@@commander31able60 I think he didn't know which math you're talking about, the first part of the video is indeed talking about area of the triangle which is indeed primary school.
Drag is proportional to the square of speed, therefore quick projectiles loose more energy on their way to the target. Heavy and slow crossbow bolts start with less energy but preserve more during their way.
Not to mention a function of damage isn't necessarily the same for firearms and crossbows. A slow moving bolt just needs to penetrate armor and flesh and cause bleeding. The larger the diameter of the bolt head the larger the wound, the more bleeding occurs. Bullets have small diameters even when dealing with huge cartridges like .50bmg (around 12.5mm). Thus when it strikes a target the initial hole isn't necessarily that large. The speed however, is enormous comparatively, and counts for much more of the damaging potential (never judge a bullet solely by its diameter, aka caliber). This means when it hits a target and dumps even a portion of its energy into a target the hydrostatic shock which creates a large temporary cavity and a smaller permanent cavity. In essence your looking at tearing a hole mostly by energy of impact to create a lot of bleeding and damage versus versus piercing a hole with a relatively large diameter. As a side note you can see this in action by watching ballistic gel tests with a slower round, say .45 acp versus a fast round like a 5.56x51 NATO.
@@thewinterasp Long, narrow bullets create more physical trauma than shorter fat bullets, because all bullets tumble on entry (see the work of Dr. Martin Fackler et al.), but a greater increase in the permanent wound cavity (as opposed to the temporary wound cavity) is caused by fragmentation of the projectile.
Well, long narrow bullets behave * Differently * than short fat bullets in Terminal Ballistics ( and external balistics for that matter ). But there are a whole bunch of additional factors , and you can't make generalizations from just one factor . The design goal of non-expanding FMJ bullets is to at least tumble upon impact, and ideally subsequently fragment . This is effected by the stability of the bullet ( rpm of spin), and multiple factors of internal bullet design . Center of gravity front to back , jacket thickness , jacket hardness , external or internal scoring of jacket, presence or absence of cannelure , and actual impact velocity . There are inherent compromises in bullet stability . To oversimplify , for maximum tumbling on impact , a bullet should be just barely stable enough to be flying point first . But for long range accuracy , accuracy in all climate conditions , and penetration of hard barriers , the more stability the better . ( Stability being a factor of bullet RPM , which is effected by both twist rate, and muzzle velocity .) ( Insert long history of evolution of U.S. ammunition, twist rates, and barrel lengths for 5.56 weapons, with terminal performance going up & down . ) If small caliber bullet performance isn't ideal , big non tumbling bullets are better than small non tumbling bullets . And throughout history generally , there have been lots of small bullets that performed poorly , or at least been designed with greater emphasis upon factors other than terminal performance . And of course , this is all within the arbitrary context of International Treaty , requiring nominally non expanding ammunition against certain Recognized Combatants . For hunting, personal defense , law enforcement , and certain Counter Terrorism , it takes a really tricked out FMJ , performing exactly as designed, under ideal conditions to match a rather mediocre expanding bullet .
True but not very relevant at distances under 200 meters or more likely under 100 meters that most warbows are regarded as being prime effective range.
I just want to say, as someone who has tutored college students for eighteen years, you did an excellent breakdown of the physics and math calculation, as well as comparison to modern weapons.
I love your honesty and clear thought process. No fuzziness, just facts backed by experimentation. If half of the "historical documentaries" would use your honesty and experimental process, would make them worth watching again.
This guy just captures my attention every time I watch his stuff. Love the precise, thoughtful experiments, and that he's a brilliant master of his craft. Cheers!
excellent video Tod, but I feel I should mention that while energy is important for punching through thin, hard materials i.e. plate, it is less important than momentum for penetrating thicker and more flexible materials, e.g. Kevlar, gambeson, and indeed flesh and bone. Sectional density is of course relevant for all materials. I bring this up because penetration is the most important data point for the "stopping power" of a round, with wound cavity a proportional secondary point. Shooting these weapons into ballistic gelatin would tell us more, though again would be inconclusive. Anyway, great vid!
Another amazing video! Thank you for all the information! We should take in mind that they didn't have the same metalwork as we do today. Also they did tend to exaggerate about their works. Your bows are among the most beautiful ones ever.
Great video. You did a great job on explaining this. Kudos for the parts about warbows. Heavy draw weights around 140 to 150 lb reaches 140-150 joules with middle to heavy arrows. Important detail there. According to a video on the Medieval Crossbow channel, composite horn crossbows in the 1276 lb range reaches 488 joules with 348 gram bolts. It's rather big in comparison to the crossbow you have here. The bolt left at 52.92 m/s. It shows that composite horn is a much better material to make a bow of than steel. The 260 gram bolt left at 57.74 m/s and gave 433 joules.
Yes, Han and other Chinese records go into quite a bit of detail on crossbows and the distances for various weights achievable and how to use the various types of crossbows. As more of these records are translated, verified, and accepted by medieval hobbyists some of the work examining the few medieval crossbows extant and reproductions will focus on how to make steel prods more efficient because while the European crossbows never quite measure up to the Chinese sources they do much better in comparison to Tod's reproduction and actually are not that different from LaCombe's results. Han crossbows had a longer stroke which as Tod demonstrates makes them more efficient but there are also many small tricks in making the limbs of bows more efficient, not only in materials, but design, and other very small factors which I do not believe we have any bowyers currently working who have fully mastered crossbow manufacture.
Nevermind the readings in that video gives me the info i need, which if im reading this right a modern recurve at 45lbs draw is putting out roughly the same energy as the medieval longbow at 95lbs which is interesting and makes me really want to do some more research on that
I asked this on another crossbow video of Tod's, but it would probably fit better here: Do you know if there is a materials-engineering reason they didn't use compounding pulleys on bows and crossbows in the medieval era, or was it just that no-one had thought of trying off-center pulley wheels? It's a really weird idea to wrap your head around, from a geometry perspective, but they had some pretty inventive people between Pythagoras and the middle-ages, and LOTS of experience with making and using bows.
All the things i a bowyer of primitive, self bows never figured out in such a scientific way,.... Low tip mass, shortest possible limbs, thin string and all that is known to increase efficiency. But this vid gives a very clear and broad insight into the matter. Thanks for posting.
Glad that you made this Video so detailed. The mathematic back up may calm down those people who say that a 1200lb crossbow could shoot through the moon.
This is without doubt a superb video! I thought you were going to dismiss the modern bows as inferior and praise the classic styles as the definitive weapons but was pleasantly surprised. This video shows a lot of understanding on the mechanics of a bow and a lot of honesty judging your own. Great work Tod, absolutely outstanding!
Hey Tod, love your videos. My son and are bow hunters. My son and I were watching your vid and some other interesting thoughts came to mind: Modern Crossbow 175lbs/131j =75% conversion Longbow 95lbs/45j = 47% conversion (approx 50%) Medieval Crossbow 450lbs/54j = 12% conversion (approx 10%) This would mean you'd need a 1000lb crossbow to deliver the same 100 joules as a 200lb longbow. Now, think as a general on a battlefield. Which weapons delivers the most joules of "death" to the battlefield per second. Working on 10 sec easy calculation. Based on our own rate of fire, we think in the hands of a expert archer, a 200lb longbow can shoot 3 arrows (each delivering 100 joules of death) in 10 seconds = 10 secs/300j = 30 joules of death per second. We've assumed 1000 crossbow can shoot 1 bolt (delivering 100 joules of death) in 10 secs = 10 secs/100j = 10 joules of death per second. I know it's simplified, but still interesting. Again, thanks for your videos. Love em!
Thanks so much for making this video! You managed to isolate some understandable maths from a device that has a massive list of variables. Those of us just beginning to enter the world of sticks'n'strings could use more like this!
The thing about the 22 vs the crossbow bolt is that bolt tends to have a very sharp and sometimes wide tip meant to slice into the target where as 22 round is like trying to push an unsharpened pencil into the meat.
Very good Video. The only thing i am missing a little is how the cams come into play because the whole trick with the compound system is that you don't have that linear relationship between draw length and poundage. So that graph would actually look quite different.
Oh Todd I LOVE IT! In fact, I was just thinking about how somebody should draw out the draw weight over powerstroke curves of some bows to calculate their energy output, and right then I see this video where you do just that! I do however have two points of criticism: 1. You are looking purely at the energy of the projectile, because this is used to characterize modern rifles. I wonder however, if the deadliness of an arrow isn't better characterized by its momentum, rather than its energy. Of course, this makes the comparison to rifles difficult, but this is to be expected, because the damage-mechanism is also a different one: An arrow cuts through the target, while a bullet pushes the mass in front of it away. The former should be far more energy-efficient. This claim could be tested by shooting bolts or arrows with different masses from bows with different draw weights, and simultaneously measuring penetration and bolt-speed. If penetration scales linearly with speed, its the momentum that counts, if it scales with the square, its the energy. 2. You remarked already that it is incorrect: You are assuming linear relationshipts for draw weight over powerstroke. Although I appreciate that this should not become too complicated and it was probably right for this video to keep it that simple, this neglects the whole purpose of the curved shape of recurve bows for example. I think it would be really interesting to measure these curves directly - for example by filming how you slowly draw the bow over a tape measure using a bow scale. (If you happen to want to do that, you are welcome to send me such a clip and I will can evaluate it and send you a nice graph and energy value ;-) ) After all, the graph for a "perfect" bow would not appear as a triangle, but as a rectangle: From zero, it would directly jump to the maximum draw weight that the archer can draw, stay there until the full draw length, and then drop back to a low value to make it easy to hold the bow drawn. I expect that the modern bow will approximate this behavior much better than the medieval ones. If such a measurement were done and compared to the actual arrow speeds, one could also calculate the actual energy efficiency of the bow :) I believe that both these points contribute to why the modern bow performed so much better than the simplified math suggested.
Thank you for this video; it has been highly educational and must have been quite a chore to do the analysis. I am trying to make my own wooden bows as well, and have learned much from your methods.
Hi Tod, awesome video and talk through. you are a true craftsman. Your maths breakdown and analysis is truly remarkable. You are really dedicated to your art/sport. Simply great to watch and to listen to, thank you so much!!
I'll have to look at the momentum change of these weapons & see how that affects their relative relationships. As the .22 comparison shows, the effectivness of a projectile can depend as much on its momentum and sectional density as it does on its kinetic energy.
