using 9 cogs with 10 cog spacing
 

Shimano makes a 11 12 13 14 15 17 19 21 23 25 cog set. Both the 11 and 12 tooth cogs have serrations for the lock ring. I took this set removed the 11 tooth cog and put it on a freehub made for 7 cogs. The 25 tooth cog is offset from the carrier placing it 1.6 mm closer to the spokes. You will need to use a 1 mm spacer behind the 25 tooth cog placing it .6 mm closer to the spokes than a standard 7 cog set. This places the 12 tooth cog .8mm closer to the dropout. I used a truvative crank made for a 9 cog chain a 10 cog chain and the system worked. This setup lets you build a stronger wheel than a standard 10 cog cassette would allow.

No offense, but this is a solution in search of a problem. A proper handbuilt built wheel with carefully selected parts will obscure any miniscule benefits you get from running a 7 speed specific freehub.

Do some research on Mavic M10 cassettes. You can make all kinds of magic with them. Shimano 9, 10 or Campy 8, 9, 10 on a Shimano HG freehub. Completely customizable.

I've done stuff like this before but not for spoke angle reasons. I do it so that I can better line up the most frequently used cogs with the big ring for less of a chain angle. If I gain on the spoke angle by using other hubs or whatever that's merely a freebie bonus.

Also don't you mean it places the 12 cog .8 CM closer and not mm?

This is often done to allow continued use of a 7-speed (126 mm OLD) hub with newer cassettes. It avoids having to respace the frame or forcing a 130 mm hub into a 126 mm frame.

It won't build a stronger wheel than a proper 8/9/10-speed hub unless the 7-speed hub spacing is already 130 mm.

Here is a formula developed by Bill McCready of santana http://www.sudibe.de/articles/wheandhub.html If you remove a gear from a 10 cog cluster and redish it will make the wheel 1.6 times stronger. All my wheels are dishless none of my wheels have ever done this http://share.ovi.com/media/currentre...resident.10018 or this http://share.ovi.com/media/currentre...resident.10050 http://share.ovi.com/media/currentre...resident.10017

Tandems typically use 140 hubs (or 160 for Santanna) so they are nearly dishless with any 8/9/10-speed freehub.

What formula are you using to calculate that? I couldn't infer the formula from the article at the end of that link.

em

Ok here is a typical calculation measure the distance from the center of the wheel to the center of the flange this will be about 20 mm on the gear side and 35 mm on the other side for a typical 10 gear setup. If we take out a gear and redish the wheel the spacing will be 24 on the gear side and 31 on the other side. For the first example take (20/35)*(20/27.5)=.4155 this gives the relative strenght of this wheel compared to a dishless wheel (27.5/27.5)*(27.5/27.5)=1.0000 where 27.5 is half the flange width. The rational for this is (20/35) gives the relative tension of the cog side spokes compared to the other side spoke. This is not the correct formula the correct formula involves vectors but it is a good approximation. The (20/27.5) gives the relative sideways pull on the rim compared to a dishless again it is not the correct formula but it is a good approximation. For the new wheel with the cog removed (24/31)*(20/27.5)= .5984 dividing .5984/.4155=1.44 my fault I quoted the 1.6 times figure from memory. Santana tandem has this problem rubbed into thier noses and every one who buys a santana tandem has enough money to sue them. Santana rates their 700c wheels with 48 spokes at 700 pounds and their 26 inch wheels with 48 DT alpine spokes at 1050 pounds. Santana has built quads and quints that carry this much weight. Smaller diameter wheels are stronger and wider flanges are stronger. Hadley racing uses 60mm wide flanges and Chris King uses 65mm wide flanges.