
How Far Can a Motorcycle Lean in a Turn? - mmastrac
http://www.wired.com/2015/09/just-far-can-motorcycle-lean-turn/
======
joeyspn
> I guess racing motorcycle tires are just awesome

This is essentially the biggest factor. And more important than the surface is
the material. When properly warmed (notice how they always prewarm the tires
in bags before any race) that stuff is basically chewing-gum.

I've worked in F1 and several circuits including the one featured in the
article (Jerez) and I remember the walls in the paddock totally splattered of
tire material at the end of the day. Some days I'd even go back to home with
small pieces stuck in my clothing.

That's the reason why engineers must wear glasses and helmets sometimes..
[https://dfp2hfrf3mn0u.cloudfront.net/879/87936_1.jpg](https://dfp2hfrf3mn0u.cloudfront.net/879/87936_1.jpg)

~~~
donjigweed
Exactly. Tire technology is unbelievable today. With track temps reaching 50C,
the tires are practically molten rubber during the race.

This was Rabat's rain tire after finishing 2nd last weekend on a track that
was mostly dry by the end of the race.

[https://pbs.twimg.com/media/CNpxNYdWIAAdD6s.jpg:large](https://pbs.twimg.com/media/CNpxNYdWIAAdD6s.jpg:large)

~~~
newman314
The surface does matter or more specifically, the suspension.

If the suspension is not properly set up for compression and rebound, guess
what? Materials mean nothing if the tire is not in contact with the ground.
And there are some bumpy tracks out there...

~~~
donjigweed
Suspension has seen less advancement than tires imo. And the greater the lean
angle the less the suspension is actually working. If the bike could lean to
90 degrees the suspension would not work at all. This is why motorcycle
handling is still something of a black art rather than pure science, because
at full lean much of the "suspension" comes from frame, fork, and swingarm
flex, rather than actual damping.

~~~
bigiain
For a long time now race bikes have run "regressive rate" rear suspension
linkages. The geometry of the suspension is set up so that when you've got the
~2G of force vertically down on the rear suspension (from the bike's frame of
reference) that a ~60degree lean angle turn implies - the effective spring
rate is significantly less than when the bike is upright and the suspension is
riding higher under only 1G of load. While it can't resolve the 90 degree
degenerate case, it's easy enough to tweak the geometry so you've still got
known and desired levels of "suspension working" at 60ish degrees. (Handwaving
away the complexities of component flex and stiction - which really is black
magic.)

Note this is opposite to what many road oriented motorcycles use - progressive
rate springs and linkages are often used to allow "more supple" suspension
around normal riding circumstances while still having enough suspension force
to deal with bumps while overloaded or leaned over hard. Race bike don't have
to have any consideration for rider comfort "suppleness" or bumps/potholes.
The sole purpose of the suspension on a race bike is to maximise the tire's
contact to the track.

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lutorm
The calculation applies to the angle between the contact patch and the center
of mass. However, since the tire has some radius to it, and the rider
typically is not centered over the bike, that angle is _not_ the same as the
bike's lean angle. So that may account for some of the discrepancy between the
"60 degree" mu and that coming from the radius of curvature calculation.

~~~
bigiain
There's two complications to that, one against our favour and one in our
favour (assuming we're trying to rationalise a Cf of 1.7 being erroneously
high).

The rider leans off the bike to the inside of the turn, and since the rider
weighs ~30-40% of the bike+rider mass, this moves the center of mass quite a
long way to an even higher angle than the lean angle sensors on the bikes
frame indicate - the rider moving makes the discrepancy worse not better.

The left/right curvature of the tires (mostly that big fat ~200mm wide rear
one) means that the location of the contact patch between the tire and the
road also moves towards the inside of the curve. This means the frame lean
angle sensor is over-reporting the angle somewhat. This moves the discrepancy
back the other way.

Another thing to consider though. Nobody assumes the rule of thumb that "the
coefficient of friction is always between zero and one" applies to sticky tape
(which it quite obviously doesn't), but a hot motorcycle racing slick has that
same tacky stickiness to it that duct tape does. Look at any bike that runs
into the gravel traps. It's tires come out _covered_ in gravel that's quite
clearly stuck to them at a coefficient of friction greater than 1. It's
perhaps non-obvious, but it shouldn't be too much of a surprise that tire
"stick" like that to the track surface as well as the gravel on the runoff
areas...

