[The following is an excerpt from a letter to Allen Meece]

[Updated 4 September 2002]

I think I've come across a potential solution for controlling the expansion of the shroud during the platform's ascent. Instead of accordian style pleats, which have little resistance to external forces from any direction and would need to be held in place with lines (demanding a more complicated control system), we can use origami style folds in the shroud fabric. Certain origami folds have offer great resistance to forces along certain directions and allow careful control of surface area.

This simple pattern, suitable for a 8.5x11” sheet of typing paper, is part of a more complex pattern for a box top. It's just one example of what's available among the techniques of this art.

I define the front of the sheet as the side marked with any measurements. The black lines represent downward or “mountain” folds, leaving raised creases across the front of the sheet when unfolded. The gray lines represent upward or “valley” folds, leaving depressions across the front of the sheet when unfolded. Folds marked with dotted lines arise as a consequence of folding layers of double or greater thickness and are only visible when the sheet is unfolded.

The procedure for folding this part of the pattern is:

A. Fold and crease folds #1 and #2. Leave the resulting pleat to lay flat against the front of the sheet.

B. Fold and crease folds #3, #4, #5, #6, #7 and #8. Leave the three resulting pleats to lay flat on each other, layered across the front of the sheet. Note that the pleats are not left at an angle to the sheet, like they would be in an accordion pleat.

C. Fold and crease folds #9, #10, #11 and #12, laying each corner flat across the back of the sheet.

D. Fold, crease and unfold folds #13, #14, #15 and #16.

E. Bring the endpoints of fold #9 together, gathering a pleat of paper between them and bringing folds #13 and #15 to right angles with each other and with the front of the sheet. Lay the pleat flat against the sheet and crease it along fold #17.

F. Repeat Step E for folds #10, #11, and #12, to create folds #18, #19, and #20.

G. I've only reproduced the part of the pattern required for this demonstration, so forget what you know about origami and secure together the new corner formed by the endpoints of fold #9 using a strip of tape. Do the same for folds #10, #11, and #12.

You should be left with a box lid with a shoddy bottom edge, but it will be adequate for this demonstration.

If you take the box by its bottom edge near the endpoints of folds #17 & #18 and pull very lightly, you'll see that the open end of the pleats behave very much like you'd expect from an unsecured accordian pleat. However, if you take the box by its top edge near the endpoints of the same two folds, a very light tug will reveal that the pleats across the top resist unfolding. This is because bending the pleats around a corner introduces surface tension that is absent from an accordiant pleat, giving the pleat greater resistance to stretching.

If you place your fingers inside the folded lid and gradually pull the pleats apart, you'll observe that they have much more resistance to lateral motion than an accordian pleat. This resistance remains until they are almost completely opened. Pleats running at right angles to each other (allowing expansion in two or three dimensions) do not prevent expansion. This simple pattern allows expansion to more than four times the starting volume of the completed box. The same principle can be extended to allow 20 times expansion by simply introducing additional rows of pleats.

If you examine the box after opening it fully, you'll see that friction and material fatique degrade the paper at the pleats, particularly along the creases. This is especially true at the point where two pleats cross at right angles because the paper there is pulled out of both pleats at once (though with relatively little extra force). However, it is equally important to note that the pleats are the only place on the sheet where this damage occurs. The friction damage could be countered by using thicker material, but this would increase the local curvature of the paper where it is creased and lead to even greater shear. The curvature of the creases can be reduced by including loose, thin sheets of paper between the folds of the pleat, which would be expelled as the pleats were opened. These would hold the pleats apart slightly, reducing the damage to the paper at the fold. And, if necessary, the square surface regions where the pleats cross each other can be cut out and removed without reducing the strength of the box.

A similar principle could be applied to the VBP platform to allow it to expand as it ascends yet still retain some surface tension for structural strength. This is an attractive alternative to using ropes and other restraints to literally hold the ship together as it ascends. If the pleats can take up part of the load, then the shroud's behavior during the ascent is a natural consequence of its own expansion and does not require an active controll system that may malfunction.

CME