Dear Jobst,
I can't make the angles work out as you suggest.
In fact, an upright seems to have a steeper and
less effective braking angle from center of gravity
to contact patch, 61 degrees versus 54 degrees
for the recumbent.
Here's how I tried to figure the angles. I gather
that the ratio of the adjacent (longer) to the
opposite (shorter) legs of a right triangle should
give the tangent of the angle that I want.
http://www.ransbikes.com/2004Bikes/Rocket.htm
When I measure things for the recumbent from where
I expect the belly button to be to the contact patch,
I get a right triangle with an adjacent side of about
75mm on my screen and an opposite side of 55mm.
(If anything, the center of gravity should be further
back than the navel, given the rider's reclining
position.)
With 75/55 = 1.3636, my tangent-angle lookup shows
an angle of about 54 degrees.
When I look at "Bicycling Science" 2nd edition and
do the same thing for figure 8.6 (the upright bike
with numerous details and an indicated center of
gravity, page. 197), I get a 45-inch adjacent side
and a 25-inch opposite side, 45/25= 1.8, and my
tangent-angle lookup says about 61 degrees.
Here's the corrected address for the blue trike:
http://www.ihpva.org/incoming/2002/dragonflyer/df1a.jpg
Carl Fogel
