What is a critical speed

During the testing to define the grade & train length impact of various HO engines, the concept of a realistic speed has emerged.  

By definition for the number of four ounce cars that the engine can not pull the velocity is zero.  What has surprised me is the shape of the velocity function as the number of cars increases to the limiting level.  It is far from linear.  As the following curve shows, it is also impacted by wheel material & size.  

As the chart shows, wheel characteristics impact the number of cars an engine will pull.  However the speed levels are very low for a number of the last successful train lengths.  Often the speed can increase moderately as the train length increases just prior to last successful train length.  

Exactly what is a useful speed is not clear.   Even if one was specified, the test process would be iterative & would only be a bottom relevant number.  The actual speed would be had to set in every test unless partial weighted cars were included.  This would require more testing supplies for questionable benefit.

A better set of speeds to focus on are the engine only level and the train length that is the car count that is 2 times the number of drive axles for the engine.  This case is 8 cars for a 4 axle engine and 12 cars for a 6 axle engine.  These values are easily defined for level and 2.5% grades.  Real engines are known to pull a train length that is 2 times the number of drive axles.  

The change in this speed is an interesting factor.  Some motors will drive the engine only to very high speeds.  However, with the requisite train length based on the axles, the speed can fall off dramatically.  For others, this reduction is not as large, as shown in the following figure:

Interestingly, the upper curve is for an 4 axle engine, so the critical speed is for 8 cars. For the other three the engines have six axles and the 12 car speed is critical. The two engines in the middle pull the same total number of cars, but show a much different velocity signature.  The speed for the expected train length is the most pertinent and should be compared.  The higher the better.  For this reason, my performance measurements will define this speed for level & 2.5% grades for all my subsequent testing.

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