Solved

# Formula to calculate optimum acceleration and deceleration

Posted on 2011-04-27

I am working on a workbook which calculates an object moving between 2 points.

The variables I have are:-

Start position - this can be any value including negative values and represzents a measurement in mm

End position - as start position

Travel. This is the distance travelled and therefore an absoute value

Accel/Decel. This represents is the same for both acceleration and deceleration and is expressed in mm/sec^2

Time - The desired time taken to complete the task

Speed - the speed of the object derived from the time variable

The object has certain minimum and maximum values which are variables

AccelMin, AccelMax, SpeedMin, SpeedMax

I am trying to find the optimum value which will essentially accelerate and then immediately decelerate without reaching the MoveSpeed or SpeedMax value (whichever is lower).

I could figure this using a loop but figure there is a much cleaner mathematical solution to this