Chassis Dynamics

For all practical purposes, it can be said that a motorcycle is under a constant state of either acceleration or deceleration. For this discussion we are going to limit our topics to those applicable to chain or belt final drives and the forces that they exert upon the chassis as they transmit the power from the engine, through the rear wheel, and ultimately converting it into friction where the tire contacts the road surface, or “contact patch”.

A motorcycle is literally “pushed” forward by its rear wheel. The point on the chassis that this pushing force propels the machine will determine the way in which the chassis and rider will react to this force. A good example of this concept is moving a refrigerator across a room. Anyone who has pushed a fridge around can tell you that there seems to be a “sweet spot” on the side where you are pushing. Too high and it wants to tip over away from you, too low and it might fall on you. It’s a balance of mechanical advantage and traction. Interestingly enough the sweet spot will be different for different sizes of people. Throw into the mix different size refrigerators and the ability to guess where the sweet spot is seems to be impossible! Fortunately for motorcyclists we have enlisted the aid of some top notch physicist to help us predict the sweet spot for bikes.

There is a simple diagram that may be applied to almost any chain driven motorcycle that will help us to predict what the motorcycle will do when we roll on the throttle, and to a lesser extent just cruising along (as cruising is still the application of power to the rear wheel). The only real flaw in the diagram is that the center of gravity is a bit of a guess, as humans come in an infinite variety of shapes and sizes, and sometimes there is more than one on the motorcycle, luggage, etc.

In the initial design phase you start with the known quantities that affect attitude, to get to the prototype phase. If it’s done right the first time, the resulting prototype will be very close, saving time and effort in the long run, as well as ensuring a quality ride that keeps the end user loyal to the brand. They will probably never know the physics behind the machine, it just “feels right”, stable, predictable.

The known quantities that affect attitude are;

Wheelbase
Wheel Size (with tire)
Gearing (sprocket diameter)
Sprocket Location on Engine (helps determine swingarm pivot point)
Swingarm Pivot size (must not come in contact with chain run)

Now let’s apply these Knowns to the diagram of our Triple to help us determine engine placement. The goal of this exercise is to find two angles, listed as “delta” and “omega”. The relationship of these angles tells us in no uncertain terms what our motorcycle will be like to ride. First draw a line across the tops of the sprockets, now draw a line from the center of the rear wheel through the center of the swingarm pivot (keeping in mind that the swingarm pivot must clear the bottom of the chain, and still be as close to the front sprocket as possible to mitigate slack in the chain as the rear wheel moves up and down), creating an imaginary swingarm.

Where these two imaginary lines intersect is called the “Pole of Moments” or POM. Our next line is drawn from the POM to the center of the rear wheel where it contacts the road surface, yielding angle Delta, or chain pull angle.

Now the guesswork comes into play when we try to find Omega. Draw a vertical line through the front wheel. Omega will run from somewhere along this line to the same spot that Delta ends, that being the center of the rear wheel where it contacts the road surface. To find where Omega intersects the vertical line through the front wheel, we must make an educated guess as to where the overall “Center of Gravity” of motorcycle and rider will be. The Center of Gravity (or CG) is the most central point of the entire mass of the motorcycle and rider. Think of it this way- if you had a plate of food, with a heavy steak on one side of the plate and a lighter salad on the other, and you wanted to balance that plate on one finger, you would do a little searching on the underside of the plate with your finger to find the balance point. No surprise then that your finger is closer to the steak side of the plate. You have just found the CG of dinner in two dimensions. But what if you wanted to find the absolute Center of Gravity in all dimensions? The point at which the weight of our dinner has an equal distribution of weight in all directions? That spot would be directly above your finger somewhere INSIDE the steak.

With a little head scratching, weight of motorcycle, estimated weight of rider and the relative position of those two, the overall CG for a normal motorcycle will usually fall somewhere just under and forward of the seat, and in the center when viewed from the front.

Now draw a horizontal line from the CG to the vertical line through the front wheel, voila! The end point of Omega, now Omega can be called the “Weight Transfer Angle”.

With our two angles on paper we may begin our analysis.

A proper handling street motorcycle will have a smaller angle Omega than Delta, here’s why; the pushing force of the rear wheel should be transmitted to the motorcycle chassis through the SWINGARM. Conversely, if Omega is greater than Delta the pushing force will be transmitted to the chassis via the SUSPENSION.

