Medieval bolt POWER!

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  • Опубліковано 5 жов 2024
  • Heavy crossbows can shoot heavy bolts; but how heavy? I have conducted a distance trial, but now I measure them with a chronograph and give all the data tables..........Then I swap out the old string for a lighter one and amazingly the bow starts to break the laws of physics!!!
    Videos I refer to
    850lbs crossbow distance trial • 850lbs Crossbow DISTAN...
    How to string a medieval crossbow • How to string a mediev...
    Assembling bow wedges • Assembling bow irons o...
    If you would like to support this channel, visiting my sites really helps as does signing up to the news letter on the websites, either one is fine
    Production replica weapons are available here todcutler.com​​
    And T shirts and Merch todsworkshop.c...
    Custom pieces and crossbows are available here todsworkshop.com
    Crossbow and bolts are made by me at todsworkshop.c...

КОМЕНТАРІ • 578

  • @sindarpeacheyeisacommie8688
    @sindarpeacheyeisacommie8688 3 роки тому +106

    It pleases me that, somewhere in the world, there is a man with crossbows willing to answer all the questions I've ever had about their use and operation. He even answers questions I never would have thought up.

    • @breembo
      @breembo 3 роки тому +1

      He is pretty great. Once I can afford to send a comission his way I will. I hope he is willing to do a cinqueda.

    • @rileyernst9086
      @rileyernst9086 3 роки тому

      Can it propel a pommel to devastating effect?
      You bet it can!

    • @rileyernst9086
      @rileyernst9086 3 роки тому

      @@breembo I've got 2 Tod Cutler daggers, they're nice and am considering a commission when he starts taking them again. A late14th century falchion would be more my jam.

    • @breembo
      @breembo 3 роки тому

      @@rileyernst9086 oh a falchion is definitely #2 on my list as well. I just hope his turn around time isnt 2 years like my cedarlore forge sword was.

  • @tlsgrz6194
    @tlsgrz6194 3 роки тому +92

    I just realized, that the steel bow on the crossbow is heavier than a longswords

    • @euansmith3699
      @euansmith3699 3 роки тому +35

      I find stuff like this a real eye-opener when looking at how much great characters in fiction lug around while sneaking past guards and scaling castle walls.

    • @tods_workshop
      @tods_workshop  3 роки тому +34

      I found it interesting, as I have neither weighed it either, I just knew it was heavy

  • @nathansears5257
    @nathansears5257 3 роки тому +63

    I love that at some point Tod goes to himself "I really got to be more enthusiastic"

    • @tods_workshop
      @tods_workshop  3 роки тому +36

      I started standing up - simple as that

    • @svensorensen7693
      @svensorensen7693 3 роки тому +7

      @@tods_workshop I've been going through your old videos and noticed the difference, been meaning to ask about it for a while.
      I guess sometimes the simple things make a big difference.

    • @ptonpc
      @ptonpc 3 роки тому +5

      @@tods_workshop I always put it down to you not being used to talking to camera. I seem to remember Jill Bearup talking about this, it's hard to get emotions across a lot.

    • @Bravohalo
      @Bravohalo 3 роки тому +4

      I really noticed when you started getting excited about things.

    • @edwardlazell3157
      @edwardlazell3157 3 роки тому +1

      I had nothing against Tod's quieter style. It was obvious there was no lack of enthusiasm there.
      Not that I mind his animated "let's shoot stuff!" lockdown pick-me-ups :-)

  • @IPostSwords
    @IPostSwords 3 роки тому +198

    "a fistfull of bolts", the highly awaited sequel to "a fistfull of dollars". Now with 100% more crossbows, but 100% less revolvers

    • @euansmith3699
      @euansmith3699 3 роки тому +16

      Having a scene, in which three rival Condottieri face each other across a piazza, attempting to draw their crossbows with windlasses, and get of the first shot, while Morricone's, "The Triple Duel", booms out of the speakers; that would be awesome. Of course, Tuco would find that Blonde had tied a knot in his windlass string while they slept the night before.

    • @daveh3997
      @daveh3997 3 роки тому +5

      "Dost thou feel fortunate, varlet?"
      (I know--wrong movie. But I couldn't resist . . .)

    • @euansmith3699
      @euansmith3699 3 роки тому +8

      @cable "Verily, it is a commonly held belief, that there be just two types of spurs in this wicked world; those that entereth the chamber by the portal [crosses himself], and those that doth risk defenestration."
      Tuco Ramirez, 1526, near Governolo

    • @undefined40
      @undefined40 3 роки тому +1

      Unless someone invents a crossbow with a revolving bolt magazine. Remember that 2004 van Helsing movie? I bet if Tod and Adam Savage work together, they can make that contraption real.

    • @daveh3997
      @daveh3997 3 роки тому +2

      @@undefined40 Sounds like a job for Jörg Sprave.

  • @patrickhuffman9632
    @patrickhuffman9632 3 роки тому +186

    The conclusion I draw: wouldn't want to get shot with any of them!

    • @larrygonzalez4375
      @larrygonzalez4375 3 роки тому +6

      Or get smacked in the head with the crossbow!

    • @Levermonkey
      @Levermonkey 3 роки тому +5

      Quite happy to be living in an age without bands of psychopaths armed with these running about.

    • @the-thane
      @the-thane 3 роки тому +4

      Now we only have to worry about psychopaths with firearms and knives running around

    • @Duiker36
      @Duiker36 3 роки тому +6

      Hey now, don't talk about American police that way. They have feelings which are very fragile.

    • @ShadowDragon8685
      @ShadowDragon8685 3 роки тому +1

      @@Duiker36 Am American. Am sad to say that our cops resemble that remark to an alarming degree.

  • @entropy11
    @entropy11 3 роки тому +56

    "crown bolt, a flying mace"
    more like a flying pommel right

    • @helloarigato
      @helloarigato 3 роки тому +5

      No, he did that in another film:
      ua-cam.com/video/hU7KJ83MfWs/v-deo.html

    • @penttikoivuniemi2146
      @penttikoivuniemi2146 3 роки тому

      Maces and pommels are actually pretty similar to one another. Unless of course we are talking about flanged maces or other more special types.

    • @ShadowDragon8685
      @ShadowDragon8685 3 роки тому +3

      No, because he actually made an END HIM RIGHTLY bolt that was like Crown Bolt++

  • @benallthetime
    @benallthetime 3 роки тому +69

    I found this channel about a week ago. I've pretty much watched everything. I regret nothing

    • @PalleRasmussen
      @PalleRasmussen 3 роки тому +7

      You would want to have a beer with Todd.

