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Where do you get these numbers? BB30 axles can be treated as a tube of 30mm OD, square taper axles typically use 6903 bearings, so can be treated as a solid rod of 17mm diameter (although some are hollow*). I was concerned with torsional stiffness, i.e. how much the axle winds up as the left crank is pressed down, since this seems to be a bigger issue than bending, certainly it dominates among BB factors when measuring total pedal deflection under load. BB30 axles are supported much further apart than typical square taper units (i.e. less overhang), so bending deflection is further reduced.

Now calculate the relative torsional stiffness of a 30mm OD 25mm ID tube versus a solid 17mm OD rod, since these are of roughly equal mass per unit length (the tube is 5% lighter). This is proportional to the polar moment of inertia, d^4 for the rod or (OD^4-ID^4) for the tube, so the ratio of torsional stiffness comes to 5:1 in favour of the tube.

The same rationale makes ISIS/Octalink axles (22mm OD 14mm ID) almost precisely the same weight as square taper and 2.3 times as stiff, which seemed like a good idea except that stuffing 22mm ID bearings inside a standard BB shell doesn't leave much room.

*If you bore through a 17mm rod with the 6.5mm pilot for the axle bolts, you need to increase the ID of a BB30 spindle to 25.5 to match the weight, and it ends up 4.7 times as stiff.

To be honest... this is going to be too much like work for me to finish it. Feel free to hire me(££) and I will be happy to!

But, 25mm standard BB, maximum circular axle is 25mm, maximum square axle to fit in this 25mm hole is... 25^2+25^2=a^2, thus a=17.68 mm. Same idea for BB30.

You should have mentioned torsion earlier then!

For flexure, BB30, will not increase stiffness by 3. See above. For torsional stiffness, I dont know, you can work that one out!

Anyway, its a wank idea. Something like a BB axle should not be composite. End of!