Asymmetric Newton's Cradle as a 'rapidly' firing medieval weapon - Is it practical [closed]

Question

I wish to project an iron or steel 'cannonball' at a fortification. I construct a Newton's Cradle but there is a very large ball at one end and a relatively small cannonball at the other.

NOTE - I use the word cannonball for convenience although there is no actual cannon.

The diameter of the large ball is about 2ft and the diameter of the small ball is about 6 inches. There may or may not be intermediate balls of gradually reducing size.

Is this practical for use as a weapon? The big ball has to be repeatedly pulled back, possibly with pulleys, by strong operators, and the firing rate must be in the order of seconds rather than minutes. Also the small ball has to be big enough and travelling fast enough to damage masonry. I need to achieve a reasonable range (say equal to that of a trebuchet casting an equally sized ball).

EDIT - I omitted to mention that one advantage I see over a trebuchet is that there is very little friction in a Newton's Cradle whereas the joints and axles of a trebuchet have constantly to be lubricated with animal grease and, even then, (given the non-existence of medieval ball bearings) experience considerable friction.

Answer 1

This is seriously impractical. The problem is, for objects larger than a few inches, Newton's cradle does not work very well. Mythbusters covered this. To transmit the energy from one ball to the next you wind up with deformation that goes well beyond the elastic limits of the balls, and into the range where the balls are plastically deforming, or even fracturing. Instead of the satisfying CLICK! from the small version, you get this disagreeable thunk from the big one. So you wind up losing a lot of energy in each collision.

And the harder you want to push the worse it gets. Eventually you wind up with flattened parts on the balls, where you lose large fractions of the energy.

Additionally, as shown in the clip, lining up large balls to get good hits is a challenge. There is a very strong tendency for the balls to hit off center and go off axis. This wastes more energy, and would make aiming very difficult. And could be a significant hazard to the operators.

........

A comment suggests springs. This won't work. The characteristic time in this system is the time a ball takes to fall from being held up at one end. If a collision begins to take a significant fraction of this time then the result is multiple balls in motion at one time. This distributes the energy over several balls and spoils the effect quite thoroughly. For it to work the balls have to be hard. The speed at which the collision propagates through the string of balls has to be very much larger than the speed a ball moves between collisions.

Another way to think about springs is this. If you are launching things with springs there are easier ways than trying to hammer on them.

Answer 2

Unfortunately, you'll fall foul of both physics and materials science

As first answer indicates, it's going to be impractical and inefficient. However, even if you do get a physics based set up that should work, you're going to hit a bigger problem.

You want a solid, 2ft sphere. For it to work well, it has to be as hard as possible - every bit of plastic deformation is going to lose you energy, and also mean replacement parts.

For that reason, you want a two foot ball of cast iron. Cast iron, as I've unfortunately tested experimentally with some nice cookware, is brittle. In the worst instances, it can shatter like china. These odds go up with a large, two foot ball. You're likely to have air bubbles, voids, impurities etc.

Stone is worse, surviving multiple collisions poorly. There are no other suitable materials in existence at this point. Brass and bronze are comparatively soft, wood is worse, steel can't be cast yet.

Crashing a 2ft ball of medieval cast iron into a 1ft ball of medieval cast iron is likely to leave you with an impressive explosion of shrapnel, and some chunks of cast iron on whatever you're hanging them with. And this is your best option for materials to use. It's not even the case that you can simply swap out the balls each shot. Chunks shattering off them will seriously reduce the energy imparted to each shot, along with seriously changing the aim.

Answer 3

[faulty argument deleted]

best case (with all energy conserved) the small ball (one sixttyfourth of the mass) will end up with 8 times the speed of the big ball

I'm not sure that that would be enough speed.

in the finite case

for an elastic collison between mass m at speed v and mass n at rest.

initial momentum mv and energy mvv/2

final momentum (conserved)

   mw+nx    = mv

final energy (also conserved)

  mww/2+nxx/2  = mvv/2

ddouble it

  mww+nxx  = mvv

divide by m

    w+xn/m =v
    ww+xxn/m = vv

let r=n/m

    w+xr =v
    ww+xxr = vv

rearrange

    w=v-xr
    xxr=vv-ww

substitute w

    xxr=vv-(v-xr)(v-xr)

    xxr=vv- (vv-2vxr+xxrr)

    xxr=vv- vv+2vxr-xxrr

    xxr=2vxr - xxrr

    xx = 2vx - xxr

    xx + xxr= 2vx 
    
    xx(1+r) = 2vx 

    xx = 2vx/(1+r)
     
    x = 2v/(1+r)

so for 6 stages, each halving the mass r will be 0.5 at each and the speed up will be 4/3 so after 6 collisions the small ball exits at about 5.7 times the speed of the large ball

That's assuming the small ball can handle the impact without plastic deformation. and that all the collisions are perfectly elastic. neither will be true.

Large ratio acceleration is easier using a lever machine like a catapult or a trebuchet.

In conclusion: to increase rate of fire, just put a larger team on your trebuchet, or get more trebuchets.

A traction trebuchet which uses most of the crew as counterweight can manage a fire rate of up to 4 rounds per minute. https://www.historynet.com/weaponry-the-trebuchet/

Answer 4

Even with a theoretically perfect set-up where the force is transferred to each ball with no loss or damage, the range on this is going to be abysmally short.

I think the best case multiplier of this is just around 8x? Artillery is generally something that can be used well outside the range of smaller weapons (bows or guns). This thing just won't have that, and little power to actually damage something that came within its puny range.

Additionally, raising the ball back into place will require at least a time equivalent to resetting a standard piece of artillery, and will likely take even more time. So this would not be a "rapid-fire" device.

To address your "very little friction" addition, I'll need to remove my first caveat of a "theoretically perfect set-up". The wear on the frame, loops, cables and balls (especially the balls) will require an enormous amount of upkeep, and @BobaFit's and @lupe's answer give excellent descriptions on how making use of the device will swiftly degrade it from its less than impressive "prime" condition.

To directly answer your question(s):

This is not a practical device. The firing rate will not be an increase over a trebuchet, the range will be much, much, shorter than that of a trebuchet, and the wear on the overall device will be much higher than on the trebuchet.

Answer 5

This isn't quite a Newton's cradle, but have a look at a light-gas gun.

A conventional gun will push a bullet forwards. The speed of sound in the heated gas puts a limit on the muzzle velocity. However, if you use the expanding gases to drive a piston, you can use the piston to propel a smaller bullet faster using hydrogen. If you wanted to achieve escape velocity from the surface of Mars, one of these could do it. It isn't a Newton's cradle, but we are transferring momentum from one body to a second body, which I hope makes it sufficiently answer-adjacent not to get marked down.