    • @benallthetime
      @benallthetime 3 роки тому +3

      @Jill Atherton I've got a BA and MA in Medieval History, and if this had been around when I was studying, I would have lost my mind

    • @benallthetime
      @benallthetime 3 роки тому +2

      @@PalleRasmussen 100% yes

    • @esoel
      @esoel 3 роки тому +2

      Welcome to the channel!

    • @tods_workshop
      @tods_workshop  3 роки тому +13

      Welcome aboard!

  • @mikurusagawa6897
    @mikurusagawa6897 3 роки тому +8

    Last time I was this early the GoPro was still working

  • @theMindwalker
    @theMindwalker 3 роки тому +37

    Man. I wish highschool would have had a class like this.

    • @Flummiification
      @Flummiification 3 роки тому +5

      I mean it's basically history, isn't it?
      And Physics...

    • @lwilton
      @lwilton 3 роки тому +3

      When I went to high school, the physics teacher did spend 20 minutes or so on bows and bolts, as an aside from the couple days on artillery shells and how they fly and are affected by things like air resistance and the rotation of the earth. But that was over 50 years ago, and I'm pretty sure things have changed in education practices since then.

    • @aaronluna4341
      @aaronluna4341 3 роки тому +2

      Yeah, we would have a blast.

    • @tods_workshop
      @tods_workshop  3 роки тому +13

      Flummification...and I loved both at school and was not great at either

    • @aaronluna4341
      @aaronluna4341 3 роки тому +2

      @@tods_workshop all this is just fascinating, isn’t it. It’s the reason why you make your videos and the reason we watch your videos. Weaponology, as I call it. I look forward to your videos and so does thousands of other people.

  • @Stevarooni
    @Stevarooni 3 роки тому +30

    Kudos to your editor. The stats for your shots being on-screen are a very nice touch. 😊👍

    • @tods_workshop
      @tods_workshop  3 роки тому +18

      Much appreciated! I will pass it on

  • @QuantumHistorian
    @QuantumHistorian 3 роки тому +9

    A possible explanation for why the lighter string gives less power: It's stretchier than the heavy string. So for the same draw distance you get more string stretching and less steel bending, meaning you have a lighter draw weight and less power. It's exactly the same impact has having a longer string, but not visible until you pull the bow back. Can this be something you measure in your workshop?

    • @lscibor
      @lscibor 3 роки тому +2

      Yeah, it's very possible that the 140 g string was just a bit too weak, so it stretched immediately, Tod's says it's probably ended up bit too long at around 6:30

    • @QuantumHistorian
      @QuantumHistorian 3 роки тому +3

      @@lscibor I thought he said that it might have always been longer? Either way, measuring the draw weight at full extension with both strings would be very interesting and resolve this quandary!

    • @kovona
      @kovona 3 роки тому

      @@QuantumHistorian Longer string will make for a lower brace height, which does reduce the potential release velocity in a bow.

    • @QuantumHistorian
      @QuantumHistorian 3 роки тому

      @@kovona Yes, obviously, nobody disagreed with that. The question is if the string is longer at rest, or only under tension.

    • @jonathan_60503
      @jonathan_60503 3 роки тому +3

      @@QuantumHistorian Even measuring that might not fully capture the issues at play; depending on whether its and issue of length at rest or an issue of string stretch. If the lighter string just happened to be fractionally longer, but no stretchier, then your draw weight measurement idea should tell the tale. But If the lighter string has more stretch to it then I'd both static and dynamic stretching; and a draw weight test would only capture the former. Because if the string stretches even more once the trigger's pulled and it's accelerating the bolt then that'd be a further reduction in energy transfer compared to whatever the draw weight test showed.

  • @martinbonniciphotography
    @martinbonniciphotography 3 роки тому +23

    Absolutely loving these videos. Thanks for making them and showing us the results.

  • @rkond
    @rkond 3 роки тому +13

    When comparing weighs of a bow, a string and a bolt one has to take into account relative mechanical advantage in the system. The ends of a bow move twice as slow as a bolt does. And the center of a bow doesn’t move at all. So the effective mass of the bow would be about 1/5 of it’s real mass. For the string it’s something like 3/4 of it’s real mass. The bow is still the most relevant part. But one has to be careful comparing the masses like this.

    • @2bingtim
      @2bingtim 3 роки тому

      Excellent point.

  • @Chasmodius
    @Chasmodius 3 роки тому +9

    I love the pronunciation of "parabellum." That's one I've not heard before.

    • @aarongreatrex-sweeney4954
      @aarongreatrex-sweeney4954 3 роки тому

      I don't think it's right. Sounds like he's pronouncing it similarly to parabola instead of para bellum

    • @Chasmodius
      @Chasmodius 3 роки тому +3

      @@aarongreatrex-sweeney4954 Probably not, but he's pronouncing it within the allowances of the rules of English pronunciation (which are VERY wide!), and we understood what word he was saying, so it's as "right" as it needs to be.

    • @tods_workshop
      @tods_workshop  3 роки тому +5

      Actually I am not a gun guy, so it was actually spelled differently to what I thought and so here we are

    • @ShadowDragon8685
      @ShadowDragon8685 3 роки тому +3

      @@tods_workshop It's cool to learn new stuff though, innit?
      It took me a few moments to get "wait, what did he mean there? Oh!" when you said that.
      "Parabellum", as in the proper name of the firearm cartridge, is a hell of a word because it's an English portmanteau of the _Latin_ words _"para bellum,"_ shortened from the phrase _si vic pacem, para bellum;_ if you seek peace, prepare for war. And of course there's all the wonderfully confusing malarkey about _how_ to pronounce Latin in the first place! So it's totally understandable that someone who didn't know it was "Para-Bellum" would look at it, immediately liken it to "Parabola," and pronounce it that way.

  • @StormEngineer
    @StormEngineer 3 роки тому +1

    I love experimental archeology. Nothing beats actually trying stuff out for real.

  • @budahbaba7856
    @budahbaba7856 3 роки тому +5

    Thank you for addressing this question, because from the arm chair i have often argued with other YT users about this! :) Love to you from across the Pond, Todd.

    • @tods_workshop
      @tods_workshop  3 роки тому +5

      The whole point of this stuff is so that we have some hard information rather than just speculation, so glad it is proving useful

  • @MrFmiller
    @MrFmiller 3 роки тому +1

    I appreciate how thorough and comprehensive your analysis is.