This was my thought as well. Momentum is the resistance to slowing down. a train rolling at 1 m/s is harder to stop than a compact car at that same speed, because it's heavier. Heavier things want to keep doing what their doing. I know American math, so check for conversion errors. Momentum is just mass x velocity and give us kgm/s. Using his values the momentum of the Compound crossbow was 2.9 The Longbow was 2.0 The Medieval Crossbow was 2.5 A .22 bullet (2.6 g, 361 m/s) was 0.9 A 9mm bullet (8 g, 381 m/s) was 3.1 A .308 (7.62 x51) (10.9 g, 770 m/s) was 8.4 A 12-ga slug (35.6 g, 488 m/s) was 17.4 A .22 isn't more deadly than an arrow or bolt. That energy value only matters the instant it makes contact. After that, the much higher density of the target will begin to slow the projectile down. Things with a higher momentum slow down more slowly, so they penetrate deeper. The compound crossbow may not have anywhere near the energy of the 9mm bullet, but it has a very similar momentum, making them comparable as far as close range damage goes. The Slingshot Channel did an old video comparing momentum of one of Joerg's slingshots to a number of handguns using a swinging metal plate to test. The only gun tested that beat the sling was a .44 Magnum. ua-cam.com/video/tLxnNP-ycVQ/v-deo.html
I know this video is quite old, but I wanted do do some calculations for myself to see if I could quantify the efficiency of the bows. I took the bow strength, the powerstroke and the weight of the projectiles for the medieval long- and crossbow from this video, as well as the Skallagrim-crossbow (I got the values from other videos: 976lbs, 160mm, 96g). I calculated the theoretical acceleration (a = F/m) for the three bows, and used that to get a theoretical projectile velocity ( v = a*sqrt((2*d)/a) ). Point is, a 423N (95lbs) longbow with a powerstroke of 0.64m (25 inch) should be able to accelerate a 45g arrow to 109m/s. You measured it at only 44.5 m/s, which is about 41% of the expected velocity. The lighter crossbow (2002N, 0.11m, 60g) should reach 87m/s but reached only 42.4m/s which is 49% of the expected velocity. Skall's heavy crossbow (4341N, 0.16m, 96g) should in theory shoot bolts at 120m/s but was measured to shoot them at 47.9m/s (39,8% of the expected velocity). Since I think, that the kinetic energy is a better measurement for the efficiency of those bows, I calculated the energy both, based on the theoretically expected and the experimentally measured velocities (the latter were basically the same that Tod calculated in the video). Because we calculate the energy by squaring the velocity and the other parts of the formula (mass of projectile and the factor 0.5) stay the same, the efficiencies of the energy were just the squared efficiency of the velocity (I should probably have seen that coming...). The surprising thing is, that the longbow appears to be less efficient than the lighter crossbow, and that even though the longbow's projectiles should in theory have more kinetic energy (268 vs 228 Joules), in practice the crossbow has the advantage here (45 vs 54 Joules). The heavy crossbow has about the same efficiency as the longbow, but with more than ten times the draw weight and twice as heavy projectiles, those projectiles have more than double the energy of either the longbow or the lighter crossbow (110 Joules). I'm kind of curious how a warbow would perform, so if anyone has the draw weight, powerstroke and projectile mass for a representative bow please let me know :)
Used to shoot metallic silhouette (firearm sport). The most fun calibers for me were the .375 H&H mag and the .458 winchester mag. Both would flatten the 50 pound or more half inch steel targets at any range you could hit them. Our range only had a clear view of 250 yards. Both would leave a decent dent where they hit. The .375 was at about 3000fps, and the .458 was more like 2000. However we had to ban calibers like the .22-250 or the .22 swift and even the .223 because they would consistently blow big holes in the half inch steel. Tiny bullets traveling at 4000fps plus requiring hours of welding the holes shut again. Even then, the targets didn’t even always fall down. Huge energy with the small fast projectiles, but very bad transfer of momentum. Most of the energy goes into vaporizing the bullet and creating the crater in the plate. For reference, the momentum of the .458 slug was about 5 times higher than the .22-250 50 grain bullet.the little round has about half as muck kinetic energy as the big one. Down range performance really depends on what effect you want. The .22=250 is a varmint round and will disintegrate inside a ground hog, where the .458 or even the .375 will easily go right through the long direction of a deer or crosswise in a bear if you are using a full jacket round.
Great job. I've been thinking about those differences for a long time. However, I don't think comparing energies of firearms to bows and crossbows makes much sense, as these projectiles work in very different ways. Unlike bolts and arrows, firearm rounds don't rely on simply piercing the target and causing blood lose through relatively small, clean cuts. Instead their tips are often blunt or even flat and hollow (and if their not, it's to do with aerodynamics as they're often designed to flatten or tumble upon impact) and tear through tissues causing massive shock waves and extensive damage. The whole process is very efficient at killing but requires far more energy to even occur. Comparing arrows/bolts to gun bullets would only make sense if done in the armor-piercing context. In therms of so-called soft targets, it doesn't really matter how much energy a projectile carries as long as it's enough to penetrate and reach the vital organs. For instance, a long knife, or any pointy object, can be slowly pushed into a body and even poke out the other side causing almost instant death even though it probably won't have more kinetic energy than a cheap air-riffle. On the other hand, a heavy rock can be thrown with more energy than many air-riffles will produce, yet won't be able to do quite as much damage.
I always wondered about the power an old crossbow might have in comparison to other weapons. I looked online and never really found anything conclusive. This video was great. I still do wonder about the projectile itself, and if that actually plays a bigger role in how "deadly" the weapon ends up being. Like you said with the heavier crossbow at 1250 lb, the joules would seem to be close to a modern .22, but I imagine the bolt itself would cause a heck of a lot more havoc on whatever it ended up hitting than a .22 round. I never tested this, of course, so I can't say for sure.
Arrows and bullets are really different.The wound types are different. The terminal ballistics are very different. I think it's hard / unrepresentative to compare them using just "muzzle" velocities. An arrow mostly pokes a little hole through you. A bullet makes a much messier hole, and stirs up adjacent tissues more than with arrows. If you look at the numbers, one .308 round is equal to (I forgot the numbers) seventy or a hundred longbow arrows. Bit if I had to choose, I'm pretty sure I would be better off being shot once with a .308 then 35-50 times with arrows, let alone 70-100. (Neither sounds enticing.)
One factor is the surface area of the missile. A pointy arrow might well have more joules per cm2 than a bullet. It might penetrate deeper despite less KE and momentum. (A 1 kg pillow going twice as fast as a bullet wouldn't penetrate much.)
Yeah, it's interesting. Because when I think of someone getting hit with a .22 pistol round to the chest, I'm not thinking "Well he's done for", but a bolt or an arrow to the chest makes me think of a much worse injury. The caliber/ammunition weight, shape and size seem to play a big part in what's going to happen when it hits, compounded by that force behind it.
*Sangh* i am just an armchair enthusiast, & so i am going to be as vague as possible to cover my tracks! :) In a very general sense, i am going to hazard that to a significant degree, some comparison of side-arm versus rifle ballistics can be instructional. Mainly in that even for most pistols, which fire bullets traveling much faster than a crossbow bolt, the single biggest operative factor to damage is the diameter of the bullet in relation to shot placement. They are still low enough velocity that wounding from fluid displacement from cavitation as the bullet passes through isn't all that significant until you start dealing with some of the magnum loads, which are more typical of revolvers than pistols. Then, overwhelmingly so with rifle loads. But, with that backdrop, i would think that by the crudest of definitions, the diameter -size -of the crossbow bolt is going to be similarly operative here too, as it is still much slower than a pistol bullet. In fact, so much so that the design of the bolt -& its ability to cause cut & bleed is going to be the biggest factor in its lethality. But that trait is where the bolt design suddenly gets funny. It might be surprising that military bolts were often not nearly so refined as good hunting bolts. Military bolts commonly have minimal fletching, utility rather than razor tips, and are weighted more for penetration rather than accuracy. In many respects i think the rough & ready design of the military bolts emphasizes wounding/disabling as the priority beyond outright bleeding/killing. This would make sense, as wounded soldiers require a lot more resources to maintain than dead soldiers, & so efficient killing function is not necessarily the most important consideration in the design of the crossbow bolts. Taking them out of the fight is. And in general, i think the design of the heavy crossbow bolt is something that i have always questioned. I am just an armchair enthusiast, but i always have this sense that they tended to not be as optimized as a projectile like, the bodkin arrow of the warbow, or even a dart & atlatl. But i could very well be wrong about that -and would venture that is more likely the case than not. But considering the abysmal rate of operation of a heavy crossbow, i would hope that designing the perfect bolt for the function of the machine would be a critical priority, as each shot counts all the more. But it appears to me that the finest bolts were probably those designed for hunting and target shooting rather than war. And like i said... don't take me too literally. All this is my sense of things! :)
As a hunter the principals taught to me go something like this: With a bow the death is caused by the cutting that the broadhead does to the animal. All the energy you need is for the tip to just pass through the heart and that isn't that much with a modern cutting broadhead especially if you don't hit bones. Cutting diameter of the tip is what causes massive blood loss and death. With a gun the damage is based on the crushing shock effect that the bullet causes. If you have ever seen a water jug for example being shot, they usually just explode even though the bullet diameter can be relatively small. If you shoot with a very low powered rifle I imagine the effect would be similar to shooting with a target tip arrow where it just cleanly goes through and easily leaves big blood vessels intact. In the past they didn't really have any ways to heal these kinds of wounds and they could easily get infected but they would probably seriously lack any kind of immediate stopping power. I guess there is still a good change if you have an arrow sticking out of your side that you would stop bullying the dude in the castle and search the local shaman for help.
This is one of the most informative bow videos I've ever seen! Thanks Tod's Stuff! (And scholagladitoria for introducing me to you!) I really enjoyed the Joules comparison as that put it into great "context." That really gives me something to think about with what "killing" power needs to be with missile weapons. Now if we could figure out how many Joules you need to defeat various armors at various ranges we'd really be in the know!
It's important to remember that missile weapons up until advanced firearms were never really used for raw stopping power either. Their role on the battlefield was as a support weapon for the main melee troops. Even the Hussites, famed more-so than the English for excessive use of missile weapons, ultimately finished off the charges with their massive flails and halberds and not their crossbows or handgonnes.
@faultroy I personally can't speak for a medieval javelin or spear, but modern olympic javelins are thrown at up to 30m/s, and weigh 0.8kg, for an initial energy of about 360 J. I'm not sure how a historical one would compare to that, but I assume it would be lower.
Thank you so much! This answers several questions I've had for a long time. Great no nonsense research, definitive no, but extremely useful and well above most youtube research.
This greatly helped me set the standards for bows and crossbows in my homebrew VtM, where we prize realism and accurate portrayal of weapons with no regard for fairness. If I can get a DnD (or simpler!) system that's a fair approximation of reality; it's more fun, slightly educational, and helps me remember the actual information for use and sharing lolz The example with the triangles on paper was particularly helpful! 18:00 There's a difference between how many joules of force an object has and how much damage it does to the various things it could hit. A 9mm FMJ and .45 ACP FMJ have the same joules of energy, but the .45 is easily demonstrable (and noted in history) to be slightly more effective. 7.45 gram (115 grain) Federal FMJ 1,180 ft/s (360 m/s) 355 ft⋅lbf (481 J) 15 gram (230 grain) FMJ, Winchester 835 ft/s (255 m/s) 356 ft⋅lbf (483 J) Both are standard pressure rounds, FMJ bullets, out of aprox. 5 inch pistol barrels, and are the most common "standard" example of each round. The Federal .45s and Winchester (presumably White Box) 9mm would do pretty much the same. More energy almost always helps, tho I have seen bullets that start to do worse in gel when given the +P+ pressure instead of just +P. See Paul Harrell for good examples of "Does this extra power (from velocity, weight, etc) translate into more effectiveness?" I presume that this holds true for all projectiles. The wound is what matters, and its all about how the projectile interacts with the target to create the wound - how the energy is used by the object to wound. If one shot deer with a Medievel or Modern crossbow or a longbow, then shot them with a .22 LR (I'll even grant it a rifle barrel), one would clearly see which is more effective! Ask any hunter. I've shot stuff with everything listed here, the difference between them and a .22 is fairly clear. What that does also show, is how relatively poor arrows and quarrels etc are at incapacitating people compared to a 12 gauge 2.75 inch 00 buck shell or 7.62x51mm (.308) FMJ round. The shotgun example is a good reason why total energy isn't all there is. There is more energy in some rounds of birdshot than the standard 00 buck I just listed, but that doesn't mean it's even close to as effective... I hope those considerations help with people's understanding of the old bows' true level of effectiveness. Great video, as always.
What a wounderfull video. It would be great to see how a normal medival bow compares go the longbow in power, range. Im so glad that I found your channel.
A point about the energy of the projectile. Low weight, high velocity will slow down more from air resistance, so perhaps down range the medieval crossbow would fair better. Bullets do ofcourse have a much smaller cross section for air resistance, but the speeds are vastly higher and the weight is vastly less so they probably lose velocity more than the medieval crossbow bolt also. Probably the gun energy is measured at the muzzle.
In addition, Kinetic energy isn't how arrows and bolts kill or do damage unless you're using rubber/wood blunts. Broadheads as a set of inclined planes are able to amplify the amount of work doable by a given force (which is measured in momentum/impulse, not KE). Related to your point, as impact velocity of any projectile increases, the resistance forces faced increase exponentially. Here's a neat research paper that talks about it in depth cpw.state.co.us/Documents/Hunting/EHU/Momentum-KineticEnergy-ArrowPenetration.pdf
This had me really wondering: could you build an effective compound bow using medieval technology? How much of their effectiveness depends on modern material science and manufacturing, and how much of it was just a matter of understanding how bow efficiency works and having the insight to use pulleys to exploit that?
