Slings and Arrows

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?
                                                                                                  – Icelander

I’ve not seen anything like that, but if I were to do it, here’s what would happen.

The key bit to model this is a calculation that would turn ST, skill, and lever arm (for sling vs. staff sling) into energy somehow. Then we could turn that fairly easily into damage.

For range, you’d take the weight of the stone and figure a velocity, and from that work out the likely arc.

We could potentially adjust penetration up slightly as a function of smaller projectile diameter, as for bullets, perhaps even using the same function (or a simplified version) of that used in my old ballistics article.

So, let’s start there . . .

Energetics

The trick would really be getting some estimate of, for a given energy of impact, what armor DR could be penetrated. That would give you a baseline from which to adjust damage as a function of impact energy.

The site I usually go to for slinging seems to suggest that the staff sling (presumably a six-foot pole and a 1-yardish sling vs a roughly 1-yard sling) only increases velocity – and thus in GURPS, damage – by perhaps 10-20%. The staff seems to get longer range through the higher start point.

However, 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 my 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.

Right. That guy.

I’d suggest an armor multiplier vs rigid armor, though. Probably (0.5) or even more.

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. Possible that David spent a few Destiny points to buy a critical success.

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).

GURPSifying the Calculations

What I might do as a start is to take the user’s ST, and increase it based on relative skill level, as I did in my article The Last Gasp through the concept of the “Training Bonus.”

You’ll see that again hopefully Real Soon Now. 🙂

Anyway, if relative skill level provides an increase in ST and a staff sling increases that further by 20%, what you probably have is something like

Damage = Constant * ST * Skill Multiplier * Staff Multiplier

So let’s say that our world record was set by someone with a sport-specific ST of 20 or so, with a 50% skill modifier, giving him a net ST 30. That’s a lot, but hey, world record.

That basically says, in round numbers, take the net ST and divide by 8 to get points of damage, or by 30 to get dice.

Hmm.

Let’s take a more-usual warrior type. ST 12, from a default (-30% ST!) would be about 0.28d, or 1 point on the average. 1d-3, with zero being a possibility. 

Train that guy up to DX, and you’re at about 1.4 points of damage, which is about 1d-2. Get him up to DX+4 and give him the equivalent of Arm ST +2 for special exercises, and a staff sling, and you’re ST 14 * 1.2 * 1.2 = ST 18.5, or 2.35 points, somewhere about 1d-1.

You’re not doing a lot of damage here.

Projectile Weight and Range

The thing is here, much with bows, there’s going to be an “optimum” weight stone that gets you the most delivered energy. Too heavy, and you can’t get it to max V. Too light, and you waste energy that you can’t couple into the projectile.

So if Mr. Effective ST 30 can fling a sling into the ring at 437m (475yds), figuring max range at about 16x your effective ST would be a quickie estimate.

Our typical guy at roughly ST 12? 134 yards. Practiced warrior with DX+4, Arm ST +2, and effective ST 18.5 would be just shy of 300 yds.

Parting Shots

This turned rapidly into an exercise in game mechanics. ST, skill multipliers to ST, and flat multipliers to effective ST for range.

Still, that might not be all bad. Basic Lift is related to the square of ST, and is a force (pounds). If energy is more or less a force times a distance – some sort of arc over which that force is applied – then the square root of energy is related to ST, and the square root of energy is how GURPS measures penetration. So a flat ST basis with multipliers is reasonably physics-based, and makes for easier math.

We handwave projectile size and weight quite a bit here. Still, if our ST 9 slinger vs our ST 30 slinger might be tossing stones with mass proportional to the effective ST you can deliver, perhaps. That would put Joe Casual at about 15 g (probably too light), Mr Warrior at 31g (almost exactly the historical average of about an ounce, or 28g), and Mr Expert at 50g or so. Just to figure out how much lead you have to haul around.

Redux


Bronco makes a nice point below, and if you don’t click on the comments, here are my thoughts after his note about the severity of the impact, as well as that the ancient guys would inscribe their sling stones with personal messages to their foes:

Yeah, I’d forgotten about the inscription thing. I should have linked to a picture of a missile with nose art, though a quick google didn’t find any (wrong terms, I’m sure).
Having the penetration be based on swing damage means that at an effective ST 14, you equal the penetration of a .45 ACP, and in a practical case matches a .380 ACP in both penetration and wounding.

The 50g sling stone at 90m/s can be compared relatively to a 145g baseball at 45m/s – a war stone compared to a major-league fastball. It’s got 1/3 the mass, but 2x the velocity. So the stone has 4/3 more energy but 2/3 the momentum . . . and a much smaller diameter. So the tendency to break stuff (and people) will be on that same order – perhaps a bit more by up to half, I’d hazard, but not a LOT more.

Still, getting beaned by a major-league (100mph fastball) is No Fun, and due to the smaller diameter and higher density of the stone, should be more likely to break stuff.
I think this is another case where the damage should be relatively large, crushing rather than piercing, but mitigated with a HT roll.