~~~
rdc12
And I assume that when a rider runs off line onto the marbles [1] they stick
to the tire as well, which reduces the ammount of sticky tire in contact with
the track. They are also probably unstable compared to the tire.

[1] Little pieces of discarded rubber

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dahart
I read hoping to see some analysis of counter-steering, for the benefit of one
or two people I know who shall remain nameless and don't believe counter-
steering exists, because of course, they've never _actually_ ridden a
motorcycle.

Went looking just now and found better explanations online than the last time
I tried, years ago, but I have yet to see a satisfactory analysis of the
physics. Many of the explanations claim that counter-steering is only done
temporarily to begin a lean, only for "setting up" a turn, and then switches
to normal steering. After a lot of experimentation, I'm pretty convinced
counter-steering is actually always happening on a bike, but relative to the
turning radius of your lean, not relative to straight, which makes it a little
subtle and harder to demonstrate. If anyone knows where a solid analysis of
the physics is, I'd love to see it!

~~~
barrkel
Counter-steering applies a torque to the bottom of the bike.

For example: when you steer to the left while having lots of forward momentum,
the contact patch of the front wheel wants to go left, so the bike starts
rolling to the right, around its centre of gravity. Gravity itself, along with
suspension, keeps the bike in contact with the ground even as it rolls over.

Once the bike is rolled over into a lean, it will start falling over, but if
you leave it at that, it won't simply fall on its side. The steering geometry
(specifically, front-loaded steering geometry, you can look it up separately)
wants to steer the bike back upright again, by steering into the turn
slightly.

Depending on how much it's steering into the turn, the bike will either turn
quickly and come upright through the same mechanism as counter-steering, or it
will turn smoothly in a circle if the steering exactly counteracts the
centrifugal ("fake") force. And if it's not steering enough into the turn,
then the bike will eventually fall over.

Counter-steering while leaned over in the steady state will increase the angle
of lean, meaning later, more steering into the turn will be required to
maintain lean angle, which will cause the described circle to tighten.
Steering more into the turn while leaned over will cause the bike to
straighten up.

Additional bonus: the width of the front tyre has a large effect on how much
the bike straightens up when using the front brake. When leaned over, braking
with the front has a torque effect on the steering axis: the contact patch is
off to the side of the tyre, and if you've got a wide front tyre, it'll have
leverage over the steering. Braking will cause the road to push back on the
side you're leaned over on, which will cause steering into the turn, which
will straighten the bike up. Steering geometry probably also affects
straightening up on front brakes, but I've always noticed it far more on big
bikes than ones with narrower, higher aspect ratio front tyres.

~~~
lutorm
This is not a correct picture. You shouldn't have to watch a GP race for long
to realize that, at speed, the bikes don't pivot around their centres of
gravity, they pivot _around the contact patch_. This is because applying
torque to the front wheel through the handlebars (essentially around the yaw
axis) results in a gyroscopic rotation around the orthogonal, roll, axis.

~~~
barrkel
The road pushes the contact patch to one side; it would be quite remarkable if
that got them to pivot around the contact patch, since the contact patch has
no leverage to use itself as the centre of the roll axis.

By centre of gravity, to be clear, I meant the roll axis running through it. I
used the word rolling precisely to refer to the roll axis.

Gyroscopic effects definitely complicate things - steering takes more effort
at speed - but the fundamentals of counter-steering is that it rolls the bike
due to torque from a reaction of the road against the angle of the front
wheel.

(FWIW, I don't own a car and use motorbikes as my main form of transport; I do
about 15k a year, a mix of city commuting and long distance touring. Smaller,
lighter bikes are easier to apply extreme countersteering to, and I do often
in the city, so I'm well aware of what actually happens when I steer harshly,
which exaggerates the effect of everything described. For example, sharply
countersteering upright will push the front of the bike into the air.)

~~~
lutorm
But that's what I'm saying, it's _not_ the force from the contact patch that
leans the bike, it leans _despite_ the force from the contact patch.

The situation at high speed is fundamentally different from the situation at
low speed. Try this experiment (this became quite long, but I wanted to make
the explanation as explicit as possible to avoid misunderstandings):

1\. Put a pebble in the road as a marker and ride towards it quite slowly,
like jogging speed. As you approach the pebble, initiate a sudden countersteer
to the left. What will happen is that the handlebars will turn slightly to the
right, the contact patch will move to the _right_ , and the bike will roll to
the _left_ as it rotates around the CM. Your front tire will likely pass to
the _right_ of the pebble.

