Art & Science: Fun With Geometry

Rake and trail are terms often used when discussing sportbike handling. Manufacturers sometimes highly tout these numbers in their brochures, and we often refer to them in testing. Trail especially affects how a bike feels, and can determine its stability, steering quickness, and in general, a large portion of the bike's handling characteristics.

Rake is the angle of the steering head with respect to a vertical axis. Trail is the horizontal distance from the front axle to where a line drawn through the steering axis meets the ground.

Trail can be calculated from triple-clamp offset (0), tire radius (R) and rake (ø). Changing any of these three variables will alter trail, but each also has other-and sometimes unfavorable-effects.

Rake is defined as the angle of the steering head with respect to a line drawn perpendicular to the ground (left). A smaller angle, or less rake, is sometimes referred to as being steeper, and production sportbikes are currently in the neighborhood of 23 degrees of rake.

Trail is the horizontal measurement from the front axle to the point at which a line drawn through the steering head intersects the ground (figure 1). Current sportbikes have 90-95mm of trail.

While the two dimensions are interrelated, trail is the number that mostly changes the steering feel of a motorcycle. Trail gives a motorcycle stability because of the self-centering effect caused by the front wheel being behind (or trailing) the steering axis. Too little trail, and this self-centering effect is decreased to the point of instability. Too much trail, and the effect is so great that steering becomes heavy. There is a lot more to trail than this (and for more detail, you can refer to the resources listed here), but these are the basics for the purposes of this discussion.

At first glance, most sportbikes appear to have a set rake and trail that cannot be changed, but that is not necessarily the case. Given a motorcycle's basic dimensions, we can calculate trail as follows (right):

(equation 1)
Trail=RSinø-0/cosø
R=tire radius
0=triple-clamp offset
ø=rake

Raising or lowering the front end of your motorcycle puts more or less weight on the front end. However, the handling change due solely to the change in weight bias is negligible.

As an example, a bike with a front tire having a circumference of 1890mm, a 23-degree rake and 27mm of offset will have 98.5mm of trail. Note that in the range of variables we are dealing with, using a tire with a smaller radius, increasing offset or decreasing rake can decrease trail. On most stock sportbikes, you cannot change two of the three variables (tire diameter and offset) without resorting to modifications, but the third variable, rake, we can change slightly by raising or lowering the fork tubes in the triple clamps.

An expert-level roadracer can notice a change in the order of 1mm in trail, and working equation 1 backward, we can calculate the change in rake required as just less than 0.2 degrees. Using an approximation based on the arc length from the rear axle to the steering head, we can further calculate that a fork-height change of just 4mm is enough to effect this angle change.

You can measure rake angle by using an inclinometer, available at hardware stores.

Many riders refer to fork height or rear-ride height change as "putting more (or less) weight on the front end," but we can calculate the change in weight bias brought about by this 4mm change.

A typical sportbike and rider combination weighing 600 pounds has approximately a 50/50 weight bias, with its center of gravity (CG) at a height 1_2 of its 1400mm wheelbase (figure 3). Front-end weight is calculated as:

W_f=W_t(L-x)/L
W_f=front-end weight
W_t=total weight
x=distance from front axle to CG
L=wheelbase

Offset is the perpendicular distance from the steering axis to a line drawn between the two fork tube centers.

In this case, the bike's weight is evenly distributed, with 300 pounds on each wheel. Raising the fork tubes in the triple clamp and changing rake by 0.2 degrees will move the CG forward by approximately 3.5mm (you can use trigonometry to calculate this), resulting in a front-end weight of 301.5 pounds. This is practically insignificant compared to the change in trail resulting from the adjustment-you would have far more of an effect on weight bias by simply moving your body a little bit forward.

Raising or lowering the front end of your bike changes much more than just rake and trail, however. It also changes the angle of the swingarm, which can play a big part in handling, especially on more powerful bikes. We will cover more rear-end geometry in a later issue, but you should know that adjustments in trail are by far the most apparent change a rider will feel when raising/lowering the bike's front end.

Adjustable triple clamps allow you to vary offset in increments. This is the preferred method for changing trail, as it affects other handling variables the least.
Photography by James Brown

Tire diameter is one of the other variables affecting geometry, and we can calculate the change in trail resulting in a switch between two brands of tires. In our last tire test ("DOT Race Tire Test," Feb. '03), the tallest front tire was the Michelin Pilot Race 2, at 1910mm in circumference. The smallest tire was the Metzeler Rennsport/Pirelli Supercorsa, at 1878mm. We always measure tire circumference and change ride heights to make the overall chassis attitude (and rake) the same (see Ask the Geek, Feb. '02), and in this case, the fork tube height would need to be changed by 5mm just to level the chassis.

Even taking that into account, however, the change in trail due only to the change in tire size is 2mm. Add in the different tire's profile (that changes trail at various lean angles), and you can see why adjusting only to keep the bike's attitude the same when changing tire brands is sometimes not enough.

The last way we can adjust trail is by changing the triple-clamp offset, and you will see that racebikes often have this adjustment. In this case, a 1mm change makes approximately the same change in trail (but opposite-more offset gives less trail, and vice versa) with very little effect on ride height and rake angle.

Resources

Motorcycle Handling and Chassis Design: The Art and Science
Tony Foale
www.tonyfoale.com

The Racing Motorcycle: A Technical Guide For Constructors
John Bradley
www.eurospares.com

This article originially appeared in the October, 2003 issue of Sport Rider.

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