On Friday, May 22, 2020 at 4:26:43 PM UTC-7, Frank Krygowski wrote:
On 5/22/2020 5:41 PM, Axel Reichert wrote:
Frank Krygowski writes:

I'm interested in the L * p^2 metric for climb difficulty. I've long
wondered if there was a widely recognized way of categorizing
hilliness.

The easiest is the average gradient over the full ride. Whether you do
two big Alpine passes or 30 nasty hills in Wales, you might end up with
3000 m vertical gain over 120 km, so 2.5 % on average (this is quite a
lot). This is of course equivalent to vertical gain per kilometer: Below
5 m/km is mostly flat, above 20 m/km (= 2 % average gradient) is
tough. All this is of course kind of arbitrary.

If out of academic curiosity you want a binary distinction, there is a
physics-based approach: You could argue that it is mountainous, if you
spend more energy for the vertical distance than for the horizontal one
and flat, if vice versa. Since aerodynamic drag is strongly non-linear
with the speed, that break-even point between flat and mountainous
depends on your speed over the ride. It did this approximately for my
"sporty tourist" style of riding, and came up with about 12..13 m/km.

Pace has some vague guidelines

If you are after an estimate for the riding time, I have an
astonishingly precise rule of thumb. If you know your flat speed, say,
25 km/h, you can try to gather the length, the total climb and the
riding time for, say, 20 rides. Then you do a linear regression
(e.g. with Excel) on

t = l/a + h/b

with t the riding time in hours, l the length in km and h the climb in
m. a is your flat speed, 25 km/h in my example, and the regression gives
you your climbing rate b (total climb per hour). Say, b is 1000 m/h for
you. Then the 30 nasty hills in Wales take 5 hours 12 min horizontally,
plus 3 hours for the vertical wall of 3 km height. (-: Makes for 8.2
hours for 120 km, with an estimated average speed of 14.6 km/h.

Usually, with my coefficients a and b, the estimate is within minutes
of the real ride. Once you have your coefficients and think that this is
a great method for years to come: Now watch these coefficients go down
...

L * p^2 may describe a single pass or long climb, but we're much more
often dealing with a seemingly endless series of short steep climbs
followed by short steep downhills.

Downhills do not count. But L * p^2 can (and should) be applied
piecewise for a roller coaster ride. Since these often are steeper than
the epic climbs (and the gradient goes in squared) you will end up with
a higher total difficulty. In my experience this formula (originated in
a Dutch cycling magazine) does an extremely good job in predicting how
you feel after a ride, no matter whether it is Wales or Wallis.

If you are touring for several weeks in a row, I would advise against
going higher than 2000 per day. 1500 might be more reasonable.

Best regards

Axel

I'm very impressed that those ideas originated in a Dutch cycling
magazine. Back in the 1970s, when I began adult riding, American cycling
magazines contained similar technical thoughts. But now they've switched
to things like "The new bike you need NOW!" or "Shorts to make your legs
look sexy!"

Your post is worth saving and pondering. Thanks for that.

Actually, Bicycling in the '70s was not like that. It was pretty nerdy with Frank Berto talking about half-step plus granny and some pretty tame bike reviews, minor race coverage and lots about camping. https://www.bikeforums.net/classic-v...-magazine.html

It changed after the sale to Rodale, but then it changed more after the next sale.

-- Jay Beattie.