Draw weight, arrow weight, speed & trajectory

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jitsuka

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Hi all

Just thinking about arrow flight.
I am wondering.
For two bows of equal design but different draw weights do you think an arrow will fly the same if it is the same grain weight in proportion to the bow's draw weight ?

Do you think that a 600grain arrow from a 60# bow will fly the same as a 400grain arrow from a 40# bow ?

Assuming that we keep other factors, size of fletching, weight of pile, f.o.c balance, etc the same.
 


moo-mop

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No.
Even if you simplified arrows as a point masses going straight out of a bow with the same drag they would not fly in a way that is proportional to the draw weight of the bow with mass - the amount of energy a bow puts into an arrow is not directly proportional to its weight, but is related to the area under the draw force curve.

However, it's even more complicated as arrows do not behave simply. The physics of flight actually involves a series of interacting variables, which you can’t keep constant between experiments (e.g. it's difficult to imagine not changing f.o.c. if you tried to keep point weight the same but change the total mass. And you would be varying the arrow spine too if you model real materials; esp if you stick with wood!). The maths is highly tricky and there is no complete model of how a recurve/longbow etc actually behaves published as far as I'm aware.

Edit: However there are some quite nice basics around to get you started thinking:
e.g. see http://margo.student.utwente.nl/sagi/artikel/bas/archghh.html
 


tinkerer

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As Moomop says, it's very complex but the two bow/arrow combinations you refer to would be expected to produce the same initial arrow speeds if they were both made to the same standard ie working at the same efficiency.

So a good wooden bow shooting 10gpp arrows and at 28in drawlength might manage 170+fps. The same draw length is key. And scaling down that good bow/arrow should still give 170fps. It's the air resistance that's the tricky bit.
In practise, there might not be a huge difference.

David
 


jitsuka

New member
The interaction is obviously complicated but I suppose what I'm getting it is,

I've swapped bows a couple of times for heavier bows. Each time I have got flatter trajectories and my point on distance has increased. I know that with my current bow (and indeed any bow) if I shoot lighter arrows they fly flatter and go further.

In trying to understand the physics the basics makes sense. Trajectory would seem to be a function of initial velocity and angle of launch affected by gravity and air resistance. If my understanding of physics is right the weight of the projectile or the amount of kinetic energy it holds doesn't affect the trajectory.

This all points to two equal design bows getting the same trajectory with arrows suitable for them. Why then do all sorts of people talk of upping their bow weight to get a better trajectory and why do the warbow people talking on the other active thread here have results showing that the heavier bows are shooting further ?
 


alanesq

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My understanding is:

A heavier bow will shoot an arrow faster, so it has less time to fall before hitting the target (i.e. flies flatter) - this is why compound bows have a very flat trajectory, they shoot arrow at very high speeds
- the old story of a bullet shot horizontal will hit the ground at the same time as one just dropped
If you increase the arrows weight so it flies the same speed then the trajectory will be about the same

The thing with the warbows is we are trying to shoot a specific arrow so to increase draw weight will increase distance because it shoots the arrow faster
i.e. launch a livery arrow as far as we can
We could just use a lighter arrow to get the same distance but then the arrow will have less "stopping power" (i.e. deliver less energy)

This is what I think people often don't appreciate about warbows - unlike target type archery it is not just about reaching/hitting the target but also (and possibly most) about how much damage the arrow would do when it gets there

btw - if you are worried about matching the arrow to the bow remember that you can adjust the arrows spine rather than it's weight
 


tinkerer

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Jitsuka, There does seem to be a paradox here, and I bet a simple explanation- but I can't think of it.

One small point is that a heavier arrow with the inertia to resist air resistance will outshoot a lighter arrow, both starting with the same speed, other things being equal, but not by a lot.

When archers move up in bow weight, they would choose their new arrows according to spine, so arrow weight wouldn't go up in proportion. In fact the same arrows could be stiffened by reducing the pile weight. David
 


steve58

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This whole area seems to be one where practical experiance is not always quite as expected!