That's awesome. I watched that catapulta video - so cool and pretty terrifying. Do you think the compound mechanism would have been achievable at hand-held scale? I don't have a great sense of what the limitations were with medieval techniques.
Sectional density and (in war or hunting heads) sharp edges promote puncturing and incision wounding in-situ, very different from the 'tearing and bruising' seen in bullet penetrations, with their considerable cavitation and (temporary) displacement of soft tissue. A handgun and arrow have similar penetration depths (at low draw weights - the 'wounding study' I have shows results for ~ 52lb bows only - and a bow of around twice the draw weight with heavier arrows (these were only 30-40g arrows - much lighter than what a heavy bow would be firing from what I understand) would show at least as good performance. Indeed, medieval/renaissance texts warn of taking broadside shots on deer because of the risk of a through shot striking hunters on the far side of the quarry on a hit - and it was preferred to take an oblique shot to maximise wound channel length.
Kinetic energy is far more informative than momentum because it is that energy that is 'used' to impact the target, ie break molecular structures. Obviously each molecular bond is far smaller in strength than a joule so it is sort of a count of how many molecular bonds it can break.
Incorrect. It is the energy that is important in a killing projectile. A large mass moving at a slow speed is nowhere near as effective as a small mass travelling at high speed. That is why is a bullet is preferred to a thrown rock.
@@paulbaumer8210 Well.... In the end a bullet isn't the same thing as an arrow, however. For instance, picture getting hit in the thigh. A sufficiently fast bullet is going to travel through and if it will kill you mostly depends on if it hits an important blood vessel or breaks your bones. If it doesn't you are left with a comparatively clean wound that can be patched up without too many complications. If you have a projectile or a bolt that isn't as fast and gets stuck instead your are in a world of trouble. Removing it can cause additional tissue damage and damage an arterie but not removing it is likely going to result in an infection of some sort or lead poisoning if it was a bullet. People dying not from getting hit with the arrow but after having the arrow removed from the wound was rather common. In the end, whilst energy does of course play a big role, it is not the sole determining factor as the type of the projectile will determine the kind of injury you receive. A full metal jacket may carry the highest overall kinetic energy but a soft point is still gonna be more lethal if you get hit by it.
the mass is already in the calculation. The slower medieval bolt had more energy than the faster arrow. He doesn`t multiply speed with speed to get to joule (v²) like you suggested.
An interesting comparison. Really puts things into perspective and hats off to Tod for a great, clear an informative explanation. One point though: Tod says that the old longbow was better made than the modern variety. This just a thought as I have no way in the means of proof. I would contend that a modern bow is better in regard to final build and tiller because of the time invested in its manufacture by a skilled modern bowyer. This is not to say that medieval bowyers were less skilled, but I suggest that emphasis was placed on the quantity of manufacture rather than quality of build. Modern customers are more demanding and expect a superb bow in all respects. Medieval bows, built for war did not have the aesthetics and perhaps the tiller was less than perfect. This did not detract from their purpose but maybe they did not last as long as the modern counterpart. Flaxen Saxon
Fantastic vid! Found it absolutely wonderfull, its a shame crosbows are illegal where I live, would love to have a medieval one. There's something very alluring with the thought of practicing marksmanship with a medieval cross in a sligthly secluded part of the countryside. Just me, my crossbow and an unfortunate assortment of fruit.
This is my first visit to your channel, Tod. Your disquisition comparing the three bows was fascinating, so much so, I am moved to ask this question: Do the numbers cited in the Penn-Galway (sp) findings factor in arc? I thought that in combat, archers sometimes fired upwards to achieve arc, to cause death at greater distances. Therefore, medieval armaments records might have been referring to distance caused by arc, ie elevated trajectory. That might account for the huge numbers. Thank you for relating your remarkable and thought provoking views.
A good video! One small point you did not cover too well though was type of Arrow / Bolts! The purpose of them was to put holes in things .... bodies, armour, horses .... and mere energy of the arrow does not compare in this respect. There were many different tips from scimitar like heads designed to disembowel horse to basic points for "normal people" to armour piercing heads. All of these were great at their design targets but poor in others. Also there is much loss in the archers paradox (flexing of the shaft in flight) which is one of the great advantages of compound bows. The draw weight varies from high at the start of the draw to light at the end. This makes the arrow speed up more as it moves to the end of the draw rather than the longbows more flat speed curve!
It's funny how you say Tod did not cover something too well, and on your comment you don't even know what archer's paradox is.... The flexing of the shaft in flight in not the archer's paradox, but a result from it, I could explain to you what it is but I will let you search the information by yourself, so you could be more considerate next time you bash on someone else's video without even knowing what you are talking about.
Excellent empirical calculation of kinetic energies. Just for interest's sake I thought it'd be interesting to calculate the momenta as well (from your numbers). For the modern crossbow, 2.86 N*s; longbow is 2.00 N*s and medieval crossbow is 2.54 N*s (the same qualitative order as kinetic energies). What I don't understand (maybe someone with an engineering background can explain this) is why longbows typically have longer ranges, even though by your test crossbows have larger momenta and kinetic energies. Is this purely a function of how streamlined the projectile is?
You made an interesting point at the end but I think you're just shy of the mark: are your bows or Joe Gibbs bows as good as the BEST bows of the time--probably not. Are they as good as the run-of-the-mill mobilize the country to arms quality of weapons that were likely made during a period like the hundred years war? Probably as good or better. The King's sword isn't measured the same as that of the yeoman, and bows I'm sure are much the same.
Looking at the efficiency of Joe's longbows in the Agincourt test, it was rather disappointing. A good bow can put out about as many joules as it has pounds of draw weight, at about a 1:1 ratio. His was at a 100:74 ratio. I once saw a 180 lb bow that barely put out any more energy than his 160 lb bow, admittedly (of course, arrows make a big difference to readings).
@@vanivanov9571 Were those recurve and/or compound bows? Longbows are self bows and are not as efficent at transfering the energy into the arrow as other types of bows.
I'll readily concede that Joe Gibbs ( or other other quality Bowyer's ) long bows have efficiency on par with military issue bows from back in the day . The big difference is the test bow has a draw weight well below historical .
@@filianablanxart8305 If we go by the Mary Rose samples then 95 is underweight with the average being around 140-150lbs but the math works similarly so long as we keep in mind what Tod says about ignoring efficiency which is actually super important and an area which causes most of the controversy from what I have seen. The heavier warbows in the 180-200lb range have thicker cross-sections which gives more potential energy but lowers the efficiency. They use heavier arrows than lighter bows which increases the amount of potential energy transferred into the arrow but still losses efficiency and all tests I have seen indicate loss of 10-20% fps but the heavier arrows have more momentum and did have higher potential energy than lighter warbows. Compared to a horn/sinew Manchu bow that has 150lb draw but is 25% more efficient but also has a shorter stroke the math indicates really similar energy delivered to a target by a slightly lighter, shorter arrow that moves at a higher initial velocity which translates into less drop (more accuracy). The result... the top end warbows of English archers and steppe warriors were really quite similar in armour penetration with the steppe bows being smaller and more accurate but also more expensive to make and more difficult to maintain. For steppe cultures that is not a huge drawback because bows were the main weapon of the steppes and there was no need for ordinances such as England created to mandate men to practice archery.
In regards to whether a great modern bowyer can match the *best* medieval bowyer, well we simply can't know for certain. But given that they're both humans doing a task with a clear goal, the answer is undoubtedly yes, what makes this question unanswerable is the fact that we don't have a point of comparison. What we do know, is that we actually have the math to PROVE that we can make the best bow possible. We can factor in all the variables; things like hysteresis, the return of the limbs, drag mechanics, the application of force over distance, etc. And we can look at that number, determine what the *theoretical* maximum efficiency of a 160# longbow should be, then keep building longbows until we get the closest tested number to the theoretical number. What we DO know about the medieval method of crafting, is that perfection was not only complete mystery, but also often times a trade secret. So the "best bow of the time" was almost certainly very regional, and literally limited to the best bow that anyone was able to produce at the time. That could have been the maximum theoretical performance of a longbow, or it could have been 70% of what a longbow is actually capable of. But they didn't have the formulae to math it out, they didn't really have the measuring equipment to quantify the results precisely (other than range and penetration), and the records of "best longbow ever made" are tenuous at best, since once an event has been removed from 1st person account, it becomes less of an actual fact and more of an arguable point: Your great grandfather claims he knew a man that could make longbows that shot 300 yards! But you tell your friend who's been made hundreds of longbows over the last 20 years, and he's never made a bow that shot more than 260 yards, and none of the bowyers he knows have ever made bows that shot more than 250-270 yards. The bias of experience results in the 300 yard claim being dismissed as crazytalk, regardless of it being true. But now, we have official records backed by photographic or even video evidence, much harder to dismiss. That being said, as Todd has mentioned, they didn't have the math, they didn't have the equipment, but they had the same brains. So a bowyer could continue to make bows, changing little things here and there, until they found the best result. So simply by trial and error, they were bound to make some pretty impressive bows eventually, as long as they kept trying. So in summary, COULD a modern bowyer make a longbow that replicated the BEST longbows made in medieval times? Absolutely. We can use the same materials, and we have the same brain. We have some scientific advantages to gauge how close we are to the end result, but ultimately it just comes down to making bows until you get the best result. And that end goal, maximum perfect result, has not changed in 600 years.
Thinking about the quality of materials the steel you use for the prods is almost certainly better than was available to medieval craftsmen whilst it seems likely there is less optimum quality yew available to contemporary bowyers.
Well done, love your brutal honesty! Romance wins with me, as my life, does not hang in the details. Besides I could not draw a real war Long bow if my life depended on it.
Excellent scientific approach to reproduction bows vs. modern variants of which I make no complaint. I would however make some comments about the quality of steel in medieval times; the process to create high quality steel was very time consuming BUT they were able to make steel that is almost as good as modern material - both Japanese and Spanish swordsmiths could create superlative blades. As regards crossbows, it might be argued that they would use time expensive methods as it was the one material they had in abundance to make as good a sprung steel as was possible - and then they would proof it to a weight far in excess of what was required. So to make a crossbow with a 400lb draw weight you could use the same forging and tempering method for a number of bows, and then test one to 600lb. If it did not shatter/shear within a few moments then you could be assured that the rest of the batch could operate to a tension the equivalent of 400lb. If anyone doubts that the armouries of nations would go to such lengths, it should be remembered that early firearms were very quickly required to be tested to withstand pressures above that needed for the ordanance they were to propel; the concept of testing a weapon to failure to determine its limits was already in place by the time cannon were fielded. I suggest that those measures were taken from experience gained in the quality control of crossbows. tl;dr; it is probable that medieval crossbows had both excellent steel bows very good quality control to enable very high draw weights in use.
Tod, I think you overlooked something. The arms of the longbow and crossbow were still moving when the projectile was shot. This means that the crossbow and longbow still retained some kinetic energy. You cannot assume that all the kinetic energy went to the arrow or bolt. The energy left would be again 0.5MVV. The velocity of the arms would be different at different parts of it. So its a little complicated to calculate. But at the maximum, it would be the same as the velocity of the projectile at the point of release. M, the Mass of the arms is likely to be heavier in the crossbow because it was made of steel, it is probably safe to say that the crossbow retains more of the energy in its moving arms than the lighter longbow.
The comparison to modern rounds and even the comparison of bolt sizes to me really changes the dynamic between modern and ancient. I think what I would like to see is impact damage per pound at various ranges per weapon as we know that this should drop off over distance as well as weight of the bolt.
