for my next frame i want my bars to sit a bit higher than now, so i'm shopping around and comparing head tubes. will a bike with a longer head tube always sit the bars higher than one with a shorter tube provided the same amount of spacers and stem length and angle? or is there some math i'm missing?

thanks

If you want higher bars, have the steerer cut so that it's longer(higher). Also try a stem with a higher angle. It'll need to be a tad shorter than what you are currently using. Best to get fitted before you buy.

You are correct, longer head tube will sit higher, all other dimensions being equal. Trek's Madone series have a "Pro" fit and and a "Performance" fit. The head tube is 3cm longer on the Performance fit. That's about 1.2 inches.

Yes they will, given your assumptions.

Spacers and stem angle can make up a lot of difference, though at the compromise of bike aesthetics. Bikes tend to look better without them, or with a minimum of spacers. But its really a matter of looks, as the integrity is not compromised assuming we are not talking extremely HT lengths (requiring lots of spacers). The old rule of thumb was that about 25mm of spacers is all you want on a steerer tube. That's probably still a criteria to go by, though modern forks can probably go to 40 without any compromise. The angled stem is also an option for higher, or lower bars.

Many bikes designed for higher handlebar position also come with a longer wheelbase in order to compensate for handling changes of the higher rider position, or so the marketing teams say. But I hear you. I have a higher head tube, about an inch of spacers, AND an angled stem. I would guess that the angled stem provides as much or more handlebar height increase as the taller head tube.

(subtle implication that your current frame might work out with an angled stem, but not meant to discourage you from buying a new frame)

Pay some attention to cockpit length, also. If you raise the bars, but extend the reach, your torso will be at the same angle you started with.

You are (pretty much) correct. If you wanted to calculate it 100%, you'd need to include fork crown height (dist between axle and fork bearing) and the head tube angle, but in practice those two can be ignored.

thanks for the info everyone. my current frame has a 135mm head tube counting the head set cups. the BMC road racer i'm looking at has 175mm head tube in my size and uses an integrated headse. t so i figure it'll be about 35-40mm difference which should put me up a little higher since i'm not really liking the aggressive drop (about 12 cm) i have over 60 miles + i have upgrade fever.