Just gone up to 55# on my fingers (compared to 53#); with the new bow the point is below the boss at 80 yards (in the shape formed by the bottom of the boss, the ground and the target stand), with the old one it's near the top of the boss. At 60 yards it makes 1/2" difference to where the rubber band goes.

Would not have expected 2# to make that big a difference and suspect that it's the 13,000+ arrows the older bow has shot that matter! Going to reserve the new one for shooting 100 yards for now
 


alanesq

New member
Steve: Have you measured the draw weights yourself?
I know from experience that what the bow claims to be and what it is can be very different
Although two identical draw weight bows are never going to be identical - I guess the best way to compare them would be to measure arrow speed ?

I don't think spine is anything like as critical for heavy bows as it is for the lighter target bows?
Using different types of wood can be one way to vary spine - I used to use birch shafts but after watching them fly in slow motion I realised these were way too stiff for my bow
see - http://homepage.ntlworld.com/alan.blackham/ewbs/hscam/shooting/shot1.avi
 


steve58

New member
Steve: Have you measured the draw weights yourself?
I know from experience that what the bow claims to be and what it is can be very different
Although two identical draw weight bows are never going to be identical - I guess the best way to compare them would be to measure arrow speed ?

I don't think spine is anything like as critical for heavy bows as it is for the lighter target bows?
Using different types of wood can be one way to vary spine - I used to use birch shafts but after watching them fly in slow motion I realised these were way too stiff for my bow
see - http://homepage.ntlworld.com/alan.blackham/ewbs/hscam/shooting/shot1.avi
That's a really clear video!

Not sure about the answer to the question. I use stiffer arrows than some would suggest, but I use a fastflight string... in any case I'd rather go too stiff than too flexible

I have seen some of our less experienced longbow archers at the club shoot quite successfully with my old arrows, spined way over for their bows (and sometimes do less well with arrows that ought in theory to have been better suited!)
 


steve58

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I mean have you measured the draw weight of your bows?
You may find that they are different to what the markings say

btw - here is a vid from after I reduced the arrows spine
http://homepage.ntlworld.com/alan.blackham/ewbs/hscam/ewbsarrw.avi
Hmmm, saw them on Bickerstaffe's scales when I collected them but not since. The behaviour of the arrows has not changed in such a way as to make me think they have dropped to any great extent.

That second vid shows the arrow flying much sweeter off the bow, very clear
 


jitsuka

New member
>Just gone up to 55# on my fingers (compared to 53#);
> with the new bow the point is below the boss at 80 yards
>with the old one it's near the top of the boss.
>At 60 yards it makes 1/2" difference to where the rubber band goes.
>
>Would not have expected 2# to make that big a difference

Is this with the same arrows ?
Are the bows the same design (you mention bickerstaff, are they both his bows, the same type of wood) ?
If so would the same effect had been got with lighter arrows ?

Certainly at some point the effect would be same, but the real question is, would the effect have been the same with the same proportional difference ?
Eg If you were shooting 530grain arrows on your 53 bow, then on your 55 bow they are 9.63grain per pound. That proportion on your old bow would be 510 grain arrows.
Now I know that whilst 20grains makes a difference, for my bows at least it doesnt make top of the boss to bottom of the boss difference.
 


tinkerer

New member
Steve, You mention that the old bow had shot over 13000 arrows and presumably has some string follow as a result. As you say, that could account for much of the improved performance. Btw, what do your arrows weigh?

It should be easy to compare the flights of a heavy and light arrow, both shot at the same initial speed, if there's a chrony to hand. Would they be like throwing a stone pebble and a polystyrene one? Something for the weekend.

David
 


tinkerer

New member
Steve, Would you be willing to shoot the same arrows from both bows for maximum distance? If you have the space. That would link that test with the position(s) of a rubber band, for example.

David
 


steve58

New member
Shooting the same arrows off both bows, 5/16" pine, rear tapered, 63 gr piles, total weight about 430 gr.

Both are the same design, single growth ring hickory back, greenheart core, osage belly. The older one is about 2" shorter than the new one and has followed the string quite a bit, at least a couple of inches.

No chrono handy and our field does not permit distance testing, shame.
 


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