MY ARROW BUILD/GUIDE: BARE SHAFT TO FULL SEND.

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WakePraySlay

WakePraySlay

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Where you say "Better Trajectory" - I think you just mean that the higher FOC arrow will drop more at long range than a lower FOC version of an arrow with the same weight (all else equal)?


This is exactly what I’m trying to get across. At short ranges the degree of FOC will not really come into play. Now at longer ranges the physics of A low vs high FOC would come into effect.

Thank you for your input!:cool:
 

Wapiti1

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FOC, total arrow weight and trajectory are unrelated. Mass doesn't affect the speed of drop because the acceleration due to gravity is a fixed value with no mass component at 9.8 m/s. What this means is that gravity pulls on the front of the arrow equally to the back of the arrow. Velocity and aerodynamics are what dictate trajectory. You input the arrow mass into the calculators to get kinetic energy. That input isn't used in the trajectory calc.

Trajectory calculations only consider velocity, departure angle, drag and gravitational acceleration in some combination depending on how the equation is arranged. Mass isn't a part of the trajectory equation.

Jeremy
 
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The foc does in fact impact trajectory, because it moves the center of mass (gravity) forward of the center of pressure, creating a moment in the arrow that causes it to tip forwards in flight, and ultimately land shorter. Increasing foc is the exact method the iaaf used to change the distance javelins could be thrown by humans in 1986. The weight was unchanged (800 Grams) but the foc was increased specifically to limit the distance it could be thrown so it could be safely thrown in the infield of a track. A javelin is essentially just a big bare shaft arrow that people throw, the physics are about the same.

Interestingly, after the foc was moved forwards and throw distances dropped by ~10% some people modified the tail of the javelin to increase drag, get a more level flight and increase throw distance. Those records have been removed from the books, but they did gain back about half of the difference lost by moving the foc forward. This does seem to indicate that with enough fletching you might be able to counteract the foc and negate the moment induced by the higher foc, get level flight and extend the distance the artow can fly.

The question still remains in my mind as to distance the arrow must fly before the foc impact on trajectory becomes relevant, as the javelin example really only tells us about absolute maximum flight distance. It's entirely possible that at bowhunting ranges, which are far less than the maximum distance the arrow could fly, the effect of foc on trajectory is irrelevant, I know I haven't tested it.

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Wapiti1

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While that is true, they also changed the aerodynamic design of the javelin to create less lift at the front. The FOC change was part of the shape redesign. Just like shooting a flat base bullet verse a boat tail of the same weight. The drag coefficient changed.

So, again, math says the trajectory is unaffected by where the mass is located all other things being equal.

Jeremy
 

IdahoHntr

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FOC, total arrow weight and trajectory are unrelated. Mass doesn't affect the speed of drop because the acceleration due to gravity is a fixed value with no mass component at 9.8 m/s. What this means is that gravity pulls on the front of the arrow equally to the back of the arrow. Velocity and aerodynamics are what dictate trajectory. You input the arrow mass into the calculators to get kinetic energy. That input isn't used in the trajectory calc.

Trajectory calculations only consider velocity, departure angle, drag and gravitational acceleration in some combination depending on how the equation is arranged. Mass isn't a part of the trajectory equation.

Jeremy

The acceleration of gravity doesn't change, but the force of gravity sure does depending on mass (Force = mass x acceleration). Gravity does not pull on the front and back of an arrow equally, the pull you are talking about would be the force of gravity and the force of gravity acts at the center of mass. On a high FOC arrow the center of mass is much more forward, thus gravity is pulling on the front of the arrow more than the back of the arrow. If we were shooting bare shafts, that would be the end of the discussion, but since vanes are also acting on the back of the arrow, there are drag forces to also take into consideration. The higher the FOC %, the longer the moment arm the fletchings have to work with, which can counteract the increased force of gravity on the front of arrow.

Think of lawn darts. They always fall head first, because they have an extremely high FOC and gravity is in fact pulling on the front of the dart more than the back of the dart. If gravity pulled on the front and back of an arrow equally, you could drop a high FOC arrow from a horizontal position and it would land horizontally. That is definitely not the case.

I'm inclined to agree with tim on this though. I don't think this comes into consideration for most compound setups even at longer shooting distances. Brendan's post also mentioned it, as long as the speed of arrow is great enough that it is creating enough drag force on the fletchings, there won't be a drop off.
 

