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Stem length by trigonometry(6 posts)

Stem length by trigonometryMGS
Feb 6, 2002 5:27 PM
I can't remember my trig well enough to do the math.
If I have a 11cm stem, with a 0 degree rise, and switch to an 11 cm stem with a 10 degree rise, How much effective length do I loose?

Can someone give me the answer and/or refresh my memory on the math. The problem confronting me is do I need to use a 12 cm stem to compensate for the apparent shortened reach?

I recall a web site with all this figured out, but can't remember the URL.

from "not pythagoras"
trig lesson 101...C-40
Feb 6, 2002 7:13 PM
The horizontal projection of a stem is calculated by multiplying the cosine of the stem's angle (relative to horizontal) times it's length.

I assume by a "zero degree rise", you mean a standard 73 degree stem which is horizontal to the ground with a true 11cm length.

A 10 degree rise, 11cm stem would have a horizontal length of 10.83cm. Not enough difference to matter.

Remember that road stems are not measured by "degrees of rise" like some mountain stems. Common road stems are 73 degrees (zero rise), 80 degrees (7 degree rise), 84 degrees (11 degree rise) and 90 degrees (17 degree rise). Most threadless stems can be flipped to produce a greater rise. An 80 degree stem when flipped, becomes a 100 degree stem with 27 degrees of rise, for example.
re: Stem length by trigonometryDaveG
Feb 6, 2002 7:16 PM
11cm with 0 rise = 10.5 effective length
11cm with 10d rise = 9.8 eff. length

try stem length * COS(stem rise + (90-head tube angle)) = length
AND Rise(in cm) = stem length * SIN(stem rise + (90-head angle))
re: Stem length by trigonometryDaniel
Feb 7, 2002 5:21 AM
I am glad I found this thread. I can use your help. I now have a 10cm threadless stem with a 73 degree angle. I am thinking of replacing it with a stem with a 90 degree angle. Should I go to a 11cm stem to achieve the same reach? My present setup is as follows. I have a steel steerer. I put in 2 inches of spacers to achieve the desired height. Being that the steerer is steel, can I leave it as is, or should I change to the 90 degree stem, and remove some of the spacers? The saving of weight is of no importance to me.


try this...C-40
Feb 7, 2002 9:36 AM
A 90 degree, 10cm stem will raise the bars almost 3cm, but the reach will be reduced to 9.5cm. An 11cm, 90 degree stem will have a reach of 10.5cm.

If you want to get rid of all the spacers, an 11cm, 80 degree stem, flipped over to 100 degrees will raise the bars a full 5cm (2 inches) and the reach would be 9.8cm.
try this...Daniel
Feb 7, 2002 12:00 PM
Thank you for your kind response. The information was very helpful. When I bought the frame, I had no experience in setting up a threadlees stem. I was fearful that I would cut too much off the steerer tube. My main concern now is whether the two inches of steerer tube is strong enough.