This is the situation you describe: at low speeds, the force from the contact
patch makes the bike rotate around the CM, which initially moves _opposite_ to
the direction you are trying to go. (It has to, the contact patch force is to
the right, and that's the only lateral force affecting the bike initially.)

2\. Now try the same maneuver at quite high speed. (Do it in a wide parking
lot or something so you don't run off the road, obviously...) What you will
find is that unlike in the first situation, when you countersteer, the
handlebars are pretty much rock solid. Even though you attempt to turn them to
the right, there is no appreciable motion. Because the wheel doesn't turn, the
contact patch continues basically a straight line. However, the bike _still_
leans over and starts turning to the left. You'll now find that the wheel will
run over or pass slighly to the _left_ of the pebble.

This behavior is impossible to understand without the gyroscopic effects. If
the bike still rotated around the CM, the contact patch would still move to
the right, actually by a _larger_ amount if you think that it takes a larger
force to overcome the stability of the spinning wheels. If that was the case,
the front wheel would still pass well to the _right_ of the pebble, but it
doesn't.

What is missing in this case is the effect of gyroscopic precession in a fixed
gyro. With the front wheel spinning rapidly, the attempt to turn it right when
countersteering will _not_ rotate it around in the steering direction, it will
cause the wheel to rotate orthogonal to the applied torque, in the roll plane,
taking the whole bike with it. If the bike was suspended in the air, it would
just rotate around its center of mass, but because friction prevents the
contact patch from moving laterally, there is a resulting force with a
magnitude that keeps the contact patch stationary. Note that unlike in the
slow-speed case, where the force from the contact patch acts to the right, it
now acts to the _left_. The resulting motion is one where the bike rotates
_around the contact patch_ , moving the center of mass in the direction of the
lean. This motion looks quite "magic" if you're not aware of what the
gyroscopic precession does.

Without the precession, you wouldn't need to go very fast until it would be
impossible to turn the bike at all. If you just imagine that the gyroscopic
effect makes the bike resist leaning over, you'd need to develop a larger and
larger contact patch force to the right as you went faster and faster. This
would make the bike track further and further to the right as you attempted to
turn to the left, which is exactly the opposite of how a bike really behaves.

Hope that explanation helps.

~~~
barrkel
I don't have enough intuition for gyroscopic precession to fully follow your
high speed case (how fast, I wonder?), but the requirement to overcome
gyroscopic stability otherwise causing tracking off line convinces me that I'm
wrong at higher speeds. I still think my picture is more explanatory at the
speeds I commute at (almost always below 45mph, with most steering at sub
25mph).

How do braking forces play into this, and do you know what kinds of speeds
we're talking about? A soft front tyre (i.e. lower than normal pressure) has a
dramatic effect on handling at street / city speeds - the extra rolling
resistance makes the steering want to steer further into the turn, causing a
countersteer upright. So you need to fight the steering to maintain line. But
of course when putting a bike on track, you run with lower pressures as a
matter of course - and I know from anecdotal experience that it is possible,
on track, to brake while leaned over a bit hard enough to start lifting the
rear, something that would require an immense effort to avoid straightening up
at street speeds.

You've given me something to think about, but unfortunately I won't be able to
solve the problem without either learning a lot more mathematics, or playing
with models...

------
jason_slack
I think this really depends upon the type of tire you have as well as the
riders ability.

Take Moto GP for instance, they lean a lot more (by training, lack of fear and
other factors) than a street rider would. Part of this is tires. They use
tires that are more rounded and don't really have a noticeable sidewall.

I have Michelin Pilot 3's on my bike and I feel safer leaning more with then
the stock tires that were on the bike.

As a side note, my bike is more upright than most, so this has a lot to do
with my ability to lean. I feel very comfortable leaning farther on a bike
where I am not already leaning really far forward to begin with.

Note: I have a 2012 Triumph Street Triple. My wife has a 2012 Triumph Daytona
Ultra sport. Mine is more upright, hers is a significant forward lean.

~~~
TrevorJ
It's also a lot safer on the track: the pavement conditions are known and
lowsiding doesn't put you into a guardrail that will cut you off at the knees.

~~~
jason_slack
You make a good point that I didn't think of. Tracks are safer, despite the
higher speeds, I think. I never took my bike to the track. I always wanted to
but never wanted to wreck it.

------
geoelectric
Easy: all the way.

Coming back up again is the tricky part.

