The reason is that the foam acts like a spring. If you build a frame using springs on rods around an end cap, the springs are in parallel. If you build a frame using foam, the foam is in series. Each performs differently.
For a parallel spring system, simply add the spring coefficients together to get the total spring constant:
The total spring coefficient is
. Force applied by the spring is then f = (k1+k2) * x, where x is the distance the spring is compressed. In other words, two (same constant) springs in parallel are equal to a spring of the same length with double the coefficient.
For a series spring system, one must add the reciprocal of the spring coefficients, then take the reciprocal to get the total spring constant:
The total spring coefficient is now
. Force applied by the spring is then f = [1 / (1/k1+1/k2)] * x. We see that two (same constant) springs in series are equal to a spring with double the length but half the spring coefficient.
Our goal with any compression frame is twofold: 1) we want to apply ~300 kgf (660 lbf) to the broad faces of the cells, and 2) we want the force to remain roughly constant over a small range of motion of our cells (generally less than 0.5mm (0.020") per cell). I think that the parallel spring case has been well discussed on this site, so let's look at the series case, and we'll use foam as the spring (since that is the topic of this thread).
I tested 1/4" 50-15250 Poron foam using a spring scale and a CNC mill to gradually compress the foam (
Post #77 of this thread). What I found was that two layers of foam are indeed the same as a series spring. The problem then was to find a combination of layers of foam that would apply the correct force (condition 1), and allow the correct amount of expansion (condition 2). What I found was that one 1/4" layer of foam per four cells was ideal, assuming one compressed the foam 50% of the total thickness.
If we roughly linearize the results I got, we see that Poron 50-15250 foam has a spring coefficient of 18#/0.15" = 120 pounds per inch of compression (per square inch of foam). Two sheets then have [1/(1/120 + 1/120)] = 60 pounds per inch, so I need to compress them twice as much as a single sheet. Since each sheet of foam has a usable range of about 2mm (0.080") of deflection, each sheet is good for compressing four cells when each one is compressed to about 40% of its original thickness.
What happens if we add more sheets? It seems like a lot of folks want to use the foam as cell spacers, so let's try nine sheets (one at each end cap plus seven more between eight cells). The total spring coefficient of nine sheets is [1/(9*1/120)] = 13.3 pounds per inch (per square inch). In order to get the 660# I want over the 56 square inches of cell face, I'll need to compress my stack of foam 660/56/13.3 = ~0.9" from an original thickness of 9*0.25" = 2.25". Note that this is still a 40% compression, but our stack of foam could now handle a total deflection of 18mm (0.70"), which is way more than we need. Granted, the force applied would be much more consistent, but with the expense and total thickness of the foam, why use more than you need?
Note: Spring images and formatted equations borrowed from
https://en.wikipedia.org/wiki/Series_and_parallel_springs.