Neat video. Not sure how versed you are in a .22? Out here in Texas, the .22 is used for a lot and is quite an under estimated round. I think the .22 is listed as a round that has killed a lot of people, likely because “it’s just a .22”. Years and years ago the us army did experiments with 1/2” plywood stating if it went through the 1/2” ply it was lethal. Would be an interesting experiment to see what that 450 pound does on 1/2” plywood at 100, 150 and 200 yards - assuming you could connect.
G'Day Tod, I carried out that experiment using a long bow, .22 rimfire and a modern .556mm assault rifle just as you did with your 3 bows. Now the age old argument between ballistic engineers is whether it is kinetic energy as in your experiment Ke=1/2 mv2 or is it Momentum M=mv that does the damage it would be great to work out the Momentum as well and see what conclusions you draw from the comparison. Love the bows and your passion for them and a great experiment. Yours aye Alan B
Great video. As much as I liked the overall discussion, the real high point for me was the chronograph test. As interesting and entertaining as it might be to debate the relative merits of various technologies from a theoretical standpoint, real-world testing captures a lot of hidden information that is difficult or impossible to capture in anything but the most complex mathematical models. If I might inquire, are you aware of any worthwhile reading on the subject of rate of fire with the different methods of spanning crossbows? There seem to be lots of somewhat reasonable modern tests of longbow rate of fire, but a paucity of information regarding crossbows. You mention a time per shot of 8-9 seconds in your latest goats foot lever video, but I can't find much about belt hooks (with and without mehcanical advantage), windlasses, or crannequins.
Fantastic, I don't think I've seen the windlass video, so I'll have to take a look. I also look forward with great anticipation to your future videos. Thank you for creating such excellent content.
i read a study done by some university students awhile back that went in to just that. They concluded that in terms of efficiency, the chinese bow was about as efficient as any traditional bow can get. Not much of a surprise considering they used it for so long, even long after european firearms outclassed the bow in terms of battlefield efficacy.
Presumably you mean the recurve design (as opposed to the compound construction)? Both had significant benefits & drawbacks Recurve bows of that period are expensive to manufacture in both cost & time & pack about as great a punch as English simple longbows. /However/ the significant comparison to draw was (?is) in the different styles of warfare: Orientals tended to prefer horse archers whereas Europeans preferred foot. Obviously a longbow is an impractical weapon to use from horseback, while the recurve can be designed to optimise the slash/attack cavalry tactics of the Eastern style /in a major battle/ (prolly a 'memento' of Ghengis' hordes: 'It worked then, so we did it this way!')
@@snafu2350 ...They were used by the scythians in the antiquity already. Nothing about ghengis' memento or whatever. Also just cavalry tactics in general. Can't use any other warbow effectively on a horse. Too big, or too weak.
@@snafu2350 longbows were used on horseback just not very often. They had mounted archers but they mostly used the horse to bring them quickly to a location
Thank you very much for that video, it answers questions I have had for a very long time. Would love to be able to send you some armour to perform tests on, I only have mild steel armour at the moment
I enjoyed this video but a quicker way would be to build two bolts and an arrow that fits each bow correctly that all weigh exactly the same and then just cronie each for FPS then you would know which is fastest/ most powerful... or am I missing something?
I'd love to see Tod make a Han dynasty style crossbow. Apparently the trigger mechanism allowed for far longer power strokes, making them almost a 'perfect storm' of the factors he outlines. i.e. a very efficient transfer of energy.
Of course, but the trigger reflects this different evolutionary path of crossbow design. I just wondered if you had an opinion on where such a chinese han crossbow would fall in the comparisons you made in the video. As you were at pains to demonstrate that simple calculations are not always a reflection of reality. The han crossbows certainly looks good on paper, but I've never seen a real world comparison!
Brother I'm not going to argue, But, The cams at the end of the limbs are what make modern compound bows so efficient, NOT the limb size or weight, or material... Change the cam's design and you can screw up the efficiency sooo bad that you won't be able to explain it with simple talk about limb quadrangles. Like you said, "We have computers these days to do the figurin for us". Thanks for another great video Tod P.S. fast and light, or slow and heavy is an argument you can't prove or win, no matter which side your on. Would you rather be hit with a small light baseball doing 90 mph, or a bowling ball doing 50 mph. 1 of them will leave a bruise... 1 of them will do much worse. Thanks for your time and effort, you make people think and that is what I like about this channel.
The argument is that the baseball will go out of the park while the bowling ball will stop short. In early times and the age of line battle and castle defense the range was a pretty huge factor.
How do composite prods compare to steel ones? I really wonder how much more efficient those would be, would they beat plain wood? An accuracy test would also be extremely interesting.
The camming on the compound bow changes the power curve from a 45 degree line to something that goes almost straight up, and then flat. So average thrust is much higher. Like the (exaggerated) curve of a stack, but reversed. More area under the curve.
My question is about composite crossbows & longer powerstrokes. Do they perform better or just same as metal crossbows? Because that would be interesting for me
I think something that's important to consider is the change in context of stopping power. Modern fighting involves weapons that even heavily injured soldiers can still use effectively, as opposed to all pre-firearm weapons which required much more physical labour from the user. A minor arm or hand injury would make a bowman essentially useless, a puncture anywhere on the body would make melee combat excruciating. The standards of damage caused by a weapon would have been much lower back then, and the ability for instant kills would be basically pointless, out of the fight is out of the fight.
Excellent video! Are you familiar with Dr. Ed Ashby and his research into arrow penetration? It would be fun to know if there are historical sources that have explored the same subject! Of course, without modern mathematics, but still. Basically Ashby shows that optimal penetration is achieved with focusing more on Forward Momentum than Kinetic Energy. A stiffer, lighter shaft with a heavy arrowhead will outpenetrate a softer, heavier shaft with a less heavy arrowhead by a fair amount. That with arrows of equal total weight and tuned for the same bow. Ashby calculates this in FOC and EFOC ((Extreme) Front Of Center) values. The subject is easy to look up, if you don't know about it. But it would be interesting to know if there is evidence of this thinking in medieval times. Anyways, thanks for the great upload, as usual!
momentum comes from the KE and Newton's law of conservation tells us the arrow get its momentum from the mass independent of its FOC. A smaller dimension shaft means less friction and surface area going in and more mass is concentrated more directly behind the pressure of the point . Foc may give you better flight that equals less lost energi and a flatter ballistics curve that lets the tip of the arrow hit at the optimal angel to avoid deflection Also you must keep in mind that the dynamic spine of the arrow changes during flight so if the foc was important to momentum the foc would change during flight making it utter useless. i
Hey Tod, old video I know, but there's more to the story than you mentioned and I feel like it should be acknowledged. Broadheads don't kill through kinetic energy like bullets, they kill through penetration, which KE is NOT a factor of. Bullets push their way through tissue, which is why they have such high KE. A basketball carries far more kinetic energy than any of these tested mediums, for example. What matters is a mixture of physiological effects (muscles retract and lubricate arrow shafts with blood when cut while an animal is still living) along with the mechanical advantage of a broadhead (or to a lesser extent a bodkin) which amplifies the work the arrow or bolt can do with the available force. This is why an arrow will penetrate a sandbag deeper than a .357 magnum will.
*Tod* have you done any material on the old style composite crossbows? I would really love to see them in action. I can imagine they were a bit tricky to assemble.
I suspect the modern crossbow actually ramps up in draw weight faster than your linear curve would indicate, at least based on my experience pulling modern compound bows. Any chance of a putting a scale on them and checking the draw vs lbs curves for all the bows?
The other thing to consider in regards to the actual numbers, is the material of the arrowhead/bolt head. Hardened steel, soft low carbon steel, is it sharpened, and even the cross section/shape of the head. While the numbers themselves are not that high in comparison to firearms, there's a whole bunch of other aspects that are also important when considering the lethality of a bow or crossbow. .22 LR might kill a person, but it would take proper shot placement, and a very unlucky individual. It has very low probability to hitting a vital structure of the body bringing about incapacitation or death. While getting shot with any one of the projectiles from the crossbows and bow you shot, the probability of killing or seriously wounding is significantly higher. Just for some additional comparison; a standard MLB regulation baseball thrown at 95 mph has a kinetic energy of 117.5 Joules. Batters get hit fairly regularly, and thankfully they aren't dying anymore (in large part due to batting helmets and other rule improvements).
i'd say on your l;ast point definately where projectile elasticity and surface area come into play. also a modern crossbow is often of materials that cant handle the very high stress of impact, since id likely say they arnt designed for it compare thast though to jeorg sprave the shloingshot guy and his 'plumbers nightmare' arrow shooter, launchinngg projectiles at aroundf 700-900 joules, ive no doubt that would pierce plate armour no trouble.
IIRC Alan Williams in his book "The Knight and the Blast Furnace" did comparisons of arrows and bullets (in this case round balls which would be worse than modern bullets) capabilities to penetrate metal plates. The balls needed a lot more energy to penetrate the same plate and of course had more energy.
When I taught Hunter Safety, we would demonstrate the difference in the mechanics of the projectiles and the impact on penetration. We would shoot at a 5-gallon pail of sand with Winchester .243 and .308 caliber rounds. The pail would always trap the rifle projectiles. When the same pail of sand wash shot with a modern compound hunting bow at 65 lb. draw weight with a broadhead arrow, the arrow would always protrude through the bucket (plastic 5-gallon pail). Projectile design and physics are very important in determining terminal ballistics.
Great video! I think that the calculation is more complicated. Because of the higher the speed and lower the mass => the higher the calculated drag. so in rifles, you lose velocity faster than in bows or crossbows. (this is why rifles don't reach underwater) On another hand, you reach the target faster. you can basically solve this by measuring the velocity at the target and then calculate the energy
Came to watch crossbows and bolts. Learnt some maths that I never paid attention to in school. Double nice.
Only rare people like Tod can teach Maths. Schools cannot afford that level of skill.
Generał WP if you learned it in school. Either you had a rare teacher, or you did not need the teacher. Which were you?
@@moscuadelendaest you calculated foot-pounds of energy in primary school? must've been nice.
@@commander31able60 I think he didn't know which math you're talking about, the first part of the video is indeed talking about area of the triangle which is indeed primary school.
Drag is proportional to the square of speed, therefore quick projectiles loose more energy on their way to the target.
Heavy and slow crossbow bolts start with less energy but preserve more during their way.
However they fall "faster".
Meaning that the archer had to account for more drop.
Not to mention a function of damage isn't necessarily the same for firearms and crossbows. A slow moving bolt just needs to penetrate armor and flesh and cause bleeding. The larger the diameter of the bolt head the larger the wound, the more bleeding occurs. Bullets have small diameters even when dealing with huge cartridges like .50bmg (around 12.5mm). Thus when it strikes a target the initial hole isn't necessarily that large. The speed however, is enormous comparatively, and counts for much more of the damaging potential (never judge a bullet solely by its diameter, aka caliber).
This means when it hits a target and dumps even a portion of its energy into a target the hydrostatic shock which creates a large temporary cavity and a smaller permanent cavity. In essence your looking at tearing a hole mostly by energy of impact to create a lot of bleeding and damage versus versus piercing a hole with a relatively large diameter.
As a side note you can see this in action by watching ballistic gel tests with a slower round, say .45 acp versus a fast round like a 5.56x51 NATO.
@@thewinterasp Long, narrow bullets create more physical trauma than shorter fat bullets, because all bullets tumble on entry (see the work of Dr. Martin Fackler et al.), but a greater increase in the permanent wound cavity (as opposed to the temporary wound cavity) is caused by fragmentation of the projectile.
Well, long narrow bullets behave * Differently * than short fat bullets in Terminal Ballistics ( and external balistics for that matter ). But there are a whole bunch of additional factors , and you can't make generalizations from just one factor .
The design goal of non-expanding FMJ bullets is to at least tumble upon impact, and ideally subsequently fragment . This is effected by the stability of the bullet ( rpm of spin), and multiple factors of internal bullet design . Center of gravity front to back , jacket thickness , jacket hardness , external or internal scoring of jacket, presence or absence of cannelure , and actual impact velocity .
