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Attack Angle
State MOM's

By: James R. Davis

I recently worked on a case where a rider and his passenger were severely injured in a single-vehicle accident when the motorcycle that was being ridden attempted to cross a trolley track that was embedded in the surface street, running parallel to the traffic lane.

That case has been settled so I have some liberty in discussing it here provided I do not identify the participants or location of the accident. This is not a case study. Rather, I will use it to demonstrate some lessons learned.

First, the issue of crossing tracks in the road that are running parallel to your path of travel.

Many, if not all, states publish and provide to the riding community a Motorcycle Operator Manual or Handbook in which many helpful, safety oriented, suggestions are made. As to railroad tracks, this is what one of those handbooks says:

The graphics at the top left of the page suggests that while you should attempt to cross tracks with an attack angle as close to 90 degrees as possible, there are times when you should not do so. For example, if in order to cross at the largest attack angle possible you will be putting your motorcycle into a path of travel that might cause you to encroach on an oncoming lane, you should better keep your motorcycle traveling in a straight line to cross the tracks.

This bit of advice makes the assumption that the tracks are already angled across your path of travel at a significant angle (as highway engineers are required to do).

I have no trouble with that advice and graphics, though I wish somewhere it was stated that "Your motorcycle should not be turning when you cross the tracks." That is, your front wheel should be pointing in the same direction as your rear wheel when you cross the tracks. In other words, your bike should be vertical and riding in a straight line when you attempt to surmount any obstacle in your path of travel.

But what if the tracks are running parallel to your path of travel and you must cross over them in order to change lanes, for example?

The graphics at the lower left part of the page and the text at the upper right attempt to convince you that you should provide an attack angle of at least 45 degrees in order to cross those tracks as safely as possible and that "Edging across could catch your tires and throw you off balance." That, too, is good advice though it is insufficient. Edging across (having a very small attack angle) could trip your bike into a spill - which can injure or kill you!

It goes on to suggest that you should first steer far enough away from the tracks so that when you then steer across the tracks, your attack angle will be at an angle of at least 45 degrees.

That, it turns out, is a virtual impossibility.

Even if you move a full lane (about 12 feet) away from parallel tracks before beginning a modest (say 0.2g) turn to cross those tracks, if your bike is moving at counter-steering speed (greater than 10 MPH), you cannot attain an attack angle anywhere near 45 degrees. Further, you cannot have completed your turn before crossing the track (your bike will not be vertical and traveling in a straight line).

I am not an accident reconstructionist, and I'm not an engineer. So the analysis which follows would not be allowed to be entered into evidence from me in a case without being challenged and probably tossed out. But I am qualified in the field of motorcycle dynamics to discuss the issues and realities as I did above, leaving the supporting calculations and analysis to be provided by a qualified engineer.

Let's look at a representation of the problem in graphic form.

Here we see a motorcycle beginning a modest 0.2g leftward turn at point 'A' and crossing a track at point 'B'. The motorcycle is traveling at 25 MPH at the time and maintains its speed.

The blue curve is a segment of a circular path that has a 215 foot radius. (Now, please, I know that to begin a turn at that speed the rider must counter-steer, and that the actual path of travel of his bike would start out turning slightly to the right and then, with a decreasing radius turn to the left, could not possibly cross the track at point 'B' as shown. The actual crossing point would be slightly higher of what is shown. I used a constant radius turn to make the analysis more straightforward for us here. Besides, it will show a maximum attack angle possible - one which is greater than actual.

The graphic shows that the motorcycle will travel 66.7 feet down the road while it travels 10.6 feet laterally (to the left).

A 0.2g turn is modest. A smaller effort would result in a smaller attack angle. Now the question is, even with our assumptions, what is the attack angle of the motorcycle relative to the track? And, by the way, we will deal only with the attack angle of the bike, not its front tire. The bike, as you can see from the graphic, has not completed its turn and is not, therefore, riding vertically and in a straight line when it encounters the track. That means that there is a steering angle of some number of degrees that must be added to the bike's attack angle in order to determine the attack angle of the front tire.

The instantaneous path of travel of the motorcycle when it encounters the track is shown below. Note that it is a tangent to the circle and must be perpendicular to the radius of the circle at point 'B'.

We need to determine the angle of that path of travel relative to vertical (the direction the track is pointed to). We will do that by finding the center angle of the line segment 'A' and 'B'. Note that if we drop a vertical line from point 'B', we can establish a point 'C' which will form a right triangle (origin, 'B', and 'C') with an adjacent side of 204.4 feet in length and an opposite side of length 66.7 feet.

The tangent of the desired angle is used to calculate that angle to be 18.1 degrees. [tan-1(66.7/204.4) = 18.1 degrees]

And now you see why we solved for that angle. The center angle is relative to horizontal and, of course, is relative to vertical for a perpendicular path.

What we have just demonstrated is that with a modest (0.2g) turning effort and starting 10.6 feet to the side of a parallel running track, at a relatively low speed of only 25 MPH, the bike's attack angle cannot be more than 18.1 degrees. An aggressive turning effort of 0.6gs would result in an attack angle of only 31 degrees - far below the MOM admonition to use at least 45 degrees.

In fact, only when you drop the speed of the motorcycle to 10 MPH or less can your attack angle be at least 45 degrees.

Those Motorcycle Operator Manuals (MOM's) and Handbooks do not mention that fact. Nor do they suggest that you slow your bike down to direct-steering speed in order to cross a parallel running obstacle as safely as possible. Their advice to motorcyclists is to cross at an angle of at least 45 degrees - but you can't, especially when there is traffic behind you.

Imagine the plight of the rider who happens to be riding right between the tracks and who tries to turn to the right or left. He or she doesn't have 10.6 feet to 'setup'; he or she has less than half that width.

Now if the tracks and particularly the roadbed next to those tracks is well maintained, has little or no height differences from the tracks, and there is neither oil nor water on the tracks, you can cross them at almost any angle (greater than about 10 degrees) with relative safety. Otherwise, any city which has a trolley system with tracks embedded parallel to a public roadway has effectively denied motorcyclists the right to use that roadway.

Copyright ? 1992 - 2022 by The Master Strategy Group, all rights reserved.

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

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