Motor and Battery Caclulations... am I doing them right?

One of my team-members approached me with a little question…

He decided he wants to use the window motors (specs and curves) as drive motors (worm gear, yeah, he knows, but he doesn’t really care) for a little mini-bot he’s making. The battery that he’s using is a 12v battery rated at 4amp-hours. The question is how long will it take for those motors to drain all the juice out of that battery.

It’s a small bot that just has to move, so I figured there isn’t going to be a lot of torque on the thing - maybe .5 to 2 Nm. From the curves, I figured that to be 5 to 8 amps per motor. Together, thats a total of 10 to 16 amps of current thats going to be drawn by those motors.

So with a 4 amp-hour battery, how long is it going to last? I figured:
4 amphours / 10 amps = .4 hours, or 24 minutes
4 amphours / 16 amps = .25 hours, or 15 minutes
So basically, I told him theoretically, 15 to 24 minutes, depending on the load. I want to know did I do these calculations right, or did I miss something.

He also said the battery’s “initial current with cyclic use” is 1amp. What exactly does that mean? Is that the max current that the battery can supply at one time, or something else?

The calculations you performed will result in some discrepancy. Amp hour rating is usually specified at a fixed load current with a specified time to fall to a certain terminal voltage. (for 12 volt batteries it is usually 8 volts) In most cases this can be assumed to be 1/10 of the rated amp hour current. i.e. a 4 amp/hour battery would last 10 hours at 0.4 amp load current. Draw significantly more than that and the amp hour rating will degrade. I am guessing that at 16 amps you might only get 5 minutes, tops to fall to 8 volts. You didn’t say if there were electronics involved but with just the motor connected the terminal voltage will continue to fall at a predictable rate until the motor slows to a halt.
The initial current of 1 amp is what the battery would be able to deliver after a full charge at 12 volts. (note it is twice the current for the amp hour rating calculated above. At 16 amps the voltage would be less. This voltage could be calculated if the internal resistance of the battery was known.) Cyclic use implies that the load is not constant and that some recharging takes place between loads. The type of battery discussed here can be found in emergency lighting where it can be expected to deliver light for a short period of time (loss of electric power) and then return to charge.