  • @mjfleming319
    @mjfleming319 3 роки тому +5

    So much fun and so much learning...thank you, Tod! Also, cant wait to see you tenderize a leg of lamb with the flying mace :)

  • @Kokoonutz
    @Kokoonutz 3 роки тому +7

    Could you make a medieval style crossbow with a metal bow ,but with a high draw length ,with it still being safe to the user?

    • @ultranium7414
      @ultranium7414 3 роки тому +3

      A cross bow made from a 200lb composite bow is better.
      Long draw length steel ,means long limbs.
      Long steel limbs=super heavy.

    • @Kokoonutz
      @Kokoonutz 3 роки тому

      i still wanna know

    • @Kokoonutz
      @Kokoonutz 3 роки тому

      Can you go long with short metal limbs?

    • @Kokoonutz
      @Kokoonutz 3 роки тому

      If so then how much untill its not safe

    • @ultranium7414
      @ultranium7414 3 роки тому

      @@Kokoonutz I cant know the limit, if you want a steel short limb long draw you will need a really springy steel,and a really strong chassis. It will be super hard to make if not impossible.

  • @MikeMaragni
    @MikeMaragni 3 роки тому +20

    I should be studying accounting, but this is honestly just morr interesting

    • @mithrandir6283
      @mithrandir6283 3 роки тому +1

      Maybe you should concentrate a wee bit, Lad. Because if do, you can go ahead and learn how to spell “more” correctly.
      PS: please read this with a Scottish accent, cause then it would sound like I’m talking directly to you.
      leis gach deagh dhùrachd, Mithrandir.

    • @simonmorris4226
      @simonmorris4226 3 роки тому +1

      If you are carrying a loaded crossbow the accountant will sign off anything you tell him to..................

    • @cykikvisage
      @cykikvisage 3 роки тому

      Maybe you should change your major to metallurgy.

    • @simonmorris4226
      @simonmorris4226 3 роки тому

      @@cykikvisage or better still engineering!

    • @michaeljohnston6811
      @michaeljohnston6811 3 роки тому

      @@simonmorris4226 As an accountant myself I have found that my curiosity was a blessing more than a curse. Although if you are pointing the crossbow at me then I confirm that I will temper my curiosity about the effect it might have on my physical (and other) integrity.

  • @TheOhgodineedaname
    @TheOhgodineedaname 3 роки тому +6

    Been waiting for this video for years!
    With regards to the string, a possibility is that a heavier mass is more effective at energy transferal.
    Heavy mass accelerating heavy mass = lots of energy transferred
    Lighter mass accelerating heavy mass = less energy transferred
    A heavy string would accelerate slower meaning the acceleration phase is longer.

  • @riffhurricane
    @riffhurricane 3 роки тому +16

    Loving these videos Tod. You (along with Ranch Fairy who's big into heavy, high FOC arrows) have inspired me to build the heaviest bolts I can for my (modern) crossbow to see the difference. Not hunting with them as I'm in the UK, but an interesting experiment all the same.

    • @garrettevans8863
      @garrettevans8863 3 роки тому

      I would highly recommend Tuffhead products, (which if you watch Ranch Fairy you’re probably already familiar with them) as they offer a wide variety of high-FOC heads and points. You should give their 400 grain dangerous game heads a try, they really have some punch! Also, if you’ve got a higher budget in mind Bishop archery makes broadheads and points in the 500-600 grain range, but unfortunately they have priced their products insanely high. Hope this information helps, and good shooting! 🏹👍

    • @riffhurricane
      @riffhurricane 3 роки тому

      @@garrettevans8863 Cheers Garrett! I am actually about to order some of the Tuffheads (+ inserts). Sadly they have to be shipped over here from the US so I'll have a little wait. I'll check out the Bishops also - I've heard them mentioned before.

  • @Bravohalo
    @Bravohalo 3 роки тому +2

    The crown bolt is not just a big load, it's going to have a really efficient energy transfer and low penetration. Should drop things really fast with minimal damage to meat/hide.

  • @peterlively8269
    @peterlively8269 3 роки тому +5

    The engineer in me loves these videos. I also think it would be great in a physics class. It teaches a lot of very important things, design of experiment, hypothesis, statistics, etc. You should take you gear to a local school!

    • @tods_workshop
      @tods_workshop  3 роки тому +2

      For the record I used to have an inspirational physics teacher who would have loved this approach - Bob Pomeroy. Amazing man

    • @stewartsherwood7769
      @stewartsherwood7769 3 роки тому +1

      Just make sure you get their permission first! 😀

  • @sandrosliske
    @sandrosliske 3 роки тому +14

    Thank you to whoever is responsible for the subtitles.

  • @somedane8879
    @somedane8879 3 роки тому +17

    I think the one of the reasons the heavy bolt is slower, is because it has a less aerodynamic tip. I'd recommend putting a pointier head on the heavy bolt and see what happens

    • @ArmouryTerrain
      @ArmouryTerrain 3 роки тому +5

      while it would be an interesting experiment, it would no longer be a historical bolt meant for hunting and not penetration.

    • @DirtyRobot
      @DirtyRobot 3 роки тому

      So, the system has x amount of energy it can give up. If you add more mass then the energy is offset by the mass.
      Think of yourself throwing increasingly more massive rocks. As the mass gets larger the distance gets smaller. Same energy, different outcome.
      I strongly recommend that you enjoy some basic physics demonstrations as they can be a very helpful tool to understand what many people take for granted.

    • @kovona
      @kovona 3 роки тому +2

      Negible effect at such a short range, mass has more to do with it. E=½mv²

    • @ABaumstumpf
      @ABaumstumpf 3 роки тому +1

      The Crono is very close by, so there is little distance for the bolt to decelerate. Then also the bolt is heavier and not as fast - so even a bit less drag. And it is heavier, so while the air-resistance is certainly higher, the extra mass means it will still not slow down as fast.
      To put that to extremes:
      A Feather as less air-resistance than a car, yet even at just 50 km/h a car could be shot way further than a feather at 200 km/h.

    • @tods_workshop
      @tods_workshop  3 роки тому

      Some dane. Baum stumpff has it

  • @michiganengineer8621
    @michiganengineer8621 3 роки тому +1

    It would be interesting to see the 3 war bolts with the same style head on them. I'm sure you'd have to add weights to get them the same as with the different heads.

