## Wednesday, March 16, 2011

### Cervelo R5-CA geometry

The Cervelo R5-CA, Cervelo's \$9000 carbon fiber frame for "experienced riders" who presumably want to ride with a lot of setback (I'm not sure if this is because of superior comfort on the bike or because of increased desire to "look pro") was designed with a 72 degree seat tube. The idea, claims Cervelo, is that the 72 degree seat tube run with a zero-setback post yields similar geometry as their canonical 73 degree seat tube run with a set-back post. Now I happen to like a zero-setback post even with my 74.5-degree seatpost. Obviously I'm not pro material. So those riding with a zero-setback post on Cervelo's 73 degree post seem to be left out of the priceless opportunity to buy this gem of a frame. Tragic: they're doomed to ride Old La Honda an extra 1.3 seconds slower than they could have by virtue of 100 extra grams.

Cervelo R5-CA in the wild. This one checks in at 5.03 kg, 26% below the UCI limit.

Or maybe this is overblown...

Here's a diagram of Cervelo of the R5-CA geometry. I've drawn a center line through the seat tube. You can clearly see it passes in front of the bottom bracket, as opposed to the R1, R2, R3, and R5 where the line passes through the bottom bracket center. From the diagram it appears the line passes 1 cm ahead of the bottom bracket along a horizontal line.

Cervelo diagram of the R5-CA. I drew the green line through the approximate seat tube center.

The relevant question, then, is if I put my saddle on an R5 with a 73-degree seat tube, move to an R5-CA with its modified seat tube, how much further back on the rails will I need to clamp the seat to get the same position?

To get the same position, the height of the rails above the bottom bracket will need to be the same. I'll define this distance as y. Then I'll assume the saddle is clamped at a distance x from the bottom bracket in the case of the 73 degree seat tube. With the R5-CA, I then need to determine the value x' with the same value of y, where positive x is behind the bottom bracket:

On the R5:
x = y / tan 73°

On the R5-CA:
x' = y / tan 72° ‒ 1 cm

I can eliminate y:

y = x tan 73°

which result in:

x' = x tan 73° / tan 72° ‒ 1 cm

Of primary interest is the difference:

x' ‒ x = (tan 73° / tan 72° ‒ 1) x ‒ 1 cm

But y is probably easier to measure than x, so:

x' ‒ x = y (tan 73° / tan 72° ‒ 1) / tan 73° ‒ 1 cm

x' ‒ x = y (1 / tan 72° ‒ 1 / tan 73°) ‒ 1 cm

which evaluates to:
x' ‒ x = y / 52.1 ‒ 1 cm

So this says if your rails are clamped 52.1 cm above the height of the bottom bracket center, then the clamp will be in the same position on both bikes. I justmeasured my commuter bike and estimate y = 64 cm. So for the same value of y, I'd need to clamp the rails 2.2 mm further back on the R5-CA than I would on the R5. Not much difference, really.

So do not fear, Cervelo fans. If you really want to spend \$9000 on this frame, the geometry probably isn't going to hold you back, assuming the Cervelo schematic is accurate. And looking at that photo, while perspective can be tricky, it seems the schematic is.

On the other hand, if I compare the R5CA to my Fuji SL1, I get x' ‒ x = 2.0 cm. That's a substantial shift. To decent approximation, each 1-degree shift in the seat tube angle will shift the rail position by the height of the rails above the bottom bracket divided by 52. So seat tube angle is important. But honestly I never could bring myself to spend that much on a racing frame anyway for almost intangibly small benefit. I'm barely even riding these days anyway.

Fit is an interesting thing, though. I should be heading up to 3D Bike Fit in Sausalito to get mine checked out. Sure, I've had my fit checked before, but it's worth getting it rechecked occasionally.