Odd question: max lean angle

DaveT319

DaveT319

Marquez FTW
Something that's been bouncing around in the cavernous void of my head: what's the slowest a bike could go at maximum lean before it just tips over from lack of centrifugal force?

For example, in the last MotoGP race, they were talking about Pedrosa having reached a lean angle of 64 degrees. They also showed onboard telemetry that indicated they go through most corners - regardless of speed - at around 60 degrees, give or take a few. So they go through a 140 MPH corner at 60 degrees, and 80 MPH corners also at 60 degrees. And I have seen them take some corners even slower than that and still all the way leaned over. So how slow could they go at that angle before there is not enough outward force to counter the downward force of gravity?

Yeah, I would imagine it's kind of a complex physics question that has to take into account the amount of grip given tires provide and the amount of grip the road surface provides, and probably other things I'm not considering. But does anyone know or have read somewhere what that minimum speed would be?
 
ElectricPrunes

ElectricPrunes

Banned
uQoznQr.gif

http://www.msgroup.org/forums/mtt/images/bike032210.xls

Other fun physics calculators: http://www.msgroup.org/forums/mtt/default.asp?CAT_ID=11
 
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louemc

louemc

Well-known member
The answer is made very clear that "it depends" when you ride a dirt bike.

You get to play at it, and you feel the variety of variables that can be put together in different ways.

Play at it till you can lean till the handle bar end touches the ground and the lean stops.. that is the limit of lean.
 
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sanjuro

sanjuro

Rider
The classic partnership of science vs skill in racing.

Before computers, everything was done, from frame welds to speed, was down by feel.

Now we have high precision in every aspect of racing.

But what Rossi or Pedrosa is doing in their heads from what they see and feel no computer can duplicate.

Yet.
 
louemc

louemc

Well-known member
The best place for some, not everyone, is in the head.

The first Calculus was done in some guys head...and then he came up with formulas that others could use.

Some people just know things...It comes to them.

Others are doomed to a fog, that never lifts.
 
DataDan

DataDan

Mama says he's bona fide
DaveT319 said:
Something that's been bouncing around in the cavernous void of my head: what's the slowest a bike could go at maximum lean before it just tips over from lack of centrifugal force?
Click to expand...
In steady-state cornering--i.e., at constant speed around a fixed turn radius--lean angle must balance centrifugal force and gravity as seen here (from MSF's Motorcycling Excellence, 1st edition):

Lean angle diagram.JPG

The trigonometric tangent of lean angle must be b/a, or centrifugal force divided by weight.

Centrifugal force is weight multiplied by lateral acceleration, which is speed^2 / turn radius.

Therefore tangent of lean angle must be proportional to speed^2 / turn radius.

IOW, the faster you're going through a given turn, the more you must lean. Duh.

To the point of your question, the slowest a bike can go at a given lean angle depends on how tight it can turn. As long as it's possible to tighten up the turn, you can maintain lean angle while slowing.
 
DataDan

DataDan

Mama says he's bona fide
sanjuro said:
Before computers, everything was done, from frame welds to speed, was down by feel.
Click to expand...
Immediately before computers (I'm thinking of the PDP-11, which became a fixture in engineering departments in the 1970s) there was the HP35:

hp35.jpg

MSRP in 1972 was an astonishing $395, more than half the price of the popular Honda CB350. But it had an extraordinarily powerful function set compared to the +-*/ calculators then available, including roots, trig, log, and exponentials. My dad got one, but only because his company bought it for him.


For decades before that, it was the venerable Keuffel & Esser Log-Log Duplex Decitrig, arguably the indispensible tool that put a man on the moon:

slide rule.jpg

I have two of them, my dad's, which he used to build fuel and oxidizer pumps for ICBMs (among other things), and my own, which I never built anything with because I took the low road and became a programmer. :wtf
 
Abyss

Abyss

Anhedonia
You need to come up with a friction coefficient to answer this question. Slicks on hot pavement will yield a different result than PR2s in the rain.
 
louemc

louemc

Well-known member
Everything is involved...
Try the friction coefficient outside the blue groove on the Mile Flat Track corner being done at 100 MPH in the marbles.
 
Gixxergirl1000

Gixxergirl1000

AFM #731
DataDan said:
In steady-state cornering--i.e., at constant speed around a fixed turn radius--lean angle must balance centrifugal force and gravity as seen here (from MSF's Motorcycling Excellence, 1st edition):

View attachment 423436

The trigonometric tangent of lean angle must be b/a, or centrifugal force divided by weight.

Centrifugal force is weight multiplied by lateral acceleration, which is speed^2 / turn radius.

Therefore tangent of lean angle must be proportional to speed^2 / turn radius.

IOW, the faster you're going through a given turn, the more you must lean. Duh.

To the point of your question, the slowest a bike can go at a given lean angle depends on how tight it can turn. As long as it's possible to tighten up the turn, you can maintain lean angle while slowing.
Click to expand...


Oh mah gawd... too much math... it makes my head hurt....

20100108063328!Exploding-head.gif
 
DaveT319

DaveT319

Marquez FTW
I guess you also have to determine what is THE max lean angle for the bike. Like with the MotoGP bikes, 60 degrees is very common, but Pedrosa hit 63 last race, and I think they said someone else has hit 64 or 65.

I guess when you get down to it, maybe there is no ONE answer? Depends too much on conditions to come up with a single number.
 
Gixxergirl1000

Gixxergirl1000

AFM #731
DaveT319 said:
I guess you also have to determine what is THE max lean angle for the bike. Like with the MotoGP bikes, 60 degrees is very common, but Pedrosa hit 63 last race, and I think they said someone else has hit 64 or 65.

I guess when you get down to it, maybe there is no ONE answer? Depends too much on conditions to come up with a single number.
Click to expand...

Well, I know for a fact that a Li'l Ninjette with 16" wheels and Dunlop GT501 sport touring tires with 5-mile sidewalls absolutely will NOT achieve the same lean angles as my Gixxer with 17" wheels and Q2's on it... :|
 
louemc

louemc

Well-known member
DaveT319 said:
I guess you also have to determine what is THE max lean angle for the bike. Like with the MotoGP bikes, 60 degrees is very common, but Pedrosa hit 63 last race, and I think they said someone else has hit 64 or 65.

I guess when you get down to it, maybe there is no ONE answer? Depends too much on conditions to come up with a single number.
Click to expand...

There is no one answer, and of course conditions are a game changer.

And If Your native country is Spain...That changes everything as well.

Marc Marquez is getting down..:thumbup a tad more than Lorenzo...at times.
 
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