Wapiti1

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Find a trajectory calculation for any object that includes mass. There isn't one because weight and weight distribution are not important for trajectory. If it was the calculation would take it into account.

All objects, regardless of mass, fall at the same speed and maintain their original attitude in a vacuum. What this means is that an external force (air resistance) is required to change the objects attitude in flight.

An arrow can't nose dive if the fletching maintain the flight path. FOC is solely about moving the steering point forward or backward to change the lever arm that the fletching act on. That's it.

Here is an example of this in practice: A .243 bullet with a BC of 0.6 that weighs 117grs launched at 3000fps has exaclty the same trajectory as a .338 bullet with a BC of 0.6 weighing 275grains launched at 3000fps. If you plot both from zero to 1000 yards, both will drop 262.1" with a 100 yard zero (per JBM Ballistics). The energy changes drastically, but the trajectories are identical. In the case of a bullet, spin from the rifling is the equivalent to fletching on a arrow. The center of gravity on these two bullets is different. One could be all copper and the other cup and core and they would still behave identically.

An arrow is not different. FOC has zero bearing on arrow trajectory.

Jeremy
 

Brendan

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While that is true, they also changed the aerodynamic design of the javelin to create less lift at the front. The FOC change was part of the shape redesign. Just like shooting a flat base bullet verse a boat tail of the same weight. The drag coefficient changed.

So, again, math says the trajectory is unaffected by where the mass is located all other things being equal.

Jeremy

Humor me on this one, pretty sure this is right:

All else isn't equal. You've got more drag (vanes) on the rear of the arrow than you do on the front. Eventually as speed drops you would get to a certain point where the vanes aren't doing as good a job stabilizing the arrow, and the front of the arrow will begin to drop faster because of the difference in drag. And, actual speed the front and rear of the arrow drop will be a combination of mass, and drag on that portion of the arrow... You're talking about acceleration due to gravity in a vacuum, but we're not talking about a vacuum...

Think about it - take an arrow in your hand, throw it up in the air, is it going to land point down? Now take a bare shaft without an insert, how is it going to land?

Probably all mental masturbation though. I honestly think any potential trajectory difference due to FOC is about the least important thing to worry about when building an arrow (And, it's going to be minimal within practical ranges)
 
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IdahoHntr

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Find a trajectory calculation for any object that includes mass. There isn't one because weight and weight distribution are not important for trajectory. If it was the calculation would take it into account.

All objects, regardless of mass, fall at the same speed and maintain their original attitude in a vacuum. What this means is that an external force (air resistance) is required to change the objects attitude in flight.

An arrow can't nose dive if the fletching maintain the flight path. FOC is solely about moving the steering point forward or backward to change the lever arm that the fletching act on. That's it.

Here is an example of this in practice: A .243 bullet with a BC of 0.6 that weighs 117grs launched at 3000fps has exaclty the same trajectory as a .338 bullet with a BC of 0.6 weighing 275grains launched at 3000fps. If you plot both from zero to 1000 yards, both will drop 262.1" with a 100 yard zero (per JBM Ballistics). The energy changes drastically, but the trajectories are identical. In the case of a bullet, spin from the rifling is the equivalent to fletching on a arrow. The center of gravity on these two bullets is different. One could be all copper and the other cup and core and they would still behave identically.

An arrow is not different. FOC has zero bearing on arrow trajectory.

Jeremy

I think in the end most of us are at the same place here. FOC should have no impact on trajectory over any reasonable shooting distance. I still believe it will have a measurable impact eventually, but not until an arrow has slowed to speeds that aren't reached until well past ranges that archers typically shoot at.

Your shooting example above is imperfect because a Ballistic Coefficient is a ratio of mass. BC = mass/(Cd x A) where Cd is the coefficient of drag and A is the cross-sectional area. The two bullets have the same BC, but they have different drag coefficients and cross-sectional areas. Too make bullets similar to arrows you would have to pick bullets with the same Cd and A, and different masses. Essentially all you could change is what the bullet is made out of, but it has to maintain the exact same drag profile or it doesn't work.

