Two recurring motorcycle topics are whether there is a threshold speed above which riding a motorcycle in sand achieves greater inherent stability, and whether aftermarket "specialists" can improve the performance of the motorcycle suspension. This short note addresses the sand threshold speed question. The suspension question is ridiculous, nonetheless most of my friends believe that "two Fred's in shed" can improve what the factory engineering specialists have delivered, and are happy to write a check for several hundred dollars for the service. So it goes.
The figure below shows the geometry of a motorcycle wheel on solid ground (left), and in sand (right). The figure assumes that the motorcycle is static, and that the wheel sinks into the sand (right hand drawing) due to the weight of the motorcycle. BTW, the commentary here follows the postulate originally made by Lyndon Poskitt (professional off road competitor). The postulate is based on the reduction, or elimination, of trail (shown in the figure). It is well known that trail, defined as the distance between a point on the ground at the linear extension of the fork tube and the actual contact patch, is needed to stabilize the forward motion of the motorcycle. Lack of trail or negative trail produces an oscillation in the wheel as the motorcycle moves forward.
Note: In the figure above the fork tube offset from the steering head is assumed to be zero.
The wheel on the right, sinking into the sand, virtually eliminates or produces a negative trail value. The value, h, is the depth of the "sink" and will vary depending on the characteristics of the sand and the weight of the motorcycle. The energy required to raise the motorcycle by the distance h is given by the well known potential energy equation "mgh". Where m is the mass of the motorcycle and rider, and g is the acceleration of gravity.
The energy needed to lift the motorcycle out of the sand can only come from the forward motion of the motorcycle. The energy of a motorcycle moving forward is given by another simple and well known kinetic energy equation "½mv²". Combining the two equations yields:
½v² ≃ gh
When a value of h of 5cm (2 inches of sink) is used in the above equation you get a value of v equivalent to walking speed, about 2 meters/second. This actually feels pretty good relative to my experience of pushing a motorcycle in sand.
Obviously if all the kinetic energy is used to raise the motorcycle there would be no forward motion when riding, and the motorcycle would tip over. So one has to allocate a fraction of the forward motion energy to raising the motorcycle. This is a debatable choice, but if one uses a conservative 10% of the forward motion goes into raising the motorcycle, the value for v (using the 2" sink) becomes about 8 mph. For 4" of sink, the speed value becomes about 12 mph.
The exact relationship between sink and threshold speed is not really important. What is important is that a threshold speed does exist, and the physics supports the existence. It should also be noted that the spinning motorcycle wheels produce additional gyroscopic stabilization which is a linear function of the wheel rotation rate. So "faster" is definitely better.
This conclusion is totally unrelated to the issue of suspension improvement by a clown or two in a messy shop with fork oil all over the floor. Disgusting.
myth busting
