Interesting twist on the scoring for Towers. I was unable to attend the meetings on Sunday to hear the rationale or comment on the extent to which this idea will weight the scoring. Hopefully, whoever came up with this one thought it through and tested some scenarios. Up through the 2001 season, structure events were scored as structural efficiency + 10% of load held. The 10% was a bonus to encourage competitors to hold more weight, but it was not so overwhelming that it discouraged teams from taking risks with lighter structures. For a given bridge mass, the scoring increased linearly with greater mass held; across a range of bridge masses, it was roughly a hyberbola. That system encouraged higher masses held while still allowing lighter bridges with lower masses held a decent chance of winning.
Scoring by using the mass held squared is not analogous to the structural design of beams, cantilevers, or bridges loaded with concentrated loads. Strength formulas for beams or bridges resisting concentrated loads use the load as a direct multiple; formulas using distributed loads use the square of the distributed load, but that's not in play here. Basic column buckling formulas such as Euler's formula use the first power of the load to predict a buckling threshold as well, and while other formulas such as Johnson's parabola or the secant formula are not first-order, they are not similar to using the square of the load either.
Aside from an arbitrary weighting scheme for scoring, was this formula intended to teach students anything about structural design or efficiency? I suspect it will simply squeeze out all of the low-load structures. It reminds me of the days when breaking at less than 15 Kg was second tiered.
Grand Haven, MI
There were days when holding less than 15kg was second tier? Who came up with that? That basically takes all risk out of the equation...and even one bad piece of wood could screw up your whole structure. That would be frustrating...