Makes sense, they wanted maximal Penetration to get their Man down for good and not a distance record while knocking lightly on his Helmet to tell him; "Hi, I'm over here and it will take me some time to reload".
I would have thought it depends on who they are fighting. If they are defending against heavy cavalry then penetration is what matters, but if they are looking at lighter armoured opponents then it may well be the earliest moment of engagement (i.e. engagement at greatest distance, preferably before they are in range to shoot back at you) might be the better option.
Hellequin, with these thick bolts they never got penetration, they generated impact, but not penetration thru armor... putting deeper dents nto a knights armor instead of a hole, that is what they did. No chance they put holes into steel armor and arrow penetrating 10cm thru hole when using 20mm arrowheads
Thanks Jason, and of course I would like to think so! There is still so much to look at with this whole area. Just for the record, this was shot a couple of weeks before yours came out. Speak soon
@@tods_workshop so weird seeing all these videos that are essentially doing babies first crossbow/longbow tests, yet they are produced by a clearly skilled, professional, craftsman who should already know the results but clearly doesn't
@@kingkarlito having watched said videos I'm baffled by why you'd think they should empirically know already. Nobody normally lofts a bolt into the next field to lose it in long grass. Nobody normally wants to spend the time, effort and cost to make period correct equipment and then smash it into other expensive gear to see what exactly happens. We've mostly come up to the skill/experience level knowing that using the gear in any other way than carefully within established safe guidelines leads to a high chance of loss, breakage and danger. Securing a location to shoot safely and consistently is difficult year round at our lattitude at any moderate+ distance. Practical 'hunt' distances are near 'point blank', targets need to be lit for half the year mid-week for most users, hard targets equate to just throwing money down range. I used to be a pretty good Town and County competitive archer and I'm not ashamed to say the majority of my practice time was indoors at sub-trial range. 90%-95% of our focus is about what happens within a 3' radius of our heads to allow us to not botch our release and miss our intended, soft target. Scientific flight data has only been delved into with modern materials because of competitive sports. These guys are testing the mechanics of technology essentially abandoned before the modern scientific model was thought of.
@@tods_workshop do you have any plans to colab a wider range of bows, crossbows, arrows and bolts to establish deminishing returns of ammo weight vs launchers of period accurate equipment? I'm fascinated to see where our ancestors balanced the performance vs logistics compromise. Afterall there's a large gap between making one bow shoot once amazingly and making thousands shoot consistently throughout a campaign.
My students (high school physics in the US) are in need of a light end of year session or two to show them how useful physics is. I've queued up about five of your crossbow (and longbow) videos for them. Thank you for them; they are wonderful.
This is all simple physics (F=ma at the bow, kE=1/2mv*2 in flight and thus at the target) but the Devil's in the details like the throw of the string, the weight distribution and aerodynamics of the bolts and so many other things. I really enjoy it when you point out how seemingly irrelevant small changes can have such large differences in outcome.
@@trevorWilkinson I think his crossbow really isn't 1000 lb, it just can't be. The string on it looks really really thin, especially compared to all these heavy crossbows you see on Tod's channel
It really is interesting to me that the limitation on range and speed at the top end of the performance curve is not poundage, or draw length, or even how mechanically 'smooth' things are but instead the material of the bow not being able to move any faster than it does.
Not really sure that's quite true. The higher the poundage (assuming constant proportions of the crossbow), the more acceleration the bolt experiences while being fired and therefore the higher the final velocity when it leaves the crossbow. This is because shooting the bolt is simply the reverse of powering up the crossbow, which requires greater and greater force the further you pull the string back, recalling that (Net) Force = mass x acceleration. The mass is constant so the acceleration 'effect' is what must grow as you power it up. The act of firing the crossbow is simply the inverse of this, where the acceleration of the bolt starts off high and then decreases to zero by the time string is back in neutral position. Despite the acceleration falling though, the speed of the arrow will continually grow because the acceleration is still always positive in the direction firing, therefore the string is in constant contact with the bolt the whole time it's being fired, imparting kinetic energy on it and speeding it up. The only way I can think of you getting a diminishing returns effect with an equally proportioned, higher poundage crossbow (firing the same bolt) would be from drag on the bolt - drag increases greatly at higher and higher speeds and you're likely to get more bending in the bolt too which wouldn't help with aerodynamism. Drag depends on the shape and velocity of an object (and also the viscosity of the medium its moving through, in this case air) but not on its weight. Therefore, a heavier bolt might experience less diminishing returns and go further at these higher poundages because its moving slower at launch thus experiencing less drag and any drag it does experience would have less of an effect because of its higher inertia (due to its higher mass). You can think about this phenomenon by imagining you had two balls of the same volume, one made of paper, the other of metal. If you made weak under-arm throws of equal force for each then you could imagine throwing the paper ball further than the metal one. Now imagine throwing them over arm with all your strength, clearly the metal ball will go further than the paper ball in this case because drag will drain the energy of the paper ball but less so the metal ball with its higher inertia. Hence, the diminishing effect is due to the drag on the bolt at higher poundages rather than some unexplained phenomenon of 'the string not being able to move any faster'.
Brings back memories of trying a flight shoot 25yrs ago, walking to and from 305yds got a bit old. Target recurve, 50lbs, alu/carbon arrows, speed unknown, slight headwind.
The adding weight to offset speed limitations thing is pretty ubiquitous in terms of black powder firearms as well, conical bullets were developed for additional accuracy, but also enabled them to fit a cylinder into the bore with more mass, because black powder only burns so fast, then you see bullets start to become smaller and faster with the advent of modern gun powder.
Yes, the Whitworth rifle is a particularly fascinating look at the beast, launching a 580gr .452" bullet, when the typical .45-70 is 405gr. That's gr as in grains (7000 per lb), not grams!
The jack you are using to check the draw weight of the limb at the end is known as a "hi-lift" jack here in the states. We use them for big vehicles like tall off-road SUVs, Jeeps, delivery vans and the like.
