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Motorcycle Dynamics
Like physics, it's a balancing act

By: James R. Davis

'Weight transfer' is well understood to exist and to occur whenever you accelerate or decelerate. However, why it happens and how much weight transfers - and even, how fast it occurs - seems to be completely beyond most riders.

I intend here to explain it all and to do so without a heavy dose of math. I will do it with an explanation of the fundamentals.

First, 'weight' and 'mass' are NOT the same thing. Weight is a FORCE, mass is not. Weight is mass times the acceleration rate of gravity. Whenever you see the symbol 'mg' it means 'weight' or 'mass times gravity')

Gravity acts through the Center of Gravity of a mass. 'Center of Gravity' (CG) is that point within the mass where an equal amount of mass if above that point as below, and an equal amount is in front of that point as is behind it.

A motorcycle is sold invariably with the claim that it's Center of Gravity is 'low' (as compared to other motorcycles.) Naturally they cannot ALL be lower than every other motorcycle. But the reason 'low' is claimed is because the lower the CG is, the more stable a motorcycle feels and easy it is to lean without falling over onto its side.

Below is a diagram that demonstrates that when a rider is on a motorcycle the CG shifts both up-wards and toward the rear. Naturally, because the rider sits higher than the bike's CG and behind it.



We will investigate weight transfer using realistic numbers in order to familiarize you with magnitudes. For example, we will assume that the motorcycle weighs 820 pounds without a rider and that the rider weighs 180 pounds so that the total weight (mg) of both is 1,000 pounds.

The height of the CG (H) stands at about 24 inches without a rider and grows to about 33 inches with the rider.

Without the rider the CG is closer to midway between the front and rear contact patches than with the rider. We will assume a motorcycle that has a wheelbase (WB) of 66 inches, and the length of the front weight bias (F) is about 37 inches while the length of the back weight bias (B) is about 29 inches. (While this is just an example, the numbers are realistic.) Why that is important is because the amount of weight on each tire is determined by dividing the alternate weight bias by the wheelbase length and multiplying that ratio by the total weight. In other words, without a rider there will be an average of 410 pounds on each tire, but the actual weights are shown below.

Front tire load =
mg * B / WB
820 * 29 / 66
360 pounds

Back tire load =
mg * F / WB
820 * 37 / 66
460 pounds

Now we add the rider and because the CG has shifted toward the rear, the lengths of F and B change. The weight on the rear tire will be about 59% of the total while the weight on the front tire will be only about 41% of that total.

We can see that by recognizing that the Front weight bias (F) has become about 39 inches instead of 37 while the Back weight bias (B) became about 27 inches instead of 29.

Front tire load =
mg * B / WB
1000 * 27 / 66
409 pounds

Back tire load =
mg * F / WB
1000 * 39 / 66
591 pounds


So, if we add lines of force to the diagram we see that for a motionless motorcycle, or one that is moving at a constant speed, gravity pulls the motorcycle and rider down (through their CG) while the ground pushes back an equal amount up-wards through the tires, though the amount of normal force up-wards is distributed about 40% through the front tire and about 60% through the back tire.

Let me remind you that gravity is a vertical acceleration force. So let's see what happens when we accelerate our bikes by cranking the throttle on. Yes, our speed increases in a horizontal direction. In fact, because our tires have traction sufficient to support it and because some of our engines are quite powerful, we can actually accelerate at rates approaching 1g (a little more than 32 feet per second per second.) Or, of course, at a rate smaller than that.

It should come as no surprise that the higher the rate of acceleration, the greater the weight transfer will be as weight transfer is a function of the rate of acceleration and the height of the CG (H) divided by the length of the wheelbase (WB). That is, the higher the CG is, or the shorter the wheelbase, the greater the weight transfer for any given rate of acceleration.

Let's add some more force lines to the diagram and explore this more closely.



Your engine produces a driving force that is felt at the rear contact patch (only) and is represented by the forward pointing red arrow. The length of that arrow is an indication of how much driving force is being sent to the rear wheel and as you can see I have made it about the same length as the length of the arrow representing gravity. In other words, we will look at what happens when you deliver the maximum acceleration force your motorcycle can handle.

Resisting this driving force is an equal amount of force (essentially inertia) that pushes toward the rear through the CG. (Forces must ALWAYS balance.)

As a consequence of the fact that the CG is higher than ground level where the driving force is being exerted, there is a natural torque developed which tries to twist the motorcycle clockwise (in the diagram) relative to the rear wheel contact patch. THAT is what causes weight on the front tire to appear to shift to the rear tire - in other words, is what accounts for weight transfer.

The down pointing green arrow at the front tire contact patch represents, by its length, how much less load the front tire is now bearing while an up pointing green arrow at the rear tire contact patch represents how much more load that tire is now bearing.

But it might occur to some that both the driving force and the resistance force are horizontal. How can they cause changes in the vertical forces on the motorcycle? I hope to show you now that you do not need to understand 'torque' to understand weight transfer.

Once again we add some force lines and shift others around to see why.



Since the gravity and resistance force lines are orthogonal (meaning perpendicular to each other) it is a simple matter to demonstrate that these forces combine via vectors into a force that points down and to the right. THAT is what shifts weight from the front tire to the rear.

Now, as to how much weight is transferred ...

The amount of weight transfer is merely the total weight times the amount of acceleration (its rate) being applied times the height of the CG divided by the length of the wheelbase (WB). So, in our example of maximum acceleration we see that the total weight transfer would be:

Weight transfer = mg * acceleration rate (1g) * H / WB
1000 * 1 * 33 / 66
500 pounds

The load on the front tire if we accelerate at the rate of 1g, therefore, would be 409 pounds LESS 500 pounds, or MINUS 91 pounds!! In other words, we have performed a wheelie and flipped ourselves onto our backs!!!

(For those of you who might think I've just described a wheelie, pay attention to the fact that I said we flipped ourselves over and onto our backs That, because as the front tire comes off the ground the CG gets higher and we have already seen that for any given amount of driving force the higher the CG, the more weight transfer occurs. A wheelie REQUIRES that as the front-end comes off the ground you ROLL OFF your throttle in order not to end up on your back.)

But if we had accelerated at only .5g's (a respectable rate) the total weight transfer would be 250 pounds and the resultant load on our front tire would be 159 pounds while our rear tire would then be carrying 841 pounds (591 + 250).

From these simple calculations we see that:
  • The greater the rate of acceleration, the greater the weight transfer
  • The higher the CG is relative to the wheelbase, the greater the weight transfer
And how fast does it occur? Instantaneously, of course. However, as you cannot increase your acceleration rate from zero to 1g instantaneously, it is THAT amount of time that determines when all the weight transfer that is going to happen occurs.

Now, please, the entirely obvious - just to finish this off ... Braking is merely negative acceleration. What we have learned about weight transfer during acceleration is equally true when braking only the weight will shift from the rear tire to the front one.

Physics is a balancing act, after all.

Copyright 1992 - 2018 by The Master Strategy Group, all rights reserved.
http://www.msgroup.org

(James R. Davis is a recognized expert witness in the fields of Motorcycle Safety/Dynamics.)

     
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