the physics of leaning a bike


This is sort of bike-related. Kind of.

My brother and I have a long-standing argument about the forces on a motorcycle when turning. Essentially, it comes down to this: If a straw, sealed at both ends, containing a ball bearing (small enough to move in the straw), was fastened to a motorcycle so that the straw was horizontal to the ground, and the motorcycle was leaned around a corner, he thinks the ball bearing would not fall to the end of the straw closest to the ground.

His reasoning is that when the motorcycle is turning and leaned over, centrifugal forces would act against gravity, so that the ball bearing would not roll to the bottom of the straw closest to the ground. Generally, I think he's arguing that centrifugal forces act opposite to the direction of lean (i.e. they act 'upward', in a sense).

I on the other hand argue that centrifugal forces act 'downward' at the angle of lean. In other words, I picture the bike describing an arc as though the driver's helmet was attached to a pivot point in the sky by a long string, with forces acting downward 'along' the string. This force acts to hold the rider on the bike, etc.

So, my view is that centrifugal forces would act in a downward way on the ball bearing through the middle of the straw (not along the straw opposite to the angle of lean as my brother thinks it would), which wouldn't be enough to counteract gravity, and so the bearing would roll down.

I also think that if he's right, we'd all fly off our bikes as we took fast corners, due to centrifugal forces acting upward and opposite to the angle of lean, as he argues.

Anyway, I know this is idiotic... but am I right or is he right?
I dunno.. never tested it.. but If I had to bet on one or the other I would probably go with your theory.
It would stay near the middle.

When you lean a bike through a turn, it stays centered with the downward force.
If the bearing in the straw would go down or up, the bike would do the same thing. In fact, it doesn't. It is a perfect balance through the center of the bike. That is why you don't fall over.

Those physics change when you lean your a$s over the seat. THEN the bearing would go up, or towards the outside of the turn.
Cache, the argument actually arose over the use of centrifugal force to create self-cancelling turn signals. I'd always pictured the straw as being offset from the spine of the bike. Of would you say it would make no difference whether the ball bearing was inline with the spine of the bike or offset?
It depends on rider style. If you sit straight up all the time, even through a turn, it would stay near center. If you lean one way or another, it would change accordingly and opposite the rider. Another factor is speed. If I am at a stop sign, turn right, the bearing would go from center, to right side of the straw, to the left, and then ultimately back to center. I suppose one way to use that as self-cancelling, is to say once the bearing returns to center for a duration of maybe 5 secs, then have it cancel the signal. Make sense?
I believe the bearing would go towards the ground . Because when you are in a turn you feel the force trying to push your head straight down towards the tank it's not like a car which is sside to side. So the bearing would fall with gravity towards the ground of what ever side you were turning.
At racing speeds the inertia of the bike pulls to right the bike (stand it back up) because it is experiencing dynamic energy. The ball would travel to the low side with gravity because it is experiencing static energy. "Only an opinion." :-) Would be neat to find out though. I have been wrong before.
It makes sense to me that speed is part of the equation - that's another area where my brother and I disagree. I can certainly see a point where the downward force I described in my first post is so high that the bearing is held against the straw at the middle of the straw (I think that's consistent with the force acting downward along the angle of lean if the straw is not too far offset from the spine of the bike). But I just can't see that happening at anything less than very high speed. Well, heck, if it's going to happen it'd happen on a busa. I do plan to test this. Yes, with a straw, a ball bearing, a camcorder and the busa. Sibling rivalry...
Too many factors really Speed of bike inertia of corner how much lean etc I assume the straw is up and down vertically on the tail light or something and the ball is ijn the bottom because of gravity at a stop No matter which way you turn the inertia of the corner forces the ball cearing down in the straw even more because the bottom of the straw is pointed to the outside of the corner you are going around .

I'm the brother...

