Motorcycle Physics
Consider, if you will, an object with a circular cross-section of radius, R, having a mass, M. (Mass is a physical property which we commonly know as weight when measured at sea level.)
Okay, let's say that object is a motorcycle wheel!
Lifting the unmounted wheel we find that it can be turned side to side about the axle axis in any direction rather easily.
Now let's mount the wheel on a motorcycle and spin it about the axle axis with a angular velocity, W. (We might measure angular velocity, for example, in revolutions per minute or rpm.) The wheel is now more difficult to tilt in any and all directions about the axle axis. In fact the force, F, which must be exerted increases as the speed at which the wheel is spun increases. (Remember that toy gyroscope you got for Christmas one year?)
This resistance to changing the orientation of the plane of rotation of the wheel (always perpendicular to the axle axis) is created through another physical property called angular momentum, L, which is a function of the mass, radius and angular velocity of the wheel:
L = f (M * R² * W)
The force, F, required to tilt the wheel side to side is, in turn, related to the angular moment:
F = L/x
where x is the distance along the axle axis at which the force is applied. On a motorcycle, x would be the horizontal distance from the center of the handlebar to the hand grip.
It is, indeed, this resistance to changing the plane of rotation of a spinning wheel that makes a bicycle or motor "stand up" when you are riding it. And, the heavier the wheel, the greater its radius and the faster its spin, the better the bike will "stand up". In other words, bigger and faster are better!
Now the really great thing about angular momentum, is that the plane of rotation will not change regardless of the angular momentum until a force in the form of a torque (F * x) is applied perpendicular to the axle axis. Once the bike is "standing up" it will do so forever until the rider does something to change the plane of rotation. Once again, bigger and faster are better when it comes to stability if you should happen to run over a hidden pothole or an indecisive rabbit. Indeed, motorcyclist are advised to increase speed in times of trouble for this very reason.
Now, riding a motorcycle down the road in a straight line isn't the reason people own motorcycles. No, Sir. We ride 'em to go around curves! And, that brings us to making a motorcycle go in a circle for which we have two methods.
Method #1 is the one used to steer automobiles. The plane of rotation stays more or less perpendicular to the road surface and the axle axis is rotated in the plane of the road.
Turn the wheel to the right to go right and to the left to go left. Simple. Uncomplicated. Deadly on a motorcycle when used exclusively except at speeds approaching zero miles per hour (as in a supermarket parking lot). When you go around a curve at any speed, a centrifugal force (the force that pulls on a string when you rotate a rock on the end of it about your head) pushes both you and the motorcycle outward, away from the inside of the curve. At the bottom, the tires of the motorcycle overcome this force by adhering to the road. At the top, your head and body pushes against nothing but thin air. The result? You topple over like a tree, crack your head on the side of the road and die. Not good.
What to do? Well, the ideal situation is to lean the motorcycle towards the inside of the curve just enough that the centrifugal force is transmitted in a straight line through your body and the motorcycle to the tires which, in turn, transmits the centrifugal force into the road. This works beautifully ... so long as the tires maintain traction with the road. Naturally, the faster ones goes, the greater this centrifugal force the tires must overcome and the greater the lean must be. (Unlike a car tire that is basically flat on the bottom, motorcycle tires are rounded for a reason: leaning!)
To execute the lean, the rider must exert vertical forces on the axle axis to tilt the plane of rotation of the tires as well as the remainder of the motorcycle and the rider toward the inside of the curve. (Remember angular momentum?) At the correct angle the rider will feel no force on his body toward the outside. He will feel as if he were riding in a straight line ...
... except the motorcycle will no longer be going in a straight line. To understand this place a circular object (like a dinner plate) in a vertical orientation and roll it. The object will roll in a straight line. Now lean the object to one side or another and it will turn in the direction of the lean. When leaned nearly 90° it will, in fact, roll in a circle with a turning radius nearly reduced to that of the plate. Exactly the same thing happens with motorcycle wheels and, accordingly, leaning is also Method #2 for steering motorcycles.
It's theoretically possible that the correct lean to overcome centrifugal forces will also produce the correct curvature for negotiating the curve in the road. In practice this seldom ever happens and then so only for a brief moment. In fact, the lean needed for counterbalancing the centrifugal forces will usually produce a turn that is too tight, causing the rider to run off the road on the inside of the curve if not corrected. How so? Well, this is the really weird part. The correction is made by using Method #1 for steering by turning the front wheel in the direction opposite the curve to produce the correct path of travel! This phenomenon is known as counter steering.
Accordingly, to correctly round a curve in the road on a motorcycle, one must simultaneously push the handle bar on the inside of the curve down to produce the lean and forward to produce counter steering in the direction opposite the curve to match the path of the motorcycle to the curve.
Now, folks, all this theory is nice but does it work?
Yup! This dude is going very fast, producing high centrifugal forces and high angular momentum. The front wheel is turned slightly away from the curve. His body and the motorcycle are perfectly aligned at a dramatically steep angle to the road. So much so, in fact, the rear wheel is driving the motorcycle forward on the side of the tire. His head is leveled with the road and held up, looking at where he is going and not where he is. Great form. And, the good news is that even if the rear wheel slips a little, angular momentum of the wheels will maintain the angle of his lean until he can regain equilibrium traction. (Otherwise he'll get run over by that bike behind him. Ouch!)
OK. that's the easy part. We still have more complicated considerations for braking (front and rear wheels) and acceleration (both increasing and decreasing) during a turn but that's for later.
It's now time to go practice making turns. With so many variables, it's really more an art than a science. And, just like driving a car, it's all done with feel as much as anything. When you do it right, you known and when you don't, well, you know that too! And while it's all going on, you just hope that God will wait to change the laws of physics until you have finished the sharp, fast turn you're in!
