dude ur forgeting the neccessory evil THE FRICTION.

The darivation u just did is in XI - physics..
a more resolved explanation was expected from mech guy ..
u should have said why tyre dont skid with nice force component diagram too . coz that darivation assumes ur on a friction less serface which is not he case and ur on soft compount + tarmec actually.

Do you want a detailed equation??
Considering friction factor, gyroscopic couples?????
I bet you don't

Any stable state of the bike while riding arises from a balance of the various forces acting on it. absorb that first.

during a turn you have traction countering centrifugal force...the one that wants the bike to carry on in a straight line...right?

now traction depends upon tyres, road surface, speed, weight and bike geometry apart from inflation pressure etc etc

if any of these factors adversely go against traction, then centrifugal force wins and the rider either slies, drops or hits something on th e outside of the turn

for example....more speed than lean...w i d e turn..crash

more lean...less speed....sliiiiide..crash

thats why even the best of riders follow the adage...slow in fast out

& suppose everything is perfect but the tyre or the road surface is not suitable to the lean angle one is making, again there would be crash



NOTE: THIS IS NOT MY WORDS BUT MY BEST EVER TEACHER'S

@OF
Thanks for the detailed explanation sir. Is there a way of knowing how much can a person lean the bike at a curve, and at what point there will be a chance of falling?

If the curves are "banked" , then that will take care of your leaning angle. For example, as a biker , you can lean your bike to the desired angle to counter the centrifugal force. But for cars , what is the solution...?
"Banking of roads" is the solution for such vehicles.

dude it is ok that i m in ET&t but man i was too crazy for Physics some time ago i would really enjoy if u bring them on.

Actually, banked curves also help bikes. While banking the tire grip has to deal with the normal forward rolling forces as well and the centrifugal force acting on the bikes mass. Go fast enough or surface with less grip and there's nothing that will stop you from going down.

Now on a banked curve the result vector of the centrifugal force and gravity is more likely to be perpendicular to the road surface. This means the tires will have to deal with much less, if any, sideways forces. Thus even on a bike you'll be able to go faster on a banked curve.

To be precise, the leaning angle is the arctangent (tan inverse) of the square of the bike's velocity divided by the turn radius times acceleration due to gravity.
(assuming frictionless surface!, if you like to include friction, the equation becomes quite complicated!!!)

In simple terms, how much one should lean depends on the speed of the bike and the radius of the road.
The beauty of Physics here is , it DOES NOT depend on the mass (weight) of the bike and the rider.

I agree with your point.

I just pointed out that ,bikes can negotiate a turn without a nescessity of a banking angle. If such an angle is available, it is better, as bikes can move fast over that corner.

Motorcycle Dynamics - Google Books

Bhai only for you, can't derive all these equations and scan them so i am posting this link any quire feel free to ask.
ENJOY

thanx for it! really a lucid language.

i am always around, just in invisible mode. and thanks for the info, i am still not sure i got the concept right but i guess i never will, if i don't have that calculative and scientific mindset and approach

thanks for the links. visual diagrams always help a nerd like me.

For what I could understand from the net search is the theory of "gyroscope" http://en.wikipedia.org/wiki/Gyroscopic which has prominent role in the leaning of the bikes. In simple english, i think the wheel is governed by 3 axis (x,y and z) where each axis tries to stay at its orginal position (if that makes sense to Einstein heads ) when ever there is a shift of the axis positions. God am i talking rubbish?

the easiest thing about bikes is riding

Very well explained OF sir, but I would like to clarify one thing from what you wrote in the beginning. Isn't centrifugal force the imaginary force supposed to act LIKE its pulling the stone away from the centre (opp. to centripetal force) whereas in actuality, its the linear velocity imparted to the stone that keeps it going and will make it go on a tangent if the thread breaks?
When we look at the free body diagram of a rider in a turn, don't we assume the centrifugal force equal and opposite to centripetal force, thats why the rider continues in his direction of the turn. If centrifugal force were to be tangential, then there's no opposing force to the centripetal one, the rider should spiral into the centre immediately. There is no 'equilibrium of forces' as you have pointed out in your last paragraph, is there? OR am I making a mistake of not taking something into account, or does the resultant of the tangential + radially inward force give it the circular path.. please clarify this.

Basically what I wanted to say : centrifugal force 'acts' or seems to act opposite to centripetal force, not tangentially but radially away from the centre. Please correct me if I'm wrong, I very strongly think so. :P

If any one can get your hands on a copy of Motorcycle Handling and Chassis Design by Tony Foale, then it will answer all your queries and then some, he explains EVERYTHING very clearly and doesn't go into complexities. I can't stress how helpful it has been to me in answering my doubts.

Well i'd just say the same reason one doesn't fall while riding a bike is behind why one not falling while cornering.since as gravity tries to pull you down the forward force due to bikes speed counters it.so if one is slow and leaning he/she will fall.as for banking of roads i don't see it being practiced in India other than approach roads for bridges.

In the purest sense of words, you are perfectly right. The ambiguity exists as I have used just words to explain a concept that begs for a diagram. With a figure, one can point arrows for different forces and their resultants. Pure words have their limitations. Centrifugal force is the virtual opposite of centripetal force. And centrifugal force will not make the stone escape on a tangent when the string breaks. It will be the stone's inertia produced by its mass and its 'linear' velocity (as you've rightly stated). Getting all these subtleties into the text would ahve made it all the more confusing and so I took the visualization-inspired short-cut by saying that the 'centrifugal force tends to make the stone go on a tangent' because thats what it 'looks' like.

And you're spot on about Tony Foale. I have the book and few could be so detailed and lucid on the subject. The Ner-a-Car and his experiments with Trail and Rake on the BMW R75/5 are a case in point. There's this useful link that has a lot of his papers and articles.

Tony Foale Designs, numerous articles of motorcycle chassis design.

OF