There are inherent compromises in bullet stability . To oversimplify , for maximum tumbling on impact , a bullet should be just barely stable enough to be flying point first . But for long range accuracy , accuracy in all climate conditions , and penetration of hard barriers , the more stability the better . ( Stability being a factor of bullet RPM , which is effected by both twist rate, and muzzle velocity .) ( Insert long history of evolution of U.S. ammunition, twist rates, and barrel lengths for 5.56 weapons, with terminal performance going up & down . )
If small caliber bullet performance isn't ideal , big non tumbling bullets are better than small non tumbling bullets . And throughout history generally , there have been lots of small bullets that performed poorly , or at least been designed with greater emphasis upon factors other than terminal performance .
And of course , this is all within the arbitrary context of International Treaty , requiring nominally non expanding ammunition against certain Recognized Combatants . For hunting, personal defense , law enforcement , and certain Counter Terrorism , it takes a really tricked out FMJ , performing exactly as designed, under ideal conditions to match a rather mediocre expanding bullet .
True but not very relevant at distances under 200 meters or more likely under 100 meters that most warbows are regarded as being prime effective range.
Always love the trademark zero bullshit production on Tod videos.
I just want to say, as someone who has tutored college students for eighteen years, you did an excellent breakdown of the physics and math calculation, as well as comparison to modern weapons.
I love your honesty and clear thought process. No fuzziness, just facts backed by experimentation. If half of the "historical documentaries" would use your honesty and experimental process, would make them worth watching again.
Exceptional video Tod. Really informative.
@nd the motion. Great explanation.
This guy just captures my attention every time I watch his stuff. Love the precise, thoughtful experiments, and that he's a brilliant master of his craft. Cheers!
It's always very nice to see a video where misconceptions are cleared up properly. Thanks for the video Tod!
excellent video Tod, but I feel I should mention that while energy is important for punching through thin, hard materials i.e. plate, it is less important than momentum for penetrating thicker and more flexible materials, e.g. Kevlar, gambeson, and indeed flesh and bone. Sectional density is of course relevant for all materials. I bring this up because penetration is the most important data point for the "stopping power" of a round, with wound cavity a proportional secondary point. Shooting these weapons into ballistic gelatin would tell us more, though again would be inconclusive. Anyway, great vid!
Another amazing video! Thank you for all the information!
We should take in mind that they didn't have the same metalwork as we do today. Also they did tend to exaggerate about their works. Your bows are among the most beautiful ones ever.
Great video. You did a great job on explaining this. Kudos for the parts about warbows. Heavy draw weights around 140 to 150 lb reaches 140-150 joules with middle to heavy arrows. Important detail there.
According to a video on the Medieval Crossbow channel, composite horn crossbows in the 1276 lb range reaches 488 joules with 348 gram bolts. It's rather big in comparison to the crossbow you have here. The bolt left at 52.92 m/s. It shows that composite horn is a much better material to make a bow of than steel. The 260 gram bolt left at 57.74 m/s and gave 433 joules.
Yes, Han and other Chinese records go into quite a bit of detail on crossbows and the distances for various weights achievable and how to use the various types of crossbows. As more of these records are translated, verified, and accepted by medieval hobbyists some of the work examining the few medieval crossbows extant and reproductions will focus on how to make steel prods more efficient because while the European crossbows never quite measure up to the Chinese sources they do much better in comparison to Tod's reproduction and actually are not that different from LaCombe's results. Han crossbows had a longer stroke which as Tod demonstrates makes them more efficient but there are also many small tricks in making the limbs of bows more efficient, not only in materials, but design, and other very small factors which I do not believe we have any bowyers currently working who have fully mastered crossbow manufacture.
Had always wondered why no one ever ended up using spring steel as a bow material and the energy thing made my day awesome video.
As a side note I would be extremely interested in seeing how a modern bow design would perform at the same weights as a historical warbow
Nevermind the readings in that video gives me the info i need, which if im reading this right a modern recurve at 45lbs draw is putting out roughly the same energy as the medieval longbow at 95lbs which is interesting and makes me really want to do some more research on that
outstanding video. well reasoned and articulate. very informative. thank you.
Mass of the arrow an important aspect. Great video
I asked this on another crossbow video of Tod's, but it would probably fit better here:
Do you know if there is a materials-engineering reason they didn't use compounding pulleys on bows and crossbows in the medieval era, or was it just that no-one had thought of trying off-center pulley wheels? It's a really weird idea to wrap your head around, from a geometry perspective, but they had some pretty inventive people between Pythagoras and the middle-ages, and LOTS of experience with making and using bows.
The first compound bow was invented in the 1960s, i guess they didnt have the technology in medievel times.
All the things i a bowyer of primitive, self bows never figured out in such a scientific way,.... Low tip mass, shortest possible limbs, thin string and all that is known to increase efficiency. But this vid gives a very clear and broad insight into the matter. Thanks for posting.
Glad that you made this Video so detailed. The mathematic back up may calm down those people who say that a 1200lb crossbow could shoot through the moon.
Very informative, and rationally backed by numbers. Top quality content.
This is without doubt a superb video! I thought you were going to dismiss the modern bows as inferior and praise the classic styles as the definitive weapons but was pleasantly surprised. This video shows a lot of understanding on the mechanics of a bow and a lot of honesty judging your own.
Great work Tod, absolutely outstanding!
Hey Tod, love your videos.
My son and are bow hunters. My son and I were watching your vid and some other interesting thoughts came to mind:
Modern Crossbow 175lbs/131j =75% conversion
Longbow 95lbs/45j = 47% conversion (approx 50%)
Medieval Crossbow 450lbs/54j = 12% conversion (approx 10%)
This would mean you'd need a 1000lb crossbow to deliver the same 100 joules as a 200lb longbow.
Now, think as a general on a battlefield. Which weapons delivers the most joules of "death" to the battlefield per second.
Working on 10 sec easy calculation.
Based on our own rate of fire, we think in the hands of a expert archer, a 200lb longbow can shoot 3 arrows (each delivering 100 joules of death) in 10 seconds = 10 secs/300j = 30 joules of death per second.
We've assumed 1000 crossbow can shoot 1 bolt (delivering 100 joules of death) in 10 secs = 10 secs/100j = 10 joules of death per second.
I know it's simplified, but still interesting.
Again, thanks for your videos. Love em!
it's nice hearing someone that knows a thing or two about bows. as long as you don't "fire" them, i will be a long term subscriber
Thanks so much for making this video! You managed to isolate some understandable maths from a device that has a massive list of variables. Those of us just beginning to enter the world of sticks'n'strings could use more like this!
The thing about the 22 vs the crossbow bolt is that bolt tends to have a very sharp and sometimes wide tip meant to slice into the target where as 22 round is like trying to push an unsharpened pencil into the meat.
Very good Video. The only thing i am missing a little is how the cams come into play because the whole trick with the compound system is that you don't have that linear relationship between draw length and poundage. So that graph would actually look quite different.
Oh Todd I LOVE IT!
In fact, I was just thinking about how somebody should draw out the draw weight over powerstroke curves of some bows to calculate their energy output, and right then I see this video where you do just that!
I do however have two points of criticism:
1. You are looking purely at the energy of the projectile, because this is used to characterize modern rifles. I wonder however, if the deadliness of an arrow isn't better characterized by its momentum, rather than its energy. Of course, this makes the comparison to rifles difficult, but this is to be expected, because the damage-mechanism is also a different one: An arrow cuts through the target, while a bullet pushes the mass in front of it away. The former should be far more energy-efficient. This claim could be tested by shooting bolts or arrows with different masses from bows with different draw weights, and simultaneously measuring penetration and bolt-speed. If penetration scales linearly with speed, its the momentum that counts, if it scales with the square, its the energy.
2. You remarked already that it is incorrect: You are assuming linear relationshipts for draw weight over powerstroke.
Although I appreciate that this should not become too complicated and it was probably right for this video to keep it that simple, this neglects the whole purpose of the curved shape of recurve bows for example. I think it would be really interesting to measure these curves directly - for example by filming how you slowly draw the bow over a tape measure using a bow scale. (If you happen to want to do that, you are welcome to send me such a clip and I will can evaluate it and send you a nice graph and energy value ;-) )
After all, the graph for a "perfect" bow would not appear as a triangle, but as a rectangle: From zero, it would directly jump to the maximum draw weight that the archer can draw, stay there until the full draw length, and then drop back to a low value to make it easy to hold the bow drawn.
I expect that the modern bow will approximate this behavior much better than the medieval ones.
If such a measurement were done and compared to the actual arrow speeds, one could also calculate the actual energy efficiency of the bow :)
I believe that both these points contribute to why the modern bow performed so much better than the simplified math suggested.
Thank you for this video; it has been highly educational and must have been quite a chore to do the analysis. I am trying to make my own wooden bows as well, and have learned much from your methods.
Thank you for putting real science to medieval and modern weapon testing. This is amazing content.
Hi Tod, awesome video and talk through. you are a true craftsman. Your maths breakdown and analysis is truly remarkable. You are really dedicated to your art/sport. Simply great to watch and to listen to, thank you so much!!
refreshing honesty. really sympathetic presentation and summary
I do enjoy your videos, they are very informative, you are quite clear and honest about your research. Thank you!
Beautiful work as usual and fantastic hand crafted bows and crossbows.
I'll have to look at the momentum change of these weapons & see how that affects their relative relationships.
As the .22 comparison shows, the effectivness of a projectile can depend as much on its momentum and sectional density as it does on its kinetic energy.
This was my thought as well. Momentum is the resistance to slowing down. a train rolling at 1 m/s is harder to stop than a compact car at that same speed, because it's heavier. Heavier things want to keep doing what their doing.
I know American math, so check for conversion errors. Momentum is just mass x velocity and give us kgm/s.
Using his values the momentum of the Compound crossbow was 2.9
The Longbow was 2.0
The Medieval Crossbow was 2.5
A .22 bullet (2.6 g, 361 m/s) was 0.9
A 9mm bullet (8 g, 381 m/s) was 3.1
A .308 (7.62 x51) (10.9 g, 770 m/s) was 8.4
A 12-ga slug (35.6 g, 488 m/s) was 17.4
A .22 isn't more deadly than an arrow or bolt. That energy value only matters the instant it makes contact. After that, the much higher density of the target will begin to slow the projectile down. Things with a higher momentum slow down more slowly, so they penetrate deeper. The compound crossbow may not have anywhere near the energy of the 9mm bullet, but it has a very similar momentum, making them comparable as far as close range damage goes. The Slingshot Channel did an old video comparing momentum of one of Joerg's slingshots to a number of handguns using a swinging metal plate to test. The only gun tested that beat the sling was a .44 Magnum. ua-cam.com/video/tLxnNP-ycVQ/v-deo.html
This is exactly what I love about your channel, no bullshit, scientific approach and lots of testing. I learnt a great deal today.
Nice job Tod.
You definitely showed efficiency matters...
I know this video is quite old, but I wanted do do some calculations for myself to see if I could quantify the efficiency of the bows.
I took the bow strength, the powerstroke and the weight of the projectiles for the medieval long- and crossbow from this video, as well as the Skallagrim-crossbow (I got the values from other videos: 976lbs, 160mm, 96g). I calculated the theoretical acceleration (a = F/m) for the three bows, and used that to get a theoretical projectile velocity ( v = a*sqrt((2*d)/a) ).
Point is, a 423N (95lbs) longbow with a powerstroke of 0.64m (25 inch) should be able to accelerate a 45g arrow to 109m/s. You measured it at only 44.5 m/s, which is about 41% of the expected velocity.
The lighter crossbow (2002N, 0.11m, 60g) should reach 87m/s but reached only 42.4m/s which is 49% of the expected velocity.
Skall's heavy crossbow (4341N, 0.16m, 96g) should in theory shoot bolts at 120m/s but was measured to shoot them at 47.9m/s (39,8% of the expected velocity).