In the swingarm pushing scenario a slight extension of the rear suspension (rebound) occurs and the steering neck remains in relatively the same place. This is desirable because it allows the suspension to do its job (isolating chassis and rider from road imperfections and increasing traction over uneven surfaces) and keeps the steering in the front as predictable as possible. Translation; smooth stable ride under acceleration, and in corners.

In the suspension pushing scenario, (Omega is greater than Delta) a compression of the rear suspension means that heavier rear springs must be used (rough ride even in a straight line) in order to keep a total collapse at bay, if there is a collapsed rear shock and you hit a pothole, contact with the road surface will be lost, with disastrous results. Another consequence of “suspension pushing” is the tendency of the chassis to squat in the rear, rotating the whole chassis around the swingarm pivot. This raises the steering neck of the motorcycle, extending the front forks, and causes severe rear weight bias. When this happens the front wheel feels skittish, and light, and a loss of both front wheel traction and directional control occur. The outcome; you will go wide in a corner, into oncoming traffic, with little or no rear, or for that matter, front suspension.

This is of course relative information, and I can already hear those who will say that their Harleys do just fine in corners, even with the suspension pushing their fatboys around corners. Three interesting points; Harleys HAVE to have low seat heights, low motors, etc. in order to lower the CG. They also do such things as; a 16″ rear wheel to lower the rear axle, and drop the swingarm, giant front and rear sprockets, to raise the top of the chain, in an attempt to compensate for an inverted weight transfer angle vs chain pull angle. Ironically, the heavier and lower they are, the less likely they are to collapse the rear suspension and go wide in a corner. The downside is that their ground clearance and cornering ability are compromised. These very low touchdown points, floorboards, kickstands, etc, become limiting factors when attempting to evade obstacles in the rider’s path. The unexpected touchdown of hard mounted chassis points is certainly a dangerous situation, especially in the hands of the inexperienced. Also the extra “ballast” reduces acceleration, and increases the effort required to corner.

The second observation is simply that the powertrain mounting points and especially the location of the front sprocket on a “Big Twin” Harley were designed in 1936. The Knucklehead was a rigid; it didn’t even have rear suspension! Hence the low sprocket and transmission, in order to merely lower the weight in the chassis. A shame that this “look” takes precedent over objective engineering realities in today’s “cruisers”

The last point is that the power to weight ratio plays a role in the extent to which the suspension push alters cornering ability. The average 800 pound Harley is only making 62 horsepower at the rear wheel. If it has a difficult time getting out of it’s own way, it’s going to have a harder time compressing the rear suspension, but double the available power, and you have a recipe for at best a product liability lawsuit, at worst people getting hurt. The “rocket powered moose” syndrome.

A fine example of the power to weight influence is the Kawasaki H1. Commonly known as the worst handling, most dangerous motorcycle of all time. Most people attribute this to a poorly constructed frame, but a deeper study reveals flaws in the dynamics of the chassis. H1 frames are certainly not “good” by modern standards, but on par with the rest of the bunch of late 60’s Japanese cheap streetbikes. It is in fact the unique combination of inverted Weight Transfer and Chain Pull Angles, a narrow and abrupt powerband, and the high power to weight ratio that amplified the other two flaws. Many a young man in the early 70’s found himself in a ditch wondering how he got there! The answer is of course that the Kawasaki chassis department wasn’t communicating with the engine department!

But back to our little triple. Like the H1 we have a very compact engine with drive sprocket sitting very close to the crank. In order to maximize the chain pull angle relative to the weight transfer angle, the engine will need to be mounted fairly high in the chassis. This however complicates things as it RAISES the center of gravity, bringing the weight transfer angle along with it! We could merely move the motor rearward, dragging the pole of moments back as well, but this violates the principle of a forward weight bias for the overall motorcycle. Since we are assuming that the gearing is fixed, the only viable solution is to lower the CG, and get that weight transfer angle down. A low seat height will help, as will placing the battery and other components low in the chassis, and close to the front wheel to help compensate for our slightly elevated and rearward motor.

Chassis dynamics are of course a study of things that are always on the move, ever changing. An interesting experiment for you to try at home; place the front wheel of your favorite motorcycle against an immovable object (brick wall, telephone pole, etc.) now with the motor idling, and in gear, let the clutch out a little. Does your bike’s seat rise, or squat? Generally speaking, chain drive motorcycles that rise have a greater chain pull angle than weight transfer angle; squatters are the other way around! You can tell how the chassis attitude of a motorcycle under acceleration will react without even riding it.
Pretty cool eh??

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