How to fold a tubular tyre

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The most convenient size to carry is probably found by folding the tub four times – so it is roughly one fifth its original ‘unfolded length’. This size will fit snugly inside a cut-off water bottle or neatly under the saddle, but makes it nearly impossible to keep the base tape from touching the tread at least somewhere.
Folding the tub in four – with three folds – makes, obviously, a longer but thinner package in which it is easy to keep base tape and tread apart.
Behind the saddle or in a bottle cage?