  • @billrock6734
    @billrock6734 3 роки тому +5

    The thinner string is more elastic and thus stretches further when being cocked,it's this that produces less bending of the bow and thus the poorer performance on being shot.

    • @tods_workshop
      @tods_workshop  3 роки тому

      as far as I know natural plant fibres aren't elastic

    • @wmyst1797
      @wmyst1797 3 роки тому +1

      @@tods_workshop Everything's elastic to some extent. But the tensile stiffness of the string _may_ be much higher than the bending stiffness of the bow, in which case it wouldn't make much difference. You could measure this.

    • @billrock6734
      @billrock6734 3 роки тому

      You could try getting two strings of identical length but different diameters and hang two weights on them and see what happens.@@tods_workshop

  • @InSanic13
    @InSanic13 3 роки тому +1

    Interesting fact; this 850lb crossbow got a very similar performance with a 93g bolt compared to the 960llb crossbow you tested a while back with a 90g bolt. The 960 had the same momentum, 4 more joules, and 2 more meters/second.

    • @tods_workshop
      @tods_workshop  3 роки тому +1

      Pretty similar weights for all parts to be honest, so at least its consistent

  • @gerardbryant4840
    @gerardbryant4840 3 роки тому +27

    Tod: "It's Tod at Tod's workshop here!"
    Target: "Oh, this is going to hurt."
    Actually, I've always wondered how they strung a crossbow.

    • @euansmith3699
      @euansmith3699 3 роки тому

      I wonder if there was another way of stringing a crossbow; or if, armies on campaign had a cart kitted out with various rigs necessary to maintain the army's weapons.

    • @lwilton
      @lwilton 3 роки тому

      @@euansmith3699 There was certainly an armorer's cart (or several) as part of the train of any substantial army. What exactly was in it would have varied with the army and age, but for most of history you can assume it would be a combination of a blacksmith's shop and a woodshop. I would also suspect there were field expedient methods of restringing a crossbow, since you likely didn't have a lot of spare bows when you were in the middle of a battle or seige.

    • @euansmith3699
      @euansmith3699 3 роки тому

      @@lwilton Especially during sieges, I guess, as those crossbow strings are going to come under a lot of repeated use.

    • @timberwolf1575
      @timberwolf1575 3 роки тому

      It's worth keeping in mind that you have a lot of men with little to do other than work at menial tasks most of the time. This gives you a huge reservoir of ability to make a bunch of field expedient pieces via a bunch of guys whittling the appropriate bits. At the end of the day, you could just get a couple of men, some rope, and a couple of closely spaced stakes or tree trunks to wedge the bow against while the men use the rope to pull the round side the bow against the trees. Enough men (or a draft horse) and even some of those HEAVY bows could be worked with in relative ease.

  • @Ghostselkie
    @Ghostselkie 3 роки тому +6

    This crossbows are just awesome.

  • @Kanner111
    @Kanner111 3 роки тому +1

    'Heavy Bolt' just sounds badass, even.

  • @exploatores
    @exploatores 3 роки тому +4

    Kind of looks like it would be intresting to test a even heavyer bolt.

  • @seth6059
    @seth6059 3 роки тому +1

    I would love to see another collaboration where Joerg Sprave, from The Slingshot Channel, tests your swords and daggers on a ballistics' jell dummy. That would be awesome!

  • @Eulemunin
    @Eulemunin 3 роки тому

    Short power stroke mean that any variation is magnified. Lovely as always.

    • @tods_workshop
      @tods_workshop  3 роки тому

      Yes I never really considered it like that before

  • @Freakismsyndrom
    @Freakismsyndrom 3 роки тому

    i read on a trad bow forum something like: not to think about the limbs transfering energy into the arrow, but about the arrow sucking energy from the limbs! To resist the limbs bending back to neutral you need an opposing force, that is inertia. Basically heavy stuff resists efforts to change its velocity. In moving objects its often called momentum.
    So a heavier bolt will always absorb a higher % of the energy stored in the limbs than a lighter bolt, because it resists the limbs for longer due to its higher inertia, giving it more time to absorb their energy.
    Regarding the string:
    If we compare the kinetic energy of each type of bolt, we can determine that the crossbow has at LEAST 4% less energy stored with the longer (lighter) string. That is assuming that the lighter string does not change limb efficiency, which it definitely WOULD.
    I think the lighter string being longer actually diminished the amount of energy stored in the limbs FAR more. Here is why:
    Lets assume during the shot the string at the nock doesnt move, and the string at the height of the bolt moves as far as the bolt, a bit like a rubber band. If the mass of the string is evenly distributed as you move along the string from nock to nock, the mass of the string moves half as far as the bolt does during the shot. That means the mass of the string moves at half the speed of the bolt at any given time. That means it carries half the momentum a bolt of the same weight would, as momentum=mass*velocity. Meaning a 80g bolt + 140g string have about the same combined inertia as a 60 g bolt + 180g string acting on the limbs, and would be draining the same amount of energy from the limbs, and would be shot at the same speed.
    That means a lighter string of the same length should cast the 80g bolt about as fast as the 60g bolt shot with the heavy string, giving it 16% more energy and bumping it up to 4.4 kg*m/s. So a 10% increase in momentum aka penetration power.***
    ***Assuming my simplifications werent too sacrilegious.
    Regardless of my quick maths, Im quite confident you could have lost 10% of total energy stored in the limbs.

  • @loupiscanis9449
    @loupiscanis9449 3 роки тому

    Thank you , Tod .

  • @russmitchell3806
    @russmitchell3806 3 роки тому

    Those are astonishing numbers.

  • @strydyrhellzrydyr1345
    @strydyrhellzrydyr1345 3 роки тому

    Great test Todd.. solidly laid out and we'll understood

  • @heitorp.c.1327
    @heitorp.c.1327 3 роки тому +1

    Your videos are always really positive for desenvolving questions and building experiments about the subject, lovely! Thank you!

  • @Daniels_unique_YouTube_alias
    @Daniels_unique_YouTube_alias 3 роки тому +8

    With energy and momentum being the highest on that blunt thicc one, I would like to see its performance with a normal botkin tip on armor or wooden doors. And make one rediculous heavy, like 400 grams and look if energy tranfer goes down again, currently it simply goes up with weight, but it would be nice to see what that strong bow can move, and when its power hits a border.

