Fan Tip Speed and Shock Waves
 

Having a few idle moments and calculated that the tip speed for the fan on a GE90-115B at 100% N1 is Mach 1.18 at sea level and 1.35 at 35,000 feet. (Just been reading "Not Much of an Engineer" by Sir Stanley Hooker). To me that means shock waves a plenty and hence inefficiency (if I read across from propeller theory correctly). Put me out of my misery, whats going on?

Are you allowing for compression in the inlet? A bit of heating there may be pushing up the speed of sound. I'd be pretty sure the tips aren't sonic, whatever the explanation ...

Turbo fans do indeed run with super-sonic tip speeds. The RB211s typically had Mach 1.4 at the design point.

Standard propeller theory is not very useful for two reasons; the blades are cascades rather than isolated airfoils (i.e. the distance between blades is only a few chords, so flow is essentially parallel between blades), and the fan is in a duct which inhibits radial flow around the tips. This leads to an aerodynamic design considerably different from a propeller.

The shock waves generated at the tips propagate non-linearly and generate the rasping 'buzz-saw' noise familiar on some types - most noticeable when the tips have only just gone sonic.