One thing I'd like to add, concerning the physics of the bolts. It isn't necessarily a fact that lighter bolts will travel farther. Air resistance and "overpower" of the bow might make a difference. If the bolt is very light, the bow might shoot it at almost the same speed as a bolt that is a bit heavier, because it's almost the speed with which the flex in the material of the bow jumps back. In that case, a lighter bolt would carry less energy, and having the same friction with the air, it will fall shorter than other, heavier bolts (a real-life example like this are airsoft bb guns. Sometimes heavier bbs make for better long-distance shots because the lighter bbs are more heavily affected by air resistance.) Another factor in play is aerodynamics. It is of great influence to air resistance how aerodynamic the bolt is that is shot. The bolts here followed the same principle in weight as they did in aerodynamics, so it's just adding to the fact that the lighter bolts will generally fly further, but air resistance greatly depends on the shape of the object flying through the air. Physically there are many things in play that might make a lighter bolt fly less far and it wouldn't break the laws of physics, even if the bow performs exactly the same for each launch (which is another possibility for variance, when regarding bolt friction during launch, bot flex, and so on.) Just wanted to add that, and also congratulate on the awesome video, very scientific with great consistency. I loved it! Thank you so much!
You are exactly correct about the absolute speed of any given limb, it's what is referred to as "cast". I do target archery, and some limbs are simply slow for any given draw weight, but they often feel nice to draw, and the really ultra-high performance limbs, such as the so-called "super recurves", like Uukha and Border, can feel very uncomfortable to some archers (personally, I much prefer the feel), but they are incredibly efficient and very very fast. The arrow you described as being like a baton or a mace had parallels with flu-flu arrows used for hunting birds in trees, they have a large heavy and blunt tip which will usually kill the bird, but doesn't break the skin, and crucially, doesn't stick into the tree. String thickness... Yep, totally correct again. We use different thicknesses of string and also centre servings to compensate. The thicker the string, the more mass it has and also creates more drag, slowing it down, however, it has less stretch, which partially compensates for this. A very thin string will stretch far more, and waste energy, but it has less mass and less drag. For heavy hunting arrows, you need the thicker string, for light outdoor target arrows, you want to minimise mass and inertia.
Two points: 1) It would be interesting to test a full-metal thin/aerodynamic bolt equivalent in weight to the "end 'em rightly" one. 2) 45 degree angle is NOT optimal for distance in the real world where there is air resistance. Optimal angles are usually somewhat lower (around 40 degrees), depending on the parameters of air resistance.
The fact that the bolts entered the ground at different angles shows that they were not at optimal angle for distance given their weight, initial velocity, and aerodynamic profile.
So Tod, Modern History TV recently did a video testing the range of a heavy crossbow he had, and he noted that his string wore out rather quickly. He speculated that over the course of a battle, a substantial number of heavy crossbows could become non-functional from the wear. How long do you find your heavy crossbow strings last before requiring repair or replacement?
I did notice on that video when Jason was loading the bow for his first shot the string looked odd (2.58) and after he fired there is clear evidence on the video of damage to the string (9,20). I wonder if the string was not already faulty before the video starts. I almost noted the string that Jason uses is much thinner than the one Tod uses in this video on a 850lbs. That may also be part of the problem
InSanic. The bow was made by a chap called Robin Knight and was old and tired when Jason got it. He asked e to service it, which I did and provided attached bolts at 80g for it and it shot OK here at short distance. I didn't weigh it, but the bow is longer than mine and the same thickness so I suspect it was more likely 600lbs but inefficient. The string was OK when here. I chatted to Jason last week and we are planning some vids together about crossbows and a particular aspect of them
I think you're very correct about the limbs being the limiting factor and not being able to push the lighter arrows faster. The same thing happened with black powder firearms. In an effort to get more power, they kept increasing shot size. They would build strong actions and longer barrels but they reached a point where black powder just wouldn't push the bullet faster. You had 50, 58, 64, 72 caliber rifles, and a bunch of others. Big bore rifles continued up until the smokeless powder became popular and then smaller, faster bullets became more common. They started out big with the 8mm and large 30 cals before working down to smaller 30 cals and now to 5.56 and 5.45. The crossbow proves that propellants have always been an issue and limitation
Kentwell Hall, I remember it well! Grew-up in South Suffolk & North Essex 70s-80s. School & family trips to Kentwell were fantastic, it did feel like genuine time travel!
Do a vid talking about how you got into history and all that stuff! Origin stories are interesting! (also: hope you got somewhere warm & dry as soon as you could)
Now we need some heavy crossbow with a very heavy anti-plate bolt for short range penetration testing. Very nice that you've added the draw weight measurement at the end of the video.
Oddly, the most important thing that I've learned from this series is the massive importance of the cams in a compound bow. I hadn't considered how much of the bow's energy was consumed by the acceleration of the limbs, and consequently how much difference a reduction in that load would make for the velocity of the arrow/bolt. I wonder if that's part of the reason why increasing the draw weight doesn't help: the bow is expending most of the increased energy into accelerating itself, leaving little to accelerate the arrow. If that's the case, it certainly backs up your theory on the solution: increase the mass of the projectile, such that it accounts for a greater fraction of the load and allows more of the bow's energy to be converted into a useful form. Finally, it's still very tempting to consider how a cam system with a longer bolt but the same massive draw weight would've looked in terms of late medieval or renaissance technology.
This channel continues to be amazing; informative and fun; science and art. I am now looking at some Tod cutlery and will order something shortly. Best advert ever haha.
The heavier bolts will decelerate due to air resistance slower, therefore if you are unable to increase the bolt velocity further you can still increase the range with bolt mass provided you can maintain that high velocity.
As someone who's just taken and interest in bow making and is somewhat of an amateur Bowyer, I actually think your theory is quite sound. In making wood bows there are all sorts of different aspects that make the bow shoot more efficiently with higher fps that wouldn't really apply to a steel limbed crossbow. Wood type, grain alignment, limb design, specific gravity (that varies even within the same species) and just overall build quality and tiller.
I don't know any formal physics at all, but I completely agree with your conclusion, Tod. If draw weight is a measure of how much energy is stored in a bow, and you observe a non-linear change in the kinetic energy of a projectile with the same weight and ballistic coefficient when shot from bows of different draw weight, the difference must be in the way the bows transfer their stored energy to the projectile. I'm guessing that the following relationships may play a part (I've probably mixed up terminology, sorry!): Inertia and other losses within the bow itself (how fast can the bow make the bowstring move when there is no projectile) vs. the inertia and ballistic coefficient of the projectile (if the bowstring is already moving as fast as the bow can make it before the projectile is released, reducing the weight of the projectile won't make it go any faster). The bow's rate of acceleration vs. its draw-length (how quickly does the unloaded bowstring achieve its peak velocity vs. how the distance over which it is transferring energy to the projectile). It would be wonderful to be able to visualise a comparison, in a hypothetical sense, of the relative dimensions, behaviors, and terminal ballistics that steel crossbows, timber longbows, and recurve composite bows of 800-1300lb might have. As always, I love what you do, and thank you so much for your work!
