Slings, realistic physics, The Deadly Spring

[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

[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.

[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.

[ErhnamDJ]

If you say someone is able to generate Watts equal to three times their Basic Lift per arm at the maximum, and that a sling has an efficiency of around ninety percent (which is just me making something up), and that attacking with a sling takes between a third of a second and three-quarters of a second (depending on swing style), then what you end up with is:

A minimum of Joules equal to nine-tenths of Basic Lift.

And a maximum of Joules equal to nine-tenths of two-and-a-quarter times Basic Lift.

So that seems to fit the data fairly well. I'd probably call the weaker attack a regular attack and the stronger attack an AoA (Strong) and leave it at that. And I'd probably come up with some Strongsling perk that mimics Strongbow, if you're using that one in your game.

[Icelander]

As usual, experimentation reveals that typical projectile weights in historical military use weren't the most effective designs, but instead some compromise between economy, logistical concerns and sufficient effectiveness.

2-3 oz. glandes outperform 1 oz. ones in more or less every way that you can mention. They even attain more initial velocity.

But they were less common because the improved performance was less important than having more ammunition for the same amount of lead.

Since adventurers often worry more about the effectiveness of each shot than economy and logistics, I'd think that looking at 100g, 200g and even 450g designs would be worthwhile.

As a GURPS rule of thumb, standardised shot are at least +1 Acc commpared to even carefully chosen stones. Found stones are -1 to hit compared to that.

I see no evidence that the staff sling rates a +1 Acc compared to any other design, especially since it is very awkward for point targets in straight flight paths. It does get longer range, though, with the same projectiles. Also, it allows for heavier projectiles without loss of velocity, which will improve both range and damage, but increase ammunition Cost and Weight.

Lead ovoid/biconical glandes outrange stones of the same weight by around 50%, fairly consistently.

[The_Ryujin]

This site might help out a bit:
http://slinging.org/index.php?page=t...eorge-alsatian

It goes into three models covering how a sling effects acceleration.

[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.

[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).

[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.