Since I think, that the kinetic energy is a better measurement for the efficiency of those bows, I calculated the energy both, based on the theoretically expected and the experimentally measured velocities (the latter were basically the same that Tod calculated in the video).
Because we calculate the energy by squaring the velocity and the other parts of the formula (mass of projectile and the factor 0.5) stay the same, the efficiencies of the energy were just the squared efficiency of the velocity (I should probably have seen that coming...).
The surprising thing is, that the longbow appears to be less efficient than the lighter crossbow, and that even though the longbow's projectiles should in theory have more kinetic energy (268 vs 228 Joules), in practice the crossbow has the advantage here (45 vs 54 Joules).
The heavy crossbow has about the same efficiency as the longbow, but with more than ten times the draw weight and twice as heavy projectiles, those projectiles have more than double the energy of either the longbow or the lighter crossbow (110 Joules).
I'm kind of curious how a warbow would perform, so if anyone has the draw weight, powerstroke and projectile mass for a representative bow please let me know :)
Used to shoot metallic silhouette (firearm sport). The most fun calibers for me were the .375 H&H mag and the .458 winchester mag. Both would flatten the 50 pound or more half inch steel targets at any range you could hit them. Our range only had a clear view of 250 yards. Both would leave a decent dent where they hit. The .375 was at about 3000fps, and the .458 was more like 2000. However we had to ban calibers like the .22-250 or the .22 swift and even the .223 because they would consistently blow big holes in the half inch steel. Tiny bullets traveling at 4000fps plus requiring hours of welding the holes shut again. Even then, the targets didn’t even always fall down. Huge energy with the small fast projectiles, but very bad transfer of momentum. Most of the energy goes into vaporizing the bullet and creating the crater in the plate. For reference, the momentum of the .458 slug was about 5 times higher than the .22-250 50 grain bullet.the little round has about half as muck kinetic energy as the big one. Down range performance really depends on what effect you want. The .22=250 is a varmint round and will disintegrate inside a ground hog, where the .458 or even the .375 will easily go right through the long direction of a deer or crosswise in a bear if you are using a full jacket round.
Great video. The numbers really put things in perspective.
Great job. I've been thinking about those differences for a long time. However, I don't think comparing energies of firearms to bows and crossbows makes much sense, as these projectiles work in very different ways. Unlike bolts and arrows, firearm rounds don't rely on simply piercing the target and causing blood lose through relatively small, clean cuts. Instead their tips are often blunt or even flat and hollow (and if their not, it's to do with aerodynamics as they're often designed to flatten or tumble upon impact) and tear through tissues causing massive shock waves and extensive damage. The whole process is very efficient at killing but requires far more energy to even occur. Comparing arrows/bolts to gun bullets would only make sense if done in the armor-piercing context. In therms of so-called soft targets, it doesn't really matter how much energy a projectile carries as long as it's enough to penetrate and reach the vital organs. For instance, a long knife, or any pointy object, can be slowly pushed into a body and even poke out the other side causing almost instant death even though it probably won't have more kinetic energy than a cheap air-riffle. On the other hand, a heavy rock can be thrown with more energy than many air-riffles will produce, yet won't be able to do quite as much damage.
VERY interisting Mister Todd!!!! CHAPEAU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Thank You Very Much!!!!!!!!!!!! Greetings.
I always wondered about the power an old crossbow might have in comparison to other weapons. I looked online and never really found anything conclusive. This video was great. I still do wonder about the projectile itself, and if that actually plays a bigger role in how "deadly" the weapon ends up being. Like you said with the heavier crossbow at 1250 lb, the joules would seem to be close to a modern .22, but I imagine the bolt itself would cause a heck of a lot more havoc on whatever it ended up hitting than a .22 round. I never tested this, of course, so I can't say for sure.
Arrows and bullets are really different.The wound types are different. The terminal ballistics are very different. I think it's hard / unrepresentative to compare them using just "muzzle" velocities.
An arrow mostly pokes a little hole through you. A bullet makes a much messier hole, and stirs up adjacent tissues more than with arrows.
If you look at the numbers, one .308 round is equal to (I forgot the numbers) seventy or a hundred longbow arrows. Bit if I had to choose, I'm pretty sure I would be better off being shot once with a .308 then 35-50 times with arrows, let alone 70-100. (Neither sounds enticing.)
One factor is the surface area of the missile. A pointy arrow might well have more joules per cm2 than a bullet. It might penetrate deeper despite less KE and momentum. (A 1 kg pillow going twice as fast as a bullet wouldn't penetrate much.)
Yeah, it's interesting. Because when I think of someone getting hit with a .22 pistol round to the chest, I'm not thinking "Well he's done for", but a bolt or an arrow to the chest makes me think of a much worse injury. The caliber/ammunition weight, shape and size seem to play a big part in what's going to happen when it hits, compounded by that force behind it.
*Sangh* i am just an armchair enthusiast, & so i am going to be as vague as possible to cover my tracks! :) In a very general sense, i am going to hazard that to a significant degree, some comparison of side-arm versus rifle ballistics can be instructional. Mainly in that even for most pistols, which fire bullets traveling much faster than a crossbow bolt, the single biggest operative factor to damage is the diameter of the bullet in relation to shot placement. They are still low enough velocity that wounding from fluid displacement from cavitation as the bullet passes through isn't all that significant until you start dealing with some of the magnum loads, which are more typical of revolvers than pistols. Then, overwhelmingly so with rifle loads. But, with that backdrop, i would think that by the crudest of definitions, the diameter -size -of the crossbow bolt is going to be similarly operative here too, as it is still much slower than a pistol bullet. In fact, so much so that the design of the bolt -& its ability to cause cut & bleed is going to be the biggest factor in its lethality. But that trait is where the bolt design suddenly gets funny.
It might be surprising that military bolts were often not nearly so refined as good hunting bolts. Military bolts commonly have minimal fletching, utility rather than razor tips, and are weighted more for penetration rather than accuracy. In many respects i think the rough & ready design of the military bolts emphasizes wounding/disabling as the priority beyond outright bleeding/killing. This would make sense, as wounded soldiers require a lot more resources to maintain than dead soldiers, & so efficient killing function is not necessarily the most important consideration in the design of the crossbow bolts. Taking them out of the fight is.
And in general, i think the design of the heavy crossbow bolt is something that i have always questioned. I am just an armchair enthusiast, but i always have this sense that they tended to not be as optimized as a projectile like, the bodkin arrow of the warbow, or even a dart & atlatl. But i could very well be wrong about that -and would venture that is more likely the case than not. But considering the abysmal rate of operation of a heavy crossbow, i would hope that designing the perfect bolt for the function of the machine would be a critical priority, as each shot counts all the more. But it appears to me that the finest bolts were probably those designed for hunting and target shooting rather than war.
And like i said... don't take me too literally. All this is my sense of things! :)
As a hunter the principals taught to me go something like this:
With a bow the death is caused by the cutting that the broadhead does to the animal. All the energy you need is for the tip to just pass through the heart and that isn't that much with a modern cutting broadhead especially if you don't hit bones. Cutting diameter of the tip is what causes massive blood loss and death.
With a gun the damage is based on the crushing shock effect that the bullet causes. If you have ever seen a water jug for example being shot, they usually just explode even though the bullet diameter can be relatively small.
If you shoot with a very low powered rifle I imagine the effect would be similar to shooting with a target tip arrow where it just cleanly goes through and easily leaves big blood vessels intact. In the past they didn't really have any ways to heal these kinds of wounds and they could easily get infected but they would probably seriously lack any kind of immediate stopping power. I guess there is still a good change if you have an arrow sticking out of your side that you would stop bullying the dude in the castle and search the local shaman for help.
This is one of the most informative bow videos I've ever seen! Thanks Tod's Stuff! (And scholagladitoria for introducing me to you!) I really enjoyed the Joules comparison as that put it into great "context." That really gives me something to think about with what "killing" power needs to be with missile weapons. Now if we could figure out how many Joules you need to defeat various armors at various ranges we'd really be in the know!
It's important to remember that missile weapons up until advanced firearms were never really used for raw stopping power either. Their role on the battlefield was as a support weapon for the main melee troops. Even the Hussites, famed more-so than the English for excessive use of missile weapons, ultimately finished off the charges with their massive flails and halberds and not their crossbows or handgonnes.
@faultroy I personally can't speak for a medieval javelin or spear, but modern olympic javelins are thrown at up to 30m/s, and weigh 0.8kg, for an initial energy of about 360 J. I'm not sure how a historical one would compare to that, but I assume it would be lower.
Very strong and interesting video with a lot of interesting and useful information, I hope in the future you will continue such powerful video.
Lots of very good information. Great video.
Thank you so much! This answers several questions I've had for a long time. Great no nonsense research, definitive no, but extremely useful and well above most youtube research.
This greatly helped me set the standards for bows and crossbows in my homebrew VtM, where we prize realism and accurate portrayal of weapons with no regard for fairness. If I can get a DnD (or simpler!) system that's a fair approximation of reality; it's more fun, slightly educational, and helps me remember the actual information for use and sharing lolz
The example with the triangles on paper was particularly helpful!
18:00 There's a difference between how many joules of force an object has and how much damage it does to the various things it could hit. A 9mm FMJ and .45 ACP FMJ have the same joules of energy, but the .45 is easily demonstrable (and noted in history) to be slightly more effective.
7.45 gram (115 grain) Federal FMJ 1,180 ft/s (360 m/s) 355 ft⋅lbf (481 J)
15 gram (230 grain) FMJ, Winchester 835 ft/s (255 m/s) 356 ft⋅lbf (483 J)
Both are standard pressure rounds, FMJ bullets, out of aprox. 5 inch pistol barrels, and are the most common "standard" example of each round. The Federal .45s and Winchester (presumably White Box) 9mm would do pretty much the same.
More energy almost always helps, tho I have seen bullets that start to do worse in gel when given the +P+ pressure instead of just +P. See Paul Harrell for good examples of "Does this extra power (from velocity, weight, etc) translate into more effectiveness?" I presume that this holds true for all projectiles. The wound is what matters, and its all about how the projectile interacts with the target to create the wound - how the energy is used by the object to wound. If one shot deer with a Medievel or Modern crossbow or a longbow, then shot them with a .22 LR (I'll even grant it a rifle barrel), one would clearly see which is more effective! Ask any hunter. I've shot stuff with everything listed here, the difference between them and a .22 is fairly clear. What that does also show, is how relatively poor arrows and quarrels etc are at incapacitating people compared to a 12 gauge 2.75 inch 00 buck shell or 7.62x51mm (.308) FMJ round. The shotgun example is a good reason why total energy isn't all there is. There is more energy in some rounds of birdshot than the standard 00 buck I just listed, but that doesn't mean it's even close to as effective...
I hope those considerations help with people's understanding of the old bows' true level of effectiveness.
Great video, as always.
What a wounderfull video. It would be great to see how a normal medival bow compares go the longbow in power, range. Im so glad that I found your channel.
A point about the energy of the projectile. Low weight, high velocity will slow down more from air resistance, so perhaps down range the medieval crossbow would fair better. Bullets do ofcourse have a much smaller cross section for air resistance, but the speeds are vastly higher and the weight is vastly less so they probably lose velocity more than the medieval crossbow bolt also.
Probably the gun energy is measured at the muzzle.
In addition, Kinetic energy isn't how arrows and bolts kill or do damage unless you're using rubber/wood blunts. Broadheads as a set of inclined planes are able to amplify the amount of work doable by a given force (which is measured in momentum/impulse, not KE). Related to your point, as impact velocity of any projectile increases, the resistance forces faced increase exponentially. Here's a neat research paper that talks about it in depth cpw.state.co.us/Documents/Hunting/EHU/Momentum-KineticEnergy-ArrowPenetration.pdf
This had me really wondering: could you build an effective compound bow using medieval technology? How much of their effectiveness depends on modern material science and manufacturing, and how much of it was just a matter of understanding how bow efficiency works and having the insight to use pulleys to exploit that?