You've probably encountered this before, but if not, you should give the wikipedia article on the Maximum Power Transfer Theorem a read. It's about electricity, but it applies to mechanics as well. To paraphrase, you need to match the resistance of the load to the power source, otherwise the power source is not efficient at transferring power to the load. Or, a big heavy crossbow needs a big heavy bolt to get all the energy out of the limbs.
Black powder is the same way. It's an inefficient propellant and you basically hit diminishing returns with regards to muzzle velocity, so more power largely meant a larger bore size and more projectile mass.
A few questions first, why weren't the bows wider, with lower draw weight? (i know that a bow the size of a long bow gets unwieldy but double or triple could work) Second how does the power stroke scale with the bow size(double the bow size double the power stroke). Double the size half the draw weight equal energy? Why this could be interesting: easier cocking= higher fire rate. i dont think bow would be that much more expensive (longer, thinner) i would love to hear your thoughts ps: amazing content
Another thing that can have an influence on how far a bolt or arrow travels through the air is your elevation relative to sea level. I know in rugby that the kickers has a much easier time kicking for goal when the match is played at high elevation when compared to near the coast. This is due to higher ambient air pressure at low elevations compared to higher up, which means less overall air resistance on the bolts as they travel. Maybe it's something interesting to keep in mind or to test in the future.
Tod - 12 blunt tip arrows, 6 archers VS knight in full armor (plexiglass over front of helmet), walking towards them for 100 feet / - would love to hear him explain the experience ! ! !
Hmm. Maybe the principle in slingshots also applies to crossbows? There is a speed limit with slingshots and the only way to take advantage of the heavier draw weight is to use heavier projectiles. Therefore is is important to match the weight of the projectile to the power of the band. Don't longbows also follow this with rules of thumb stating you should use about 8-10 grains per pound of draw weight?
The electrical engineers call it "impedance matching". For the annual cottage "shoe kick" event, I taught the kids to experiment to get the "right" weight of shoe for their kick in order to maximize (in this case) distance.
I think you're right with your theory Todd, and from a physics standpoint it's impressive to see it in action. If we look at Newton's 2nd Law of Forces (F = m*a), then the functional force of the arrow will be intrinsically bound by its weight and the launch capacity of the crossbow. It could also explain the functional limitation of the amount of kinetic energy smaller arrows could absorb, and why said arrows and crossbow sizes had to increase in order to harm more heavily armored targets.
As several others have commented, 45 degrees isn't actually the ideal angle. Love all your videos btw! I show them to my students at times. Optimal angle is I think (if I remember my physics) 35-42% in atmosphere depending on altitude, weather, projectile etc..
"I shot an arrow in the air, She fell to ground in Berkley Square." Yikes, how deeply those bolts penetrated in to the soil; which, I assume, is less dense than flesh. This was yet another great video. Thank you for sharing.
Drag will also have a massive effect. IE it's proportional to the speed squared. So a 10% increase in speed which in a vacuum would give you 10% more range, in air makes just a little difference as at launch they have 21% or there abouts more drag. So the additional speed bleeds off very quickly. The other thing to remember is projectiles only follow a parabolic curve in a vacuum. If you compare first graze and first fall on musket tables they are remarkably close together. First graze is where the first shot is likely to hit the top of the head. First Fall is where the first shot is likely to hit the ground. As no army uses volley fire any more (that I know of) these terms are obsolete but the science still holds.
I like your theory, I really hope you can spend some more time investigating it. Testing heavier pound bows with heavier bolts to see what differences in distance and power you can achieve and leading to some really interesting discussions on how these war cross bows were used. Keep up the good work!
Cool stuff Todd! Could you perhaps paint arrows for video tests with neon colors (or maybe even glow-in-the-dark arrows to shoot in the evening) so we can see them shoot?
I just want to say that measuring in yards is ok. It's a sensible choice and if we're not being pedantic about exactitude we can just consider them as metros. BTW, great video as always, sir.
The big, heavy projectile theory matches what is done in guns with subsonic rounds. You're limited by speed (because you want to keep it effectively suppressible), so, instead, you bump up the weight of the projectile to increase the energy. In fact, for some calibers, density of available materials becomes the limiter; for a round to cycle it needs to fit within certain physical parameters (the bolt built for Skal's crossbow fails on this with this new crossbow), including overall length, so you can only have a projectile that is so big; to add weight you have to add density within that same physical size.
If you take the range the bolt traveled you get an idea of the launch velocity (an idea, because it can't account for wind resistance). For the needle bodkin it says about 46 m/s, while for the crown bolt, only 36.4 m/s. Those can be converted into energy, and there is quite a spread, 69 J for the needle and 105 for the crown bolt. You can also find the energy stored in the crossbow. With a draw length of 288mm and a force of 850 lbf, that means an energy of 544J. So the rest of the energy that doesn't go into the projectile, goes into moving the string and the arms of the bow. For everything except the crown bolt, that is about .45kg (depending on which bolt). For the crown bolt it was 0.66 kg (which means the crown bolt took a much larger hit from drag, not a big surprise). Using a chrono to get exit velocity would allow a better estimate of the dead-weight of the bow, as well as a way to calculate the drag on the different bolts.
I am a mathematician with some knowledge of physics, and while I can't promise anything, I think your theory is correct. The crossbow is going to launch projectiles at reasonably similar velocities, simply because a lot of the energy goes towards accelerating the limbs (and the string!). As such, a very light projectile would in fact travel less distance due to wind resistance!
Very reasonable hypothesis. With the design, steel limbs and the type of string, it seems likely that crossbows like that will have very similar maximum contraction speeds, due to material limitations. Conceivably then they should have similar max ranges and the main difference between a 850 and a 1200 would be that the latter can shoot a heavier to maximum range.
So, great video (as usual). I started thinking about the holes in the metal socket of the windlass. Are they meant to have a functional use other than perhaps lightening the object? I'm think perhaps to make sure that the thing doesn't get stuck on the crossbow if it gets full of mud or as an egress point for dirt. Kind of like the sand groves on the bolt of an L1A1 SLR (couldn't thik of a better example, sorry)?
"Now we all have a metal box in the house that carries out the same function." What, hiding corpses from Belgium Detectives during early 20th century house parties?
While shooting them all at the same angle might give results that are easy to compare, but are we sure the optimum angle of flight is the same for each weight of bolt?
