What follows is technical, and requires heavy use of the brain. The enterprising reader takes a couple of aspirin in advance, to ward off the pain that is coming.


Furthermore (forewarned is forearmed) this article is written for fitters: those who fit for a living, bike shop fitters, coaches who fit their subjects. This is going to be hard even for them. If you’re the hobbyist expressing casual interest, by all means read on, but what you’ll read in the paragraphs below is the technical equivalent of taking a soldering gun to your computer’s motherboard.


When the curriculum for the F.I.S.T. Tri Bike Fit Workshops was first constructed, bike fitting was a one-step process. What you got at the end of the process, if the fitter did his job, was a set of “fit coordinates” specific to the rider.


The curriculum is now two-step, and that second step is determining the bike or bikes that best match that customer’s fit coordinates. In order to do that, we determine the “stack” and “reach” of the bike that fits underneath the aerobars that sit aboard our fit simulator.


Stack and reach are the vertical and horizontal spatial relationships, respectively, between the bottom bracket and the head tube top. Stack and reach is a sort of Esperanto of bike geometry, that is, it grants us the ability to compare all bikes one against the other without having to normalize for wheel size, seat angle, bottom bracket drop and the like.


Some F.I.S.T. fitters report placing their customers on a bike one size up from that which our fit protocol would indicate. The culprit here is finding the right “reach” measure. Why is this any more complicated than the protocol we teach at our workshops? It’s because of the change that happens to a bike’s reach when you “stack up” the stem. There is some fudge factoring required when you use the sorts of X/Y fit tools that we advocate, and fitters who don’t account for this will find a variance between the fit metrics our protocol spits out versus the actual size of the bike the customer needs.


There are three components to the fudge factor, some of which you control, some which you don’t. What this all means, in the end, is that you have to look for a bike with a slightly longer reach than your X/Y axis fit bike would indicate. Typically, it’s about a centimeter, and that’s if you have pretty much no spacers under the stem. If you do anticipate spacers (and typically that’s the case) you’re looking for an even longer bike, that is, you’re looking for a bike that might have 1.5cm more reach than the fit session indicates. You might even be looking for a bike with 2cm of additional reach.


In other words, if your fit session spits out a stack & reach of 53cm and 40.5cm, let us say, what you’re really looking for in your stack & reach tables is a bike with 41.2cm to 41.5cm of reach. That’s if you’re anticipating no spacers under the stem. If you place even minimal spacers under the stem, you’re looking for a bike with a somewhat shorter stack and an even longer reach. I’ll explain why this is so.

Remember what an X/Y fit bike looks like. The head angle is 90 degrees, as in the adjacent illustration. If you stack the stem with spacers underneath it, this does not change the length relationship between the bottom bracket and the aerobars. The bike’s “cockpit” is unchanged on these X/Y fit bikes.


But bikes aren’t built with 90 degree head tubes. They’re built with 72- or 73-degree head tubes. As spacers are placed underneath the stem, the stem rises, yes, but it also travels backward toward the bottom bracket to some degree. This is the basis for the fudging, and the amount we need to fudge is illustrated by that small aqua colored right triangle in the illustration.


If we take 72 degrees as our baseline head angle, the X and Y coordinates of the bike’s front end alters based on high school trigonometry. The sine of 72 degrees is .31. The cosine is .95. This means that if you stick a 10mm spacer under the stem, you’re not raising the bike’s front end 10mm. You’re raising it 9.5mm. Furthermore, your bike’s front end is now sitting 3mm back toward your bottom bracket. This 3mm represents negative reach, and you have to account for that.

But, let’s say you put no spacers under the stem. You’re still not out of the woods. Remember that the stem itself is sitting at that 72-degree head angle. If you executed the fit with a 9cm stem on the fit bike that stem, measured center to center, has its “center” sitting halfway between the top and bottom of the stem clamp. Most stems are about 4cm tall (if “height” is determined by the length of the clamp that attaches to the steerer). Your stem’s midpoint is halfway along that height gradient. The setback, or “negative reach,” of that position is the sine of half the length of the stem clamp. In most cases, that’s the sine of 2cm, which is 6mm. In other words, right out the gate you’ll have to look for a bike that’s got a 6mm longer reach than the fit protocol indicates.


But that's not all. There’s the headset top cap. But it’s integrated, you say, so there is no elevation above the head tube top! If you’re a retailer, go out on your showroom floor and take a look. That top cap is at least 5mm tall and as much as double that, and that’s not counting the top caps that are spacers in disguise.


So, before you add any spacers at all, with the stem sitting right on the headset top cap, we see that we’re looking at about three quarters of a centimeter of reach variance. Maybe a centimeter. That’s why you have to start, right out the gun, even with no spacers at all under the stem, looking for a bike that has about a centimeter more reach than that which your fit process indicates.


Now, if you add spacers, then you’re adding additional complexity. If you’re like most people, you’d like a new bike to go out the door and into the garage with some moderate amount of spacers under the stem, to afford the rider a bit of leeway, in case a slightly lower position be in his future. Mind, I’m not advocating the 30mm or 50mm of spacers we often find on bikes, maybe just 15mm. But even this will cause the fitter to again adjust the reach for which he’s looking another 5mm.


Let’s consider an example. Let us say a fitter executes a fit, resulting in our needing to find a bike with a stack & reach of 53cm and 40.5cm respectively (the process having been executed on his X/Y fit bike). The fitter now considers what new model bikes will work for that customer, and he assumes that the “perfect” bike will have 15mm of spacers under the stem, because every new bike out the door needs a little room for the stem to go up or down in height. He understands that he’ll be searching his stack and reach tables for a bike with something like 51.5cm and 42cm respectively. This, because the extra reach is needed to counteract the “negative reach” incurred by the stem, the headset top cap, and even minimal spacers; and the frame stack is lessened to make room for that 15mm of spacers.


If your favorite fit simulator is that made by Exit Cycling (this X/Y axis bike is my favorite), my rule of thumb is to execute the fit session, derive the reach number, and then add 1.5cm of reach to that number, and look for bikes on my stack & reach tables that match this number. Likewise, I’m subtracting that same amount from the stack, because, again, I’ve got to make room for the 1.5cm of spacers anticipating placing under the stem.


Fitters typically remember to subtract from the stack the 1.5cm of spacers they have to make room for. What they forget is that you must add the following to the reach: .31 x (half the stem clamp + headset top cap + spacers).


But, really, this 11mm to 20mm (15mm on average) worth of negative reach, how much difference will this make in determining bike sizes? Cervelo P3C sizes differ in reach only by an average of about 13mm, P2Cs by 12mm. Felt in 52cm, 54cm and 56cm differ from each other in reach only by 10mm. Kuota’s Kalibur differs in reach by 17mm from M to L, and only 11mm between L and XL. QRs are about 15mm or 16mm apart in sizes. From Scott’s M to XL these three sizes are only 23mm apart in reach. Trek’s Equinox TTX are only 11mm apart from M to L.


So, you see, you jump up a bike size on average when it comes to reach, through normalizing for the negative reach generated through the bike’s stem, its headset cap, and 10mm to 15mm of spacers under the stem. That’s why many retailers report sizing up from that which their fit simulators indicate.