Stability
or Control?
By Doug Milliken, first published in Human Power, The
Technical
Journal of the IHPVA. Spring 1989, Vol. 7, No. 3.
After the IHPSC in Visalia, I stayed on a week in
the Bay Area with my good friend Max Behensky. The conversation often turned to
practical HPVs and at one point I brought up the old question, "Where
should the center of pressure be on a streamlined bicycle to deal with cross
winds?"
We both knew that on three and four wheelers a center of pressure (CP) near the
center of gravity (CG) is desirable in cross winds. This has been established
for years in the automotive business, perhaps by Dr. Kamm and associates in
Germany, pre-W.W.II. The basic effect of a cross wind on an
"aerodynamically neutral" car is to move the car sideways with little
change in heading direction. If the CP is aft of the CG (big tail fins?) the
cross wind will produce a yawing moment (about a vertical axis through the CG)
that rotates the car slightly up-wind. This in turn produces a tire side force
that counteracts the side force due to the side wind. If the CP is ahead of the
CG (most common) the yawing moment rotates the car down-wind and the tire forces
add to the aero side force. With some knowledge of the aerodynamic and
tire/suspension properties, it should be possible to produce cars (and
non-banking HPVs!) that "go straight", hands-off the wheel, in cross
winds. References 1 and 2 are suggested.
The situation is not so simple for a two-wheeler because the roll (lean) degree
of freedom counts as much or more than the yaw degree of freedom.
Max is a "quick-and-dirty" experimentalist of the first rank and he
quickly suggested that I roll slowly along on the Moulton while he jogged
alongside and applied simulated side force to the frame at different points. A
suitable string was found and it was attached to the frame at various points to
simulate different CP locations for frame-mounted fairing/rider combinations. We
located the string about .8 meter (32 inches) above the ground to get the CP
height about right for an upright bike like the Moulton.
This experiment is so easy to do that I hope you repeat it. I am tempted to
leave out the results but, for the curious, here is what we found.
-
With the string tied at the head tube, Max
pulled sideways (gently at first!) and I found that it was very easy to make
a slight steering correction to return the bike to roll-and-yaw equilibrium
and to keep the path essentially straight. With a little practice, I was
steering and rolling the bike slightly and could resist as much side force
as he could pull. Sharply varying side forces (gusty winds) were tried next
with the same ease of control.
-
Next, we moved the string back to the seat post
simulating a CP aft of the CG. We kept the height above ground the same.
Here the control required was much more difficult. With practice, I could
steer and roll the bike to counter this side force but there always were
several big swerves and the heading always changed. A varying
"gusty" side force was very difficult to
control -- most of the effort went into roll stability (keeping balanced)
and the heading went all over the road!
-
Finally, we moved the string back to the head
tube and reversed the front forks to increase the trail. Now the side force
also produced a large steering torque. This torque steered the bike
"down-wind" which resulted very quickly in a roll angle
"up-wind", just what is required to "lean into the
wind". With a loose grip on the handlebars, the bars wiggled around as
the string was jerked but the bike kept going nearly straight.
The interesting conclusion is that the
"aerodynamically unstable" location of the CP forward of the CG is the
easiest to control and appears preferable over an "aerodynamically
stable" configuration! Control appears more important than stability for
this situation. The experiment we tried did not go to very high speeds so I am
not suggesting that this result is valid at higher speeds. My experience with
large, frame-mounted front fairings has generally been good at speed (on long
hills) in moderately gusty winds.
One variant of this experiment would be to attach the string to the handlebars
to simulate a bar-mounted fairing (ZZipper(TM) or Breeze Cheater(TM)); because
the Alex Moulton AM-7 lends itself so nicely to frame-mounted fairings, this was
not of direct interest to us. If a large paved area was available, you could
ride at higher speeds in a big circle while the assistant stayed near the center
and provided the simulated side-wind force.
I am sure that some of you more theoretical people will be able to work out a
mathematical model for this situation. It must be dynamic and has to include
some type of rider control, perhaps "force control", where the
steering angle is a function of both the rider control torque and the steer
torque arising from the trail. The motorcycle dynamics and aerodynamic data and
models in References 3-4 may be a good starting point but bicycles differ in
several respects, especially speed range, tire performance and weight of rider
relative to machine. Reference 5 comes close but the effects of moving the CP
are not treated.
With a suitable dynamic model, it may be possible to predict a "best"
location for the CP relative to the wheelbase and/or the CG. Likewise, it may be
possible to recommend a desirable CG location for best disturbance response
(this may conflict heavily with other design considerations!!) It may also be
possible to choose a steering geometry that minimizes the control workload for
the rider, given known CP and GC locations.
Doug Milliken is a long-time HPV builder,
wind tunnel junkie (bikes and race cars), and former IHPVA VP-Water. He is also
the co-author of the book, "Race Car Vehicle Dynamics", which can can
be seen on the SAE Online Bookstore (www.sae.org). He is a dealer for Alex
Moulton Bicycles, accessories and parts (USA). For information on AM products,
he can be reached through his engineering company Milliken
Research.
References:
1. I don't read German but the figures are pretty obvious. Cn is the standard
nomenclature for yaw moment coefficient and plots are shown of Cn against alpha,
(angle of attack due to a side wind) for cars of different shapes and with big
rear vertical tails:
Koenig-Fachsenfeld, F. R., "Aerodynamik Des Kraftfahrzeugs"."
Frankfort: Umschau Verlag Frankfort, 1951.
2. In English (but again from Germany):
Hucho, W-H, ed., "Aerodynamics of Road Vehicles". Cambridge,
England: University Press, 1986. See pages 214 and following. Available in the
USA through the Society of Automotive Engineers (SAE), 400 Commonwealth Drive,
Warrendale, PA 15096.
3. Here is some motorcycle wind-tunnel data and some analysis:
Cooper, K. R. "The Effect of Aerodynamics on the Performance and
Stability of High Speed Motorcycles" in "Proceedings of the Second
AIAA Symposium on Aerodynamics of Sports and Competition Cars". Ed. Bernard
Pershing. Los Angeles, 1974.
4. A collection of papers with an excellent bibliography:
"Motorcycle Dynamics and Rider Control", 10 SAE papers
published as SP-428, 1978. Available from the SAE.
5. As a teenager I rode a mini-bike with a small rocket engine attached to the
frame at the CG to simulate a side wind for the following authors; someone else
rode the instrumented bicycle described in this paper. Very complete and complex
model with correlation experiments:
Roland, R. D., and R. S. Rice, "Bicycle Dynamics, Rider Guidance
Modeling and Disturbance Response". Calspan Corp. Report ZS-5157-K-1, April
1973.
