Geometry Question
 

I'm trying to compare the reach of two bikes. I like the fit of Bike A with 52.5cm top tube. I am trying to set up Bike B to fit like Bike A so I need to know what the reach is in relation to the bike that fits me well.

Bike A: 72.5 head tube angle, 75 seat tube angle, 52.5cm top tube
Bike B: 72.0 head tube angle, 73.5 seat tube angle, 53.6cm top tube

I've read that .5 difference of seat tube angle = .5cm of tube tube

There a 1.5 degree difference in seat tube and .5 difference of head tube. Bike B has both slacker angles. Does this mean Bike B has a reach of 51.6cm relative to Bike A???

Any formula that I can use to figure this out?

You mean, .5cm of top tube? I say that is off. On my bike which is larger, it equals about half that one degree equals 6mm. That said, on bikes you want to be similar, and ridden the same way, you will need the same seat to pedal position. So seat tube angle is zero change, unless it was so great, that you couldn't adjust it out, in which case the frame is unridable for you. So all you have to worry about is the head tube change, and that looks within stem range. Also the head tube and top length changes will to some extent net, so you should have about 1cm to deal with. At a guess.

In any case, all you need to do is get a large piece of paper and draw it out. Or do it in cad

It can be figured out, but not by a simple formula. If you want the two bikes to feel the same, we have to get your saddle into the same position on both bikes, and the saddle to bar reach to be the same.

The 1.5 degree seat tube angle change will result in a saddle setback change of about 1.7 cm, assuming your saddle height to BB is 68.5 cm (close to my setup). With the shallower seat tube, you'll need to position your saddle 1.7 cm farther forward to get your knee to BB relationship the same as it is on the steeper bike.

The difference between top tubes is 1.1 cm. With the shallower-angle frame, you'd need a top tube 1.7 cm longer with the same stem to put your hands where they are on the steeper bike. A stem that is 0.5 cm longer than on the steeper bike would get your reach about the same as you have now.

The reduction in head tube angle in the shallower frame will move the front wheel farther away from the BB, I think it will be more than a centimeter. This will reduce any tendency for toe overlap with the front wheel. This will have a very small effect on the handlebar clamp position.

Hmm, you're right, I just ran the trig on that, and it is 1.79 cm. I'm surprised because that 1/4" figure I thought was straight from a CAD drawing I recently did. Oh well, I misremembered. Tan for 1.5 degrees is .02618. I still think it is likely to net out with a different post, and seat position.

I think these calculations are precise, but the input data are not. I can get as many decimal points as one would like, but it makes no sense to go below a millimeter. Besides, for better or worse I made an assumption about the likely saddle height.

There is a spreadsheet called "bg101" that will answer questions like these if you don't feel like doing the trig by hand. Of course you need to know the other angles and tube lengths.