Doug Goncz
Apr8-06, 04:01 AM
Hello, spr.
I rode to the Hoffman Building Thursday to see the hubbub surrounding
the Moussawi trial and meet with some friends from XP class to watch
Failure to Launch. I selected my route based on slope using mapping
software. I stayed on high ground until I needed to descend. It seemed
a useful strategy and I made good time. I wondered if a "comfort
eikonal" could be encoded into a future software package to provide
bicycle riders with decent routing between arbitrarily chosen points A
and B.
"Comfort" is a vague term having a lot to do with work to capacity at
rates determined by an exponential relationship documented in
mechanical engineering handbooks. For example, a laborer can do around
80 watts of work for around 8 hours, or around double that for half the
time, up to the point of an instantaneous capacity of very rough order
1000 watts. So let's think of what kind of eikonals are available
between points A and B on terrain in the presence of normal gravity:
An eikonal is the path minimizing a parameter of the path. Some
measurable parameters of bicycle travel are, in rough order of
decreasing measurability, time, distance, speed, and energy cost. Time
is easy to measure in the moment with a clock, but more difficult to
predict over terrain with little exact knowledge of wind and rider
performance. Distance is something we have a pretty good handle on both
as an odometer function and from existing terrain databases. Speed,
instantaneously, or as an average readable from a display, is
available, but average speed difficult to predict because energy cost
and human performance are both difficult to measure and difficult to
model.
It seems to me that converting a terrain database from altitude to
local slope with the grad function would give a "medium" through which
paths could be found connecting points A and B while minimizing effort.
A ray of light travels from point A to wherever it ends up in such a
medium of varying "refractive index". Simply "shooting" at point B
might be entirely futile. However, with points A and B fixed in the
medium, starting with the direct route, it seems to me that paths could
be evolved towards those minimizing effort in steps and the
computations abandonded when sufficient progress was made.
For example. DeLorme's Topo software offers profiling along either
direct and road/trail routes. When I had that software running, I
extracted some profiles and analyzed them in Mathcad using its
fourth-order Runge-Kutta solver to get estimates of travel time with
simulated bicycle performance including wind resistance, gear shifts,
rolling resistance, human power input, and other factors.
What I am after here is a Smart Bike that will give the operator of a
bicycle the ability to make effective decisions about Which Way to Go,
weighing various factors relevant to the decisions, but mostly
following the slopes along roads to minimize energy cost and so to
maximize range or comfort. A courier would have different priorities
from a tourist.
I'd like to start with Farfax and Arlington counties in Virginia, and
Falls Church and Alexandria cities. Northern Virginia, in other words.
About ten miles square at 100 foot intervals. It's only 250,000 data
points, a matrix size easily handled in Mathcad. 500 pixels square when
displayed.
Can any of you say where to get the data for conversion from altitude
to slope? USGS?
Might slope data already be available?
Doug Goncz
Replikon Research
Falls Church, VA 22044-0394
I rode to the Hoffman Building Thursday to see the hubbub surrounding
the Moussawi trial and meet with some friends from XP class to watch
Failure to Launch. I selected my route based on slope using mapping
software. I stayed on high ground until I needed to descend. It seemed
a useful strategy and I made good time. I wondered if a "comfort
eikonal" could be encoded into a future software package to provide
bicycle riders with decent routing between arbitrarily chosen points A
and B.
"Comfort" is a vague term having a lot to do with work to capacity at
rates determined by an exponential relationship documented in
mechanical engineering handbooks. For example, a laborer can do around
80 watts of work for around 8 hours, or around double that for half the
time, up to the point of an instantaneous capacity of very rough order
1000 watts. So let's think of what kind of eikonals are available
between points A and B on terrain in the presence of normal gravity:
An eikonal is the path minimizing a parameter of the path. Some
measurable parameters of bicycle travel are, in rough order of
decreasing measurability, time, distance, speed, and energy cost. Time
is easy to measure in the moment with a clock, but more difficult to
predict over terrain with little exact knowledge of wind and rider
performance. Distance is something we have a pretty good handle on both
as an odometer function and from existing terrain databases. Speed,
instantaneously, or as an average readable from a display, is
available, but average speed difficult to predict because energy cost
and human performance are both difficult to measure and difficult to
model.
It seems to me that converting a terrain database from altitude to
local slope with the grad function would give a "medium" through which
paths could be found connecting points A and B while minimizing effort.
A ray of light travels from point A to wherever it ends up in such a
medium of varying "refractive index". Simply "shooting" at point B
might be entirely futile. However, with points A and B fixed in the
medium, starting with the direct route, it seems to me that paths could
be evolved towards those minimizing effort in steps and the
computations abandonded when sufficient progress was made.
For example. DeLorme's Topo software offers profiling along either
direct and road/trail routes. When I had that software running, I
extracted some profiles and analyzed them in Mathcad using its
fourth-order Runge-Kutta solver to get estimates of travel time with
simulated bicycle performance including wind resistance, gear shifts,
rolling resistance, human power input, and other factors.
What I am after here is a Smart Bike that will give the operator of a
bicycle the ability to make effective decisions about Which Way to Go,
weighing various factors relevant to the decisions, but mostly
following the slopes along roads to minimize energy cost and so to
maximize range or comfort. A courier would have different priorities
from a tourist.
I'd like to start with Farfax and Arlington counties in Virginia, and
Falls Church and Alexandria cities. Northern Virginia, in other words.
About ten miles square at 100 foot intervals. It's only 250,000 data
points, a matrix size easily handled in Mathcad. 500 pixels square when
displayed.
Can any of you say where to get the data for conversion from altitude
to slope? USGS?
Might slope data already be available?
Doug Goncz
Replikon Research
Falls Church, VA 22044-0394