~~~
roflchoppa
nah, just use the throttle to return upright.

~~~
function_seven
I think the joke is that "all the way" is making full contact with the ground,
i.e. crashing.

Kinda like falling out of a skyscraper doesn't kill you. It's the sudden stop
at the end that does.

(But I'm not defending the joke :)

~~~
mikeash
Or after an engine failure in an airplane. "How far can we get on the other
engine?" "I'd say it should take us all the way to the crash site."

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lnanek2
I don't see anywhere in his calculations where he takes into account that the
more you lean the larger the tire surface against the ground gets. Motorcycle
tires are actually intentionally designed for this nowadays.

~~~
aidenn0
The classic coefficient of friction you learn in freshman physics is
independent of surface area; the larger the surface area, the lower the
pressure, so it evens out. With sticky materials though, this doesn't hold.

~~~
newman314
Hence, area of contact patch will make a difference.

~~~
aidenn0
But TFA did not ever use a single model from physics where it would make a
difference.

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confiscate
I think this largely depends on the tire's "side surface" as well.

For instance, my motorcycle's tires are not race tires, but street tires. The
bottom of the tire only goes up the "side" for a limited distance. If I lean
too far the side of my tire no longer touches the ground

Also, the lean angle would have to be related to the foot peg size. My current
foot peg is quite long--even for mild lean angles somestimes I can feel the
road scratching on my boots and the foot peg.

~~~
agumonkey
Ha foot peg. No need for a motorcycle to enjoy them. A steep downhill lane
with a large roundabout. A young self not willing to brake on his mountain
bike. The pegs only kissed the ground a split second, enough for me to die a
little inside while my rear tire lost contact.

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latchkey
Love this animated gif where the guy touches his helmet on the ground around a
corner on the track...
[http://www.gifbin.com/bin/072011/1311056598_biker_touches_gr...](http://www.gifbin.com/bin/072011/1311056598_biker_touches_ground_with_head_during_turn.gif)

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akcreek
Many racers, including the referenced GP crowd use 16.5" wheels instead of the
more standard OE 17" since you can mount a wider/taller tire. That profile
allows increased lean angle due to better grip from the additional surface
area of the tire contacting the track surface.

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gpsx
I haven't thought about motorcycles or rotating bodies in a while so I am
afraid to say this, but I think there is a missing force in that diagram. As
the motorcycle sweeps through the turn, the angular momentum of the tires is
changing directions. This tries to push the bike up, the same way counter
steering tilts the bike opposite the direction you turn. If this is true, the
lean needs to to compensate both the "fake" force (acceleration) and the
change in angular momentum of the wheels as direction of the bike changes.

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abakker
I'm not sure if this matters, but with the aggressive profile of motorcycle
tires, I assume the effective diameter of tire changing might matter. The
effective diameter at 90° is maybe 26 inches (guessing). Leaned heavily into a
turn though, the diameter might be substantially less, say 18".

I am not a physics person, but it would seem that the change in diameter that
corresponds with the change in angle might change the effective CoG. Can
anyone tell me if this is correct?

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aidenn0
This neglects to mention aerodynamic downforce; does anyone know if that plays
in at all for motorcycles (it certainly does for race cars).

~~~
ablation
Some manufacturers are experimenting with added downforce with the addition of
winglets. See Ducati's example here:
[http://www.bikesportnews.com/uploads/news_images/_G104079%28...](http://www.bikesportnews.com/uploads/news_images/_G104079%281%29.jpg)

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thecrumb
The author also fails to mention a few things...

Bikes slide while leaned over and electronic traction control.

How far could you lean one of these bikes over without the computer helping?
:)

~~~
anigbrowl
I used to ride an old bike with no electronics (a Honda 400/four). It does
drift but you can feel that and control it with countersteering in good
weather conditions (in bad weather conditions I would cut speed significantly
or just not ride).

You can still lean an all-mechanical bike with ordinary tires quite a ways.
When I would be turning through very long curves on freeways and so I would
get back fatigue from the fake force (the one that's trying to make the bike
stand up vertically again), requiring me to sit on the upper side of the bike
to keep it leaned over with less effort. I have a very slim build so this is a
trick that might not be familiar to most male riders.

------
mirimir
Better yet is racing on ice, with spiked tires :)

It works for bicycles too!

