# Impossible/wrong frame length calculation?

I have been riding daily a Holland style bike (upright posture) for quite a long time. I now ordered a new e-bike online, with a more conventional shape (so I don't have a good body feeling for how I would sit on it) and for the first time in my life, tried adjusting the bicycle fit myself.

The seat worked well enough. The trouble came with fitting the handlebars to get the right arm angle.

This is a picture from the bike's user manual. It agrees with several online sources that the arm-to-torso angle should be 90°. This is confirmed by info provided by a made-to-measure bike manufacturer, and an article based on an interview with a bike sport physician (both in German).

The problem with that: when I measured myself and used drawings and Pythagoras, I got to to the result that my top tube should be somewhere between 77.5 and 89 cm (depending on drawing realism and handlebar height). Sitting on the new bicycle visually confirms these results - it has a "top tube" distance of 60 cm, and I would easily need 15 to 20 cm more for a 90° angle.

An online calculator wasn't able to work with my measurements - if I read it correctly, it recommends a top tube of negative 7 cm length.

Now, I was quite prepared for a scenario where the ordered bicycle turns out to not be a good fit, so I would have to send it back and go offline shopping. But the problem is, when I browse different bicycle brands online, even the large frames are well under 70 cm in length.

What is the problem? Is it that producers just don't create bicycles for people with my ape factor? Or did I make a mistake in my calculations? Or is that 90° angle a weird rule that nobody achieves in reality? And if it is indeed that I have too unusual proportions, what are my options?

• It would help if you told your measurements. A normal-shaped person who needs 77-89 cm top tube would be 2.5 to 2.9 m tall :) I have never heard of the 90 degree rules except from those who think it's elbows that should be at that angle.
– ojs
Commented Sep 3, 2021 at 15:33
• That's why I asked here :) I'm 1.73 tall, but I have quite long arms, at 63 cm from the shoulder joint pivot point to the inside of the knuckles. My torso measurement is also 63 cm (groin to sternum notch). Calculating a simple right triangle with these lengths gives the highest estimate (89 cm length) while drawing more realistic models give the lower estimates. But even with the "shortest" model, if I want to keep the 90 degrees angle, a 60 cm tube means the handlebar would have to go 21 cm below saddle height, which on my new bicycle is the lower edge of the front tube. Commented Sep 3, 2021 at 15:49
• What type of hat is the illustrated model wearing? Commented Sep 3, 2021 at 19:35
• General comment: we don't generally size most frames by the actual top tube (TT) length unless they're old-style road frames with a horizontal TT. Bikes these days have sloped TTs, and you don't know the slope angle, which influences how long the TT is. It would be better to use the effective/virtual TT (what the TT length would be if it were horizontal) or the reach (search the site for "stack reach" if interested; there are answers referencing these concepts). I second all those who say that 90deg arm angle is maybe not correct and should be treated as an approximation Commented Sep 5, 2021 at 14:27
• The actual and virtual TT lengths have relation of cos(TT angle). So, for 10 degree angle that is quite a lot, the difference is roughly 1.5%.
– ojs
Commented Sep 6, 2021 at 6:41