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Consequences of Physical Growth

The way the Palladium system deals with physical growth (as a Super Ability) is inaccurate. In practice, game play is balanced, making the problem somewhat academic. The trouble is that the solutions intended to preserve game balance aren't always consistent or logical. A basic algebraic concept lends a great deal of insight into this issue. The concept is called scaling.

Imagine a square, with sides of a fixed value L. This square has an area A1 = L * L = L2.

If we make another square, this time with sides of length 2L (twice as long),  our square has an area of:

A2 = (2L) * (2L) = (2 * 2) L2 = 4 L2.

The second square has an area four times as large as the first. If we now make, in a similar fashion, cubes with sides of length L and 2L respectively we see that the volume of the first cube is:

V1 = L * L * L = L3

while the volume of the second cube is:

V2 = (2L) * (2L) * (2L) = (2 * 2 * 2) L3 = 23 L3 = 8 L3.

If we double the length of our cube's sides, we get eight times as much volume! The implication for mass is that, assuming the cubes have the same density, the larger cube will have a mass eight times greater than the smaller cube. This concept, while easily dealt with mathematically, has been greatly underestimated in the setting of rules for the Palladium system.

A further complication comes from the way strength factors into the concept of scaling. Physical strength is largely determined by muscle cross section. Therefore, when one doubles their size, they quadruple the area of their muscles, quadrupling their strength. The character has four times the strength, but needs to manipulate eight times his usual mass! Very large characters will fatigue quickly due to the extra exertion.

Of course, characters don't often settle for a mere doubling of their size. If one increases the size of their character by a multiplicative factor through some type of growth, the mass of the character will increase by that factor cubed. The strength of the character will increase by that factor squared.

Imagine a character using the Growth ability. If the six foot tall character has a PE of 27, he can increase his height by 54 ft to a total of 60 ft. The character is ten times taller than a moment earlier! This means that the character's strength will increase by an amazing factor of 100 (10 squared), but their mass (and hence their weight) increases by a factor of 1000 (10 cubed)! Let's say the character originally had a PS of 20, and a weight of 200 lbs. The character now has an unbelievable PS of 2000! If the character's strength were ordinary he would be able to lift 40,000 lbs. Since the growth gives the character Superhuman Strength, he can carry 400,000 lbs. Unfortunately for the character, his own weight has increased to 200,000 lbs, which may cause problems (sidewalks collapsing, giant footprints....). If it weren't for the Superhuman Strength given to him by the transformation the character would collapse under his own weight!

Think of the damage bonus that goes along with this incredible PS! One punch does over 2000 points of damage! A body slam could destroy a city block! Of course, these results are entirely inconsistent with the way Growth is dealt with in the Palladium system. This character, according to the rules, would have a PS of 74 and a weight around 10,000 lbs.

These are big increases, but not nearly what the math above dictates. The only logical explanation is that the character is much less dense in his enlargened state. In this case, the character's density is twenty times less than before growth occurred! The 60 foot tall character would very easily float on water.

After this long note, one can see that there are several points that need to be further explored or entirely rewritten in the Palladium system. Powers involving Growth need to be either strictly kept in check or allowed to go full-tilt in order to gain some consistency with reality.