If someone had asked me some time ago about bicycle frame geometry I would have answer simply in terms of 19”, 20” for MTB or 56, 58 for a road bike. I was of course aware of basic measurements such as Top Tube length or Standover Height and have passed a few times my measurements through a fit calculator but I haven’t given much thought from a geometric, or trigonometric to be more precise, point of view.
However comparing bicycle frames online I realized there are a lot of subtle changes which ultimately affect your riding style and comfort which are not contained in an information such as: “This is an 18” frame”. For this reason I started digging through my math old knowledge and wrote a small app to sketch and compare bicycle frames.
Everything starts with the bicycle:
Based on the above, real, bicycle, one can then create a theoretical bicycle based on the following measurements: Wheel size (WS), Bottom bracket offset (BB), Chain stay length (CS), Seat tube (ST), ST center-center (STCC), Seat tube angle (STA), Wheel base (WB), Head tube (HT), Head tube angle (HTA). These measurements are the ones usually provided as the bicycle geometry. Depending on the manufacturer, sometimes either the Reach (RE) and Stack (SK) or the Top tube horizontal (TT) and Top tube sloped (TT’) are provided. The meaning of the above measurements should be obvious from the image above, if not, a good place to start is on wikipedia.
Some things are ignored in the process, such as the frame tubes width, their shapes or their position on the head tube. It should be possible however, within the theoretical model above, to calculate and sketch frames with an informative degree of accuracy.