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<blockquote data-quote="Cheiromancer" data-source="post: 75432" data-attributes="member: 141"><p>I began with geometry. If you have two cubes of equal density, one twice the size of the other, each supported by a horizontal surface, the larger exerts twice the weight per unit area on the supporting surface than the smaller one does (each supporting face has two cubes on top of it, not just one). As far as the smaller object is concerned, doubling its size is much like doubling the gravity it experiences. Similarly, tripling an object’s size is like tripling the gravity it experiences, and so on.</p><p></p><p>A Large or Medium-size creature who doubles in size increases its weight eightfold, and it’s size category increases by one (MM 5). Its carrying capacity is automatically doubled (PH 142 “Bigger and Smaller Creatures”) and its Strength increases by 8 points (MM 12). 8 points of strength triples its carrying capacity (PH 142, Table 9-1; e.g. from Str 15 to 23, or from Str 20 to 28). With a doubling of carrying capacity due to size, the net increase in carrying capacity is six fold. </p><p></p><p>Note that the Strength increase is a trifle anomalous; if a creature’s weight increases eightfold, its carrying capacity should increase proportionately. A Strength increase of +10 would make more sense, since that quadruples the carrying capacity. </p><p></p><p>The table would make more sense if a tripling of the creature’s size resulted in two size increases, since two size increases corresponds to a +16 to strength, or (from PH 142, Table 9-1) a ninefold increase in carrying capacity. If the “Bigger and Smaller Creatures” rule of PH 142 is generalized, tripling a creature’s size should automatically triple its carrying capacity. Thus a creature three times as big should carry 27 times as much. Since it also weighs 27 times as much, this is exactly as it should be.</p><p></p><p>Now remember the cube? A creature who triples in size is like a creature who experiences three times normal gravity. But a creature who triples in size must increase its strength by 16 points in order for everything to scale properly. So if 16 points of strength exactly balances a tripling in gravity, what increase of gravity balances an increase of one point of strength? Since 1.0711 is the 16th root of 3, it must be a 7.11% increase.</p><p></p><p>If doubling in size increased Strength by +10 (which it probably should), a +1 to Strength would correspond to an increase of 7.18% (1.0718 is the 10th root of 2). So either way a 7% increase in gravity needs to result in a +1 increase of Strength for the situation to remain the same.</p><p></p><p>Another way of looking at it is to say that if gravity increases by 7%, the creature’s strength effectively decreases by 1. This would be for purposes of determining encumberance and strength based checks (climb, balance, jump and tumble at least, things like Ride and Swim involve other considerations).</p><p></p><p>The relationship between encumberance and strength is a problem. Specifically, the weight of the creature doesn't figure into its own encumberance. But it should; old or overweight people often do not have sufficient strength to move their own bodies around efficiently, and so they move slowly, can't run very well, and tire more quickly. Even if they are not carrying anything, they are moderately or heavily encumbered.</p><p></p><p>Even if you were in the best of shape, suddenly adding 40% to your weight would be an encumberance. Suppose you weighed 175 lbs; your weight will suddenly increase by 70 lbs. Now, this is weight and not mass; you start, stop and turn corners as if you were your old weight, but you need more energy to remain standing.</p><p></p><p>The best way to conserve energy while moving would be to move more slowly; the way the encumberance chart shows this is by making your speed go down.</p><p></p><p>Another way of looking at the problem was to consider encumbrance. After all, if you weigh 175 pounds and the gravity suddenly doubles, you are now carrying around an extra 175 pounds. Well, not quite. Your mass hasn’t changed, so the inertia you feel when you try to turn a corner or come to a stop- that won’t change. In fact you may find it easier to turn a corner, since your increased weight means better traction between your feet and the ground; you are less likely to slip. But when you are standing still, it will feel like you have an extra 175 pounds on your shoulders.</p><p></p><p>I decided to handle this with a combination of strength reduction (for the purpose of determining encumberance) and reduction in base movement rates. This worked out quite nicely for the damage caused by falling, since if it is linear to distance it is probably linear in acceleration as well. And 2ad=v^2, so this has to do with the kinetic energy (1/2 m v^2) that a person has when they hit the ground.</p><p></p><p>I wouldn't expect DM's to use the 7.1% (adding 7.1% is the same as multiplying by 1.071); they would probably use "nice" increments as given above. 4 or 6 or 10 or something.</p></blockquote><p></p>
