Will two different size balls travel the same distance?

[Dr.Strangelove]

@Chronos

Hm, that’d be true. The point of diminishing returns would probably be at about the point where the mass of the arrow were comparable to the mass of the bowstring, though, which I imagine we’re still far above, even with the lightweight arrows.

It also depends on the bow itself. With no mass or string on it, it will still only straighten at a maximum rate. There’s some lever action going on, so this is probably pretty fast, but it’s still a theoretical factor.

@Chronos

And the same energy will mean that the lighter arrow will have a higher initial speed, and even though it’ll feel greater drag as a result, it’ll still at any given moment of time always have a higher speed than the heavy one.

That’s not true–the lighter arrow will have greater deceleration than the heavy one. The aerodynamic *force * is constant for a given speed (given the constraint of equal shapes), and F=ma, so a lowered m means a greater a. So there will be a time where the lighter arrow equals the speed of the heavier, and after that point it will be going slower.

Of course, the light arrow is going faster to start with, so at a given moment of time it may have gone farther–but that depends on the intricacies of the aerodynamics. I ran a little Excel simulation and found that it was fairly easy to find values where decreasing the mass made it worse.

This also ignores the fact that the arrow has to travel in a parabola. If there is sufficiently low drag (like in a vacuum), then the distance will simply be a function of starting speed, and (as you originally said), it’s simply the lighter the better.

So I dunno. 50 grains is 3.2 grams–pretty dang light. I’m inclined to agree that for all practical purposes, lighter is better.

[Chronos]

It also depends on the bow itself. With no mass or string on it, it will still only straighten at a maximum rate. There’s some lever action going on, so this is probably pretty fast, but it’s still a theoretical factor.

I’m not entirely sure: As the bow approaches its equilibrium shape and the string approaches a straight line, the mechanical advantage approaches infinity. I wouldn’t be surprised if it were possible to design a bow to waste an arbitrarily small amount of energy in the wood (or whatever material they’re made from now). The 80% efficiency HoneyBadgerDC mentions might plausibly come from the bowstrings, if the arrows are really only 3 grams-- Do you happen to know what the mass of a typical bowstring is?

In any event, we’re talking about a sufficiently-complicated system here that it probably can’t be modeled well by a generalist physicist: You’d probably need a specialist who was firsthand familiar with the sport and equipment to recognize all of the factors which are significant.

[HoneyBadgerDC]

When I said about 80% efficient I was thinking in terms of hunting weight arrows so I mispoke. As the arrow weight drops so does the efficiency of the bow. Each bow has a unique easy to calculate virtual bow mass. If the virtual bow mass happens to come out at 150 grains and the arrow weighs 150 grains the bow would be about 50% efficient. In reality the virtual bow mass seems to climb as arrow weights drop instead of staying constant I think because of the additional momentum of the limb tips and maybe some added air resistance on the string. So even though the arrow speed continues to climb as the arrows get lighter the amount of kinetic energy going into them drops rapidly with reduced arrow weights.

[Quercus]

@Chronos

And the same energy will mean that the lighter arrow will have a higher initial speed, and even though it’ll feel greater drag as a result, it’ll still at any given moment of time always have a higher speed than the heavy one.

Not sure I follow, here. Yes, if two arrows are the same weight, and one started faster, the faster one will have higher drag at every moment, but will also be going faster at every moment (because drag depends on speed). But a lighter arrow has higher decceleration for a given drag force, so it’s not clear to me that a lighter arrow will always be going faster.

[ZenBeam]

The total energy for the system, prior to firing the arrow, does not depend on the arrow mass. It’s initially all contained in tension the bow and string, since the arrow is not moving. I’ll call that energy E.

Based on HoneyBadgerDC’s post about virtual bow mass, I think that energy gets split between the arrow mass and the virtual bow mass using
E = 1/2 (Mb + Ma) * V^2
This is a bit of a leap, but it would justify even having a quantity called virtual bow mass in the first place.

The initial velocity of the arrow would then be
V = sqrt(2 * E / (Mb + Ma))

It has nice features like the arrow velocity going to zero as the mass becomes large, and the velocity staying finite as the arrow mass goes to zero.

[HoneyBadgerDC]

I apologise for not being able to read the formula you posted as it might be right on. Just in case I will tell you how we arrive at virtual bow mass. Suppose we shoot a 500 grain arrow through a chrono and it registers 185 fps. We know that takes about 38ft#'s of ke. Now we measure the energy stored in the bow at the same draw length the arrow was shot at say 28inches and determine that the 50# bow is storing about 52ft# of kinetic energy. We simply find out how many grains of arrow weight it would take to equal 52# of ke and be moving at the same 185 fps. In this case 685 grains of arrow weight moving at 185 fps will equal 52ft#ke. I subtract the 500 from the 685 and know that the bow has a virtual mass of 185 grains.