In the case of an arrow, Cd and A are staying the same, and only mass is changing. This actually shows that a heavier arrow will have a better BC. Of course, in the real world, heavier arrows means slower speeds, so they balance and the decrease in velocity overcomes the superior BC of the heavier arrow giving a more arching trajectory. This now makes me curious to see if that would change with arrows being shot at maximum distances. If eventually the heavier arrow would pass up the speedier arrow because of its higher BC like you see happen with bullets.

For a real world example, if we used two identical arrows, but one was heavier than the other and they were both launched at 280 fps, would they have the same trajectory? No, they wouldn't. Even though they have the exact same aerodynamics, the heavier arrow will have a better trajectory because heavier things are harder to slow down. They maintain their velocity better than lighter weight objects due to Newton's laws of physics. Mass is very much involved in the trajectory of an object, because it effects the velocity of that object.

I'd also like to point out that the BC calculation above also can be a proving point for the fact that FOC has no bearing on trajectory, as two arrows with the same mass would have the same BC no matter where the mass was focused. I tend to think BC is an imperfect representation for an arrow all together, and it would take a whole different system to determine whether FOC does have an effect on arrow trajectory at all.

I like to think about things and that is the only point for my discussion here. Talking about things helps me understand them better and I like to understand how things work. I'm not trying to promote hard feelings or anything. Just trying to fine tune my own understanding. I've always enjoyed that there are a good number of engineers and other people on this page who understand physics and keep my mind working.
 
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Last post on this.

Find a trajectory calculation for any object that includes mass. There isn't one because weight and weight distribution are not important for trajectory.

Jeremy

Let's take a closer look at the trajectory of a bullet example. Consider a rifle with a 0" sight height, a 1 yard zero, shooting 150 gr berger match flat base at 3000 fps, G1 bc of 0.398. This bullet is fired perfectly flat, and it takes 1.647 seconds to make it to 1000 yards and drops 390.7" (all according to jbm). The drop of this bullet in a vacuum would be:

drop = 1/2 * g * t^2 = 0.5 * (32.8 ft/s^2)*(12 in/ft)*(1.647 s)^2 = 533.8" which is no where close to what jbm predicts. Clearly, there's more to the story than just the time of flight and gravity.

There are at least two additional forces, lift and drag that play a significant role in this problem, and it turns out both of those forces are functions of the objects shape, and thus included in the ballistic coefficient, which you mentioned.

The ballistic coefficient is a simplified way to account for the lift and drag (and all other aerodynamic characteristics) a given shape will produce relative to a known, standard shape who's precise aerodynamic characteristics are known. You may recognize a couple of these shapes, G1 and G7, and the different b.c. numbers the same object will have relative to each of those standards. Also included in ballistic coefficient is mass, here's an excerpt from Kestrel's website: "For the more technically minded, ballistic coefficients are derived from the mass of the object divided by its diameter in the airflow squared, divided by the form factor, i, that relates to the aerodymanics of it's shape. " By including the mass and the shape, the ballistic coefficient by default also takes into account the center of pressure and the center of gravity, which are simply functions of the shape (COP) and the mass distribution (COG) of the projectile.

Because of the standardized shapes required to achieve the same bc, the relationship between the COP and the COG (ie the foc) is essentially identical between similarly constructed bullets with identical BC's. If you change the bc, you change the relationship between the COP and the COG (i.e. the shape of a bullet) the drop changes, even for the same time of flight. One of the reasons for this difference is because of the difference between the COP and the COG, although there are other more significant factors, namely the lift and drag characteristics of the bullet.

For example, lets now consider another bullet in flight for 1.647 seconds: a 270 cal berger 150 gr vld at 2960 fps. again with 0" sight height and a 1 yard zero (level bullet flight), the drop at 1100 yards and 1.647 seconds is 412", which is different once again than how the bullet would free fall in a vacuum. The difference? The shape, which determines the lift, the drag, the center of pressure, and the center of gravity for that particular bullet. This 270 cal bullet produces less drag and less lift, so it travels further, despite starting slower, and falls more than the initial 30 cal example in the same amount of time.

The takeaway here is that bullet shape, which also determines the center of gravity and the center of pressure, has a direct impact on the trajectory of the bullet.

