From: jsr@TorreyPinesCA.ncr.com (Joe Riel 3752)
Subject: Front Brake Usage
Organization: NCR (Torrey Pines Development Center)
Disclaimer: This posting does not necessarily reflect the opinions of NCR.
Distribution: usa
Date: Tue, 15 Dec 92 02:45:26 GMT

As John Forester states, at maximum braking the brake lever force 
(more accurately the brake pad frictional force) is essentially 
independent of the grade.  For example, for a 15% grade (quite 
steep for a road bike) the maximum frictional force is 98.87% of
that for a level surface, an insignificant difference (1.13%).  

Two questions seem relevant:  (1)what sensed variables are used to
control braking, and (2)how closely does a trained cyclist come to
achieving optimal braking?  Following is some speculation about the 
first.

Since, as mentioned above, the maximum braking frictional force is
essentially independent of the slope of the road, brake lever force 
would at first seem a desirable method of achieving optimum braking.
Cable brakes are quite lossy, however, and for a given force at the
hand lever the force at the calipers can vary over a large range.  
Consider a front brake efficiency of 70%, for a given force at the 
brake lever, Flever, the normalized force at the calipers will be between 
Flever/0.7 and Flever*0.7, a range of 2:1.  This is too large a range
to achieve consistent, near optimal results.  

Sensing the deceleration directly, by using our built-in accelerometers,
and adjusting the lever force accordingly can reduce the effect of the
brake system hysteresis (though the closed loop analysis could get
tricky :-) but is liable to send us over the handlebars when the slope is
downhill.

Sensing the onset of pitch over by detecting a skidding rear wheel
seems a reasonable strategy to pursue since it is almost independent of 
the brake force transfer function (there is some dependence on the
rear brake, but the forces are low so that the effect on total 
braking force should be rather small).  The technique is to apply a light
force on the rear brake lever and then progressively increase the
front brake force until the rear wheel begins to skid.

Which method, or combination of methods, if any of these, we really use
(not just what we think we use) is an interesting question and can 
probably be determined with some reasonably simple experiments.

--------

John points out, as I admitted, that my estimate for the effect of
sliding off the back seat was based on hypothetical values; previous
experiments by him indicate that the actual values are somewhat
less.  Experimental values, in my book, carry far more weight than
arbitrary guesses so I'll defer to his judgement but will investigate
this a bit further to see where the discrepancy lies.  We both will 
agree, I think, that in a "panic stop" the purpose is to achieve a 
rapid and controlled, but not necessarily maximum, deceleration; if 
sliding off the seat causes the rider to delay the application of 
braking or to lose some control then it is probably better to remain 
in the original position.

There is a case where maximum braking is required, and that is during
mountain bike technical descents; sliding off the seat is often the
only reasonable way to ride down some sections.  A relevant difference
between this case and that of a panic stop is that the rider has time
to prepare.

Joe Riel