One property of matter which we rarely think about, but greatly influences motorcycle design and how they are ridden, is inertia. Yet it is this property that allows engines to run, stops our bikes from falling over and lets us steer them around corners. Newton's first law states that a body at rest will remain at rest and a body in motion will remain in uniform motion in a straight line, unless acted upon by an outside force.
The unwillingness of something to have its state of rest or motion changed is measured by its inertia. (Picture our man "Six-Pack" Brasfield at rest on his couch-he ain't going anywhere-as having a lot of inertia.) For straight-line motion, the inertia of an object is simply its mass or, because we're on earth, its weight. The heavier something is, the more force required to accelerate or stop it (Newton's second law).
For spinning bodies, the moment of inertia takes into account an object's mass as well as how that mass is distributed about the axis of rotation. The higher an object's moment of inertia, the harder it is to turn about an axis. For a point mass (essentially an object without size dimensions, Figure 1), the moment of inertia is:
Where I is the moment of inertia (or MoI which is measured in lb ft2), m is the object's mass (in pounds) and r is the distance of the object to its center of spin (in feet). From this basic equation, the MoI for some basic shapes can be derived. Of most interest to us, however, is a simple disc, (Figure 2) which has a MoI of:
Obviously, the heavier an object of a given size, the greater its moment of inertia. But notice inertia increases with the square of the distance from the axis, meaning it is important to keep something small, as well as light, for a low MoI number. The lower the MoI, the less torque required for acceleration. You can experiment with the following: take a small object, weighing approximately a half-pound, and tie it to the end of a short string, about one foot long. Spin the object over your head-this works best if tried outside. Notice how quickly you can accelerate the rpm of the spin, and the strength required. Now, lengthen the string to a few feet and repeat (hopefully, the string stays tied and the experiment doesn't turn into a centrifugal force/linear trajectory experiment). More force is required to accelerate the spin for a longer string because the object is moving farther to complete each rotation and its arc velocity (or its equivalent linear speed) must be higher.
Enough of the physics, what about your bike? There are many ways in which rotational inertia affects the handling of a motorcycle, but the two which we will deal with are the moment of inertia of spinning parts, such as wheels and crankshafts, and the MoI of the whole motorcycle when turned into a corner. To show the importance of inertia as it pertains to rotating parts, consider your bike's front wheel/tire/disc assembly as a solid disc (Figure 3, not a great approximation, but close enough to show the significance of the concept). A front tire's radius is approximately 12 inches (half the diameter of a 17-inch wheel with a tire mounted), and the assembly weighs roughly 20 pounds, giving a MoI of 10 lb ft2. To put this into perspective, recall from last issue's dyno story ("Dyno Might!") the torque (T, in foot-pounds) required to spin an object at an angular acceleration of a (in radians per second) is:
The torque required to accelerate just the 20-pound wheel from a stop to a road speed of 100 mph in 10 seconds is 4.3 foot-pounds.
Now, lighten the assembly by three pounds by hollowing out its center (Figure 4). The MoI drops to 9.75 lb ft2, hardly any savings in inertia at all from the 10 lb ft2 calculated above. However, taking the three pounds off the outside of the rim (by dropping the diameter), will lower the inertia to 7.1 lb ft2-a 30 percent savings for only a 15 percent drop in weight (Figure 5). Now, only 3.08 foot-pounds of torque are required for a similar acceleration, unused torque that can be put to better use for linear acceleration of the whole bike.
The same theory applies to any part of a motorcycle that spins-sprockets, transmission gears, clutch plates, crankshaft. Not only is the weight important, but also how that weight is distributed about the axis of rotation. Now for the quick test: Which saves more inertia, a two-pound lighter set of brake discs (12-inch diameter), or a one-pound lighter tire (24-inch diameter)?
Not only are objects with a high MoI harder to spin, but also they are more affected by gyroscopic reactions, which can in turn adversely affect handling. The gyroscopic moment is a reaction felt when a spinning, body is rotated along the axis of spin (we've all done the bicycle wheel trick), and, essentially it redirects your input into a different orientation. The reaction is proportional to the inertia of the body, its spin velocity and how quickly the axis is rotated. In short, lowering the MoI of any spinning parts will lessen the gyroscopic reactions introduced, making your bike easier to turn from side-to-side.
Considering the entire motorcycle as an object now (Figure 6), there are three axes around which it can rotate: roll (side-to-side), pitch (front-to-back) and yaw (left-to-right). While pitch and yaw certainly affect handling to an extent, what we are most interested in is the roll MoI, because it determines how quickly a motorcycle can be leaned from one side to another, a measure of its "flickablilty." One part of the inertia equation, the mass, is addressed easily-less mass means easier turning. But the motorcycle's roll axis, the line about which it rotates when turning from side-to-side, is defined less easily. In a simplified analysis, the motorcycle rotates about the tires' contact patches, so it would make sense to centralize as much mass as possible close to that axis (low to the ground).
We will discuss gyroscopic effects as they pertain to cornering a motorcycle in a future issue, but consider for a moment that the front wheel is steered from under the motorcycle-in the opposite direction of the corner-entering a turn. This would mean that the axis of rotation (the roll axis) lies above the ground and closer to the bike's center of gravity (CoG) during at least a portion of the turn. But having the CoG too low affects a bike's behavior in the middle of a corner, once the bike is leaned in. Honda's 1984 NSR500, with its fuel tank underneath the engine and pipes over top, is an extreme example of lowering the CoG-and Honda reverted to a more conventional layout the following year. In this light, the current trend toward mass centralization (compacting a bike's heavier parts nearer to the CoG with less emphasis on simply placing everything as low as possible) makes sense.
Oh, the answer to the test. The lighter tire drops twice as much rotational inertia as the lighter discs.