    • @tods_workshop
      @tods_workshop  3 роки тому +3

      how about 510g? try this one ua-cam.com/video/hU7KJ83MfWs/v-deo.html

    • @Daniels_unique_YouTube_alias
      @Daniels_unique_YouTube_alias 3 роки тому +2

      @@tods_workshop Yes, i saw that one. Sadly no Chrono to compare it to the other bolts, and since it is blunt, I don't know how effective a 'sharp' version (please mount a spearhead on a bolt 😅) would be compared to the 90ish grams bolts. Since crossbows are not the most mobile and range-defining things, i wonder if a 'breach commando' could have used some rediculous bolts like that, as range would be neglectable and pure energy transfer is all you need sometimes. (Full metal bolts perhaps? They probably are not as top heavy as the pommel one...)

    • @YouPlague
      @YouPlague 3 роки тому +1

      That one is thicker, so more metal would need to be bent and the four 'cuts/leaves' would need to be longer, so I would think there would be diminishing returns. But having numbers to prove that would be sweet.

    • @Daniels_unique_YouTube_alias
      @Daniels_unique_YouTube_alias 3 роки тому +1

      @@YouPlague agreed, and seeing the smile on Tod's face when shooting something rediculous is priceless as well 🤣

  • @johnbeauvais3159
    @johnbeauvais3159 3 роки тому

    I’m very pleased to learn what the historical meaning of bastard was and how it applies.
    I know that high velocity stabbing would really be unpleasant, but I’d be way more scared of seeing one of those crown bolts flying through the air around me.

  • @Subcomandante73
    @Subcomandante73 3 роки тому +3

    £850 bow? I thought a hand crafted historical replica would be more expensive.

    • @dbKneecapped
      @dbKneecapped 3 роки тому +1

      850 lbs. Draw weight, not currency.

    • @M0T0M451
      @M0T0M451 3 роки тому +1

      lbs (draw weight), not £ (value)

    • @InSanic13
      @InSanic13 3 роки тому +4

      A couple of his lighter "munitions" crossbows sell for around £830; this sells for about £2400.

  • @henrymarris8832
    @henrymarris8832 3 роки тому +2

    started the video and couldnt stop laughing at the T-shirt, Love it! and loved this eagerly awaited follow up on the bolt distance vid! keep them coming!

  • @juanixinauj
    @juanixinauj 3 роки тому

    I love this sort of content and I'm so very happy to see numbers explaining the mechanics going on with shooting bolts. When you shot using the lighter string and you got less velocity, at first I was very surprised. After you proposed an explanation, it all became clear. Now it seems quite obvious that if the final string length varies (with crossbow drawn), the bow will be differently deflected, affecting the deformation energy it's storing before release. And I say final length, because the string can be longer or shorter, but also more or less elastic. Accounting for this might be out of the scope of these videos, I think, but it's probably good to know for a better understanding of the whole thing.
    In any case, cheers!

  • @tanfosbery1153
    @tanfosbery1153 3 роки тому +2

    Would be interesting to know the retained velocity and energy of the bolts at 100 yards

  • @AxDhan
    @AxDhan 3 роки тому +6

    you should consider doing your test by triplicate, three times the same thing and average your results.

    • @chubbymoth5810
      @chubbymoth5810 3 роки тому

      I was thinking the same thing. But it will take a lot more time to retrieve the bolt and shoot again.

    • @johndowe7003
      @johndowe7003 3 роки тому

      @@chubbymoth5810 gotta use more bolts or get a helper

    • @tods_workshop
      @tods_workshop  3 роки тому

      Yes I should, but to be honest that would improve accuracy of results, but would still be very very far from good statistical set and ~I simply don't have the time, so I figure either 1 or three shots depending is good enough to illustrate the point which is all I am really trying to do

  • @bbotelhoHI
    @bbotelhoHI 3 роки тому

    I love the fact that Todd is conducting these tests purely for the pursuit of knowledge.

  • @zethron1173
    @zethron1173 3 роки тому

    If the lighter bolt was made at Tods Workshop, damn right it has more power!

  • @bostonrailfan2427
    @bostonrailfan2427 3 роки тому +1

    lighter bot = faster speed, faster speed = more impactful
    basic physics at work

    • @bostonrailfan2427
      @bostonrailfan2427 3 роки тому

      @@JorgTheElder the point impacts faster leading to more penetration allowing the mass to do more damage. it’s why modern tank shells fire a smaller arrow-like bolt than a large bullet-like shell, the force to penetrate is less but it also goes deeper and causes more damage on the backside of the point of entry: like flesh and body parts

  • @hitobite
    @hitobite 3 роки тому

    Changing the string had the biggest difference for the heavy bolt.
    That makes sense: if the lighter string is more elastic (reduces the force), then there should be less energy in the bow. We don't see this for the lighter bolt, since the weight of the string starts having a bigger influence.

  • @Mishkola
    @Mishkola 3 роки тому

    my answer before watching the video: to the degree that making the bolt lighter makes the bolt faster, it should be the case that lighter bolts have more energy. The relationship between energy and mass is linear, but the relationship between energy and velocity is a curve.

  • @parallaxe5394
    @parallaxe5394 3 роки тому +1

    Hello. Tod from my observation and background (material science) it seems that the main limitation of xbows is the elasticity (rate of deformation) of the metal bow. Depending on the metal (or other material) a vast amount of the stored energy in the bow is lost to internal friction and the maximum deformation speed also limits the maximum speed the bolt can reach. Because of this the lighter bolts only move a bit faster than heavier bolts.
    If you would really put money into R&D I bet you could design a modern xbow with terrifying power and momentum. But at the same time we have fully automatic firearms, so nobody will put down the money for such an adventure.

    • @parallaxe5394
      @parallaxe5394 3 роки тому

      @Michael Smith Hello. I set the performance of the bolt as standard for the comparison. Of course there are ways to improve the bolt too. My main focus was the xbow and why the lighter bolts did not show a far greater speed.
      Modern xbows solve a lot of these problems already (I'm aware of that) but they are doing this with more or less basic materials. CFRP's are by today's standard basic materials by the way.
      Besides that Michael your intuition was not wrong, the effects you describe are important too and are based on material properties and mechanical solutions. It takes a whole bunch of different engineers and technicians to produce a top rated product.

