Geometry specifications can be frustrating. It seems like there's always at least one number missing from what you'd need to map everything into an arbitrary coordinate space. Beyond that, I've heard that there is some disagreement among sites that specify reach and stack as to exactly what those numbers mean.

I take "reach" to mean the effective horizontal distance from a point directly above the bottom bracket to the top of the top tube. Salsa appears to indicate it this way in their diagrams. Trek's diagram is a little vague, and might be referring to the top of the steerer rather than the top of the top tube. This same problem of point-of-reference exists for effective top tube specifications. But lets pretend that everybody means the same thing and we're measuring to the top tube since that's fixed.

Now brace yourself. I'm about to geek out.



To calculate reach, you'd need to know the distance along the seat tube from the bottom bracket to the point at which the effective top tube measurement is taken. I'll call this distance H. Given the seat tube angle as A and the effective top tube length as T then reach, R, can be calculated as

R = T - [H * sin(90 - A)]

Of course, you don't really know H. Another possibility is if you knew the veritical height difference, S, between the bottom bracket and the top of the top tube (which I believe is the stack). Then,

R = T - [S * tan(90 - A)]

In theory, you can calculate S if you know fork rake, fork length, head tube length and bottom bracket drop. There is a bit of variability based on the headset stack, but you can get close. If you have bottom bracket height instead of drop, you also need wheel size and tire size. The calculations here are messier so I won't post them.

[/geek]

Now, if you aren't currently wearing a plaid shirt with a pocket protector, it's probably much easier to use the rule of thumb that one degree increase in seat tube angle virtually reduces the effective top tube length by about 1 cm. This rule of thumb can usefully compare frames in a way similar to frame reach if you already have a bit whose fit you know. You can, of course, also vary the practical reach by changing stems. Similarly, bottom bracket drop/height, top tube length and fork length together tell you most of what you want to know about frame stack.