Acceleration is the rate at which the decoder increases speed from one speed step to the next in response to a new increase speed command. The acceleration rate (CV03) can be set to simulate train weight. Deceleration is the rate at which the decoder decreases speed from one speed step to the next in response to a new decrease speed command. The deceleration rate (CV04) can be used to simulate inertia. Just like the prototype, you can set your locomotives to get off to a slow start because of a heavy load and to take a long time to come to a stop because of the inertia of the train once it is moving.

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Back EMF
Acceleration and Deceleration Rates
The Throttle Response Curve, Adjusting

Adapted from "Digital Command Control: The Wave of the Future", by Zana and A.J. Ireland.