That actually would be a good test - take a variety of bow weights and a series of standardized bolt weights. Measure speed at each bow at each draw weight. If your theory is (and I'm interpreting on this) that the heavier bows were entirely to bring up heavier bolts up to the same speed as the lighter ones could be, and there's a maximum speed achievable that doesn't depend on bow draw, then you should see a consistency with the lighter bolts hitting that limit and the heavier ones travelling faster until they also reach a limit. A ballistic chronograph would give you the speed but I'm not sure how well the usual firearm ones work on crossbow bolts. I would imagine they should still work.
Sounds like a very reasonable conclusion there mate. I was in Berlin not all that long ago when one of the museums was running a crossbow exhibition. It seemed to suggest the later years of the war crossbows were an arms race over plate armour and penetration power crossbows, with crossbows getting heavier along with plate getting thicker. I have no idea if that brief exhibition aligns with evidence in the production specs of plate and crossbows at the time though. But it seems reasonable that you'd only make such insane bows for a specific reason and super high mass bolts would for pure penetration sounds likely.
Gotta factor in the aerodynamics of the bolt tip as well. And they probably all cap out at a certain range no matter what the draw weight because of terminal velocity. Just horizontal terminal velocity instead of vertical
Great channel. Man deserve respect for interesting researches. There is some museums were placed some Arabic or Turkish Bows and Crossbows that made from composition materials and with interesting engineering, and it is clear that it all done with the aim to increase speed of projectile. Interesting to see "Ziyyar" that was actually machine used quite sophisticated construction to increase velocity of spear sized bow. Also China archives saved illustrations of machines with combination of several bows, that also served for arrows speed increase.
This phenomenon about the arrow speed/distance is real thing. In bow making there is such a thing as a lighter out shooting a heavier bow using the same arrow. It has to do with the dry fire speed of each bow. The lighter bow usually dry fires faster than the heaver bow do to reduced mass on the limb tips. But the heavier bow will send a heavier arrow just as far or even further than a light bow with a light arrow because it has more residual energy left in the slower moving limbs to transfer to the heavier arrow. It's quite interesting. And you could spend weeks testing the little nuances of it.
Your statement at 8:15, "You can't do it quickly, but you can make it heavy." I think that may have quite a bit of merit. I'm not terribly well versed with historic bows, and especially not crossbows, but I've done a lot of shooting with black powder firearms and a similar limitation exists. Black powder is an explosive, and as such there is more or less a hard limit on the velocity that a projectile can be propelled with it, that limit is about 2100fps (~640m/s) and so what you see with black powder arms is a focus on making larger and larger caliber rounds but maintaining a relatively consistent velocity. It makes sense to me that once you start to reach the upper limits of what you are capable of speed wise you'd start to make heavier projectiles but retain that same or similar speed.
About the mace arrow, I don't pretend to know anything about this stuff, and I don't shoot at animals. I will ask a question that might be silly. Would a bolt for shooting an animal wanting to preserve its fur not better have a flat surface on the tip and could that non-flat tip be intended to not just glance off the helmet of a cavalry man charging at you? What would it do to an armoured rider if you hit his helmet at a range of ten meters, could it incapacitate him?
The increase of mass to increase kinetic energy was extremely prevalent in guns prior to the invention of smokeless powder. Before 1886, black powder had a low max velocity so to compensate large caliber bullets were used to compensate. That's why African Safari rifles were often .60 cal (~15 mm) or bigger.
I see you're going for the casual pope look 😂
😂
😂
😁😁
🤣🤣🤣
Well, God did indicate his blessing with that rainbow...
"But it got me thinkin'...", it always gets good after that!
No pot of gold at the end of the rainbow, but a Tod with a crossbow. Poetic!
What was not shown in this video was dead leprechaun with crossbow bolt in his back, next to a empty pot.
@@IamOutOfNames well of course what else do you think he was aiming for
"Faith and Begorrah! "
Makes sense, they wanted maximal Penetration to get their Man down for good and not a distance record while knocking lightly on his Helmet to tell him; "Hi, I'm over here and it will take me some time to reload".
Old crossbows have very little draw length
@@heldermonteiro2718 but you do need a windless to load most of them
I would have thought it depends on who they are fighting.
If they are defending against heavy cavalry then penetration is what matters, but if they are looking at lighter armoured opponents then it may well be the earliest moment of engagement (i.e. engagement at greatest distance, preferably before they are in range to shoot back at you) might be the better option.
max distance of turkish bow ~400 meters, but what an arrow was used.. for practical pusposes unusable.
Hellequin, with these thick bolts they never got penetration, they generated impact, but not penetration thru armor... putting deeper dents nto a knights armor instead of a hole, that is what they did. No chance they put holes into steel armor and arrow penetrating 10cm thru hole when using 20mm arrowheads
Looks like the Wizard of Crossbows is at it again...
We're off to see the Wizard
The Wonderful Wiz of Arroz!
Arrowmancer.
@@yajurka Beware, Bodkin, the Boltomancer!
"I cast Crossbow Bolt!"
@Alorand I thought of sth along of Todstradamus, but yours is better ^^
I love the sound the spinning nut makes
nicely done, and a much better bow than I used!
Thanks Jason, and of course I would like to think so! There is still so much to look at with this whole area. Just for the record, this was shot a couple of weeks before yours came out. Speak soon
@@tods_workshop so weird seeing all these videos that are essentially doing babies first crossbow/longbow tests, yet they are produced by a clearly skilled, professional, craftsman who should already know the results but clearly doesn't
@@kingkarlito having watched said videos I'm baffled by why you'd think they should empirically know already. Nobody normally lofts a bolt into the next field to lose it in long grass. Nobody normally wants to spend the time, effort and cost to make period correct equipment and then smash it into other expensive gear to see what exactly happens. We've mostly come up to the skill/experience level knowing that using the gear in any other way than carefully within established safe guidelines leads to a high chance of loss, breakage and danger. Securing a location to shoot safely and consistently is difficult year round at our lattitude at any moderate+ distance. Practical 'hunt' distances are near 'point blank', targets need to be lit for half the year mid-week for most users, hard targets equate to just throwing money down range. I used to be a pretty good Town and County competitive archer and I'm not ashamed to say the majority of my practice time was indoors at sub-trial range. 90%-95% of our focus is about what happens within a 3' radius of our heads to allow us to not botch our release and miss our intended, soft target. Scientific flight data has only been delved into with modern materials because of competitive sports. These guys are testing the mechanics of technology essentially abandoned before the modern scientific model was thought of.