That's awesome. I watched that catapulta video - so cool and pretty terrifying. Do you think the compound mechanism would have been achievable at hand-held scale? I don't have a great sense of what the limitations were with medieval techniques.
You should do a bit on those heavy linen strings your big crossbows use, im very curious as to their construction!
it's not just about the kinetic energy, but also the momentum of the projectile, which is m*v (not v²), there the heavy bolts are actually quite good.
Sectional density and (in war or hunting heads) sharp edges promote puncturing and incision wounding in-situ, very different from the 'tearing and bruising' seen in bullet penetrations, with their considerable cavitation and (temporary) displacement of soft tissue.
A handgun and arrow have similar penetration depths (at low draw weights - the 'wounding study' I have shows results for ~ 52lb bows only - and a bow of around twice the draw weight with heavier arrows (these were only 30-40g arrows - much lighter than what a heavy bow would be firing from what I understand) would show at least as good performance.
Indeed, medieval/renaissance texts warn of taking broadside shots on deer because of the risk of a through shot striking hunters on the far side of the quarry on a hit - and it was preferred to take an oblique shot to maximise wound channel length.
Kinetic energy is far more informative than momentum because it is that energy that is 'used' to impact the target, ie break molecular structures. Obviously each molecular bond is far smaller in strength than a joule so it is sort of a count of how many molecular bonds it can break.
Incorrect. It is the energy that is important in a killing projectile. A large mass moving at a slow speed is nowhere near as effective as a small mass travelling at high speed. That is why is a bullet is preferred to a thrown rock.
@@paulbaumer8210 Well.... In the end a bullet isn't the same thing as an arrow, however. For instance, picture getting hit in the thigh. A sufficiently fast bullet is going to travel through and if it will kill you mostly depends on if it hits an important blood vessel or breaks your bones. If it doesn't you are left with a comparatively clean wound that can be patched up without too many complications. If you have a projectile or a bolt that isn't as fast and gets stuck instead your are in a world of trouble. Removing it can cause additional tissue damage and damage an arterie but not removing it is likely going to result in an infection of some sort or lead poisoning if it was a bullet.
People dying not from getting hit with the arrow but after having the arrow removed from the wound was rather common.
In the end, whilst energy does of course play a big role, it is not the sole determining factor as the type of the projectile will determine the kind of injury you receive. A full metal jacket may carry the highest overall kinetic energy but a soft point is still gonna be more lethal if you get hit by it.
the mass is already in the calculation. The slower medieval bolt had more energy than the faster arrow. He doesn`t multiply speed with speed to get to joule (v²) like you suggested.
Extremely informative, thank you very much.
An interesting comparison. Really puts things into perspective and hats off to Tod for a great, clear an informative explanation. One point though: Tod says that the old longbow was better made than the modern variety. This just a thought as I have no way in the means of proof. I would contend that a modern bow is better in regard to final build and tiller because of the time invested in its manufacture by a skilled modern bowyer. This is not to say that medieval bowyers were less skilled, but I suggest that emphasis was placed on the quantity of manufacture rather than quality of build. Modern customers are more demanding and expect a superb bow in all respects. Medieval bows, built for war did not have the aesthetics and perhaps the tiller was less than perfect. This did not detract from their purpose but maybe they did not last as long as the modern counterpart.
Flaxen Saxon
Fantastic vid! Found it absolutely wonderfull, its a shame crosbows are illegal where I live, would love to have a medieval one. There's something very alluring with the thought of practicing marksmanship with a medieval cross in a sligthly secluded part of the countryside. Just me, my crossbow and an unfortunate assortment of fruit.
Johan where do you live that crossbows are illegal? You can’t even make one and have it in your house?
This is my first visit to your channel, Tod. Your disquisition comparing the three bows was fascinating, so much so, I am moved to ask this question: Do the numbers cited in the Penn-Galway (sp) findings factor in arc? I thought that in combat, archers sometimes fired upwards to achieve arc, to cause death at greater distances. Therefore, medieval armaments records might have been referring to distance caused by arc, ie elevated trajectory. That might account for the huge numbers. Thank you for relating your remarkable and thought provoking views.
A good video!
One small point you did not cover too well though was type of Arrow / Bolts! The purpose of them was to put holes in things .... bodies, armour, horses .... and mere energy of the arrow does not compare in this respect. There were many different tips from scimitar like heads designed to disembowel horse to basic points for "normal people" to armour piercing heads. All of these were great at their design targets but poor in others.
Also there is much loss in the archers paradox (flexing of the shaft in flight) which is one of the great advantages of compound bows. The draw weight varies from high at the start of the draw to light at the end. This makes the arrow speed up more as it moves to the end of the draw rather than the longbows more flat speed curve!
It's funny how you say Tod did not cover something too well, and on your comment you don't even know what archer's paradox is.... The flexing of the shaft in flight in not the archer's paradox, but a result from it, I could explain to you what it is but I will let you search the information by yourself, so you could be more considerate next time you bash on someone else's video without even knowing what you are talking about.
Great video👍🏼 Personally I enjoy a field recurve and some stumping
Excellent empirical calculation of kinetic energies. Just for interest's sake I thought it'd be interesting to calculate the momenta as well (from your numbers). For the modern crossbow, 2.86 N*s; longbow is 2.00 N*s and medieval crossbow is 2.54 N*s (the same qualitative order as kinetic energies). What I don't understand (maybe someone with an engineering background can explain this) is why longbows typically have longer ranges, even though by your test crossbows have larger momenta and kinetic energies. Is this purely a function of how streamlined the projectile is?
What I learned from this is that .22 LR is surprisingly effective.
.22 lr can kill deer and people (not humanely tho)
@@comradesoupbeans4437 how do you kill someone humanely tho?
@@TheIlidius i meant the deer lol, people are just basically the same in terms of firepower needed
Extremely effective at very close range, reference the Bain family murders :-(
A .22 revolver was considered a fine self defense weapon a century and change ago.
great work Tod, very thorough approach!
This was fantastic and I would like to see more of this.
You made an interesting point at the end but I think you're just shy of the mark: are your bows or Joe Gibbs bows as good as the BEST bows of the time--probably not. Are they as good as the run-of-the-mill mobilize the country to arms quality of weapons that were likely made during a period like the hundred years war? Probably as good or better. The King's sword isn't measured the same as that of the yeoman, and bows I'm sure are much the same.
Looking at the efficiency of Joe's longbows in the Agincourt test, it was rather disappointing. A good bow can put out about as many joules as it has pounds of draw weight, at about a 1:1 ratio. His was at a 100:74 ratio. I once saw a 180 lb bow that barely put out any more energy than his 160 lb bow, admittedly (of course, arrows make a big difference to readings).
@@vanivanov9571 Were those recurve and/or compound bows? Longbows are self bows and are not as efficent at transfering the energy into the arrow as other types of bows.
I'll readily concede that Joe Gibbs ( or other other quality Bowyer's ) long bows have efficiency on par with military issue bows from back in the day . The big difference is the test bow has a draw weight well below historical .
@@filianablanxart8305 If we go by the Mary Rose samples then 95 is underweight with the average being around 140-150lbs but the math works similarly so long as we keep in mind what Tod says about ignoring efficiency which is actually super important and an area which causes most of the controversy from what I have seen. The heavier warbows in the 180-200lb range have thicker cross-sections which gives more potential energy but lowers the efficiency. They use heavier arrows than lighter bows which increases the amount of potential energy transferred into the arrow but still losses efficiency and all tests I have seen indicate loss of 10-20% fps but the heavier arrows have more momentum and did have higher potential energy than lighter warbows. Compared to a horn/sinew Manchu bow that has 150lb draw but is 25% more efficient but also has a shorter stroke the math indicates really similar energy delivered to a target by a slightly lighter, shorter arrow that moves at a higher initial velocity which translates into less drop (more accuracy). The result... the top end warbows of English archers and steppe warriors were really quite similar in armour penetration with the steppe bows being smaller and more accurate but also more expensive to make and more difficult to maintain. For steppe cultures that is not a huge drawback because bows were the main weapon of the steppes and there was no need for ordinances such as England created to mandate men to practice archery.
In regards to whether a great modern bowyer can match the *best* medieval bowyer, well we simply can't know for certain. But given that they're both humans doing a task with a clear goal, the answer is undoubtedly yes, what makes this question unanswerable is the fact that we don't have a point of comparison.
What we do know, is that we actually have the math to PROVE that we can make the best bow possible. We can factor in all the variables; things like hysteresis, the return of the limbs, drag mechanics, the application of force over distance, etc. And we can look at that number, determine what the *theoretical* maximum efficiency of a 160# longbow should be, then keep building longbows until we get the closest tested number to the theoretical number.
What we DO know about the medieval method of crafting, is that perfection was not only complete mystery, but also often times a trade secret.
So the "best bow of the time" was almost certainly very regional, and literally limited to the best bow that anyone was able to produce at the time. That could have been the maximum theoretical performance of a longbow, or it could have been 70% of what a longbow is actually capable of. But they didn't have the formulae to math it out, they didn't really have the measuring equipment to quantify the results precisely (other than range and penetration), and the records of "best longbow ever made" are tenuous at best, since once an event has been removed from 1st person account, it becomes less of an actual fact and more of an arguable point: Your great grandfather claims he knew a man that could make longbows that shot 300 yards! But you tell your friend who's been made hundreds of longbows over the last 20 years, and he's never made a bow that shot more than 260 yards, and none of the bowyers he knows have ever made bows that shot more than 250-270 yards. The bias of experience results in the 300 yard claim being dismissed as crazytalk, regardless of it being true. But now, we have official records backed by photographic or even video evidence, much harder to dismiss.
That being said, as Todd has mentioned, they didn't have the math, they didn't have the equipment, but they had the same brains. So a bowyer could continue to make bows, changing little things here and there, until they found the best result. So simply by trial and error, they were bound to make some pretty impressive bows eventually, as long as they kept trying.
So in summary, COULD a modern bowyer make a longbow that replicated the BEST longbows made in medieval times?
Absolutely.
We can use the same materials, and we have the same brain. We have some scientific advantages to gauge how close we are to the end result, but ultimately it just comes down to making bows until you get the best result. And that end goal, maximum perfect result, has not changed in 600 years.
Thinking about the quality of materials the steel you use for the prods is almost certainly better than was available to medieval craftsmen whilst it seems likely there is less optimum quality yew available to contemporary bowyers.
Yew is used in expensive furniture, more money to be made there because women throw wads of money at useless trivial shit. It is that simple.
@@AKlover Yew is ground up and used in very expensive pills now too.
Well done, love your brutal honesty! Romance wins with me, as my life, does not hang in the details. Besides I could not draw a real war Long bow if my life depended on it.
Excellent scientific approach to reproduction bows vs. modern variants of which I make no complaint. I would however make some comments about the quality of steel in medieval times; the process to create high quality steel was very time consuming BUT they were able to make steel that is almost as good as modern material - both Japanese and Spanish swordsmiths could create superlative blades. As regards crossbows, it might be argued that they would use time expensive methods as it was the one material they had in abundance to make as good a sprung steel as was possible - and then they would proof it to a weight far in excess of what was required. So to make a crossbow with a 400lb draw weight you could use the same forging and tempering method for a number of bows, and then test one to 600lb. If it did not shatter/shear within a few moments then you could be assured that the rest of the batch could operate to a tension the equivalent of 400lb. If anyone doubts that the armouries of nations would go to such lengths, it should be remembered that early firearms were very quickly required to be tested to withstand pressures above that needed for the ordanance they were to propel; the concept of testing a weapon to failure to determine its limits was already in place by the time cannon were fielded. I suggest that those measures were taken from experience gained in the quality control of crossbows. tl;dr; it is probable that medieval crossbows had both excellent steel bows very good quality control to enable very high draw weights in use.
I’ve really been enjoying your videos Tod. Keep it up!
Thanks Tod! That really put things into perspective.
