Thanks everybody for the feedback.

@All The unfold tool did help. There is still distortion around the tip of the spinner that I just can't get rid off. It's almost a catch 22. When I correct the distortion on the tip, then the rest is distorted. When the rest are OK then the tip is distorted. I have kept both versions of the UVs in separate UV sets and when I get to texturing the spinner I'll be able to see which one is going to give me less problems. What I did notice about the unfold tool is that it had almost no effect if "Weight solver to" was set to a non-zero value (Even .0001 produced little effect).

@Dave, my only prior experience with UVs was the haunted house tutorial and that was all nice flat, unsmoothed geometry.

@bullet, you are wicked! Spiral pattern! Thanks to the Germans I actually have a choice among no pattern, split straight in two or spiral.

@Chavfister, I have just mapped the individual pieces of geometry and scaled each to fit within 0,0:1,1. I still have to scale them in relation to each other. I did have a look at RoadKill and Headus but unfortunately there isn't a Mac version of Roadkill. I'll stick to doing UVs manually until I can create good UVs. Then I'll automate.