[Space] GURPS

[Rabek]

I did a search and couldn't find an answer, so I apologize if this was answered elsewhere.

In GURPS Space, there is a formula:

L=1/G^(2/3)

Where L is the linear dimension (height or length) and G is the local gravity.

What unit is L in? How am I to utilize this formula? With Earth-like gravity, that gives an L of 1. The base unit for length in GURPS seems to be yards, but there are definitely things on Earth longer than 1 yard.

I know it probably doesn't matter in the grand scheme of the book, but I'm really curious as to the intent of the formula. I suspect it means my randomly rolled 80 yard long critter should not be so large if I wish to be true to biology and physics as we know them, but I don't know what the cap should be on a world with Earth-like gravity.

[Anthony]

Originally Posted by Rabek

What unit is L in?

G^2/3, apparently. It's a multiplier on typical creature sizes -- i.e. at 0.5G typical creature sizes are (0.5)^-2/3 or about 1.58x larger. I'm not entirely sure where that value comes from, though, there's no obvious reason for an exponent of -2/3.

[RaRaRasputin]

Originally Posted by Anthony

I'm not entirely sure where that value comes from, though, there's no obvious reason for an exponent of -2/3.

It's the result of applying the Square Cube Law.

http://en.wikipedia.org/wiki/Square_cube_law

[Anthony]

Originally Posted by RaRaRasputin

It's the result of applying the Square Cube Law.

I know what the square/cube law is. However, a -2/3 power of gravity vs linear scale doesn't follow from that (in fact, the expected ratio, based on the square/cube law, is 1/G).

[roguebfl]

Originally Posted by Anthony

I know what the square/cube law is. However, a -2/3 power of gravity vs linear scale doesn't follow from that (in fact, the expected ratio, based on the square/cube law, is 1/G).

GURPS fantasy has a good section on how it works under it's scaling rules p.51

[whswhs]

Originally Posted by Brett

Weight/cross-sectional area is limited by tissue strength.

For scaling with regard to buckling strength, though, the length of a pillar varies as the fourth root of its mass (so its cross-sectional area varies as the three-fourths power of its mass). How much significance this has for biomechanics is debated, but some biomechanicists take it seriously. Using the two-thirds power may be a gamable approximation rather than a physical reality.

Bill Stoddard

[Anthony]

Originally Posted by Brett

Weight/cross-sectional area is limited by tissue strength.

Yes, but this produces an exponent of -1. Using very simple square/cube law proportions, a ST 10 creature (125 lb) in 1G has a BL of 16% of its weight. In 0.5G, a ST 20 creature (1,000 lb in 1G, so 500lb) has a BL of 16% of its weight. ST 10 vs 20 corresponds to a factor of 8 in mass and thus a factor of 2 in linear scale, if we keep proportions constant.

Now, there are a bunch of non-gravitational reasons for creatures changing shape as size increases, so you wouldn't expect 0.5G creatures to look just like double-sized 1G creatures. This might result in a 2/3 power producing plausible results, but it's not an obvious outcome.

Originally Posted by Brett

Yes, and also cross-sectional area of muscle is required to accelerate extremities and torque joints, and those needs scale with mass and moment of inertia respecitvely, not with weight….

Actually, they scale with weight, because desirable movement speed varies with gravity.

[Anthony]

Originally Posted by Brett

Is this because of pendulum gaits?

That's one factor, but in general you only need to be able to move fast enough to catch yourself while falling. You may want to be faster, but it's not critical and thus doesn't influence maximum size.

[Rabek]

It appears you are all vastly more knowledgeable than me in a wide variety of matters!

So it appears it's a multiple for length in worlds of alternate gravity to Earth's?

Is there a feasible cap to creature size at various levels of gravity, then?

I very much appreciate the responses so far.

[Anthony]

Originally Posted by Rabek

Is there a feasible cap to creature size at various levels of gravity, then?

Almost certainly. Figuring out what that cap is, however, is not trivial, because size limits are a function of both structure and metabolism, and those scale differently. It's possible that the -2/3 power is an adequate rule of thumb, it's just not immediately obvious why it would be correct.