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Re: Motorcycle Steering



Dan MacIsaccs, I believe you are a biker (on beautiful AZ highways, no
less) please read and comment if you have time.

Thanks to Jim McLean for his response to my question about the physics of
motorcycle steering. I'm posting my response to his response on Phys-l in
case it may be of interest to others:

Jim writes:

Although the *forces* of gravity and centrifugal force don't balance, their
*torques* do (i.e., about the pivot point where tire meets road). Although
that idea would be easy to explain (even to someone who hasn't heard of
angular momentum), in this case I think most people would regard the
distinction between force and torque as a detail of little importance. So
I would suggest that it would be more important to focus on the other
factors in a letter.

I will accept the explanation that the *torques* exerted by gravity and
centrifugal *forces* balance as *valid* only in the non-inertial,
accelerated frame of reference of the rider who has to invent the concept
of centrifugal force to make Newton's Laws of Motion for inertial frames of
reference vaild in this non-inertial F of R. In the rider's F of R, the
force of gravity is balanced by the normal force of the road and the inward
force of friction is balanced by the outward centrifugal force and, as
mentioned above, the torques balance while the bike is leaning into the
curve.

Since most people believe in *centrifugal* force is why I asked:

QUESTION: Should I even bother to respond to the article since the "common
sense" (which isn't common) of the vast majority of the readers will agree
that outward centrifugal force balances gravity and they will never have
heard of angular momentum?

Even my dear father passed away at age 83 years believing that his physics
teacher son with the fancy BS, MAT, and MS degrees in physics (Thanks to
NSF) didn't know what he was talking about when he said that centrifugal
force was fictitious, that they only force acting on a satellite was
gravity. His explanation was that it was in orbit because that is where
gravity was balanced by centrifugal force. Same thing with mud flying off
the wheel of a bicycle - "centrifugal force". And yet he couldn't find any
centrifugal force on baseball thrown horizontally and curving towards the
ground. His physics made sense to him.

Getting back to motorcycle steering: In the inertial F of R of the
spectator watching the motorcycle rounding a curve, the force of gravity is
balanced by the normal force of the road (which are anti-parallel but not
colinear). The horizontal force of the road (friction) is unbalanced and
is the centripetal force causing the direction of the velocity to change
direction. What about the torque exerted by the force of gravity on the
bike WRT the point where the tire makes contact with the road (obviously, a
moving point). If you find the torque of normal force WRT the tire contact
point, the torque is zero. It *seems* as though torques are unbalanced and
the bike should fall over, which it doesn't.

AH-HA, one can only pick the tire contact point about which to write
torques in the non-inertial frame of reference of the rider and we're back
to that fictitious centrifugal force again (fictitious to the stationary
observer).
Let's pick the center of curvature of the road as a fixed point (WRT the
stationary observer) as a point about which to write torques due to gravity
and normal force of the road. r cross Fg points towards the rear of the
bike. R cross Fn points towards the front of the bike and R > r since the
bike is leaning. This unbalanced forward torque causes the L of the wheels
(pointing left and up because the bike is leaning) to slowly move forward,
which, of course, it must do as the bike gradually changes it direction of
travel.

If I were the average motorcycle rider (or my dad), I would choose to
believe in centrifugal force rather than believe in the above explanation.
My response to the author of the motorcycle magazine writer would not
include the above, only why push right creates lean to the right rather
than push right car-steers the wheel to the left, moving the contact patch
to the right, creating lean to the right.

Quoting me, Jim writes:


A SECOND INTERESTING ASIDE: If you do not ride a motorcyle, you can
demonstrate counter-steering to yourself while riding a bicycle.

Then he adds,

I don't know the first thing about motorcycles, but I know for sure that
*during* a turn on my bicycle, the handle bars are car-steered. I assume
that the same is true of motorcycles, and that counter-steering applies to
*starting* a turn?

Again quoting me:

While
riding at a safe, reasonable speed, gently push forward on one of the
handgrips and notice what happens to the bicycle.
....

I have a Multi-Track bicycle and I live in the country with lots of hills
and winding roads, and believe me, I've tried to analyze how I steer my
bicycle since I did fine for years before I ever heard of counter-steering.
So I started by riding *no hands*. Riding *no hands*, I create lean by
shifting my body weight and the front wheel car-steers itself becoming less
noticeable at higher speeds. Even with my hands on the handle bars, I do
indeed car-steer my bicycle at low speeds just as I do riding one of my
motorcycles at low speed. As a Motorcycle Safety Foundation instructor, I
teach students how to start up from rest making a sharp right or left hand
turn: Lean bike over slightly and turn front wheel in the direction of the
turn.

