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For example, with a 20% power variation (+/-
average power target) whenever the road tilts up
or down by 7%, a little more than 10 seconds
would be lost to the theoretical minimum time to
cover the course. Similarly, a 0% power
variation at a 0% grade (constant power effort)
would result in slightly more than a 20 second
time loss. The theoretical best way to go
up Couser Canyon road would be to vary power by
60-80% above the average power constraint level
whenever the road tilted up/down by 6% (as
indicated by the 0 second contour on the plot).
Several case results have been tabulated below:
An example of the instantaneous power versus
distance plot for some of the modeled cases
looks similar to this:
The above profile is not very useful, other than
showing that the initial section was done below
the average power target of 289 watts and that
power should go up on the steep sections and
down on the flat/downhill sections. This
plot becomes slightly more interesting when a 30
second rolling average is computed and then
compared to the “real” data acquired during the
pace-by-feel effort.
The above plot (red is actual data, black is
simulated data) shows my best guess at the
variable power strategy that I employed during
the effort (50% power variation at +/- 6%
grade). This variable power effort would
have resulted in being a mere two seconds off
the computed, optimal time. The plot shows
that up until 500 seconds the actual and
simulated data tracks exceptionally well.
The subsequent 500 seconds shows some
significant deviation – trends and magnitudes
are pretty good on an overall level, though.
The following plot is an overlay of several
different cases that were modeled:
Probably the most interesting thing about this
plot is to notice the 289 watt constant power
line (green) and the minimum time power line
(light blue) – not very similar, huh?
Section 1 of the course is done primarily below
the average power target; section 2 has a
gradually increasing slope to its power.
Section 3 is again below the target power,
allowing the body rest up for the above average
power target period during the last 5-6 minutes
of the effort.
It should be noted that all the simulated trials
and the actual power generated over the course
exhibited the same general patterns – one should
go slightly harder when the road tilts up, and
slightly easier when the road is level/tilts
slightly down for optimum performance.
More importantly, the results show that a
variable power pacing strategy can make a
significant difference in the total time to
complete a course.
While instantaneous speed may not be
particularly valuable for identifying general
trends in performance, instantaneous speed can
demonstrate the accuracy of the mathematical
model. The first plot below is an overlay
of actual speed, speed determined without an
inertial term in the equation of motion (power
consumption due to speed changes is not
accounted for), and speed determined while
considering inertia effects:
It should be clear that the red line is the no
inertial term result. If the no-inertia
red trace is removed and the data is re-plotted:
we can see that mathematical modeling does a
pretty darn good job of measuring “real-world”
performance. Isn’t math cool?
Conclusion
While some may describe doing time
trials/training tests as “I was just going as
hard as I could”, this should not be construed
as “I used a constant power pacing strategy
during the effort”. It should be clear
that the results of this obscure analysis
suggest that if the terrain is variable, a
variable power pacing strategy will result in a
significantly faster time to complete the
course. The best way to determine this
variable power pacing strategy is to practice on
the course and see what works – a power meter
should help to accelerate this whole process of
pacing optimization.
During the Mars project, JPL engineers used a
lot of elbow grease, smarts, and the power of
supercomputers to iterate on design concepts.
As a result, the evolution of the Mars landing
system was sped up until it had reached a near
“optimal” state. On “race” day, the hugely
challenging task of landing on Mars was made to
look easy.
It’s also kind of the same with racing bikes
– if one rides enough, sooner or later, that
supercomputer between one’s ears will figure it
all out and tell your legs, heart, and lungs
just the right time to step on the gas and just
the right time to ease off, making the
complicated task of pacing by feel look easy.
So get out there and ride your bike - “optimal”
performance is just around the corner…
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