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Old 12-15-13, 12:06 PM
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wphamilton
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I'm not a frame design expert by any means, but I think I've boiled it down to the rule of thumb basics.

Rider position is determined by the three points: bottom bracket, seat, hand position. The three points are rotated and adjusted for every riding style, (except for trick bikes where you're standing up a lot but I leave that out of the scope). The three points also determine the center of gravity.

Given the rider configuration, seat tube length and height of the top tube depends on leg length. Top tube length is torso and arms.

Where the wheels are relative to the rider center of gravity determines the handling characteristics, and the foot clearance. Head tube angle affects trail, which means responsiveness and stability. And clearance with the feet from the front wheel, generally less of an issue. Chain stay length positions the rear wheel, longer for more straight stability and heel clearance (with panniers), at the expense of "nimbleness".

Some other measurements are more specialized. Bottom brackets are raised (cross bikes) for more clearance (feet and rear derailleur) over curbs, tree logs etc, sometimes pedal clearance when turning. The sloping top tube is mainly for standover clearance - there may be some impact on strength and rigidity, but I don't really see it. Level top tubes are usually prefered for cyclocross since they're easier to carry that way.

I'll probably take some heat for this, but I don't think that the seat tube angle really matters much. It roughly positions the saddle, otherwise is cosmetic.

Although I categorize these for different aspects, they're all inter-related for a given style of bike. A cruiser for example has the upright rider position and therefore doesn't strain to position the wheels to facilitate handling at high speeds, and so on.
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