If I'm ×4 strong and my club is ×4 heavy, do I hit you with ×16 force?
 

This is more physics than GURPS, I suppose, but I want to know because of GURPS. It's more of a thought experiment, but it's because of GURPS that I have these thoughts, which means I should really blame the GM who introduced me to it in the first place.

You have ST 10 (BL 20) and a knobbed club that weighs 2 lb.

I have ST 20 (BL 80) and a knobbed club that weighs 8 lb.

I don't care about the damage yet, but I want to know if I'm hitting you with ×16 amount of force because I'm four times as strong and my club is four times as heavy. Of course, I'm sure physics is a bit trickier than just that, but do I have the right idea? If not, I'd love to be corrected. If I'm right, wouldn't giants kill each other too easily? At ST 20, I am assumed to have four times the mass, but I'm hitting with 16 times the force. Doesn't that mean me and my other ST 20 friend pose a greater threat to each other than you and your other ST 10 friend? Is this why larger creatures (bears, elephants, etc.) seem to have higher DR on top of their higher HP?

On the other end of the spectrum, what about those two ST 5 goblins in my backyard? They are ×1/4 as strong and their knobbed clubs are ×1/4 as heavy. So, it seems they are ×1/4 the mass but hitting each other with ×1/16 the force. Is it going to take them forever to knock each other out? Does that make sense? Do small creatures (ants, squirrels, etc.) have that same issue? (It seems like some ants have Striking ST on their mandibles, which might offset that a bit.)



Does that make sense? Again, it's more of a thought experiment than anything else. While the GURPS numbers don't line up with my assumptions (and I didn't expect them to), they do trend in those directions, which makes me feel like I can't be far off.

Thanks.

Re: If I'm ×4 strong and my club is ×4 heavy, do I hit you with ×16 force?
 

No. Most likely you're hitting with 4x the force.

Re: If I'm ×4 strong and my club is ×4 heavy, do I hit you with ×16 force?
 

If you are 4 times stronger than you will do twice the damage.

ST 10 (20) vs ST 20 (80). ST 20 is 4 times stronger, and the damage should be based on the square root of that, which means the damage should be 2 times what ST 10 can do.

with a more massive weapon, maybe a little more than that.

Re: If I'm ×4 strong and my club is ×4 heavy, do I hit you with ×16 force?
 

My eyes have been opened! Square roots are so important. With them being so important in GURPS, it's a wonder that I forget about them so often. So, then, damage would scale normally?

Re: If I'm ×4 strong and my club is ×4 heavy, do I hit you with ×16 force?
 

In gurps Terms, you're doing a little over x2 damage. Most of that is from ST. The weight increase grants a flat but not insignificant bonus. One of the low tech compendiums covers increasing weapon weight. But in general, st drives damage, and weapon weight is secondary.

Re: If I'm ×4 strong and my club is ×4 heavy, do I hit you with ×16 force?
 

Hitting with 'force' is pretty shaky physical ground to be starting from. Calculating actual forces involved in an impact depend on body deformation physics and that's going to be pretty gross to work with.

Usually we're more likely to look at energies or cross-sectional energy densities or maybe momentum.


But personally, I'd start by looking at Basic Set p355, throwing.

By the rules there the range you get varies fairly closely with BL/weight * ST. Since BL varies with the square of ST, that means that throwing range varies with the cube of ST for a given weight. (When the weight is close enough to BL, it tails off when it's more than a factor of 4 away.)

Maximum range is proportional to the square of velocity, so when you scale up ST and weight together the implication is that throw velocity goes up proportionate to the scaling factor until the projectile gets too small. That would mean momentum goes up with the square and energy with the cube.

On the other hand, those clubs are much too small compared to BL to match that calculation. For things so light, range more or less just varies linearly with ST. So energy would go up with the square of scaling factor, and momentum with the 1.5 power of it.

Re: If I'm ×4 strong and my club is ×4 heavy, do I hit you with ×16 force?
 

The short answer: GURPS doesn't tackle melee damage with any sort of "here's how the physics works out" approach. I think it could do so (to some degree), and so I've played with all kinds of melee weapon design systems and other hacks, but the system itself didn't take such an approach from the start, and so it is what it is. (And for melee damage stats, etc. apparently created through the "just eyeball it" method, what the system offers isn't bad, IMO! Plus, any sort of fancy-pants physics-based approach is destined to make things some degree more complex, even after lots of reluctant simplifications.)

But your suggestion of "x16 amount of force" is problematic. I don't know what your exact meaning of "force" might be, but just going with the general idea of "how hard I smack ya":

The idea that x4 strength lets you hit with x4 "force" is fine.
The idea that x4 strength lets you hit with x4 the weapon mass is fine.
The idea that x4 strength gives you both of these together is fishy!

You need to pick one: the x4 strength lets you hit with no added mass, but way more speed . . . or with lots more added mass, but at the expense of speed. Not that the end results of the two need to equal out to the same damage, but there's gotta be a tradeoff.

(Keep in mind that, whether the chosen weapon is big or small, the energy going into the blow - the strength - is unchanged. So the work done by the energy - the "damage" - shouldn't vary hugely. Speaking in very general terms, anyway.)

Re: If I'm ×4 strong and my club is ×4 heavy, do I hit you with ×16 force?
 

The first thing you should do with the throwing rules is never look at them again.

Re: If I'm ×4 strong and my club is ×4 heavy, do I hit you with ×16 force?
 

I don't think there's anywhere better to look for what the ST stat translates to in terms of actions faster than weight lifting.

Re: If I'm ×4 strong and my club is ×4 heavy, do I hit you with ×16 force?
 

Well, the first problem is that the distance table implies that a thrower puts more energy into an object the heavier it is, yet the damage table implies that there's a point of peak efficiency, and above and below that weight ratio less energy is put into the object. Then there's the way the distance table says doubling your ST lets you throw an object four times the weight twice as far (for eight times the energy).

A start would be giving a fixed distance for a given weight ratio, not multiplying ST by the distance modifier.

If one assumes that large creatures can accelerate an object over a longer distance for more speed (like the bonus long arms give to damage), then that can be added in separately in some way.