Did any of you guys do that simple test in Physics class? Weigh a feather, find something equivalent in weight but smaller in size with less drag, we used a dime. Drop them from 2ft, dime hits first, feather second. Do the same in a vacuum chamber, some fancy rigging with magnets was done, drop them, they hit at the same time...

Another good one was to shoot an arrow parallel to the ground and drop an arrow from the same height, they hit the ground at the same time, every time...