Clarification of Answer by
28 Nov 2004 21:04 PST
Your further questions led me to some very useful additional
material. The previous articles include passages that describe the
correlation of speed and force with depth. The second article mentions
spacing or "pitch", as typically 7-8". I found additional material
below that includes information about why spacing tends to be typical,
as well as a study describing how and why corrugations initially form.
Weight is a combination of mass and gravity, and force is a
combination of mass and speed. Increased speed means increased force.
The articles make the point that speed is the more significant factor
rather than weight, though I do include additional material below on
the factor of the weight of vehicle or load. Google Answers guidelines
to respect copyright are that only limited passages can be quoted from
sources, so the full articles can be read for further information.
The articles describe how increased speed means increased force,
resulting in greater suspension and tire bounce and depth of ruts. The
Straight Dope article discusses this in terms of the tire and
suspension "downstroke" and the speed of the driver and vehicle:
"Wouldn't variations in speed affect the washboard pattern?
Sure...Drive too fast on a washboard road and the downstroke exerted
by the car wheels may meet the road at a point where a bump is ramping
upwards. You know what that means: You bounce off the ceiling.
Instinctively most drivers slow to a speed at which the downstrokes
coincide with the troughs between bumps, reinforcing the
pattern...**Forced oscillation overcomes minor variations in
oscillation rate that might otherwise arise due to differences in car
The "Ripples in the Road" article says about speed, force and depth:
"**High speeds increase both tire force and bouncing. Fast moving
vehicles, therefore, quicken the formation of corrugations and
increase their depth**. [Which is why a solution is that]
Municipalities can encourage some residents to slow down by informing
them of the effect that speed has on washboarding."
And this about spacing, or "pitch":
"The **pitch is the length of a corrugation measured from crest to
crest**, typically 7 to 8 inches."
US Dept of Energy
Ask A Scientist©
"When a **heavy load** passes over the spot it can sink in partially
and then the gravel is displaced from the soft spot."
Geophysical Institute, University of Alaska Fairbanks
Alaska Science Forum
Why Do Roads Corrugate?
"The January 1963 issue of Scientific American contains an article by
Dr. Keith B. Mather, now Vice Chancellor for Research and Advanced
Studies at the University of Alaska, which puts the matter to rest
once and for all."
[See website for description of experiment and further information]
"Among the more significant findings were that:
-**If the wheel moves slowly, no corrugations were formed**, but a
deep rut instead;
-it did not matter whether the wheel was driving or idling, **at
sufficient speeds, washboarding occurred**;
-**the trough-to-trough distances between ruts increased linearly with
-sand was not pushed ahead of the wheel and then overridden to begin
another cycle, as had been commonly believed.
The most important contribution to understanding washboarding lay in
the observation of how the corrugations are actually formed. When the
wheel reaches a certain critical speed, it begins to move in short
hops, bounding on random irregularities of the surface. Hitting an
obstacle, even a small one, propels the wheel into the air for a
certain distance. When it lands further down the track, it sprays sand
forward and to the side, thus creating the beginning of a crater. Each
time it digs itself in at a crater it has to ride out again and thus
repeats the pattern. **If traffic were to move at widely diversified
speeds, different "hop-lengths" might tend to cancel each other out,
but depending on road conditions, all traffic tends to travel in a
rather closely constrained speed range, thus compounding the problem
with each successive vehicle**."
You might check your library catalog for this January issue of
Scientific American and if not, you can request the specific article
through your library's Interlibrary Loan Service.
Here's an online New Scientist question on this topic with a response
by the same Keith Mather, that includes the "periodicity" or spacing
of the corrugations:
"Corrugations may form whenever the force at right angles to the
surface is sufficient to cause permanent deformation. In the case of a
wheel on a road, when the wheel encounters any bump or irregularity,
it is projected upward, moves through an arc, and impacts further
along the road, where it tends to dig in and produce a small crater.
Subsequent wheels that ride up from this crater are likewise projected
and again form a little crater beyond. The corrugations already formed
are reinforced by the repeated passage of vehicles, and new
corrugations continue to propagate down the road from the initial
bump. You can watch the pattern develop on a test track. The
periodicity, averaging about 70 centimetres (27 inches) on dirt roads,
depends on the average vehicle speed (which determines the impact
force), the material of the road, and the tyre and springing constants
of the vehicle."
For more complete information, a popular account appeared in
Scientific American (January 1963), and a more technical version in
Civil Engineering & Public Works Review (May 1962, p 617 and June
1962, p 781).
I hope this is helpful. Let me know if I can be of further assistance. jdb-ga