Cascade Elevator Gearbox Calulations

I was trying to figure out how to calculate the gear ratio requirements for a cascade elevator. Last year my team built a continuous lift and it worked fine (on the drive part). However, this year, we wanted to do cascade to avoid all the tensioning issues we had with continuous. However, I was trying to use JVN calculator, but if I understand correctly the cascade would need to be geared 3 times higher (for a three stage lift)? Is this correct?

Approximately, yes. The cascade lift multiplies the force needed to lift the later stages in exchange for having all stages rise at the same rate. This tends to mean that a cascade lift will hit max height faster than a continuous lift run at the same speed.

Ok thanks, this answers my question.

Maybe drawing a free body diagram will help get you started. Depending on the design, some multi stage lifts will have varying loads, and some will have a constant load.
In the varying load example, you will be lifting one stage from lowest to highest, then lifting the next stage and the first stage together from the second stages lowest to highest and so on.
In the constant load example, you will lift all stages at the same time from lowest point to highest point. The free body diagram may look like this (sorry for the bad picture):

You will have to use a 3:1 ratio to account for the cascading effect I believe.

Maybe I’m thinking about this wrong, but wouldn’t a 3-stage cascading elevator be an effective 4:1 reduction? The first cascade doubles the force, then the second doubles that doubled force (i.e. quadruples the force)

Either way, once you figure this out I recommend using the Mechanism tab on my design calculator for these kind of calculations. It does everything JVN’s calculator does, plus some additional helpful calculations like stall voltage, reduction for max power, reduction for max efficiency, etc.