   By adding the virtual mass to the actual arrow weight lets say 150 grains I am able to find out the highest possible speed and arrow of any weight can be shot from a particular bow, in reality the virtual mass slightly rises as arrow weights go down due to increased momentum of limb tips and air resistance.

[doorhinge]

@HoneyBadgerDC

I am interested in the balls flying through air not a vacuum. I am trying to come up with a strategy for building flight arrows for this years competition. I am limited to arrow length, and size of my fletchings. I am not limited to the weight of the arrow or the thickness of arrow or fletching beyond that they have to be made from natural materials. I have physical limitations in that they have to be stiff enough to withstand the acceleration forces of the bow.

Last year I succeeced in getting my arrow weight down about 75 grains in weight and still maintain good flight, this gave me about 30 fps gain in speed comming out of the bow. My distances fell flat even though I had greater speed and good flight. 

My thoughts now are that I need to figure out the optimum shape for the arrrow and try to find a thinner fletching material. Would a torpedo shape possibly have an advantage over a long needle tip?

@HoneyBadgerDC

Maintaining Forwaard center of gravity is one the arrow makers biggest challenges. The further forward the weight the better flight we get, but it also requires more stiffness to resist the acceleration forces so the weight starts going up. Most of us have settled for about 5% FOC to maintain lower arrow weights where from a standpoint of flight you cannot have too much FOC.

@HoneyBadgerDC

Thse are primitive all wood bows as the velocity is at best about 260 fps. The diameter of the arrows at the center is right around 5/16’ never below 1/4". I am at the point now where I am thinking I may have to give up a little to him in arrow weight if I can make it up somehow with a better shape. I just can’t seem to find the tipping point weight I need to be concentrating at.

What are the contest limitations for arrows? (28" max?) (definition of "natural materials?)
What is the length of your bow, tip to tip?
What is the draw weight at what length draw?
Are arrow rests required, banned, optional?
Are manual releases allowed or is this fingers only?
Are thumb rings allowed? (The arrow launches from the “wrong” side of the bow.)

Using a Thumbring

Are you familiar with the term “ballistic coefficient”? It’s mostly used for bullets and artillary shells.

Ballistic coefficient

Bullets with similar BC, regardless of weight or diameter, will follow the same trajectory if they’re started with the same muzzle velocity. The higher the BC, the more “aerodynamic” the bullet’s form would be. Higher BC numbers indicate flatter shooting bullet and longer ranges.

*For the precise establishment of BCs (or perhaps the scientifically better expressed drag coefficients), Doppler radar-measurements are required. The normal shooting or aerodynamics enthusiast, however, has no access to such expensive professional measurement devices. Weibel 1000e or Infinition BR-1001 Doppler radars are used by governments, professional ballisticians, defense forces, and a few ammunition manufacturers to obtain exact real world data on the flight behavior of projectiles of interest.

Doppler radar measurement results for a lathe turned monolithic solid .50 BMG very-low-drag bullet…

…The initial rise in the BC value is attributed to a projectile’s always present yaw and precession out of the bore. The test results were obtained from many shots, not just a single shot. The bullet was assigned 1.062 for its BC number by the bullet’s manufacturer, Lost River Ballistic Technologies*.

An arrow point that dupicated the BC of the Lost River .50 BMG would slip thru the air very efficiently. The ogive is important both for how the point enters the air and how the air leaves the point (and later, the feathers, vanes, and nock). Laminar flow vs turbulent flow. A needle point would eventually have to transition to the shaft. Too sharp of a curve would allow the air to leave the point’s surface creating turbulance (aka drag).

FOC makes a difference in arrow flight. Too low and the arrow won’t track straight. The front and back will try to swap ends. Arrows or javelins with extremely high FOC will drop quickly. IIRC, Easton suggests 5% to 15% FOC.

Then there is the ol’ Archers Paradox to consider. The bow string wants to travel in a straight line to the bow face. The arrow has to bend around the bow. Some arrow shaft flex is required. Too little flex and the arrow will shoot left (for a RH archer). Too much flex and you’ll have no idea where the arrow will go.

