On say a 90mm stem with 10 deg rise, roughly how much higer are the bars than the steerer assuming the steerer end of the stem is flat?

Are we talking 10mm or less?

90mm sin 10deg is very roughly approx 9mm.

So in response you your either/or question, the answer is yes. :p

Sin 10 deg x 90mm = 15.624 mm

Bit of a discrepency there 😕

Inbred456 is correct:
a: sine 10deg = 0.17364817766693
therefore: the rise = 15.62833599mm

Excellent, mathematics to back up the answer 8)

Useful link if any ones interested http://calculator3.sdsu.edu/calculator3.php

It's more than 10 degrees though isn't it, because of the angle of the head tube don't you already start at about 20 odd degrees? Or am I full of the usual guff? 😉

What shermer said.

Think sine 30 ie 0.5

Shermer

My thoughts I'd go for 90*(sin30-sin20) assuming a 70 degree head angle. Thats 14.2 mm

Sorry same answer really

CynicAl

you have to allow for the rise of the zero rise stem

So that's 45mm? That seems a bit much! 🙂

EDIT: oops- looks like someone's already got there…

Shermer see my post, thats only half the calculation

oops you saw it