  • @louisfkoorts5590
    @louisfkoorts5590 3 роки тому

    Thanks Tod. 👋🏻

  • @trexfishtec7375
    @trexfishtec7375 3 роки тому +1

    Interesting theory. With air guns usually the heavier projectile the more power due to the extra time the heavier projectile has under load before leaving the weapon. In airsoft we call this joule creap

  • @PeterGriffin-gh8dz
    @PeterGriffin-gh8dz 3 роки тому

    I am for real making a 4000+ pound Crossbow this winter... wish me luck. I need it !

  • @RC-bl2pm
    @RC-bl2pm 3 роки тому

    food for thought:
    no mention here of sectional density.
    Energy and momentum are part of terminal ballistics but only part of the story...
    A fastball and a .22 round have samey energies but different effects on target.
    Higher energies would matter more on the blunts you have there.
    Rifle shooters have argued energy versus penetration basically the whole time.
    Don't get all worked up like them but it might be good to take sectional density into account.
    fun study thanks for the video.

  • @Novum_YT
    @Novum_YT 3 роки тому +1

    Tod - I'd love to see you do a theory video on how medieval warfare would have been altered if they had compound bow technology.

  • @exoterric
    @exoterric 3 роки тому

    Don't ever stop.

  • @wumbumtm3138
    @wumbumtm3138 3 роки тому +1

    That crown bolt has to be the most painful looking bolt i've seen on this channel

  • @shaidrim
    @shaidrim 3 роки тому +4

    Your videos are always so informative. I really love them. But seeing all the numbers you have provided with your vids, I started to wonder why crossbow are considered so much more powerful than bows. Easier to use I can understand, but talking about speed and energy, they looks very close to bows, if not inferior. Am I missing something?

    • @thomasjackson8737
      @thomasjackson8737 3 роки тому

      I think you have hit on something here. Per time period, I do not think there would be much difference in power between bows and crossbows, but crossbows could throw a heavier weight? I will have to go back to lockdown longbow vids to see the arrow weights, but even then not all armies used longbows, so the difference in projectile weight and energy transfer may have been a larger factor.

    • @ziggarillo
      @ziggarillo 3 роки тому +2

      You're not missing anything, you need to practice for years and build up very specific muscles to shoot a warbow, you just have to wind up a windlass on a crossbow and point.

    • @shaidrim
      @shaidrim 3 роки тому +1

      @@thomasjackson8737 that’s interesting. I will check darts and arrow weight again too, ‘cos energy wise they didn’t look so different. But your point could answer why crossbows were considered the most powerful between the two

    • @shaidrim
      @shaidrim 3 роки тому

      @@ziggarillo yeah, easiness of use was clearly the main advantage of crossbows, even if genovese men had a mandatory training requirement like the english bowmen had (meaning they were highly trained soldiers and not some peasants levy troops of sort)

    • @lscibor
      @lscibor 3 роки тому +2

      Generally those crossbows with huge draw weight but very short draw length are one piece of puzzle available to us.
      Probably because they're best preserved in museums, collections, etc. and best studied.
      But they are obviously limited design, because they just can't store than much energy when they're being bent just by about 6 inches.
      So I suspect they're quite misleading.
      Take a look at this magnificent bows by Andreas Bichler, it's about 1200 pounds, like one of Todd's crossbows. It has about 15 inches of draw lenght instead though, so energy ends up being 3 times higher.
      ua-cam.com/video/AA5M0QKXtWU/v-deo.html

  • @rjeffm1
    @rjeffm1 3 роки тому +1

    A interesting test would be to see how fast the bow can move an effectively weightless string. Perhaps use a string made of kevlar or similar very light modern material with effectively no stretch, or measure the movement of the bow with no string at all - that might need a fancy jig, measuring kit, and
    some equally fancy math. This would establish the limiting velocity of the steel bow itself.

    • @ScottKenny1978
      @ScottKenny1978 3 роки тому

      You'd have to use a very light string, dry firing a bow is a quick way to break it.

  • @Grand-Massive
    @Grand-Massive 3 роки тому

    It seems like you should choose your bolt based on distance, using heavier and heavier projectiles the closer the enemy/target gets

  • @simonbrooke4065
    @simonbrooke4065 3 роки тому +2

    I think I made a similar comment when you posted your range tests on these bolts, but I'd be very interested to see the results of a bolt as heavy as your crown bolt but a deliberately aerodynamic shape. I suspect what kills the range on it is air drag. I also (for the same reason) wonder what difference polishing or varnishing the bolts might make.

  • @arasin.staubly
    @arasin.staubly 3 роки тому +2

    "...through the chronograph..."
    ...might be another set of famous last words....

    • @tods_workshop
      @tods_workshop  3 роки тому +1

      Already did for it with a sling and took out the shields

    • @ScottKenny1978
      @ScottKenny1978 3 роки тому

      Yeah, I snickered at that.
      People shoot a chronograph on a regular basis.

  • @stanpotter7764
    @stanpotter7764 3 роки тому

    The heaviest bolt has the same K.E. as a 100 mph fastball in baseball, but focused into a much smaller surface area. Ouch!

  • @Loki_Firegod
    @Loki_Firegod 18 днів тому

    I know I'm really late, but the thinner/lighter bowstring might also have a bit more flexibility. I know bowstrings are made from rather inflexible material (interestingly, in Germany it's called "Sehne" which translates to "sinew", but material like sinew or guts or other animal-derived strings weren't used much in central and western Europe; according to any evidence they preferred hemp or flax for its rigidity) but hardly any material has zero lateral give. And the thinner you make it, the more it can (slightly) stretch, which then reduces the efficiency.
    So basically I'm saying: unstrung the length of the two strings may have been virtually identical, but once you put them on the bow the lighter one may have ended up a few millimetres short - and once you've loaded the crossbow, that effect may have increased to the point where you lose a significant amount of power.

  • @schonnj
    @schonnj 3 роки тому

    I was rather surprised how stiff the bowstring was. It's almost like a coil-spring made of rope...

  • @angrypotato_fz
    @angrypotato_fz 3 роки тому

    Thanks for providing a neat chart :)

  • @tommylitchfield3450
    @tommylitchfield3450 3 роки тому

    And now we want to see just how much difference in speed various brace heights make! Keep up the great content, Mr. Todd

    • @tods_workshop
      @tods_workshop  3 роки тому

      Now that would be niche!

    • @ScottKenny1978
      @ScottKenny1978 3 роки тому

      The way to see that is on Mister Watts' big ballista. Firefly is a beast, 5000lb draw weight and some 30" draw length!
      With a sawtooth/gear tooth rig for variable draw length.
      wattsunique.com/blog/

  • @nilo70
    @nilo70 3 роки тому

    God , I love these Tod !

