How small can a folding bicycle be? How light? I'd like to carry one in my shirt pocket for emergencies, or for travel by bus.
Perhaps the frame could consist of waterproofed fiberglass fabric tubes filled with water, pressurized with a thumbscrew, maybe with a little bit of air to support elasticity. Any frame mass over 20kg is probably unreasonable, and let's say 80% of that is the water. That's about 16kg of water. If the water-filled frame comprises 7 segments, each around half a meter, for 3.5 meters total, that's 4.6 liters per meter, a cross-sectional area of 46 cm^2. That makes the tubes about 7.7 cm across. If one of the tubes is under bending stress, the tensioned part of the tube is about 4 cm wide, and we just have to keep the water pressure high enough to keep both walls in tension (so the "compression" wall won't buckle). The tensile strength of glass fibers is around 300-650kpsi (see http://www.roymech.co.uk/Useful_Tables/Matter/Glass.html for details.) Only half of that (or so) is available to resist the bending stress, since the other half of the fiber runs around the circumference to keep the tube from splitting lengthwise. So how much force do we need to apply bending a tube to rip the fabric? We have 4kg of glass over 3.5m of tube. I think that's somewhere around 1000cc of glass, or 285 cc per meter. 7.7cm diameter means 24cm circumference, or 2400 cm^2 per meter, for a thickness of 285/2400 cm, about 1.2 mm. 1.2 mm over 4 cm of the circumference gives a cross section for the tensile stress of 0.48 cm^2, or about .074 square inches --- with a tensile strength of, say, 150kpsi, that gives us 11000 pounds of strength. That's working on a lever arm of 7 cm against a force potentially applied in the middle of the strut, with a lever arm of 25 cm, so that force has to be 3000 lbs. to break the fabric. So we could probably get by with one tenth of that strength, and thus one tenth that amount of glass: 0.4kg, occupying about 100cc. There are still practical problems: how do you make wheels that fold, or do you just use tiny scooter-like wheels? Do you make legs with some kind of mechanical linkage that produces a smooth gait instead? How do you keep the fabric from creasing and breaking glass fibers when you put it in your pocket? (Maybe you unzip the tubes lengthwise and roll them up around a dowel?) Wouldn't even an 0.12-mm-thick layer of fiberglass be pretty stiff? Maybe it would be better to make water-filled fiberglass stilts instead.