@@tods_workshop do you have any plans to colab a wider range of bows, crossbows, arrows and bolts to establish deminishing returns of ammo weight vs launchers of period accurate equipment? I'm fascinated to see where our ancestors balanced the performance vs logistics compromise. Afterall there's a large gap between making one bow shoot once amazingly and making thousands shoot consistently throughout a campaign.
Glad to see this cross pollenization. Came to watch Tod's test immediately after watching yours.
"But really, it's a mace on a stick."
Isn't that just a mace?
What he has there is the handy snack size Mace on a Stick.
In this case, it's a projectile mace.
@@StergiosMekras a missile mace sounds much cooler
Yes, it's just a mace
A flying finned mace ? Finned flying mace? Arrow mace. Mace arrow? The clobberer!
Have fun with a crossbow in an open field, with the rainbow ... What more could you ask for? 😁
Dressing up adds to the level of authenticity. PS I bought one of your daggers to support the channel. Love your work!
Others have remarked Tod, but you resemble a cardinal of the crossbow.
I love it.
Imagine what a strategic asset Tod would have been. Wars would have been won using his knowledge of the technology of the time.
I love how it requires an off-road car jack to test.
heavy stuff
My students (high school physics in the US) are in need of a light end of year session or two to show them how useful physics is. I've queued up about five of your crossbow (and longbow) videos for them. Thank you for them; they are wonderful.
Good timing, with Modern History's last video on his crossbows lackluster range :)
This is all simple physics (F=ma at the bow, kE=1/2mv*2 in flight and thus at the target) but the Devil's in the details like the throw of the string, the weight distribution and aerodynamics of the bolts and so many other things. I really enjoy it when you point out how seemingly irrelevant small changes can have such large differences in outcome.
Modern History TV Collab coming up? :P
Just watched his distance video the other day, definitely something wrong with his bow after seeing this.
@@trevorWilkinson I think his crossbow really isn't 1000 lb, it just can't be. The string on it looks really really thin, especially compared to all these heavy crossbows you see on Tod's channel
2 of my fav youtubers, can't wait
@@trevorWilkinson He was shooting into a reasonable head-wind in his video.
@@CountCrapula. could be different materials of string?
Maintaining that level of enthusiasm in that much rain is impressive :)
It's an essential quality for being british
Crossbow, big bulky robes and an agile mind... Looks like Chancellor Ridcully is having fun outside again xD
That's ARCHChancellor Ridcully to you, me lad...🤨
@@Lucius1958 It's all about the hat, you see
@@Lucius1958 He'd be an Archancellor if he had the Hat. Without it, he's just good old Hughnon.
@@DjDolHaus86 Exactly !
ARCHchancellor Ridcully testing his latest acquisition from a shop in the Street of Cunning Artificers. Shame there's nothing left to shoot at!
big props to the video-bombing rainbow in the background, btw
Would have been interesting to see a chronograph of the launch speeds on those bolts.
That is coming
I love your use of a cell phone as an inclinometer...brilliant
Indeed, a cell phone inclinometer and a laser ranger-finder; truly this is a high-tech medieval experiment.
It really is interesting to me that the limitation on range and speed at the top end of the performance curve is not poundage, or draw length, or even how mechanically 'smooth' things are but instead the material of the bow not being able to move any faster than it does.
Not really sure that's quite true. The higher the poundage (assuming constant proportions of the crossbow), the more acceleration the bolt experiences while being fired and therefore the higher the final velocity when it leaves the crossbow. This is because shooting the bolt is simply the reverse of powering up the crossbow, which requires greater and greater force the further you pull the string back, recalling that (Net) Force = mass x acceleration. The mass is constant so the acceleration 'effect' is what must grow as you power it up. The act of firing the crossbow is simply the inverse of this, where the acceleration of the bolt starts off high and then decreases to zero by the time string is back in neutral position. Despite the acceleration falling though, the speed of the arrow will continually grow because the acceleration is still always positive in the direction firing, therefore the string is in constant contact with the bolt the whole time it's being fired, imparting kinetic energy on it and speeding it up. The only way I can think of you getting a diminishing returns effect with an equally proportioned, higher poundage crossbow (firing the same bolt) would be from drag on the bolt - drag increases greatly at higher and higher speeds and you're likely to get more bending in the bolt too which wouldn't help with aerodynamism. Drag depends on the shape and velocity of an object (and also the viscosity of the medium its moving through, in this case air) but not on its weight. Therefore, a heavier bolt might experience less diminishing returns and go further at these higher poundages because its moving slower at launch thus experiencing less drag and any drag it does experience would have less of an effect because of its higher inertia (due to its higher mass). You can think about this phenomenon by imagining you had two balls of the same volume, one made of paper, the other of metal. If you made weak under-arm throws of equal force for each then you could imagine throwing the paper ball further than the metal one. Now imagine throwing them over arm with all your strength, clearly the metal ball will go further than the paper ball in this case because drag will drain the energy of the paper ball but less so the metal ball with its higher inertia. Hence, the diminishing effect is due to the drag on the bolt at higher poundages rather than some unexplained phenomenon of 'the string not being able to move any faster'.
Brings back memories of trying a flight shoot 25yrs ago, walking to and from 305yds got a bit old. Target recurve, 50lbs, alu/carbon arrows, speed unknown, slight headwind.
The adding weight to offset speed limitations thing is pretty ubiquitous in terms of black powder firearms as well, conical bullets were developed for additional accuracy, but also enabled them to fit a cylinder into the bore with more mass, because black powder only burns so fast, then you see bullets start to become smaller and faster with the advent of modern gun powder.
Yes, the Whitworth rifle is a particularly fascinating look at the beast, launching a 580gr .452" bullet, when the typical .45-70 is 405gr.
That's gr as in grains (7000 per lb), not grams!
The jack you are using to check the draw weight of the limb at the end is known as a "hi-lift" jack here in the states. We use them for big vehicles like tall off-road SUVs, Jeeps, delivery vans and the like.
Here is a handy guide to their use for those who want to know more.
th-cam.com/video/xPLrHw2At7s/w-d-xo.html
Finally distance test ...👍 Please more distance test of crossbows
Always with a great experiment, Tod !!
Congrats !!!!
One thing I'd like to add, concerning the physics of the bolts.