  • @nigelmacbug6678
    @nigelmacbug6678 3 роки тому +6

    last time l was this early, stones were the highest tech, missile weapons

  • @tensense5872
    @tensense5872 3 роки тому

    Perhaps you could do one with different length bolts perhaps weighted the same and see how length effects things?

  • @nickdavis5420
    @nickdavis5420 3 роки тому

    Can’t wait for a fistful of bolts more

  • @suedavenport7793
    @suedavenport7793 3 роки тому

    I feel totally properly dressed watching this. Me and Tod wearing the same tee shirt! Lol

  • @IanZainea1990
    @IanZainea1990 3 роки тому

    I had sent a suggestion for graphics, I sent an example along with it. I'm not sure if you decided to do it independent of my suggestion it if you saw it, but I'm glad you started putting up the stats, makes it easier to follow along

  • @lmaolmoo4147
    @lmaolmoo4147 3 роки тому

    These have more energy than a .25 ACP or .22 but way better cross section density. That's pretty insane considering the time period when you think about it.

  • @MartinGreywolf
    @MartinGreywolf 3 роки тому

    According to Fragment Hazard Criteria, energy is meaningless when it comes to blunt impacts (at these low velocities, at least, it could be driving factor for hydrostatic shock with bullets) - so anything that doesn't go through mail. The findings were that there were three categories of blunt impact injuries, and the thing that mattered how badly it injured you were either m*v (so, momentum), m*m*v*v (both speed and weight squared) and m*m*m*m*v*v*v*v (speed and momentum to the fourth power). This is especially important with the heavy weight bolt, because that one will be fearsome in these three categories, much more so than the energy alone would suggest.
    If you are wondering, Fragment Hazard Criteria gives us even the lightest bolt above the 50/50 odds of causing a major injury (cracked skull, breaking ribs enough to lacerate insides), and has even odds of going through a thigh even when blunt. Wear armor when getting shot at, is what I take from that.
    Another thing I noticed is that the heavy bolt is about 150 grams at 45 meters per second - which is about as fast as I can sling a baseball, which weights 150 grams. And there were clay and lead sling projectiles found in that weight category, probably meant as a siege ammo or anti-armor. It's interesting to note that once you get to cranequin crossbows, you can use them to make all but the most elite slingers obsolete, and with almost no training required at that.

  • @kenthesparky178
    @kenthesparky178 3 роки тому

    That is one steep learning curve.

  • @olivermcneice8440
    @olivermcneice8440 3 роки тому +2

    Advert comes up of someone smacking the shit out of a potato, sounds just like a crossbow 😂

  • @Erikreaver
    @Erikreaver 3 роки тому

    One thing to consider with the choice between light and heavy quarrels is that weight of them doesn't matter only in flight. There is going to be the cost of metal, but of course, even to carry them. Which is a massive concern even today. Some quick math and rounding made me realise that with a 60gram bolt you will fit ~83 into an arbitrary allowance of 5kilograms. With the 93gram one? Only ~54. You only get two thirds of number of bolts downrange! I am sure each crossbowman had a different preference and probably even had multiple types of bolts on his person, just thought that it is a good argument for consideration of the light bolts, even though I like lobbing big hunkin' chunks of steel myself as well. Lovely video and looking forward to more of them as always! Have a good one, Tod!

    • @ScottKenny1978
      @ScottKenny1978 3 роки тому

      Yep, that's a significant concern even today.
      I suspect that the crossbowmen would have maybe a dozen or so specialty arrows and a fixed weight of war shots. Total equipment weight is going to be about 35lbs/15kg

  • @nick_steele9790
    @nick_steele9790 3 роки тому +3

    Amazing as usual! You made my day!

  • @Crimsonedge1
    @Crimsonedge1 3 роки тому

    Weight increases, speed decreases. Weight decreases, speed increases. Initial "power/energy" remains the same.

  • @user-ii5im7zm2t
    @user-ii5im7zm2t 3 роки тому

    Sometimes I wish you had a friend named Todd Cutler, just so he could poke his head in for video introductions.

  • @eurodon8532
    @eurodon8532 3 роки тому

    Just remember that force is the product of mass and acceleration. If you decrease mass you need to increase acceleration by a factor that's greater than the reduction, if you want to generate a greater force.

  • @jeice13
    @jeice13 3 роки тому

    While the second string did lower energies it also got them much closer to each other so it may still help with lighter bolts. The 80 and 60 lost virtually no emergy compare to the 10 the 2 heavies lost due to length

  • @Goatcha_M
    @Goatcha_M 3 роки тому

    Also, medieval techniques, everything is going to be approximate, they aren't going to be weighing strings to the gram, potentially the ounce, but more likely they just make them to a pattern and set, especially as every village in Europe had its own slightly different measures. Same goes for the crossbowmen on the field, he isn't going to be measuring angle with a protractor , he is going to aim roughly 45 and shoot.

  • @vinojmarotickal4134
    @vinojmarotickal4134 3 роки тому

    Todd I have seen ones of the video in which you have shown a half moon type arrow head and lam from India and I asked my grandpa about this arrow head and he told me that it's is used to hunt deer and he also told me that an experienced hunter can hit the deer neck and calculate how the arrow head spin and hit the deer without damaging the spin

  • @kamilrenczewski5151
    @kamilrenczewski5151 3 роки тому

    You should consider to record shooting both strings with ultra slow motion. It may be that lighter string is smashing the arrow and bouncing back a little and not accelerating the arrow over full draw length. Maybe stiffness of both strings are considerably different?

  • @hawkname1234
    @hawkname1234 3 роки тому

    I watch these videos compulsively now. I don't even know what Tod's talking about half the time. I for sure don't know before I click the video. Doesn't matter. All cool.

  • @michaelvanbenschoten2165
    @michaelvanbenschoten2165 3 роки тому

    With an unloaded dry fire, the string will only move so fast. no mater how light the projectile, you cannot exceed that speed. Diminishing returns means heavier bolts are able to have more of the potential energy transferred to them.

