FROM BOWING TO HUMIDITY

Rohacell expands with ambient relative humidity. The level of expansion is of order 1 part in 10**4 for each percent relative humidity change. This would not be a big deal if the expansion were uniform, but Silicon glued onto all three inner surfaces, but not onto 2 of the 3 outer surfaces constrains the expansion. There is information on the relation between humidity and cage expansion in Eric's Rohacell paper. For a relative humidity increase from 30% to 92%, the cage width expands by 0.62% if the foam is free, like on the outer surface, but only by 0.21% when Silicon is glued on. The picture below shows this effect:

If we now line up 8 of these cages (the outer 4 have silicon on all sides, and are not expected to contribute), they form the bowed assembly that we are worried about. A schematic diagram of half of the arc is shown below.

Here alpha = (8x0.094)/2 degrees, and d = 4 cagewidths, about 21 cm. The total bow is d(1-cos(alpha))/sin(alpha) = 0.07 cm

If we assume the effect is linear, as I do in the figure below, we can put the 5% and 10% limits, calculated on the previous page, on the plot below, and derive maximum humidity excursions.

The bowing limits, derived on the previous page, can be translated into constraints on longterm humidity excursions of 9 and 18 % for the 5% and 10% efficiency losses, respectively.

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