Lift always acts through the center of pressure, just like gravity always acts through the center of mass. If you increase the separation between these points, you increase the moment because the force * distance becomes larger. This increased moment tends to make the arrow tip down more in flight, absent another moment to cancel it out. Again, this is super apparent with a javelin because it's big and slow enough to see, watch a javelin be thrown you can very clearly see it tip over in flight.

It is admittedly less of a factor with an arrow, especially at useful ranges and with fletching, which applies some moment to counteract the tip weight due to the air resistance on the side profile of the fletching as the tip tries to pivot down. As I mentioned earlier, it is at least theoretically possible, albeit likely impractical, to use enough fletching to achieve perfectly level arrow flight, and thus maximize the distance an arrow could travel when fired from a bow. I will not be performing that experiment.
 

Beendare

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Jeremy is correct on this...good posts Wapiti1!

Ashby has many folks confused. When his study on very high FOC first came out [about 20 years ago] he claimed these arrows flew further than the same weight arrow with lower FOC.
FALSE

There was a group of physics guys on the UC Berkeley archery team that called him on it....wanted his data as it defied the laws of physics. Newton was rolling in his grave. Turns out Ashby "Proved" his theory with rubber bands and soda straws.

Wapiti1 is correct- its physics.



Easton agrees with the OP, their recommendation is 8%-16%. Every single pro in every archery discipline shoots avg FOC under 20%. Most top hunters have figured this out too. These are the folks that know arrows..........one guy with rubber bands is telling us different. You pick. grin.

______
 

Read1t48

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WakePraySlay -
Thanks for the write-up and article. I read it today and picked up some great tips for my spring arrow build. Your timing was perfect. Good luck in your upcoming season. I hope we can all make it out.
 
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WakePraySlay

WakePraySlay

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WakePraySlay -
Thanks for the write-up and article. I read it today and picked up some great tips for my spring arrow build. Your timing was perfect. Good luck in your upcoming season. I hope we can all make it out.
Thank you for reading it! I hope your arrow build goes well!

and exactly if there is a season:oops:!!!

sorry I got lost in the debate above haha! Good luck to ya!
 
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WakePraySlay

WakePraySlay

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Excellent write up!

Maybe I missed it in the 49 pages but what are you going to be hunting with a 730 grain arrow?
A little overboard huh? And well this upcoming season I’m going to go and hunt western Washington for a Roosevelt pending the season will be open?

But in reality I just put new limbs on my bow (75#) and I had to get new arrows because my current spines were too weak. I opted for a 250 spine because I was on the line for a 250 or 300. Rather have a stiffer spine than being under Spine’d.

but I will be using them for elk, bear, and deer. And just Incase I see a squatch:ROFLMAO:
 

Brendan

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Jeremy is correct on this...good posts Wapiti1!

Ashby has many folks confused. When his study on very high FOC first came out [about 20 years ago] he claimed these arrows flew further than the same weight arrow with lower FOC.
FALSE
______

One comment on this - the idea isn't that it's what Ashby said. It's the reverse. Higher FOC arrows should nose dive and come up shorter after a point. Check out the Javelin article I linked earlier that talks about Center of Mass vs. Pressure and the changes they made to induce a shorter flight and make sure the javelin went into the ground nose first.

But, if you have a detailed physics based explanation or test that debunks it, I'm all ears.

(I still think this is mostly theoretical and you're not going to see any difference with any range reasonable FOC arrows)
 

Zac

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Thanks so much for posting this. A youtube video would have been epic. I will definitely be using your wax paper trick. Also I think you may have posted the wrong gpi number for your dangerous game shafts. I was thinking you were probably using the 300 spine until I saw your overall weight. Also what broadhead are you using? Is that an Evolution Outdoors?
 
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WakePraySlay

WakePraySlay

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Thanks so much for posting this. A youtube video would have been epic. I will definitely be using your wax paper trick. Also I think you may have posted the wrong gpi number for your dangerous game shafts. I was thinking you were probably using the 300 spine until I saw your overall weight. Also what broadhead are you using? Is that an Evolution Outdoors?
Thought about doing a vid but maybe next time!!! I’m glad you could benefit from this! And yeah I’m shouting tje 250’s.

as for my broadheads I’m shooting rage. They’re the SS model meant for lighter draw bows or better penetration for big game. Shot a little buck a few years ago clean pass through and he went about 60 yards and took a dirt nap.
 
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