Tod, I think you overlooked something. The arms of the longbow and crossbow were still moving when the projectile was shot. This means that the crossbow and longbow still retained some kinetic energy. You cannot assume that all the kinetic energy went to the arrow or bolt. The energy left would be again 0.5MVV. The velocity of the arms would be different at different parts of it. So its a little complicated to calculate. But at the maximum, it would be the same as the velocity of the projectile at the point of release. M, the Mass of the arms is likely to be heavier in the crossbow because it was made of steel, it is probably safe to say that the crossbow retains more of the energy in its moving arms than the lighter longbow.
The comparison to modern rounds and even the comparison of bolt sizes to me really changes the dynamic between modern and ancient. I think what I would like to see is impact damage per pound at various ranges per weapon as we know that this should drop off over distance as well as weight of the bolt.
Neat video.
Not sure how versed you are in a .22? Out here in Texas, the .22 is used for a lot and is quite an under estimated round. I think the .22 is listed as a round that has killed a lot of people, likely because “it’s just a .22”.
Years and years ago the us army did experiments with 1/2” plywood stating if it went through the 1/2” ply it was lethal.
Would be an interesting experiment to see what that 450 pound does on 1/2” plywood at 100, 150 and 200 yards - assuming you could connect.
G'Day Tod, I carried out that experiment using a long bow, .22 rimfire and a modern .556mm assault rifle just as you did with your 3 bows. Now the age old argument between ballistic engineers is whether it is kinetic energy as in your experiment Ke=1/2 mv2 or is it Momentum M=mv that does the damage it would be great to work out the Momentum as well and see what conclusions you draw from the comparison. Love the bows and your passion for them and a great experiment. Yours aye Alan B
Great video. As much as I liked the overall discussion, the real high point for me was the chronograph test. As interesting and entertaining as it might be to debate the relative merits of various technologies from a theoretical standpoint, real-world testing captures a lot of hidden information that is difficult or impossible to capture in anything but the most complex mathematical models.
If I might inquire, are you aware of any worthwhile reading on the subject of rate of fire with the different methods of spanning crossbows? There seem to be lots of somewhat reasonable modern tests of longbow rate of fire, but a paucity of information regarding crossbows. You mention a time per shot of 8-9 seconds in your latest goats foot lever video, but I can't find much about belt hooks (with and without mehcanical advantage), windlasses, or crannequins.
Fantastic, I don't think I've seen the windlass video, so I'll have to take a look. I also look forward with great anticipation to your future videos. Thank you for creating such excellent content.
Definitely enlightening Tod. 👍🏻
'You couldn't make a longbow twice this length'
- Au Contraire! Meet the VERY longbow!
Longerbow!
@@InSanic13 :)
How efficient is the Mongolian type bow over the Long bow, i was going to ask this in another video you showed.
You mean recurve vs long bow?
i read a study done by some university students awhile back that went in to just that. They concluded that in terms of efficiency, the chinese bow was about as efficient as any traditional bow can get. Not much of a surprise considering they used it for so long, even long after european firearms outclassed the bow in terms of battlefield efficacy.
Presumably you mean the recurve design (as opposed to the compound construction)? Both had significant benefits & drawbacks
Recurve bows of that period are expensive to manufacture in both cost & time & pack about as great a punch as English simple longbows. /However/ the significant comparison to draw was (?is) in the different styles of warfare: Orientals tended to prefer horse archers whereas Europeans preferred foot. Obviously a longbow is an impractical weapon to use from horseback, while the recurve can be designed to optimise the slash/attack cavalry tactics of the Eastern style /in a major battle/ (prolly a 'memento' of Ghengis' hordes: 'It worked then, so we did it this way!')
@@snafu2350 ...They were used by the scythians in the antiquity already. Nothing about ghengis' memento or whatever.
Also just cavalry tactics in general. Can't use any other warbow effectively on a horse. Too big, or too weak.
@@snafu2350 longbows were used on horseback just not very often. They had mounted archers but they mostly used the horse to bring them quickly to a location
Absolutely fascinating... Be interested to know your thoughts on the modern reverse draw crossbows??
interesting, rigid limbs and elastic element into string givs good results too.
Very nice and clear information. ¿Can you tell me what modern crossbow did you use there, please?. Regards!
Would be cool to add composite bow for the comparison as well
Great content dude. Love how in depth you go!
It would be really interesting to see exactly what it looked like when they made and tuned bows/crossbows
Thank you very much for that video, it answers questions I have had for a very long time. Would love to be able to send you some armour to perform tests on, I only have mild steel armour at the moment
Amazing information and presentation! Thank you!
I enjoyed this video but a quicker way would be to build two bolts and an arrow that fits each bow correctly that all weigh exactly the same and then just cronie each for FPS then you would know which is fastest/ most powerful... or am I missing something?
I'd love to see Tod make a Han dynasty style crossbow. Apparently the trigger mechanism allowed for far longer power strokes, making them almost a 'perfect storm' of the factors he outlines. i.e. a very efficient transfer of energy.
Of course, but the trigger reflects this different evolutionary path of crossbow design. I just wondered if you had an opinion on where such a chinese han crossbow would fall in the comparisons you made in the video. As you were at pains to demonstrate that simple calculations are not always a reflection of reality. The han crossbows certainly looks good on paper, but I've never seen a real world comparison!
Ah! So because it behaves more like a composite bow then you can use them as a proxy for comparison. Stupid of me not to see that. Much appreciated!
Very very good video!!! Thank you!!
Brother I'm not going to argue, But, The cams at the end of the limbs are what make modern compound bows so efficient, NOT the limb size or weight, or material... Change the cam's design and you can screw up the efficiency sooo bad that you won't be able to explain it with simple talk about limb quadrangles. Like you said, "We have computers these days to do the figurin for us". Thanks for another great video Tod
P.S. fast and light, or slow and heavy is an argument you can't prove or win, no matter which side your on. Would you rather be hit with a small light baseball doing 90 mph, or a bowling ball doing 50 mph. 1 of them will leave a bruise... 1 of them will do much worse. Thanks for your time and effort, you make people think and that is what I like about this channel.
The argument is that the baseball will go out of the park while the bowling ball will stop short. In early times and the age of line battle and castle defense the range was a pretty huge factor.
How do composite prods compare to steel ones? I really wonder how much more efficient those would be, would they beat plain wood?
An accuracy test would also be extremely interesting.
Awesome! Great to hear you're making more quality videos. Who is going to be shooting the 160lbs longbow if I might ask?
DushinSC not you
all depends on weight and disztribution of weight per power..
DushinSC I’m guessing Joe gibb...
Did Todd just shoot a 95 LB BOW?!!! Dude is a beast!
Yes he is hehe
@@alexwang2419 Yes. A lighter Danish longbow draw...
The camming on the compound bow changes the power curve from a 45 degree line to something that goes almost straight up, and then flat. So average thrust is much higher. Like the (exaggerated) curve of a stack, but reversed. More area under the curve.
My question is about composite crossbows & longer powerstrokes. Do they perform better or just same as metal crossbows? Because that would be interesting for me
I think something that's important to consider is the change in context of stopping power. Modern fighting involves weapons that even heavily injured soldiers can still use effectively, as opposed to all pre-firearm weapons which required much more physical labour from the user. A minor arm or hand injury would make a bowman essentially useless, a puncture anywhere on the body would make melee combat excruciating. The standards of damage caused by a weapon would have been much lower back then, and the ability for instant kills would be basically pointless, out of the fight is out of the fight.
Excellent video! Are you familiar with Dr. Ed Ashby and his research into arrow penetration? It would be fun to know if there are historical sources that have explored the same subject! Of course, without modern mathematics, but still. Basically Ashby shows that optimal penetration is achieved with focusing more on Forward Momentum than Kinetic Energy. A stiffer, lighter shaft with a heavy arrowhead will outpenetrate a softer, heavier shaft with a less heavy arrowhead by a fair amount. That with arrows of equal total weight and tuned for the same bow. Ashby calculates this in FOC and EFOC ((Extreme) Front Of Center) values. The subject is easy to look up, if you don't know about it. But it would be interesting to know if there is evidence of this thinking in medieval times. Anyways, thanks for the great upload, as usual!
momentum comes from the KE and Newton's law of conservation tells us the arrow get its momentum from the mass independent of its FOC. A smaller dimension shaft means less friction and surface area going in and more mass is concentrated more directly behind the pressure of the point . Foc may give you better flight that equals less lost energi and a flatter ballistics curve that lets the tip of the arrow hit at the optimal angel to avoid deflection Also you must keep in mind that the dynamic spine of the arrow changes during flight so if the foc was important to momentum the foc would change during flight making it utter useless. i
Brilliant video. Truly top drawer. Thank you very much indeed.
Hey Tod, old video I know, but there's more to the story than you mentioned and I feel like it should be acknowledged. Broadheads don't kill through kinetic energy like bullets, they kill through penetration, which KE is NOT a factor of. Bullets push their way through tissue, which is why they have such high KE. A basketball carries far more kinetic energy than any of these tested mediums, for example. What matters is a mixture of physiological effects (muscles retract and lubricate arrow shafts with blood when cut while an animal is still living) along with the mechanical advantage of a broadhead (or to a lesser extent a bodkin) which amplifies the work the arrow or bolt can do with the available force. This is why an arrow will penetrate a sandbag deeper than a .357 magnum will.
*Tod* have you done any material on the old style composite crossbows? I would really love to see them in action. I can imagine they were a bit tricky to assemble.
I suspect the modern crossbow actually ramps up in draw weight faster than your linear curve would indicate, at least based on my experience pulling modern compound bows. Any chance of a putting a scale on them and checking the draw vs lbs curves for all the bows?
Brilliant . very well explained Tod 👍
The other thing to consider in regards to the actual numbers, is the material of the arrowhead/bolt head. Hardened steel, soft low carbon steel, is it sharpened, and even the cross section/shape of the head.
While the numbers themselves are not that high in comparison to firearms, there's a whole bunch of other aspects that are also important when considering the lethality of a bow or crossbow. .22 LR might kill a person, but it would take proper shot placement, and a very unlucky individual. It has very low probability to hitting a vital structure of the body bringing about incapacitation or death. While getting shot with any one of the projectiles from the crossbows and bow you shot, the probability of killing or seriously wounding is significantly higher.
Just for some additional comparison; a standard MLB regulation baseball thrown at 95 mph has a kinetic energy of 117.5 Joules. Batters get hit fairly regularly, and thankfully they aren't dying anymore (in large part due to batting helmets and other rule improvements).
i'd say on your l;ast point definately where projectile elasticity and surface area come into play. also a modern crossbow is often of materials that cant handle the very high stress of impact, since id likely say they arnt designed for it
compare thast though to jeorg sprave the shloingshot guy and his 'plumbers nightmare' arrow shooter, launchinngg projectiles at aroundf 700-900 joules, ive no doubt that would pierce plate armour no trouble.
IIRC Alan Williams in his book "The Knight and the Blast Furnace" did comparisons of arrows and bullets (in this case round balls which would be worse than modern bullets) capabilities to penetrate metal plates. The balls needed a lot more energy to penetrate the same plate and of course had more energy.
That makes sense. Bullets aren't as pointy & usually of softer metals.
When I taught Hunter Safety, we would demonstrate the difference in the mechanics of the projectiles and the impact on penetration. We would shoot at a 5-gallon pail of sand with Winchester .243 and .308 caliber rounds. The pail would always trap the rifle projectiles. When the same pail of sand wash shot with a modern compound hunting bow at 65 lb. draw weight with a broadhead arrow, the arrow would always protrude through the bucket (plastic 5-gallon pail). Projectile design and physics are very important in determining terminal ballistics.
Great video!
I think that the calculation is more complicated. Because of the higher the speed and lower the mass => the higher the calculated drag.
so in rifles, you lose velocity faster than in bows or crossbows. (this is why rifles don't reach underwater)
On another hand, you reach the target faster.
you can basically solve this by measuring the velocity at the target and then calculate the energy