It isn't necessarily a fact that lighter bolts will travel farther. Air resistance and "overpower" of the bow might make a difference. If the bolt is very light, the bow might shoot it at almost the same speed as a bolt that is a bit heavier, because it's almost the speed with which the flex in the material of the bow jumps back. In that case, a lighter bolt would carry less energy, and having the same friction with the air, it will fall shorter than other, heavier bolts (a real-life example like this are airsoft bb guns. Sometimes heavier bbs make for better long-distance shots because the lighter bbs are more heavily affected by air resistance.) Another factor in play is aerodynamics. It is of great influence to air resistance how aerodynamic the bolt is that is shot. The bolts here followed the same principle in weight as they did in aerodynamics, so it's just adding to the fact that the lighter bolts will generally fly further, but air resistance greatly depends on the shape of the object flying through the air. Physically there are many things in play that might make a lighter bolt fly less far and it wouldn't break the laws of physics, even if the bow performs exactly the same for each launch (which is another possibility for variance, when regarding bolt friction during launch, bot flex, and so on.)
Just wanted to add that, and also congratulate on the awesome video, very scientific with great consistency. I loved it! Thank you so much!
You are exactly correct about the absolute speed of any given limb, it's what is referred to as "cast". I do target archery, and some limbs are simply slow for any given draw weight, but they often feel nice to draw, and the really ultra-high performance limbs, such as the so-called "super recurves", like Uukha and Border, can feel very uncomfortable to some archers (personally, I much prefer the feel), but they are incredibly efficient and very very fast.
The arrow you described as being like a baton or a mace had parallels with flu-flu arrows used for hunting birds in trees, they have a large heavy and blunt tip which will usually kill the bird, but doesn't break the skin, and crucially, doesn't stick into the tree.
String thickness...
Yep, totally correct again. We use different thicknesses of string and also centre servings to compensate. The thicker the string, the more mass it has and also creates more drag, slowing it down, however, it has less stretch, which partially compensates for this. A very thin string will stretch far more, and waste energy, but it has less mass and less drag. For heavy hunting arrows, you need the thicker string, for light outdoor target arrows, you want to minimise mass and inertia.
I'm happy to see some period clothing in the video. It really adds to the experiments that you're doing.
Lovely garb. Enjoy seeing Tod in his mating plumage.
🤢🤮
Two points:
1) It would be interesting to test a full-metal thin/aerodynamic bolt equivalent in weight to the "end 'em rightly" one.
2) 45 degree angle is NOT optimal for distance in the real world where there is air resistance. Optimal angles are usually somewhat lower (around 40 degrees), depending on the parameters of air resistance.
The fact that the bolts entered the ground at different angles shows that they were not at optimal angle for distance given their weight, initial velocity, and aerodynamic profile.
So Tod, Modern History TV recently did a video testing the range of a heavy crossbow he had, and he noted that his string wore out rather quickly. He speculated that over the course of a battle, a substantial number of heavy crossbows could become non-functional from the wear. How long do you find your heavy crossbow strings last before requiring repair or replacement?
I did notice on that video when Jason was loading the bow for his first shot the string looked odd (2.58) and after he fired there is clear evidence on the video of damage to the string (9,20). I wonder if the string was not already faulty before the video starts. I almost noted the string that Jason uses is much thinner than the one Tod uses in this video on a 850lbs. That may also be part of the problem
I thought this video is an immediate silent response to Modern History TV about distances and going wrong
InSanic. The bow was made by a chap called Robin Knight and was old and tired when Jason got it. He asked e to service it, which I did and provided attached bolts at 80g for it and it shot OK here at short distance. I didn't weigh it, but the bow is longer than mine and the same thickness so I suspect it was more likely 600lbs but inefficient. The string was OK when here. I chatted to Jason last week and we are planning some vids together about crossbows and a particular aspect of them
lol the one on Todd's can't even be called a "string", look at the SIZE of it! Looks almost as thick as my wrist. "Bow rope".
@@BobT36 Or a chonker plonker, as it were.
I think you're very correct about the limbs being the limiting factor and not being able to push the lighter arrows faster. The same thing happened with black powder firearms. In an effort to get more power, they kept increasing shot size. They would build strong actions and longer barrels but they reached a point where black powder just wouldn't push the bullet faster. You had 50, 58, 64, 72 caliber rifles, and a bunch of others. Big bore rifles continued up until the smokeless powder became popular and then smaller, faster bullets became more common. They started out big with the 8mm and large 30 cals before working down to smaller 30 cals and now to 5.56 and 5.45. The crossbow proves that propellants have always been an issue and limitation
Kentwell Hall, I remember it well! Grew-up in South Suffolk & North Essex 70s-80s. School & family trips to Kentwell were fantastic, it did feel like genuine time travel!
Do a vid talking about how you got into history and all that stuff! Origin stories are interesting! (also: hope you got somewhere warm & dry as soon as you could)
Now we need some heavy crossbow with a very heavy anti-plate bolt for short range penetration testing. Very nice that you've added the draw weight measurement at the end of the video.
It's just crazy to me to think at 230lbs I could hang on that crossbow and it wouldn't even be close to full draw.
That's a good point. Gearing is an amazing invention.
You need to eat more cake, also makes you harder to kidnap.
Some of your plays aren't half bad, can go on a bit, but definitely have potential.
I love the Rainbow in the background as you're doing this.
Oddly, the most important thing that I've learned from this series is the massive importance of the cams in a compound bow. I hadn't considered how much of the bow's energy was consumed by the acceleration of the limbs, and consequently how much difference a reduction in that load would make for the velocity of the arrow/bolt. I wonder if that's part of the reason why increasing the draw weight doesn't help: the bow is expending most of the increased energy into accelerating itself, leaving little to accelerate the arrow. If that's the case, it certainly backs up your theory on the solution: increase the mass of the projectile, such that it accounts for a greater fraction of the load and allows more of the bow's energy to be converted into a useful form.
Finally, it's still very tempting to consider how a cam system with a longer bolt but the same massive draw weight would've looked in terms of late medieval or renaissance technology.
People walking by at 6:48 "Who's the bloke in the funny outfit with the crossbow?"
"Shhhh...That's Tod...Don't make eye contact." 😄👍
oh my, the rainbow in the backgrounds makes it the perfect scenario.
Superb work, scares the shit out of me when you measure the bow pull weight at the end, if that gives way it's going to hurt 🤪
I came to ask a question but after watching this and the mechanics of how it works it was answered so thank you for that
Medival man trying to shoot leprechaun RECOLOURED
This channel continues to be amazing; informative and fun; science and art. I am now looking at some Tod cutlery and will order something shortly. Best advert ever haha.
The heavier bolts will decelerate due to air resistance slower, therefore if you are unable to increase the bolt velocity further you can still increase the range with bolt mass provided you can maintain that high velocity.
also every bolt weight will have its optimal angle for getting maximum range.