    • @michaelvanbenschoten2165
      @michaelvanbenschoten2165 3 роки тому

      @@JorgTheElder the premise of the video is; "does a lighter bolt equal more power?" Because energy is M(V^2) lighter projectiles usually mean more velocity. However a heavy crossbow is more like a train engine on a short track than a gun.
      The train engine has a top speed of say 10mph, but can shove a lot of mass around. If that engine pushes a ping-pong ball as a projectile, it will achieve top speed as fast as it can, but its still a ping-pong ball moving at 10mph.
      The engine could then push a single train car to top speed just as it reaches the end of the track, maximizing its energy efficiency.
      A lighter string won't necessarily give a noticeable increase in speed in a heavy poundage bow. The physical speed limit of the bow makes more difference than an ounce of mass saved when you are close to top speed.

  • @michaelguerra5888
    @michaelguerra5888 6 місяців тому

    Hell, if you go by the 12 grain per pound rule looks like you could shoot about a pound and a half bar of steel as an arrow.

  • @elchinodecai
    @elchinodecai 3 роки тому

    Could you make a really thick and heavy pointy bolt just for the sake of tasting it and see how it compares to historical ones?

  • @SeraphElrick
    @SeraphElrick 3 роки тому +3

    As someone who never did this in school: what exactly is the difference in kinetic energy and momentum? Isn´t it both just a relationship between the mass of the projectile and its speed? And how does a change in one or the other affect the damage sustained by the target? I´d be glad if someone would educate me^^

    • @ultranium7414
      @ultranium7414 3 роки тому +4

      When it comes to penetrating armor, you need both momentum and kinetic energy.
      1-A really high speed, really light projectile
      Will scratch a thick hard armor.
      2-A really low speed ,really heavy projectile
      Will push a thick hard armor.
      Num 1 is a high kinetic energy low momentum projectile
      Num 2 is a low kinetic energy high momentum projectile.
      I hope that I could inform you

    • @QuantumHistorian
      @QuantumHistorian 3 роки тому +6

      Good question! These are all terms whose popular usage is different from their technical physical meaning, so it can get confusing. Here is a very brief overview, do feel free to reply with more questions.
      First, some basic definitions:
      *momentum =* mass * velocity
      *kinetic energy =* 0.5 * mass * velocity * velocity
      *velocity =* speed and the direction of movement
      Essentially if you know any two out of {mass, velocity, momentum, kinetic energy} you can work out the other two. Mass is useful because it's constant no matter how the thing is moving or not moving. Velocity is useful because it tells you the kinematics (where something is when). Momentum and Kinetic Energy are useful because they are both (independently) conserved as things travel and bump/crash into each other. That means that if you know the momentum or energy before some complicated event (say many billiard balls bouncing off each other), you know what the momentum or energy are later, without having to worry about the detail of what happened in the middle. However, some of that momentum/energy might be transferred to air or to vibrations inside a material where it's so hard to measure and keep track of it that we essentially consider it "lost".
      As an aside, these 4 quantities are all related to force in the following way
      *force =* mass * acceleration = mass * change_in_velocity / time_for_that_change
      *kinetic energy =* force * distance_that_force_is_applied_through
      *momentum =* force * time_that_force_is_applied_over
      (where I'm assuming everything is constant to avoid calculus, but you can replace all multiplications by integrals and division by differentiation if you want the most general version). It's not so hard to check that these definitions are all consistent with each other, which is why that otherwise mysterious 0.5 in thee definition of kinetic energy comes in.
      Saying which one of those is more deadly or penetrates deeper is *very* complicated because the shape and material of the projectile and target comes into play. You can no longer consider them as single point-like objects but (almost) have to deal with how individual atoms react during the impact. That's sufficiently difficult that accurate theoretical predictions are not worth attempting, and instead people do tests of various projectiles on various targets and various speeds, draw up tables of the results, and then come up with some heuristic rule that fits the data. Hence why this channel is so interesting!

    • @torhacs
      @torhacs 3 роки тому

      Basicslly "momentum" that their refer actualy is the inertia of the object as the first law of fisics says any object without external forces tend to keep is trajetory/speed know as "momentum" that is product of it weight and is applied initial aceleration, the kinetic energy is a abstract term in form of a energy, joules that include its momentum force, to the object that can cause phisical changes if transfered to others object like target or people

    • @QuantumHistorian
      @QuantumHistorian 3 роки тому +1

      @@torhacs I'm sorry, but that's absolute butchering the physics. Inertia is mass, not momentum. Momentum is mass times velocity, not weight or acceleration. There's no such thing as a "momentum force" and neither momentum nor force is the same thing as energy. Energy is not more linked to physical changes than momentum or acceleration. See my reply above for what these things mean. I'm not trying to be rude, but in a discussion about this these terms *have* to be used correctly, or we get nowhere at all.

    • @TNaizel
      @TNaizel 3 роки тому

      @@QuantumHistorian that was a great explanation! I have a question: can two objects with the same kinetic energy have different momentum? (or vice versa)

  • @whitewalker9622
    @whitewalker9622 3 роки тому

    I just love your videos! Great work!

  • @themadscientest
    @themadscientest 3 роки тому

    Crown bolt vs coconut in jelly!

  • @synoche4275
    @synoche4275 3 роки тому

    Regarding the lighter String: Maybe trying a different material could change velocity and momentum. So sinew, flax, hemp, bast, maybe even leather are all different in elasticity and could influence the dynamic of the bow and therefore the bolts. Worth a try?

  • @laki7480
    @laki7480 3 роки тому

    Now I am curious to see how the difference in power and range when shooting a "light crossbow" with lighter and heavier bolts and how much a heavy crossbow helps those heavy bolts

  • @leighrate
    @leighrate 3 роки тому

    I would expect that your dealing with a number of different factors.
    Inertia, friction , wind resistance etc.
    Personally I think you are going to approach the point of diminishing returns fairly quickly.
    Plotting the data points on a graph might give some indication.

  • @martynasskrabulis729
    @martynasskrabulis729 3 роки тому

    Great video! Assuming a flat plane and no air drag(could be accounted for if we knew the drag coefficients of the arrows), you could calculate their energy from the distance they traveled, no need to measure their velocity. Since their launch angle was 45 degrees, the energy can be calculated as m(mass)*g(free-fall acceleration)*d(distance traveled)/2. According to my calculations, the energy of the 159g bolt was 105J, 93g was 91J, 80g was 80J, 65g was 69J. So pretty close to yours. I'm sure taking air drag into account wouldn't be that difficult

    • @wmyst1797
      @wmyst1797 3 роки тому +1

      Depends what you mean by "pretty close". Your estimates are all about 20% below the measured values, so air resistance is significant.