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 Post subject: Crossbow experiment
PostPosted: Tue Apr 15, 2008 1:13 am 
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I wanted to follow up on some interest from previous threads:
http://belegarth.com/board/viewtopic.php?t=18412

As I say, I'm from Amtgard/HFS with a great deal of experience with LARP crossbows. We went with 450 inch-pounds as safe even for close range use, compared to about 650 ip for a 35#*" handbow. Recently I was wondering how best to equate what is a safe energy, since "half draw" is undefined and means a different pull to different people and thus basically a meaningless term.

Well, what we DO have common to most groups is that fulldraw 35#*" is officially acceptable at >20ft. Therefore, by comparing the speed from an arrow from that arrow at 20 ft versus the exact same arrow out of a crossbow at close range, if the crossbow is slower then it tends to show it's acceptable since there is no difference between the two hits. On top of that, a crossbow bolt will generally have a lighter shaft which certainly helps the situation even more, although there's nothing stopping a person from using a solid fiberglass crossbow bolt shaft which would be even heavier than most 28" graphite arrows.

The data's below, but the short story is that a 450ip (45 lbs at 10" of power stroke, 56 lbs * 8" of power stroke, etc) is about 20%-30% less impact energy than getting fulldrawn at 20ft, even with widely differing examples of arrows. It's possible to go higher, but IMHO this is ok and if you have aerodynamic arrows they can be made light and thus fast and have good range. Unfortunately Bel/Dagorhir have that "protrusion" term that mostly prevents such construction, but that's another story. Anyhow, 450ip is something I've worked with extensively and found to be effective with my gear anyways with no notable complaints and I do my best work at around 20ft. If the Marshal's measurement is off and allows something even 10%-20% over the limit, it's still pretty safe as things go, just kinda stingy at worst.

The Test
======

I used 3 different arrows here, the first two were just picked up from the unclaimed junk cleaned up after a large event and I think they're fairly good examples of what people build. "Yellow" a heavy aluminum-shaft design with a 2.77" flat face. It weighs 75.1 grams. "Black" uses a thick Beman 500 carbon shaft with a 2.75" dia head which is somwhat rounded but I believe this would also meet Dag/Belegarth's "protrusion" rule (barely). It weighs 57.2g. MS2K is my own Meatseeker 2000 design, using a thin graphite shaft. It a 2.725" dia ball front and tapered cone backside and weighs 43.9g.

I measured speed on a Chrony F1 chronograph from a 34#*" Beak Kodiak Magnum, 7.25" brace height for a 19" power stroke for 646 ip total (* good bow, btw), shot it right off the bow at fulldraw, then measured the speed with the chrono 20 ft away at fulldraw. Then I put the same arrow on a recurved fiberglass prod crossbow measured at 44.4 lbs, 10" power stroke, for 444 ip. Measurements are averaged from several shots. The (% energy) listed is a calculation of how much of the fulldraw close-range energy for that arrow type is in that shot. Note that energy is velocity squared times mass, mass is constant for these comparisons so it's just a ratio of squared velocities.

Yellow:
Mass: 75.1g
Aerodynamics: poor
Fulldraw close: 93.2 fps
Fulldraw from 20ft: 79.4 fps (72.6% energy)
Crossbow 444ip close: 72.4 fps (60.3% energy)

Black:
Mass: 57.2g
Aerodynamics: fair
Fulldraw close: 107.35 fps
Fulldraw from 20ft: 94.06 fps (76.8% energy)
Crossbow 444ip close: 81.37 fps (57.5% energy)

MS2K:
Mass 43.9g
Aerodynamics: excellent
Fulldraw close: 124.2 fps
Fulldraw from 20ft: 110.3 fps (78.9% energy)
Crossbow 444ip close: 91.625 fps (54.4% energy)

Comments: Distance * ft was pretty hard to get with great precision, trying to both hit a fairly small target area while holding exactly a 28" draw. The MS2K full-length arrow may suffer somewhat from being on the crossbow because its shaft spine is too flexible for a 44 lb draw, the long shaft may be bending more than usual and buffering some of the shot energy.

Conclusion: the absolute flat-face of yellow is an aerodynamic fiasco, despite its slower speed and greater mass it loses the most energy of the bunch. My MS2K I'm proud to say conserves more of its energy despite dramatically lower weight and far higher speeds.

But anyways, the impact energy at 20ft, where LARPs usually allow unrestricted fulldraws, varies by arrow type but was measured as 72.6%-78.9% of fulldraw energy for a fairly comprehensive list of probable arrow types.

In all cases, at 444 ip a crossbow will fire the same projectile with substantially less energy even at pointblank range than a target would get at 20ft from a legal fulldraw. But, you may note, a crossbow bolt is somewhat different. No group allows crossbow heads to be constructed differently than arrows so we will assume the head design has comparable diameter, padding, and mass. A crossbow bolt has less than half the shaft length of an arrow, thus half the shaft mass for a particular shaft type. Buffering and spreading out the shaft's energy is almost the entire safety issue in archery. With half the shaft mass, the arrow will be faster, but the portion of energy in the shaft will always drop significantly and there is significantly less impact as a result. This principle is only true when comparing similar head designs and shaft types. For example, if a builder were to use solid fiberglass rod for crossbow bolts, the mass would be even higher than a graphite arrow and is thus more stress on the padding.


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 Post subject: Re: Crossbow experiment
PostPosted: Sun Apr 20, 2008 12:05 am 
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You mentioned that people don't agree on what a half-draw is. I don't agree. Since a full draw is 28", a half-draw would be 14".