As someone who's just taken and interest in bow making and is somewhat of an amateur Bowyer, I actually think your theory is quite sound. In making wood bows there are all sorts of different aspects that make the bow shoot more efficiently with higher fps that wouldn't really apply to a steel limbed crossbow. Wood type, grain alignment, limb design, specific gravity (that varies even within the same species) and just overall build quality and tiller.
I don't know any formal physics at all, but I completely agree with your conclusion, Tod.
If draw weight is a measure of how much energy is stored in a bow, and you observe a non-linear change in the kinetic energy of a projectile with the same weight and ballistic coefficient when shot from bows of different draw weight, the difference must be in the way the bows transfer their stored energy to the projectile.
I'm guessing that the following relationships may play a part (I've probably mixed up terminology, sorry!):
Inertia and other losses within the bow itself (how fast can the bow make the bowstring move when there is no projectile) vs. the inertia and ballistic coefficient of the projectile (if the bowstring is already moving as fast as the bow can make it before the projectile is released, reducing the weight of the projectile won't make it go any faster).
The bow's rate of acceleration vs. its draw-length (how quickly does the unloaded bowstring achieve its peak velocity vs. how the distance over which it is transferring energy to the projectile).
It would be wonderful to be able to visualise a comparison, in a hypothetical sense, of the relative dimensions, behaviors, and terminal ballistics that steel crossbows, timber longbows, and recurve composite bows of 800-1300lb might have.
As always, I love what you do, and thank you so much for your work!
Perfect timing. I needed a short video before nodding off.
You've probably encountered this before, but if not, you should give the wikipedia article on the Maximum Power Transfer Theorem a read. It's about electricity, but it applies to mechanics as well.
To paraphrase, you need to match the resistance of the load to the power source, otherwise the power source is not efficient at transferring power to the load. Or, a big heavy crossbow needs a big heavy bolt to get all the energy out of the limbs.
Something satisfying about shooting arrows and bolts at distance
Great plug for Kentwell!
Black powder is the same way. It's an inefficient propellant and you basically hit diminishing returns with regards to muzzle velocity, so more power largely meant a larger bore size and more projectile mass.
I'd love to see a tutorial how you make that monster spring steel bow of yours in the near future! Amazing video man, keep them coming!
Wow! How strong are you to be able to pick up and wield that 850lb crossbow, so easily?!?!
The weight of this joke is astounding.
@@epauletshark3793 You're really drawing out this joke as far as it will go
Sorry but I didn't get it, it flew right past me
A few questions
first, why weren't the bows wider, with lower draw weight? (i know that a bow the size of a long bow gets unwieldy but double or triple could work)
Second how does the power stroke scale with the bow size(double the bow size double the power stroke).
Double the size half the draw weight equal energy?
Why this could be interesting: easier cocking= higher fire rate.
i dont think bow would be that much more expensive (longer, thinner)
i would love to hear your thoughts
ps: amazing content
Another thing that can have an influence on how far a bolt or arrow travels through the air is your elevation relative to sea level. I know in rugby that the kickers has a much easier time kicking for goal when the match is played at high elevation when compared to near the coast. This is due to higher ambient air pressure at low elevations compared to higher up, which means less overall air resistance on the bolts as they travel. Maybe it's something interesting to keep in mind or to test in the future.
Tod - 12 blunt tip arrows, 6 archers VS knight in full armor (plexiglass over front of helmet), walking towards them for 100 feet / - would love to hear him explain the experience ! ! !
Oh my, did I spot a rainbow in the backgroudn there? :D
Hmm. Maybe the principle in slingshots also applies to crossbows? There is a speed limit with slingshots and the only way to take advantage of the heavier draw weight is to use heavier projectiles. Therefore is is important to match the weight of the projectile to the power of the band. Don't longbows also follow this with rules of thumb stating you should use about 8-10 grains per pound of draw weight?
The electrical engineers call it "impedance matching".
For the annual cottage "shoe kick" event, I taught the kids to experiment to get the "right" weight of shoe for their kick in order to maximize (in this case) distance.
I think you're right with your theory Todd, and from a physics standpoint it's impressive to see it in action.
If we look at Newton's 2nd Law of Forces (F = m*a), then the functional force of the arrow will be intrinsically bound by its weight and the launch capacity of the crossbow. It could also explain the functional limitation of the amount of kinetic energy smaller arrows could absorb, and why said arrows and crossbow sizes had to increase in order to harm more heavily armored targets.
As several others have commented, 45 degrees isn't actually the ideal angle. Love all your videos btw! I show them to my students at times. Optimal angle is I think (if I remember my physics) 35-42% in atmosphere depending on altitude, weather, projectile etc..
"I shot an arrow in the air,
She fell to ground in Berkley Square."
Yikes, how deeply those bolts penetrated in to the soil; which, I assume, is less dense than flesh. This was yet another great video. Thank you for sharing.
Drag will also have a massive effect. IE it's proportional to the speed squared. So a 10% increase in speed which in a vacuum would give you 10% more range, in air makes just a little difference as at launch they have 21% or there abouts more drag. So the additional speed bleeds off very quickly. The other thing to remember is projectiles only follow a parabolic curve in a vacuum. If you compare first graze and first fall on musket tables they are remarkably close together. First graze is where the first shot is likely to hit the top of the head. First Fall is where the first shot is likely to hit the ground. As no army uses volley fire any more (that I know of) these terms are obsolete but the science still holds.
I like your theory, I really hope you can spend some more time investigating it. Testing heavier pound bows with heavier bolts to see what differences in distance and power you can achieve and leading to some really interesting discussions on how these war cross bows were used. Keep up the good work!
Cool stuff Todd! Could you perhaps paint arrows for video tests with neon colors (or maybe even glow-in-the-dark arrows to shoot in the evening) so we can see them shoot?
So this is what Timothy Claypole from 'Rentaghost' gets up to in his later years! Just teasing Tod, I enjoy your vids!
I just want to say that measuring in yards is ok. It's a sensible choice and if we're not being pedantic about exactitude we can just consider them as metros. BTW, great video as always, sir.
Great video, in my research in slings its seems like they heavier the projectile the more damage they do
The big, heavy projectile theory matches what is done in guns with subsonic rounds. You're limited by speed (because you want to keep it effectively suppressible), so, instead, you bump up the weight of the projectile to increase the energy. In fact, for some calibers, density of available materials becomes the limiter; for a round to cycle it needs to fit within certain physical parameters (the bolt built for Skal's crossbow fails on this with this new crossbow), including overall length, so you can only have a projectile that is so big; to add weight you have to add density within that same physical size.