[QUOTE="Cheiromancer, post: 75432, member: 141"] I began with geometry. If you have two cubes of equal density, one twice the size of the other, each supported by a horizontal surface, the larger exerts twice the weight per unit area on the supporting surface than the smaller one does (each supporting face has two cubes on top of it, not just one). As far as the smaller object is concerned, doubling its size is much like doubling the gravity it experiences. Similarly, tripling an object’s size is like tripling the gravity it experiences, and so on. A Large or Medium-size creature who doubles in size increases its weight eightfold, and it’s size category increases by one (MM 5). Its carrying capacity is automatically doubled (PH 142 “Bigger and Smaller Creatures”) and its Strength increases by 8 points (MM 12). 8 points of strength triples its carrying capacity (PH 142, Table 9-1; e.g. from Str 15 to 23, or from Str 20 to 28). With a doubling of carrying capacity due to size, the net increase in carrying capacity is six fold. Note that the Strength increase is a trifle anomalous; if a creature’s weight increases eightfold, its carrying capacity should increase proportionately. A Strength increase of +10 would make more sense, since that quadruples the carrying capacity. The table would make more sense if a tripling of the creature’s size resulted in two size increases, since two size increases corresponds to a +16 to strength, or (from PH 142, Table 9-1) a ninefold increase in carrying capacity. If the “Bigger and Smaller Creatures” rule of PH 142 is generalized, tripling a creature’s size should automatically triple its carrying capacity. Thus a creature three times as big should carry 27 times as much. Since it also weighs 27 times as much, this is exactly as it should be. Now remember the cube? A creature who triples in size is like a creature who experiences three times normal gravity. But a creature who triples in size must increase its strength by 16 points in order for everything to scale properly. So if 16 points of strength exactly balances a tripling in gravity, what increase of gravity balances an increase of one point of strength? Since 1.0711 is the 16th root of 3, it must be a 7.11% increase. If doubling in size increased Strength by +10 (which it probably should), a +1 to Strength would correspond to an increase of 7.18% (1.0718 is the 10th root of 2). So either way a 7% increase in gravity needs to result in a +1 increase of Strength for the situation to remain the same. Another way of looking at it is to say that if gravity increases by 7%, the creature’s strength effectively decreases by 1. This would be for purposes of determining encumberance and strength based checks (climb, balance, jump and tumble at least, things like Ride and Swim involve other considerations). The relationship between encumberance and strength is a problem. Specifically, the weight of the creature doesn't figure into its own encumberance. But it should; old or overweight people often do not have sufficient strength to move their own bodies around efficiently, and so they move slowly, can't run very well, and tire more quickly. Even if they are not carrying anything, they are moderately or heavily encumbered. Even if you were in the best of shape, suddenly adding 40% to your weight would be an encumberance. Suppose you weighed 175 lbs; your weight will suddenly increase by 70 lbs. Now, this is weight and not mass; you start, stop and turn corners as if you were your old weight, but you need more energy to remain standing. The best way to conserve energy while moving would be to move more slowly; the way the encumberance chart shows this is by making your speed go down. Another way of looking at the problem was to consider encumbrance. After all, if you weigh 175 pounds and the gravity suddenly doubles, you are now carrying around an extra 175 pounds. Well, not quite. Your mass hasn’t changed, so the inertia you feel when you try to turn a corner or come to a stop- that won’t change. In fact you may find it easier to turn a corner, since your increased weight means better traction between your feet and the ground; you are less likely to slip. But when you are standing still, it will feel like you have an extra 175 pounds on your shoulders. I decided to handle this with a combination of strength reduction (for the purpose of determining encumberance) and reduction in base movement rates. This worked out quite nicely for the damage caused by falling, since if it is linear to distance it is probably linear in acceleration as well. And 2ad=v^2, so this has to do with the kinetic energy (1/2 m v^2) that a person has when they hit the ground. I wouldn't expect DM's to use the 7.1% (adding 7.1% is the same as multiplying by 1.071); they would probably use "nice" increments as given above. 4 or 6 or 10 or something. [/QUOTE]
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