Slings, realistic physics, The Deadly Spring

[Icelander]

Has anyone had any luck modelling slings in a slightly more plausible manner than the current one?

Can one plug them into Douglas Cole's The Deadly Spring in any way?

[ErhnamDJ]

We could probably come up with some rough estimates if we had any empirical data at all on slings. What we really need to know is the efficiency with which the energy is transferred to the bullet and also the amount of time that the energy is being applied to the bullet.

It's not as easy to do this with the sling, though, as it is with the bow. With the sling you don't have uniform acceleration. It's completely different from a bow. It's more like swinging a baseball bat.

I found this after a Google search. I don't understand most of it, though.

He's talking about propelling a 100g stone to 32m/s.

That's only about fifty Joules.

If you care to guess this guy's ST score, I can try to apply my melee damage house rules to get you a rule you can use. All I'd be doing is figuring his arm's wattage for his Basic Lift and then applying an efficiency modifier to get the final energy, but that should work okay enough for what we're doing. I just need to know that particular example's Basic Lift to get the efficiency of his examples that we can then form into a generalized rule.

[Icelander]

I've got a decent study where the author compares previous experiments and performs some of his own. It's called Expertimentation in Sling Weaponry by Eric T. Skov and is available online. It's an Anthropolgy MA thesis from the University of Nebraska, this year.

Unfortunately, only fairly light projectiles are used, but even so, it's light-years ahead of the other literature I've read.

[The_Ryujin]

Hmmmm, from what (little) I know about slings is that they seem to act mostly like a pendulum arm, increasing the torque of your throw, with a bit of a spring like action going on at the end so I would think that you'd need to do some heavy retooling of Mr. Cole's Deadly Spring engine to make one work.

[whswhs]

There is some published work on modelling of one-armed catapults (both onager-style, with springs made of wound tendons, and trebuchet-style, with big damned weights) that looks at the gain in efficiency from having the missile in a sling at the end of the arm, rather than in a rigidly fixed cup. That's effectively equivalent to a human arm holding a conventional sling. I would recommend looking at the mathematical modeling for that case, at least as an intuition aid.

Bill Stoddard

[Icelander]

Originally Posted by The_Ryujin

Hmmmm, from what (little) I know about slings is that they seem to act mostly like a pendulum arm, increasing the torque of your throw, with a bit of a spring like action going on at the end so I would think that you'd need to do some heavy retooling of Mr. Cole's Deadly Spring engine to make one work.

To begin with, I was thinking I'd input some real world experimental results into his firearms model, to check what our performance benchmarks ought to be.

At least it would guide me toward quick and dirty fixes to slings, before they become relevant in my campaigns.

[Anthony]

The problem with a sling is that it's a messy biomechanics problem; muscle isn't as simple to model as springy materials.

For a very simple throwing arm, the total energy is (torque) * (angle between minimum and maximum), and the efficiency is (moment of inertia of the projectile) / (moment of inertia of projectile and arm). Unfortunately, the amount of torque an arm can apply is time-dependent. Using a constant-power approximation instead of a constant-force approximation, energy scales as P^2/3 * I^1/3. A sling increases the moment of inertia of the projectile without a corresponding increase in arm inertia or projectile weight; the combination of increased total inertia, increased efficiency, and no increase in projectile mass results in a faster, higher energy projectile.

Note that this is basically the same as the physics of swinging weapons, and the virtue of tip-weighted weapons is that they have a greater moment of inertia for the same weight.

[DouglasCole]

Originally Posted by Icelander

To begin with, I was thinking I'd input some real world experimental results into his firearms model, to check what our performance benchmarks ought to be.

At least it would guide me toward quick and dirty fixes to slings, before they become relevant in my campaigns.

I looked around a bit, and Chris Harrison presented some numbers that suggested sling bullets could hit as fast as 90 m/s.

That's a lot more than the 38 m/s provided by a staff sling in Richardson's website. I will admit I find 90 m/s somewhat optimistic, but some of the ranges claimed by slingers (and the actual Guiness Book world record of over 437m with a 52g projectile from a 51" sling) suggest an impressive ability. Using a simple trajectory calculator, this could be achieved at a 45-degree release angle at just above 65m/s (no air resistance), or as little as a 16 degree angle at 90 m/s.

Let's assume a 50g projectile at 75 m/s, then.

That's about 140J and an effective diameter on the order of 18.5mm.

Penetration by the firearms model would be 1d (3.5pts) and the wound modifier would be north of 3.6, so if we call it 1d pi++ that probably understates the impact a bit.

I'd suggest an armor multiplier vs rigid armor, though.

For the 30-40m/s and 28g that Thom Richardson usually throws down, you'd be in the neighborhood of 1.2 points on the average; call it 1d-2 pi++

So if the higher-end limits are to be believed, against an unarmored man, you would look at an average of about 3.5*3.5 = 12 points, with an upper end on the order of 21 points, enough to reduce an average man to -HP in one shot at the extreme, and KO him on the average with a "torso" hit. That breaks the RAW max of pi++ for GURPS, though. more rationally, you'd only approach the upper end on a vitals hit.

I was thinking 90m/s was pretty darn optimistic, and certainly "world record" is upper end. But it does suggest that imparting such energy is feasible (and a strong bow is on that order as well).

[Icelander]

To take a simple benchmark to start with, fairly typical lead glandes are ovoid or biconical in shape, measuring 29mm x 18mm x 13mm and weigh just over one ounce or 35-40g. Call it an ounce precisely, or 28g, if that makes it simpler, as that is very close to a median weight of discovered examples.

Experiments suggests that they attain a speed of 45m/s, even with inexpert users, assuming they are willing to practise for a few weeks. If not, speeds of 30m/s are more common.

It seems that anyone with the skill at DX+2 in GURPs terms, which is fairly likely for professional military slingers, would attain at least 45m/s and likely more.

Range is at least 100m and up to 300m, depending on methods. The longest cast, not yet verified by the Guiness Book of World Records, is 505m, using just such a 40g ovoid lead glans.

Striking with the pointed end, what kind of damage ought that be doing?

Edit: The impact cross-section of such a biconical projectile is 0.79 cm2.

[The_Ryujin]

Oh yeah, that would give you good bench marks to work off of but the hard part would be you would have to come up with a whole new way to translate ST into damage or more correctly into velocity (we can fub things a bit here and just count final velocity at the point of launch and use Dice rolls to simulate throws with more or less oomph).

As a base I'd say that arm velocity could equal ~8m/s*SQRT(ST/(2.6*cube root(body weight + weight of stone in KG))) then times that by how much of a boost the sling gives you. As for how much of a boost it gives you, well as a start we can fudge around with how much of a lever the sling acts like and compare it to known results. One way to bench mark this is to get throw a couple rocks with your hand and measure the velocity at release and then use a sling and do the same.