Joe Riel said:Quoted message said:Quoted message said:> All this has no bearing on Doyle's suggestion that the direction
> of a passing bicycle can be assessed from the track it leaves on
> a dirt road.
Quoted message said:Quoted message said:Quoted message said:It should certainly be possible. The rear track follows a curve
of pursuit of the front track. The relation between the two
curves depends on the direction. It's easy enough to figure out
which is the front wheel, start with the front wheel on the given
front wheel track, the rear on the other track, and see if they
continue to match as you trace the front wheel track. Then try it
going the other direction.
Quoted message said:Quoted message said:Quoted message said:I just tried this using the water trails left by wet tires. It
does appear to work, however, it happens to be a sunny day here,
so I had to work quickly. More testing later...
Quoted message said:Quoted message said:You'll need to explain that in more detail. When I ride a curve,
the front wheel always takes a greater radius than the rear. That
the front wheel proceeded the rear wheel in time and space is also
clear. What is unclear is how the direction of this tracking
occurred. If you can point out the physical trace that reveals in
which direction the two tracks were made, I could better understand
it.
Quoted message said:One way to imagine it is to assume that the front wheel follows a
perfect sine wave. The rear wheel will then (eventually) also
follow a sine wave (actually, not quite, but close enough) with the
same wavelength, but a smaller amplitude. If the wavelength is
greater than (about) the wheel separation, the sine wave generated
by the rear wheel should have a small lead with respect to the front
wheel. So the direction of the bike must be such that the phase of
rear track leads that of the front track. That is:
Quoted message said:front track = A*sin(x/L)
rear track ~ B*sin(x/L+phi) with 0 <= phi <= Pi and B < A.
Quoted message said:If you are looking at this backward (x -> -x) then the phase
difference would be negative (i.e. phase lag).
Quoted message said:A practical way to deduce the direction with just a yardstick (which
is a good approximation of the wheel separation of a standard bike)
is to lie the stick so that one end is on the front wheel track, the
other end on the rear wheel track, then make the front edge of the
stick follow the front wheel track. If the other end follows the
rear track, you're moving the stick in the proper direction. I will
test this on my walk tonight (part of the walk is along a dirt path
with bike tracks).
That assumes the rider is riding an exaggerated wavy course on a
smoothly paved road, which isn't the norm, nor does it leave a visible
track. Beyond that, I ride on roads with recently swept wide
shoulders by street sweeping machines (the bike lane) because there
are construction projects along the route. This leaves a dusty
shoulder where every bicycle leaves a visible track. These are all
single lines of slightly varying width as the riders make minor
corrections. You cannot distinguish tires or tread profile... nor
direction, although these folks probably follow right hand traffic.
The whole story is an extension of Doyle's character that claims to
see more than there is to see. Holmes should have known though not to
go to Hotel Zwirgi at the top of the Reichenbach Falls near Meiringen
where he and Dr. Moriarty had to plunge over the falls in order to
free Doyle from writing further adventures. The faithful demanded
that Holmes could not die that way and forced Doyle to write that
Holmes saved himself at the last moment by grabbing onto a branch.
http://switzerland.isyours.com/E/guide/berner_oberland/sherlockholmes.html
http://en.wikipedia.org/wiki/Reichenbach_Falls
http://www.ne.jp/asahi/mayumi/watanabe/rtw/9/shstamd/shstamd.htm
Jobst Brandt