As I understand it: centrifugal force would act horizontally on the motorcycle in the opposite direction to the direction of turn.  It occurs because all objects want to travel in a straight line.  If some force pushes them off that line the inertia of the object pushes against it.  ("every action causes and equal and opposite reaction" - Newton I think)  You feel this in a car when you turn the steering wheel.  That force would tend to push the ball "up" the straw (in the same way that pushing a child on a swing backwards actually makes it go up).  Meanwhile gravity would be pushing it down, however, which, as Cache said, is why we don't all fall off when we go around in circles.

The interesting question is what would happen if the straw were off center.  This is where it gets strange:  I think that which ever side of the motorcycle you put the straw on the the ball would roll further away from the motorcycle when you went around corners.   You know how your legs always feel like they want to fly off the motorcycle no matter which way you are leaning?  Maybe it is just me.  I think you would have to be a physicist to care why but the formula for centrifugal force is (I believe) mass times velocity squared divided by radius.  So if you want to work out the vectors...

Unfortunately the forces involved are so small that that you probably couldn't differenciate them from the general two and frowing of the motorcycle.  

Hopefully my brother is going to do the test this weekend...  Should be interesting!  (Yes, I'm a nerd)
I do believe this is relative to the actual speed of the lower speeds it should higher speeds, if it is in the bottom of the straw, it should move towards the top at a certain speed.
Just a question, why argue about a ball bearing in a straw? Easy way to solve this problem is take your brother out on the road and spank him with the busa. If he has one a busa too, then whoever has the fastest color (black and blue) would settle it.
Now know that you thought this thread was interesting and would like to know the outcome.
I'm making a few assumptions: 1.the straw is perpendicular to the length of the bike. 2.the rider is travelling fast enough that he/she will need to countersteer into the corner.

I think when you start the turn the ball would roll to the inside of the turn.  You don't have all the centrifugal force working yet.  When it does come into play, the ball will stay at the inside end.  It's being "pushed" down parallel the centerline of the bike.  The centrifugal force is pushing down, not out to the outside of the turn. Swing a bucket of water in a circle with your arm 45 deg out from your body, the water will stay level in the bucket, not sloshing up the outside side. That being said, it shouldn't matter if the straw is off center or not.
Anybody, anybody, Bueller?
You know, Paistes5, I'd do that, but then I'd just feel like a bully. I mean, he has a BMW R1100S.... It'd be taking candy from a baby... or a boxer.. whatever...

brennanop, I think you're right on target. I realized I was wrong about being suspended from the sky, and the forces do act laterally (not downward), but that the ball was still going to do what I thought, because:

When you turn the bike centrifugal forces and gyroscopic forces want to hold the bike up, but gravity wants to put it on the ground. Clearly, as your lean increases, gravity is winning. But at some point centrifugal forces and gyroscopic forces come into a balance with gravitational forces and you maintain your lean angle. I think, if this happened instantly, the ball bearing would stay fixed in position by the forces acting on it. However, because gravitational forces exert a constant force, while gyroscopic and centrifugal forces need to build up, the ball would roll with gravity before the forces were balanced. Go fast enough, and hey, maybe it would roll back up again.

Still plan to test this though.
OK I must have made a wrong assumption here I belived the straw was vertical say mounted on the rear tailight up and down twards the ground while stopped the ball bearing is in bottom of straw . If you mount it horizontally across the seat the bearing being in the middle when you lean the bike over it depends on lean angle etc but the straw would be vertical in a hard lean situation and gravity would pull the ball bearing to the bottom while inertia or CF would pull the ball bearing into the side of the straw at that point because the straw is not at the correct angle to allow the ball to go to the other end so you see it would still depend on speed angle of lean weight of ball bearing how the straw was mounted and where and of course color of bike the Blue and silver is the fastest color you know hehehehe I couldnt resist
Okay guys, for what it's worth; I have a friend who is a Physics professor, and he rides MCs. He said the ball would roll towards the ground. Speed has an affect, but only on how fast the ball would roll towards the ground. Issue settled?

All i lean the wrong way.."some more than others"
But bikes always feel right..butt planted straight into the seat
..just feels right,,,,unless yer hanging off like a proffesional superbike rider..bikes feel good,,in a turn...."natural" just love it..who invented two wheeler's..I'd give him a hug if i could.