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William P

Posted: Tue 11 Jul, 2017 7:05 am Post subject: Q: the physics of crossbow draw weight / energy discrepancy 


an interesting topic that i find hard to concisely convey is the subject of bow vs crossbow energy and draw weight etc etc
and i hope to use this discussion as data or even a quick reference for those unbclear/ curiopus about the subject to learn more since i KNOW theres several big threads on the subject, their sheer size makes it very hard to get what you are actually looking for without sitting down for half an hour, so i thought id set this thread up
one question issuch as, why does a 150lb crossbow, not equal the same energy as a longbow of the same poundage
similarly the question arises about efficientcy of say, steel prods vs wood or composite structure how does that effect efficiency and bolt weight as well? what would happen if you put a longbow arrow, for example in a high powered medieval crossbow (like a 1200lb bow.




Leo Todeschini
Industry Professional




Arne G.

Posted: Tue 11 Jul, 2017 9:19 am Post subject: 


One quick answer: it is not just the draw weight, but also the draw length, that matters. A typical crossbow only has a draw length of 6" or perhaps a bit more, which is considerably less then the ~30" or so of a war bow. Thus, a crossbow may develop very roughly as little as 1/5th the power of a war bow for the same draw weight.
Other smaller but significant factors include projectile design and the material properties of the wood/metal/etc. used for the bow or prodd.
Tod can explain this much better and in much greater detail.




T. Kew
Location: Cambridge, UK Joined: 21 Apr 2012
Posts: 186

Posted: Tue 11 Jul, 2017 10:16 am Post subject: 


As noted above, it's not just draw weight but also draw length that matters.
To explain this a bit: if you draw a graph of the 'drawforce curve' of a bow, the energy stored that is available for a projectile is the area under that curve (this can be proved mathematically). For modern compound bows you can make all sorts of exciting shapes, which mean that the calculations can be a bit difficult, but traditional bows are normally fairly simple. As you draw the bow, it will start at some low poundage, and slowly increase until it reaches the maximum poundage at full draw.
I've attached a quick graph I doodled, showing three potential missile weapons: a 100lb bow, a 100lb crossbow, and a 150lb crossbow. Let's quickly work through the basic maths:
Assume they all start at 0 lbs, and all the lines are straight. This means we can just use the formula for the area of a triangle to work out the power available in all three weapons, which is 1/2 * width * height
The 100lb crossbow (red) has a width of 6 inches and a height of 100lbs, meaning the overall energy is 300 inchpounds  which is a silly unit, but we only really care how it relates to the other bows on the chart.
The 1000lb crossbow (green) is unsurprisingly much more powerful  with a width of 6 inches and a height of 1000lbs, the overall energy is 3000 inchpounds. That's 10x as much energy as the 100lb crossbow, which fits exactly with what we'd expect.
Now for the 100lb bow (blue). This has a height of 100lbs again, but a width of 30 inches, and that makes the overall energy 1500 inchpounds  5x as much as the 100lb crossbow, but only half as much as the 1000lb crossbow. It's not any taller than the 100lb crossbow, but it is so much wider that it still can store a lot more energy.
In reality, of course, it's much more complicated than this: efficiency is a feature, and drawforce curves aren't as simple as the very artificial example I've provided. But the basic reasons why a bow can keep up with a crossbow should be clear.
Overall, most medieval war bows seem to have had pretty similar stored energies, whether they were crossbows or longbows. They basically represent two ways to get enough power from a missile weapon: either apply a moderate amount of force over a nice long distance, or apply much more force but over a very short distance.
Attachment: 214.32 KB
Illustration of drawforce curves [ Download ]
Instructor and scholar, Cambridge HEMA




Timo Nieminen

Posted: Tue 11 Jul, 2017 1:18 pm Post subject: Re: Q: the physics of crossbow draw weight / energy discrepa 