Oznog wrote:
As I say, I'm from Amtgard/HFS with a great deal of experience with LARP crossbows. We went with 450 inch-pounds as safe even for close range use, compared to about 650 ip for a 35#*" handbow.


Help me with your physics calculations please. It has been a few too many years since college physics 102. I know inch-pounds is a measure of work and that, for a constant amount of force, work=force*distance. But for a bow, force isn't constant so you arrived at 650 ip for a full draw instead of 980 ip. What is the correct formula?

I know that most people forget that the force is reduced at a 14" half-draw (I think it is 17.5 pounds for the handbow above at half-draw, but could be wrong about that as well). You did some impressive experimentation, but because you compared a crossbow to a handbow at full draw instead of half-draw, I'm a bit doubtful about the quality of your results.

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PostPosted: Sun Apr 20, 2008 12:12 pm 
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I wish that I knew what kind of spring to approximate a bowstring as.

If I knew it were linear, I could easily calculate the spring factor from the full draw weight and length. Then I could find the poundage at any point during the draw and the integral of the force curve over the distance to get the work done throughout the stroke.

Anyone want to gather some force data for me so I can plot the force curve of a bowstring? A draw weight measurement every inch from full draw to no draw would be all I need.


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PostPosted: Sun Apr 20, 2008 1:56 pm 
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Arrakis wrote:
I wish that I knew what kind of spring to approximate a bowstring as.

If I knew it were linear, I could easily calculate the spring factor from the full draw weight and length. Then I could find the poundage at any point during the draw and the integral of the force curve over the distance to get the work done throughout the stroke.


It is safe to approximate is as linear when used within the designed draw length. Longbows are slightly under the curve. For a longbow and recurve both selected to be 35#*" the recurve is linear and the longbow is slighly curved downward thus it has less force at the lower end (but we specifically chose a bow that would be 35# so we know they match up at that point). There is a type of static tip recurve bow called a horsebow that is actually above linear and thus stores more than the typical recurve.

But, for typical recurve, a linear approximation is quite value, thus the graph is a triangle and the integration to determine energy is 1/2*distance*peak force. In practice there's not a lot of practical value to including the "1/2" part, we just call it "inchpounds" and be discard the 1/2 part. SCA did it, Amtgard did it, it makes sense to do this.


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 Post subject: Re: Crossbow experiment
PostPosted: Sun Apr 20, 2008 2:39 pm 
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Thomas MacFinn wrote:
You mentioned that people don't agree on what a half-draw is. I don't agree. Since a full draw is 28", a half-draw would be 14".

Help me with your physics calculations please. It has been a few too many years since college physics 102. I know inch-pounds is a measure of work and that, for a constant amount of force, work=force*distance. But for a bow, force isn't constant so you arrived at 650 ip for a full draw instead of 980 ip. What is the correct formula?

I know that most people forget that the force is reduced at a 14" half-draw (I think it is 17.5 pounds for the handbow above at half-draw, but could be wrong about that as well). You did some impressive experimentation, but because you compared a crossbow to a handbow at full draw instead of half-draw, I'm a bit doubtful about the quality of your results.


First a bit of history trivia:
A 28" draw is measured from the FRONT of the bow, because it was meant to define arrow length with a broadhead. However, the guy who can comfortably draw 28" on a bow with a thin handle now has a 29" draw just if the bow's designed with a thicker handle but everything else is the same. So Archery Mfg Association (AMO) simply defined the handle as 1.75" thick. A 28" draw is 26.25" from the deepest part of the handgrip.

On top of that, the brace height of the string is an even larger distance which does not contribute to the draw and has no business in an inchpounds calculation. I took a brace height of about 7.5" which is typical. Thus technically a bow is "drawn" 9.25" just sitting on a table, the archer only adds 18.75" of power stroke to bring it to 28". 18.75" of power stroke * 35#= 656 inch-pounds. 980 would be using the distance from the front of the bow which includes the distance the force will be drawn over plus empty brace height distance plus the empty handle width which is not really a meaningful number.

As such 14" is not really a candidate to picture as "half draw". That's only pulling back 4.75" and will reach 8.9lbs, this is only 6.4% of full-draw energy and is far slower than if you had simply thrown the arrow by hand. Actually half energy is reached at a 22.5" of draw which is 24.7# on a 38#*" bow.

AFAIK no archer is aware of 22.5" draw being the half energy point, nor do they measure and use this limit on the field. And even that makes no sense, since a fulldrawn arrow of the type Bel uses striking someone 20ft away is about 73% energy not 50% energy. In fact people just learn to draw some unmeasured, undefined reduced subjective amount and I don't think any speculation into a typical number for it is especially meaningful. The only thing I could determine was that groups typically allow 20ft+ as completely legal to fulldraw from and I can objectively measure what that arrow energy is when getting hit with a legal fulldrawn shot from 20ft away. This is an objective number I see as consistent with the actual application of the rules.

FYI, the reduced draw to actually achieve the same velocity right off the bow as it would have when hitting something 20ft away with a fulldraw is about 25.25" draw and about 30 lbs. Just under 3" of let-off.


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PostPosted: Sun Apr 20, 2008 8:02 pm 
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Excellent.

I don't see any reason to discard the .5x portion of that calculation. If you use inches of distance and pounds of force, you already have inch-pounds. the way people seem to be calculating it, it's in half-inch-pounds.

But, cool. Build us a great awesome crossbow at the right poundage and power stroke and bring it to a national event and show people how safe it is. Nothing makes your point like shooting someone with a full-draw bow and then with your crossbow and it feeling lighter.


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