House rules for gravity

[jeff_wilson]

Originally Posted by Brett

I think that is correct, yes. The distance by which a ball comes in low or high is proportional to the absolute difference between gravity encountered and gravity expected, not the proportional difference. If the difference between 0.4 gee and 0.6 gee is that the ball is three inches lower than you expected and you don't catch it, then the difference between it you expect 1.4 gee it will take 1.6 gee to produce the same result, not 2.1 gee.

I do not think that is right outside of the narrow special case where the ball is being given identical initial velocity, the catcher is not tracking it during flight, and duration aloft is on the close order of 1/10 of a second. If the pitcher is familiar with 0.6 gee he's going to compensate with more upward velocity, catchers with better eyesight will be able to usefully watch the ball until its closer in time and space from interception and thus less divergence from the expected arc is possible. The difference in position is also proportional to both the difference in gravity and the time aloft, which generally means it will be greater at longer distances, especially there is a trade-off between upward and lateral velocity by the pitcher.

[Agemegos]

Originally Posted by jeff_wilson

I do not think that is right outside of the narrow special case where the ball is being given identical initial velocity

In the case of catching at given throw we are within the special case, and when throwing a given ball at a given backboard with a given arm close enough, I think.

[jeff_wilson]

Originally Posted by Brett

In the case of catching at given throw we are within the special case, and when throwing a given ball at a given backboard with a given arm close enough, I think.

For biomechanical reasons, almost certainly not; the arm and ball will be heavier, which is going to require more muscle tone to support them, detracting from the lateral portion of the windup in non-linear ways. Of course, playable rules won't model this with any detail, but such considerations are still important in choosing which playable abstraction will be used.

An example of this is the 4/e rule for jumping in different gravities, which I helped write. The original, simple rule to divide distances by local gravity was mostly accurate, but made low gravity running high jumps approach 100% too high. Kromm acknowledged this, but also noted:

...you'll have to explain it for
flat critters that the average reader does not think of as having "height,"
and use language that's generic enough that gearheads will not complain
about it for blob-men and Weeble-like machines with oddly placed centers of
mass. However, I am willing to see your attempt. If you can add a 10- to
15-word sentence to what we currently have for high jump that generically
addresses center-of-mass vs. ground clearance for all geometries, in words
that someone with an F in physics can grasp, then I will use it.

My answer to his challenge does a pretty good job, without explaining in detail that half of a high jump's clearance is from raising the legs up to the center of mass, and of course legs don't get appreciably longer in lower gravity. The weird, legless things are accommodated because they don't have legs to run with in the first place, and the ground-hugging things with legs are presumably planting one edge and flipping up as they jump or otherwise exploiting an anatomical advantage that doesn't scale with gravity either. But none of that shows on the page because it's all under the hood except for:

"Exception: Do not multiply the improvement in high-jump distance from a running start."

[Agemegos]

Originally Posted by jeff_wilson

An example of this is the 4/e rule for jumping in different gravities, which I helped write. The original, simple rule to divide distances by local gravity was mostly accurate, but made low gravity running high jumps approach 100% too high.

I'm not proposing to change the rules for high jumps and long jumps.

My rule for DX modifiers scales in exactly the same way as the the 4e rule for DX modifiers that you helped to write, i.e. linearly with difference in gravity.

What, then, do you propose that I do differently, and how do you propose that I do it?

[jeff_wilson]

Originally Posted by Brett

I'm not proposing to change the rules for high jumps and long jumps.

My rule for DX modifiers scales in exactly the same way as the the 4e rule for DX modifiers that you helped to write, i.e. linearly with difference in gravity.

What, then, do you propose that I do differently, and how do you propose that I do it?

(BTW, I didn't help with or even comment on the DX mods IIRC, but that was also eight years and three semesters of physics ago. )

I'd say that a bell curve or sigmoid would be more appropriate, with changes near a reference gravity being more important than those farther away on the scale of single second turns. The ratio between lifting effort and thrusting effort changes most quickly in the middle, then as the extremes are approached, they only get slightly more extreme for the same change in absolute local gravity. I believe this should be true for both your absolute reference gravity and the book's character-relative reference gravity.