Floating Discs
Loose fitting discs on racing machines. The front disc on my Riii is a loose fit, about 1.00mm of radial movement, as are all others that I have checked. The technical people at Triumph said that it was how they were designed but when I asked what the dimension of the designed radial float and maximum permitted radial float due to wear, the chap I spoke with said that the design department would/could not say but that the disc would wear out before the radial movement became excessive. Your comments in "What's stopping you" explain why sometimes when I apply the front brake the lever travels further than I would have expected. On a road bike the brakes are often used to prevent a bike from rolling backwards on a hill. When the front brake is next applied, the disc will first take up the radial slack an thus a suddenly applied load will be generated on the disc, pins and carrier. Suddenly applied loads have twice the effect as a gradually applied load. This means greater stresses on all the brake disc fixing components. The pins and carrier n my Riii look very similar to the pins etc on other bikes. I asked my Triumph tech person if the had taken "the effect of suddenly applied loads" into consideration when this feature was designed into the breaking system. He could not say. Racers of course won't have this problem of suddenly applied loads.
Sorry, it's my pretentions to appear as though I have a classical education. Triumph Rocket Three (iii).
I think I recall that they mentioned Tokico as the supplier. I agree with all your comments but wonder why a fully floating disc was fitted

Ah no, that was me being thick, sorry! Actually I'm surprised they have fully floating discs on that or any road bike, most bikes have what are called semi-floating discs, where the steel disc is located on buttons on the carrier but you can't actually wobble it. Even high end superbikes like the 1198, Fireblade etc only have semi-floating discs. These allows for some heat expansion but not as much as race discs. I guess it's because the R3 is so heavy and also very powerful. You can be sure Tokico will have thought of pretty much everything you're likely to do with the bike though, and quite a lot that you're not - imagine the lawsuits you'd get from bad brake design...
I haven't checked the axial movement but will. It is certainly not possible to "wobble it" but the radial movement is quite obvious

By wobble I didn't mean moving it in any particular direction, just that it was loose enough to move about, as distinct from semi-floating discs which you can't move by hand even when they're cold.
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Discs are looser on race bikes because they run hotter and expand more - when they're up to heat the clearances close right up. All the forces you're ever likely to apply to them are taken into account at the design stage, and in fact brakes are designed with much bigger load and stress tolerances than most other parts of a bike, just because it would be so disastrous if they failed. In fact Triumph and other manufacturers don't design the brakes anyway, they get them from the handful of specialist manufacturers like Tokico, Lockheed, Brembo and so on, so they wouldn't know much about the design parameters. What the bike designers do is specify what they want from the brakes, tell the brake manufacturer who then comes up with something appropriate. As far as someone like a Triumph bike designer is concerned, he'll just draw an arrow to the wheels on his blueprint and write 'good brakes in here'!
Brake failure through fracture or some other breakage is extremely rare, I wouldn't worry about it. The problems that do occur are usually some sort of maintenance error or neglect, although sometimes a tank slapper on a race bike can get floating discs rattling and they'll knock the pistons back in the callipers, so when you come to the next corner suddenly you have no brakes unless you squeeze the lever four times... by that time you're in the gravel!
What bike you mean by an Riii btw?