[doorhinge]

More BC info.

http://www.precisionshooting.com.au/downloads/ballisticcoefficients-explained(4).pdf

[HoneyBadgerDC]

@doorhinge

What are the contest limitations for arrows? (28" max?) (definition of "natural materials?)
What is the length of your bow, tip to tip?
What is the draw weight at what length draw?
Are arrow rests required, banned, optional?
Are manual releases allowed or is this fingers only?
Are thumb rings allowed? (The arrow launches from the “wrong” side of the bow.)
http://www.youtube.com/watch?v=FXE2yaO9lYQ

Are you familiar with the term “ballistic coefficient”? It’s mostly used for bullets and artillary shells.
Ballistic coefficient - Wikipedia

Bullets with similar BC, regardless of weight or diameter, will follow the same trajectory if they’re started with the same muzzle velocity. The higher the BC, the more “aerodynamic” the bullet’s form would be. Higher BC numbers indicate flatter shooting bullet and longer ranges.

*For the precise establishment of BCs (or perhaps the scientifically better expressed drag coefficients), Doppler radar-measurements are required. The normal shooting or aerodynamics enthusiast, however, has no access to such expensive professional measurement devices. Weibel 1000e or Infinition BR-1001 Doppler radars are used by governments, professional ballisticians, defense forces, and a few ammunition manufacturers to obtain exact real world data on the flight behavior of projectiles of interest.

Doppler radar measurement results for a lathe turned monolithic solid .50 BMG very-low-drag bullet…

…The initial rise in the BC value is attributed to a projectile’s always present yaw and precession out of the bore. The test results were obtained from many shots, not just a single shot. The bullet was assigned 1.062 for its BC number by the bullet’s manufacturer, Lost River Ballistic Technologies*.

An arrow point that dupicated the BC of the Lost River .50 BMG would slip thru the air very efficiently. The ogive is important both for how the point enters the air and how the air leaves the point (and later, the feathers, vanes, and nock). Laminar flow vs turbulent flow. A needle point would eventually have to transition to the shaft. Too sharp of a curve would allow the air to leave the point’s surface creating turbulance (aka drag).

FOC makes a difference in arrow flight. Too low and the arrow won’t track straight. The front and back will try to swap ends. Arrows or javelins with extremely high FOC will drop quickly. IIRC, Easton suggests 5% to 15% FOC.

Then there is the ol’ Archers Paradox to consider. The bow string wants to travel in a straight line to the bow face. The arrow has to bend around the bow. Some arrow shaft flex is required. Too little flex and the arrow will shoot left (for a RH archer). Too much flex and you’ll have no idea where the arrow will go.

It sounds like you know your way around a bow and arrow, as for the rules they vary greatly with different classes so I will only address the primitive classes.

Arrow length minimum 22", no overdraws are legal and arrow rest cannot exceed 2" in length.

Only 2 weight classes 50# and unlimited.

No limits on arrow weights beyond the physical limitations of natural materials.

Finger releases only a glove or other finger protection is legal.

String material must be natural, usually we use linen or gut.

No restrictions on bow length however we do have restrictions such as a self bow must be made from a single piece of wood, a simple composite may only have a backing strip of wood or other natural material, a complex composite may use an unlimited amount of natural materials and will also be allowed an overdraw up to 4" long.

A bows weight is measured at the point where the arrow is about to fall off of it's rest, it is measured using the archers longest arrow. 

 We are not allowed the use of elevated rests.

[eltro102]

they wouldn’t travel the same distance in a vaccum because the gravity field of the larger ball would interact differently (slow it down faster by radiating energy away as gravity waves?)

[doorhinge]

I don’t shoot flight. Just between you and me, I opted for training wheels. I know, I know… I’m a wuss, but I shoot sooooo much better with a compound. I do tinker with my equipment and have robin hooded a few shafts at 30 yds. Ouch.

I’ll just throw out a few idea’s and hopefully they’ll be of some use to you.

The lighter the arrow, the more shock, stress, and vibration will be transmitted to the bow. Zero grains per inch = a dryfire and a dryfire can destroy a bow.

For maximum distance, it’s seems reasonable to maximize the poundage. Are you pulling 50lb and to what anchor point? You’re not limited to a point on your face or to your ear or to your back shoulder.

War bows were shot by “bending the bow”. Push with the bow hand and rotate your string hands ELBOW until it either can’t rotate around any farther or the shaft is near your face. DO NOT WEAR GLASSES, HATS, EAR RINGS, OR PIERCINGS if you intend to try this. I bought an inexpensive 25# @ 28" recurve to practice this. This technique will remove eye glasses very quickly and painfully. My draw is 31" to the corner of my mouth. Finding ready-made arrow shafts 8" - 10" longer was impossible, so I “attempted” to make my own out of cedar and hardwood dowels. I did manage to “bend the bow” but the shafts weren’t accurate. Oh well.

You might want to build a draw board to see how well your bow limbs responds to bending. At one end of the draw board, peg(s) hold the bow at the grip throat On the other end of the draw board you attach a small boat winch or pulley arrangement. Attach one end of a scale to the end of the winch rope. Attach the other end of the scale to the bowstring and slowly pull the string back. The scale should should show a somewhat linier progression. Some bows “stack” or plateau at different points which makes the bows more difficult to shoot and may waste energy.