Okay, let's say that object is a motorcycle wheel!
Lifting the unmounted wheel we find that it can be turned side to side about the axle axis in any direction rather easily.
Now let's mount the wheel on a motorcycle and spin it about the axle axis with a angular velocity, W. (We might measure angular velocity, for example, in revolutions per minute or rpm.) The wheel is now more difficult to tilt in any and all directions about the axle axis. In fact the force, F, which must be exerted increases as the speed at which the wheel is spun increases. (Remember that toy gyroscope you got for Christmas one year?)
This resistance to changing the orientation of the plane of rotation of the wheel (always perpendicular to the axle axis) is created through another physical property called angular momentum, L, which is a function of the mass, radius and angular velocity of the wheel:
L = f (M * R² * W)
The force, F, required to tilt the wheel side to side is, in turn, related to the angular moment:
F = L/x
where x is the distance along the axle axis at which the force is applied. On a motorcycle, x would be the horizontal distance from the center of the handlebar to the hand grip.
It is, indeed, this resistance to changing the plane of rotation of a spinning wheel that makes a bicycle or motor "stand up" when you are riding it. And, the heavier the wheel, the greater its radius and the faster its spin, the better the bike will "stand up". In other words, bigger and faster are better!
Now the really great thing about angular momentum, is that the plane of rotation will not change regardless of the angular momentum until a force in the form of a torque (F * x) is applied perpendicular to the axle axis. Once the bike is "standing up" it will do so forever until the rider does something to change the plane of rotation. Once again, bigger and faster are better when it comes to stability if you should happen to run over a hidden pothole or an indecisive rabbit. Indeed, motorcyclist are advised to increase speed in times of trouble for this very reason.
Now, riding a motorcycle down the road in a straight line isn't the reason people own motorcycles. No, Sir. We ride 'em to go around curves! And, that brings us to making a motorcycle go in a circle for which we have two methods.
Method #1 is the one used to steer automobiles. The plane of rotation stays more or less perpendicular to the road surface and the axle axis is rotated in the plane of the road.
Turn the wheel to the right to go right and to the left to go left. Simple. Uncomplicated. Deadly on a motorcycle when used exclusively except at speeds approaching zero miles per hour (as in a supermarket parking lot). When you go around a curve at any speed, a centrifugal force (the force that pulls on a string when you rotate a rock on the end of it about your head) pushes both you and the motorcycle outward, away from the inside of the curve. At the bottom, the tires of the motorcycle overcome this force by adhering to the road. At the top, your head and body pushes against nothing but thin air. The result? You topple over like a tree, crack your head on the side of the road and die. Not good.
What to do? Well, the ideal situation is to lean the motorcycle towards the inside of the curve just enough that the centrifugal force is transmitted in a straight line through your body and the motorcycle to the tires which, in turn, transmits the centrifugal force into the road. This works beautifully ... so long as the tires maintain traction with the road. Naturally, the faster ones goes, the greater this centrifugal force the tires must overcome and the greater the lean must be. (Unlike a car tire that is basically flat on the bottom, motorcycle tires are rounded for a reason: leaning!)
To execute the lean, the rider must exert vertical forces on the axle axis to tilt the plane of rotation of the tires as well as the remainder of the motorcycle and the rider toward the inside of the curve. (Remember angular momentum?) At the correct angle the rider will feel no force on his body toward the outside. He will feel as if he were riding in a straight line ...
... except the motorcycle will no longer be going in a straight line. To understand this place a circular object (like a dinner plate) in a vertical orientation and roll it. The object will roll in a straight line. Now lean the object to one side or another and it will turn in the direction of the lean. When leaned nearly 90° it will, in fact, roll in a circle with a turning radius nearly reduced to that of the plate. Exactly the same thing happens with motorcycle wheels and, accordingly, leaning is also Method #2 for steering motorcycles.
It's theoretically possible that the correct lean to overcome centrifugal forces will also produce the correct curvature for negotiating the curve in the road. In practice this seldom ever happens and then so only for a brief moment. In fact, the lean needed for counterbalancing the centrifugal forces will usually produce a turn that is too tight, causing the rider to run off the road on the inside of the curve if not corrected. How so? Well, this is the really weird part. The correction is made by using Method #1 for steering by turning the front wheel in the direction opposite the curve to produce the correct path of travel! This phenomenon is known as counter steering.
Accordingly, to correctly round a curve in the road on a motorcycle, one must simultaneously push the handle bar on the inside of the curve down to produce the lean and forward to produce counter steering in the direction opposite the curve to match the path of the motorcycle to the curve.
Now, folks, all this theory is nice but does it work?
Yup! This dude is going very fast, producing high centrifugal forces and high angular momentum. The front wheel is turned slightly away from the curve. His body and the motorcycle are perfectly aligned at a dramatically steep angle to the road. So much so, in fact, the rear wheel is driving the motorcycle forward on the side of the tire. His head is leveled with the road and held up, looking at where he is going and not where he is. Great form. And, the good news is that even if the rear wheel slips a little, angular momentum of the wheels will maintain the angle of his lean until he can regain equilibrium traction. (Otherwise he'll get run over by that bike behind him. Ouch!)
OK. that's the easy part. We still have more complicated considerations for braking (front and rear wheels) and acceleration (both increasing and decreasing) during a turn but that's for later.
It's now time to go practice making turns. With so many variables, it's really more an art than a science. And, just like driving a car, it's all done with feel as much as anything. When you do it right, you known and when you don't, well, you know that too! And while it's all going on, you just hope that God will wait to change the laws of physics until you have finished the sharp, fast turn you're in!
Comments
Post a Comment