William P wrote:  similarly the question arises about efficientcy of say, steel prods vs wood or composite structure how does that effect efficiency and bolt weight as well? what would happen if you put a longbow arrow, for example in a high powered medieval crossbow (like a 1200lb bow. 
If the prod is heavier, but the same draw weight, the efficiency will be lower (IIRC, steel will give you lower efficiency than composite, but not hugely lower. Steel is OK.) You can increase the efficiency by using a heavier bolt. Too heavy, and you have low velocity and short range. Choose the right bolt weight.
If you put a longbow arrow in a 1000lb crossbow, the question is whether it will survive being shot.
Arne G. wrote:  One quick answer: it is not just the draw weight, but also the draw length, that matters. A typical crossbow only has a draw length of 6" or perhaps a bit more, which is considerably less then the ~30" or so of a war bow. Thus, a crossbow may develop very roughly as little as 1/5th the power of a war bow for the same draw weight. 
The draw length is measured from the bow; this is not the distance over which the arrow/bolt is accelerated. That distance is the draw length  brace height = power stroke. The 30" you give for a war bow is the draw length; the brace height would be about 67", so 2324" power stroke. Still a lot more than the 6" power stroke of a European crossbow.
Han Dynasty crossbows typically had 1820" power strokes (approx 24" draw length). So, at the cost of greater size, would store/deliver more energy than a typical European crossbow of the same draw weight.
"In addition to being efficient, all pole arms were quite nice to look at."  Cherney Berg, A hideous history of weapons, Collier 1963.




William P

Posted: Wed 12 Jul, 2017 9:13 am Post subject: 


T. Kew wrote:  As noted above, it's not just draw weight but also draw length that matters.
To explain this a bit: if you draw a graph of the 'drawforce curve' of a bow, the energy stored that is available for a projectile is the area under that curve (this can be proved mathematically). For modern compound bows you can make all sorts of exciting shapes, which mean that the calculations can be a bit difficult, but traditional bows are normally fairly simple. As you draw the bow, it will start at some low poundage, and slowly increase until it reaches the maximum poundage at full draw.
I've attached a quick graph I doodled, showing three potential missile weapons: a 100lb bow, a 100lb crossbow, and a 150lb crossbow. Let's quickly work through the basic maths:
In reality, of course, it's much more complicated than this: efficiency is a feature, and drawforce curves aren't as simple as the very artificial example I've provided. But the basic reasons why a bow can keep up with a crossbow should be clear.
Overall, most medieval war bows seem to have had pretty similar stored energies, whether they were crossbows or longbows. They basically represent two ways to get enough power from a missile weapon: either apply a moderate amount of force over a nice long distance, or apply much more force but over a very short distance. 
tis leades me to a question that didnt occur to me, when we say a arablest crossbow is 1000 lb draw weight.. how is that calculated, is that 1000lb's at 6 inches or is it an attempt to draw 1000lb of bow 28 inches and realising its draw force is a lot less at such smaller distances?




T. Kew
Location: Cambridge, UK Joined: 21 Apr 2012
Posts: 186

Posted: Wed 12 Jul, 2017 10:57 am Post subject: 


William P wrote:  tis leades me to a question that didnt occur to me, when we say a arablest crossbow is 1000 lb draw weight.. how is that calculated, is that 1000lb's at 6 inches or is it an attempt to draw 1000lb of bow 28 inches and realising its draw force is a lot less at such smaller distances? 
Typically* the quoted weight will be at full draw, whatever that distance is for the bow in question. So a 1000lb crossbow will be 1000lbs of force at six inches.
*Not for modern compound bows.
Instructor and scholar, Cambridge HEMA




Leo Todeschini
Industry Professional




William P

Posted: Thu 13 Jul, 2017 12:02 am Post subject: 


funnily enough i just watched it
now im very curious to see your gastraphetes and your 11th12th century bows and see how THEY perform joules wise.
i was also watching skallagrim test his 350lb crossbow against repro helmets and watching it fail dismally and i am quite curious now.
also you mentioned the energies for a 1250lb crossbow doing something in the realm of 140 150 lb of energy, thats the biggest one you have made but what is the biggest of the 'handheld' crossbows that we know about, ive heard up to 4000 lb's quoted but i assume thats a swivel mounted seige engine... and i dont know where that sort of figure is from,





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