EngineerBenchEstimating the time for a printer move
Distance divided by requested speed is accurate only when speed stays constant. Short moves often spend most of their time accelerating and decelerating. This model includes both phases and checks whether there is enough distance to reach the requested speed before slowing down.
Entry and exit speeds affect the answer
A move that starts and ends at rest takes longer than the same move between two continuous segments. Enter speeds that match the move being studied. When the requested speed cannot be reached, the profile is triangular rather than having a constant-speed section.
One move is not a complete print
Firmware look-ahead, cornering rules, jerk limits, extrusion limits, and neighboring moves can change execution time. This estimate is useful for understanding acceleration limits or comparing settings. It does not replace a slicer's whole-file estimate or measurements from the actual printer.
Recognizing a triangular speed profile
Acceleration requires distance. Starting from rest, reaching a speed v at constant acceleration a takes v divided by a seconds and uses v squared divided by twice a of travel. A move must also reserve distance to decelerate to its exit speed. If the two ramps would consume more than the move length, the requested top speed is never reached.
For a symmetric move that starts and ends at rest, short travel can therefore be dominated by acceleration rather than the chosen speed limit. Raising requested speed beyond the reachable peak may have no effect on the model's move time. Entry and exit speeds change the available ramp distances, so use values consistent with the surrounding path. A slicer may join several segments with nonzero junction speeds, while firmware limits can reduce those speeds at corners. Use the result to understand one idealized move and to compare acceleration assumptions, not to add independently optimized segment times and call that sum a verified print duration.
Formula
Phase distances use v² − u² = 2as; total time sums acceleration, cruise, and deceleration.