However, riding my bicycle at greater than, say 6 m/s, I notice that I
don't car-steer my bicycle. Rather, it seems to be a subtle, almost
instinctive, combination of minor body weight shift and unconscience pushes
and pulls on the handgrips, learned so long ago via immediate feedback that
I don't even think about what I'm doing just as I don't think about how to
swim when I fall off the dock while my wife,who doesn't swim cannot imagine
not thinking about what to do should she fall off the dock. (She does ride
her own Harley Low-Rider). Going around a sharp curve at 10 m/s, I notice
that the front handle bars don't seem to be car-steered at all but the bike
is leaned over alot with road friction creating the centripetal force.
Since a car doen't lean (or leans the wrong way, centripetal force from
road friction must be created turning the front wheels. In doing your own
demo on a bicycle, the key word is *gently* since, if I push too hard on
the right handgrip, the front wheel car-steers to the left but the bike
leans to the right, as Jim noticed, creating a seemingly unstable wobble.


Re-performing the experiment confirmed my previously formed opinion based
just the sort of thing you mentioned above. My explanation is somewhat
different than yours.

Pushing on the right handle bar causes the bicycle to turn left just as a
car does; there is no counter-steering effect directly attributable to the
push on the handle-bars. However, the bicycle is now turning while
vertical: in the bicycle's reference frame, there is a torque from
centrifugal force tending to tip the bicycle over to the right, and no
torque due to gravity. If this condition persisted, the bicycle would
indeed fall over to the right - ouch!


The phrases I disagree with is:

there is no counter-steering effect directly attributable to the
push on the handle-bars.

in the bicycle's reference frame, there is a torque from
centrifugal force tending to tip the bicycle over to the right, and no
torque due to gravity. If this condition persisted, the bicycle would
indeed fall over to the right - ouch!

Try this with a bicycle wheel in the physics lab which has handles mounted
on the axle. Suspend this wheel on strings from the ceiling or just hold
the wheel on two fingers. Get the wheel spinning as fast as you can. Then
gently push forward on, say, the right axle. The wheel will lean to the
right (much to the surprise of your students) and this lean cannot be
*explained* by centrifugal force since any centrifugal force (to a bug on
the tire) is outward in all directions in the plane of the wheel and
therefore no net centrifugal force.

Trying to visualize your "torque due to centrifugal force", I get this:
Push right on right handgrip, bicycle turns left, centrifugal force to the
right causes bike to lean right, bike is now going around a right hand
curve due to inward centripetal force of friction and the centrifugal force
now switches to the left to balance gravity (via torques). I'm glad you
noticed and realized that if you continue to push on the right handgrip,
then-=>

If this condition persisted, the bicycle would
indeed fall over to the right - ouch!

You are correct when you state:

To summarize, the initial counter-steer is just a way to tip the bike to
the right, so that a balanced turn can then follow.

At one time I had 4 bikes but now I'm down to 2 (not counting my wife's
Harley) since I found it difficult to ride all four bikes at the same time.
At low speeds, I car-steer. At higher speeds, I counter-steer. To go
around a right hand curve, I push right to lean right. Once the lean is
estabished, I relax my push and slowly roll on the throttle (my speed is
the slowest at the very beginning of the curve) increasing the push as
needed. Sometime the curve tightens (exit ramp) or there is an obstacle in
the road and I push on the right or left handgrip as needed to either lean
over more or to straighten the bike. If, for some reason, I have to roll
off the throttle (poor planning due to not looking through the curve)
causing the suspension to shift forward, I try to straighten the bike as
much as possible first.

I still disagree with:

To summarize the differences from David's understanding, the torque on the
front wheel (about the steering column) from the initial counter-steer is
not the main cause of the bike tilting - instead the tilt is due to
centrifugal force.

Maybe Dan MacIsaacs can help us out here. Dan??



Thanks for your patience reading this. I'll try to not think of how many
papers I could have graded while typing this (this was more Phun)

Bye, David

PS: If I can find the time to draw the diagrams with a Mac paint program,
maybe I can encode it as a .gif file and paste it into a phys-l post. I
enjoyed Donald's picture of the Leyden Jar.

I'M SPENDING TOO MUCH TIME ON THIS MOTORCYCLE STEERING STUFF, JUST BECAUSE
OF BAD PHYSICS IN A MOTORCYCLE MAGAZINE WHICH I WOULD NOT HAVE HAD TIME TO
READ HAD IT NOT BEEN WINTER BREAK !!!!!!!!!!! But it's phun !!

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David R. Thiessen FUN + PHYSICS = PHUN
Science Department PHYSICS IS PHUN !!
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dthiessn@nslsilus.org (Quote sources long forgotten)
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