[concept] Basic lift and scaling considerations

[pierseb]

While waiting for DF, I’ve decided to freshen up my GURPS. Reading the basic lift section, my thoughts drifted toward the usual scaling considerations: x2 size, x8 mass thus x8 the basic lift…

But then it struck me. Basic lift definition has 3 components for a specific strength. 2 are fixed, weight and 1 sec time interval, but the third one, height, is variable…

Since basic lift height component is define as what can be lifted over the head, this will drastically change for character of the same strength but of various sizes. Meaning that a creature twice the size (+2 SM) will have to accelerate the same mass twice as fast to reach over his head.

Simple solution, sweep it back under the carpet and ignore it.

Another one would be to redefine BL with a fix dimension. Let’s say 2m/2 yards. If you’re bigger, it takes you more time to reach your maximum reaching height. A creature twice the size can reach its maximum 4m/4 yards in twice the time. Maybe allow half the load in the same time interval. That would match the slow moving giant cliché. Should there be a threshold on how long you can take to lift base on your size? For example, in weightlifting, either snatch or the clean and jerk, there is a transition from pulling the weight off the ground to pushing it over your head. Not counting the rest once the lifter as repositioned himself, there a clear time limit to be efficient. Scaling up in size, maybe this also scale in time since gravity doesn’t? What about smaller creatures that can’t reach 2m/2 yard? They could do it faster, even attempt a maximum two hands lift in less than 4 sec?

Going further, is the cube law even relevant to strength scaling? It holds true for supporting static structures but when adding movement, like lifting, it doesn’t appear to be nearly enough. Let’s say we want to scale creatures but let them able to execute a one handed lift in a second.

Disclaimer: I can handle both imperial and metric units for cooking, carpentry and day to day occupations. But for physics, I’m sticking to the metric system, sorry. Also, I’ll approximate 1G to 10m/s², good enough for comparison.

Let’s say a regular human wants to use his BL (10kg) to do a one hand lift from the ground to above his head (2m) in 1 second. What force would this involve? Reaching 2m in 1s is a 4m/s² acceleration.

10kg * 4m/s² = 40 N

Now assume a character x2 the size and x8 the mass (80kg) that is trying the same lift scaled to his height, 4m. Reaching 4m in 1s is a 8m/s² acceleration.

80kg * 8m/s² = 640 N

Again for a x4 size and x64 (640kg) mass for a 8m lift. Acceleration would need to be 16m/s².

640kg * 16m/s² = 10240 N

The progression is regular for even bigger or smaller creatures. That’s a x16 force increase or a ^4 progression. But this is only for mass inertia. Considering gravity, things gets funky. You have to add:

First case,
10kg * 10m/s² = 100 N
Second case,
80kg * 10m/s² = 800 N
Third case,
640kg * 10m/s² = 6400 N

This part follows the cube law but we need to add both.

40 N + 100 N = 140 N
640 N + 800 N = 1440 N
10240 N + 6400 N = 16640 N

That’s a ^4+^3 progression…
My physics notions goes way back and I might be completely off.

As this been discussed before? Your thoughts?

[RyanW]

Originally Posted by pierseb

While waiting for DF, I’ve decided to freshen up my GURPS. Reading the basic lift section, my thoughts drifted toward the usual scaling considerations: x2 size, x8 mass thus x8 the basic lift…

Usual scaling, IME, is x2 length, x4 BL, x8 mass.

[Anthony]

Realistically, you should probably have altered time rate based on size. It's not particularly practical to implement, however; I suggest just giving larger creatures lower DX to represent this.

It's worth noting that damage should also scale with size independently of weight, meaning a large creature does attacks that are slower but higher damage.

[pierseb]

Originally Posted by RyanW

Usual scaling, IME, is x2 length, x4 BL, x8 mass.

You are right. If you double a creature size (x2), its mass would be x8 (x2³). If you don't do any other adjustments, its muscle power would be x4 (x2²) since it's related to muscle cross section.
The problem with this approach is that mass/weight increase way faster than its strength. A x2 size creature following these principals would barely be able move around. Of course RAW GURPS doesn't account for body weight/mass for encumbrance. This where the cube law comes in. It suggest that strength should also proportionally follow mass increase to keep the creature as nimble than its smaller counterpart. A x2 creature with x8 (x2³) BL made of the same muscle structures would need way bigger muscle cross sections. Bone structures would also have bigger than x4 cross section increase. This would certainly make a bulkier creature. TBone’s Gulliver http://www.gamesdiner.com/gulliver is an excellent reference on the subject.
It doesn’t seems to address the BL size component issue or that cubing BL probably isn’t nearly enough.

[pierseb]

Originally Posted by Anthony

Realistically, you should probably have altered time rate based on size. It's not particularly practical to implement, however; I suggest just giving larger creatures lower DX to represent this.

It's worth noting that damage should also scale with size independently of weight, meaning a large creature does attacks that are slower but higher damage.

Interesting approach I wouldn’t have thought of. But if the goal is to keep the creatures as nimble, independently of their size, this would be an advantage only applicable to BL.
The more I think of it, to properly resolve the issue, it would require something similar to TBone’s natural encumbrance table, with a BL to Size ratio component. A major undertaking, added to “what would my ideal version of GURPS should be” musing. Adding natural encumbrance, redefining BL independently of size, adopting logarithmic strength and damage…
It will probably end up under the carpet. :)

[whswhs]

Originally Posted by pierseb

You are right. If you double a creature size (x2), its mass would be x8 (x2³). If you don't do any other adjustments, its muscle power would be x4 (x2²) since it's related to muscle cross section.
The problem with this approach is that mass/weight increase way faster than its strength. A x2 size creature following these principals would barely be able move around. Of course RAW GURPS doesn't account for body weight/mass for encumbrance. This where the cube law comes in. It suggest that strength should also proportionally follow mass increase to keep the creature as nimble than its smaller counterpart. A x2 creature with x8 (x2³) BL made of the same muscle structures would need way bigger muscle cross sections. Bone structures would also have bigger than x4 cross section increase. This would certainly make a bulkier creature. TBone’s Gulliver http://www.gamesdiner.com/gulliver is an excellent reference on the subject.
It doesn’t seems to address the BL size component issue or that cubing BL probably isn’t nearly enough.

The last time I looked into it, the actual scaling relationship was a little off from limb length as the fourth root of body mass, and limb cross-section as the three-fourths power. This might be related to the mechanical relationships for buckling strength, though I don't think limb bones actually buckle. But the math gets really complicated. And if you take BL as the 3/4 power of weight, instead of the 2/3 power, the two curves are actually fairly close together, at least for a fairly wide interval around humans. So I've treated it as a gamable approximation. You could deal with it by giving bigger creatures a small boost to lifting ST, I suppose.