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.
@@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
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.
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'.
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!
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!
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 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.
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.
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.
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
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.
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)
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 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!
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.
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!
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.
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.
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.
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.
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 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!
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.
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.
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!
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.
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 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.
Physics student (second year) here: your explanation for the lack of speed difference between the heavier and lighter drawwheight crossbows seems good. Your firing angle however, is a bit too high. The 45 degree angle is the ideal angle, if there is no wind resistance, in which case the projectile path is a perfect parabola. Wind resistance is proportional to the velocity squared, so it is definetly relevant here. A slightly sharper angle if maybe 41 degrees should give better results, however the exact angle is very difficult to calculate. The path in the extreme case of a super thick atmosphere is more like an upside down hockeystick. This image should help explain why a slightly lower angle is better for fast moving projectiles Excellent video overall
200 yards doesn’t sound impressive at first but then you picture yourself standing at the end of a football field looking down the field and imagine sending a bolt over twice that distance and it suddenly feels much more impressive.
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.
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.
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.
It is obvious that the crossbow is a much more sophisticated and powerful and destructive weapon than what most people, including myself, have learned from ancient history. What is more evident is that the bolts that Tod has fired for long range would have made some very serious injuries on a charging or standing infantry ready or already engaging in warfare.
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 ! ! !
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.
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.
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.
Cantilevered beam stiffness is proportional to its ((width * height^3) / length^3), meanwhile inertia grows proportionally to (width * height * length^3). So ignoring all of the engineering details, as the bow's dimensions grow to make a larger draw weight bow there's definitely going to be diminishing returns. What you'd gain from a more massive bow is exactly what Tod says, a bolt of a given mass becomes a less significant part of the overall inertia of the system.
I think your theorie is correct. It must be the limited speed of the steel throwing limbs. Because they have a certain speedlimit in returning to relaxed position, a 1000lbs crossbow will accelerate a bolt to the same speed as a 500lbs crossbow would. The difference is that the 1000lbs crossbow would be able to shoot a much heavier bolt, without the bolt loosing speed.
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.
So apparently people were talking about how 45° isn't actually as efficient as possible based on air resistance but at least your results were measured consistent
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?
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.
You should try 35-45 degree launch angles with same bolt. Optimal launch angle will vary,depending on the ballistic coefficient of the bolt, but it will be always UNDER 45 degrees. Unless you shoot in a vacuum. The more drag, the less elevation is optimal for maximum distance. I'd estimate about 38-40 degrees optimal launch angle for a tipical bolt for max distance.
Just an FYI: The optimal angle for shooting is not actually 45°, but closer to 30° or even 20°, depending on the shape of your projectile. Reason being that 45° is only the best angle in a perfect vacuum. But due to drag losses you want a bit more forward than upward momentum. That said, for a rough comparison 45° does good enough.
I shot an arrow in the air, It fell to earth, I knew not where; But, strangely, at my journey's end, I found it again in the neck of a friend. Misattributed to Longfellow
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.