If you take the range the bolt traveled you get an idea of the launch velocity (an idea, because it can't account for wind resistance). For the needle bodkin it says about 46 m/s, while for the crown bolt, only 36.4 m/s. Those can be converted into energy, and there is quite a spread, 69 J for the needle and 105 for the crown bolt. You can also find the energy stored in the crossbow. With a draw length of 288mm and a force of 850 lbf, that means an energy of 544J. So the rest of the energy that doesn't go into the projectile, goes into moving the string and the arms of the bow. For everything except the crown bolt, that is about .45kg (depending on which bolt). For the crown bolt it was 0.66 kg (which means the crown bolt took a much larger hit from drag, not a big surprise). Using a chrono to get exit velocity would allow a better estimate of the dead-weight of the bow, as well as a way to calculate the drag on the different bolts.
My retirement dream job, id totally hang out with this cat every week.
I am a mathematician with some knowledge of physics, and while I can't promise anything, I think your theory is correct. The crossbow is going to launch projectiles at reasonably similar velocities, simply because a lot of the energy goes towards accelerating the limbs (and the string!). As such, a very light projectile would in fact travel less distance due to wind resistance!
Very reasonable hypothesis. With the design, steel limbs and the type of string, it seems likely that crossbows like that will have very similar maximum contraction speeds, due to material limitations. Conceivably then they should have similar max ranges and the main difference between a 850 and a 1200 would be that the latter can shoot a heavier to maximum range.
I always enjoy the videos which, like this one, Tod makes in his back garden.
So, great video (as usual). I started thinking about the holes in the metal socket of the windlass. Are they meant to have a functional use other than perhaps lightening the object? I'm think perhaps to make sure that the thing doesn't get stuck on the crossbow if it gets full of mud or as an egress point for dirt. Kind of like the sand groves on the bolt of an L1A1 SLR (couldn't thik of a better example, sorry)?
Talking of old technology, nice view of the icehouse behind you. Now we all have a metal box in the house that carries out the same function.
"Now we all have a metal box in the house that carries out the same function." What, hiding corpses from Belgium Detectives during early 20th century house parties?
Well done Todd, thanks for sharing.
i always enjoy your videos, even the ones i've already watched.
While shooting them all at the same angle might give results that are easy to compare, but are we sure the optimum angle of flight is the same for each weight of bolt?
Love the rainbow in the background.
Be interesting to see just how hard that Mace on a stick would hit using a force/ G-sensor of some kind. Would not like to get hit by that thing.
Easy done - get a pandulum target. You can directly read out by how much it swings out on impact.
Part medieval, part angle meter on my phone. Love it. amazing how its only been a few hundred years.
Yesssss...all is coming together
Your theory makes sense to me. It's almost like a torque/rpm thing in IC engines.
It looks a great way to work out your arms
That actually would be a good test - take a variety of bow weights and a series of standardized bolt weights. Measure speed at each bow at each draw weight.
If your theory is (and I'm interpreting on this) that the heavier bows were entirely to bring up heavier bolts up to the same speed as the lighter ones could be, and there's a maximum speed achievable that doesn't depend on bow draw, then you should see a consistency with the lighter bolts hitting that limit and the heavier ones travelling faster until they also reach a limit.
A ballistic chronograph would give you the speed but I'm not sure how well the usual firearm ones work on crossbow bolts. I would imagine they should still work.
Post credit scene added to the Tod Cinematic Universe!
Sounds like a very reasonable conclusion there mate.
I was in Berlin not all that long ago when one of the museums was running a crossbow exhibition. It seemed to suggest the later years of the war crossbows were an arms race over plate armour and penetration power crossbows, with crossbows getting heavier along with plate getting thicker.
I have no idea if that brief exhibition aligns with evidence in the production specs of plate and crossbows at the time though. But it seems reasonable that you'd only make such insane bows for a specific reason and super high mass bolts would for pure penetration sounds likely.
I think that is the story, but then the heaviest bows I know of were for hunting - go figure?
Thank you , Tod .
Gotta factor in the aerodynamics of the bolt tip as well. And they probably all cap out at a certain range no matter what the draw weight because of terminal velocity. Just horizontal terminal velocity instead of vertical
Great channel. Man deserve respect for interesting researches. There is some museums were placed some Arabic or Turkish Bows and Crossbows that made from composition materials and with interesting engineering, and it is clear that it all done with the aim to increase speed of projectile. Interesting to see "Ziyyar" that was actually machine used quite sophisticated construction to increase velocity of spear sized bow. Also China archives saved illustrations of machines with combination of several bows, that also served for arrows speed increase.
This phenomenon about the arrow speed/distance is real thing. In bow making there is such a thing as a lighter out shooting a heavier bow using the same arrow. It has to do with the dry fire speed of each bow. The lighter bow usually dry fires faster than the heaver bow do to reduced mass on the limb tips. But the heavier bow will send a heavier arrow just as far or even further than a light bow with a light arrow because it has more residual energy left in the slower moving limbs to transfer to the heavier arrow. It's quite interesting. And you could spend weeks testing the little nuances of it.
loving the yarmulka
Your statement at 8:15, "You can't do it quickly, but you can make it heavy." I think that may have quite a bit of merit. I'm not terribly well versed with historic bows, and especially not crossbows, but I've done a lot of shooting with black powder firearms and a similar limitation exists. Black powder is an explosive, and as such there is more or less a hard limit on the velocity that a projectile can be propelled with it, that limit is about 2100fps (~640m/s) and so what you see with black powder arms is a focus on making larger and larger caliber rounds but maintaining a relatively consistent velocity.
It makes sense to me that once you start to reach the upper limits of what you are capable of speed wise you'd start to make heavier projectiles but retain that same or similar speed.
About the mace arrow, I don't pretend to know anything about this stuff, and I don't shoot at animals. I will ask a question that might be silly. Would a bolt for shooting an animal wanting to preserve its fur not better have a flat surface on the tip and could that non-flat tip be intended to not just glance off the helmet of a cavalry man charging at you?
What would it do to an armoured rider if you hit his helmet at a range of ten meters, could it incapacitate him?
The increase of mass to increase kinetic energy was extremely prevalent in guns prior to the invention of smokeless powder. Before 1886, black powder had a low max velocity so to compensate large caliber bullets were used to compensate. That's why African Safari rifles were often .60 cal (~15 mm) or bigger.