You might want to build a wind tunnel to test your points, vanes, shafts, and completed arrows. A blower, 2 - 3 sides of plywood and 1 or 2 sides of plexiglass. Screw them together but leave an access port. Use a box(es) of plastic straws to channel and smooth the air flow. You’ll need a solid stand to hold your arrows or drill a hole thru the shaft at various FOC locations.

Vane placement and straightness is also important. I put a slight spin on my arrows with a Bitzenburger. They do have straight clamps. There are other jigs also. Consistancy, consistancy, consistancy.

I find an arrow “spin tester” usefull when sorting shafts and fletched arrows. Some shafts have a “heavy” side. Some glued vanes are heavier than others.

There are also arrow spine testers but those are kinda expensive.

I seem to remember an old article by an English flight shooter (champion?) who said that 28" barreled shafts where the most efficient size and shape. I know that longer canoes and sailing ships are smoother and therefore faster thru the water and air is just thin water. I could shoot 28" arrows with an overdraw or extended mechanical release.

[Chronos]

Quoth eltro102:

they wouldn’t travel the same distance in a vaccum because the gravity field of the larger ball would interact differently (slow it down faster by radiating energy away as gravity waves?)

Even in a vacuum, there are many, many effects which would be far, far larger than this.

[HoneyBadgerDC]

Doorhinge, I don’t want to mislead you in anyway. I have actually been around flight and have even been a world record holder in the broadhead classes for several years. Last year I missed the record by 10".

  You are right on about the releases, I think I may have perfected the quick release by actually adding 24 fps to the speed of a bow shot from a machine. I throw a well timed left jab from a bent arm just as I release the string and rip my fingers off the string with no forward creep. I think I have the fastest recorded primitive bow that was actually recorded in a formal test. Even though I know of others including myself who have built them faster than that particular test.

   The reason for the short arrows is that a short limbed bow has a greater capacity for efficiency even though it gives up some in stored energy and will beat out a longer stroke bow with the very light arrows. Also every inch you add to an arrow you also need to add mass to increase the stiffness. For the most part about 22" to 24" arrows drawn 2" past the back of the bow seem to give overall best results.

   My buddies arrows have been kicking everyones asses even though they are being shot by a variety of shooters. Most all of the recent records have fallen to this one mans arrows. I am at the point of believeing unless we can make arrows like his competing will be very tough. After reading th above posts and putting thaty with what I allready know and not having anymore time to think about it I think I will go with the bullet shaped tip, taper to the rear, use the heaviest and stiffest wood I can find for higher sectional density. What I give up in weight I might be able t make up for with a better release and slightly faster bow. And hopefully an arrow with reduced coefficient of drag. 

   The heavier arrow will likely give up about 30 fps comming out of the bow, maybe better flight can overcome this.

[njtt]

Ther is a young man of Devizes who might be able to answer this question.

[doorhinge]

@HoneyBadgerDC

Doorhinge, I don’t want to mislead you in anyway. I have actually been around flight and have even been a world record holder in the broadhead classes for several years. Last year I missed the record by 10".

I didn’t see anything misleading, just general questions that I enjoyed answering in a general kinda way. I find your release interesting. Sounds like a modern version of some of the warbow techiques I’ve witnessed. Your timing/rhythm far exceeds anything I could accomplish.

Congrats on holding the broadhead head record.

Soooo, what broadhead(s) did you use to set the record? Store bought or homemade? Modified how? If it’s a secret, I don’t need to know, I’m just curious.

[Sicks_Ate]

@njtt

Ther is a young man of Devizes who might be able to answer this question.

Oh shit…I’m gonna be there all day.

[HoneyBadgerDC]

@doorhinge

I didn’t see anything misleading, just general questions that I enjoyed answering in a general kinda way. I find your release interesting. Sounds like a modern version of some of the warbow techiques I’ve witnessed. Your timing/rhythm far exceeds anything I could accomplish.

Congrats on holding the broadhead head record.

Soooo, what broadhead(s) did you use to set the record? Store bought or homemade? Modified how? If it’s a secret, I don’t need to know, I’m just curious.

We are very open about how we do things. I used a standard 67" osage self bow 50#@28". I had the basic skinny tips and about 3" reflex. The arrows weigh 500 grains and the broadhead is a homemade piece of sheet metal 7/8 wide by 1 1/4" long. A few years back I came up with a method for monitoring the condition of the wood durring the tillering process that if properly excecuted substantially reduces hysterisis in the wood. I call it no set tillering. It’s worth about 10 fps if we get it right.