CV3/CV4 Momentum Calculator
Description
CV3 (acceleration) and CV4 (deceleration) give a locomotive simulated momentum — a gradual ramp up to speed and coast down to a stop, instead of snapping instantly. The CV value itself doesn't mean anything in seconds on its own; it only becomes a real-world time through the formula below, which makes it awkward to dial in by trial and error. This calculator converts directly between "how many seconds I want the ramp to take" and the CV value that produces it.
One genuinely useful fact falls straight out of the formula: the total time to go from a stop to full speed depends only on the CV value, not on whether the decoder is running in 14-, 28-, or 128-speed-step mode — the per-step rate changes with the step count, but it exactly cancels out over the full ramp. This calculator shows both numbers so you can see that for yourself.
Sources
The acceleration rate formula is reproduced directly from NMRA Standard S-9.2.2, "Configuration Variables For Digital Command Control, All Scales" (July 2012), Configuration Variable 3: rate (sec/step) = (CV value × 0.896) / speed steps in use — including the standard's own worked example (CV3 = 2 at 28 speed steps gives exactly 0.064 sec/step). CV4 (deceleration) "uses the same fashion as acceleration," per the same standard. The full-ramp-time independence from speed-step mode is a direct algebraic consequence of that formula (the speed-step count cancels out), not a separately sourced claim.
Disclaimer: this is the NMRA's own formula for how CV3/CV4 should behave, but manufacturers implement it with varying precision — treat the CV value here as a close starting point, and fine-tune by testing on your actual locomotive.