Problem regarding photo panning

[thatguy]

Hi there,

Hoping someone can help with a math problem for a practical application. My apologies, but I don't know for certain this is an algebraic question.

http://pointofviewcameras.co.uk/camalapse-time-lapse-mount.html

This device is basically an egg timer designed to mount a camera on top so it can pan across for time lapse photography. If you have one of these with a camera mounted on top and wind it up, it takes 60 minutes for a full 360 degree turn (1 revolution).

These timers are stackable because they will screw in to each other (refer to pics in the link above). If you were to stack two of these timers together with a camera on the top and wind both up to the max, the camera will:

1) do 1 revolution in half hour, and
2) do 2 revolutions in one hour

So here is the question. What happens if you stack a 3rd timer, or 4th timer to it? What is the equation to determine the outcome if you were to stack 10 of them?

Thanks for any and all comments,
Tony

 

[thatguy]

I ask for an equation because there is a disagreement in our office about what happens to the 3rd and 4th timer.

1) Some folks seem to think that the time for 1 revolution as the number of timers increase is based on "time of 1 revolution" / "number of timers". Therefore:
1 revolution for 1 timer = 60 minutes (60 / 1 = 60)
1 revolution for 2 stacked timers = 30 minutes (60 / 2 = 30)
1 revolution for 3 stacked timers = 20 minutes (60 / 3 = 20)
1 revolution for 4 stacked timers = 15 minutes

2) Others say the time is halved with each additional timer, and therefore:
1 revolution for 1 timer = 60 minutes
1 revolution for 2 stacked timers = 30 minutes
1 revolution for 3 stacked timers = 15 minutes
1 revolution for 4 stacked timers = 7.5 minutes

Assuming you are saying option (2) is correct, how do you prove it?

 

[stapel]

I ask for an equation because there is a disagreement in our office about what happens to the 3rd and 4th timer.

1) Some folks seem to think that the time for 1 revolution as the number of timers increase is based on "time of 1 revolution" / "number of timers". Therefore:
1 revolution for 1 timer = 60 minutes (60 / 1 = 60)
1 revolution for 2 stacked timers = 30 minutes (60 / 2 = 30)
1 revolution for 3 stacked timers = 20 minutes (60 / 3 = 20)
1 revolution for 4 stacked timers = 15 minutes

2) Others say the time is halved with each additional timer, and therefore:
1 revolution for 1 timer = 60 minutes
1 revolution for 2 stacked timers = 30 minutes
1 revolution for 3 stacked timers = 15 minutes
1 revolution for 4 stacked timers = 7.5 minutes

Assuming you are saying option (2) is correct, how do you prove it?

Maybe you could try attacking this from the perspective of the total number of revolutions for the "top" timer in one hour. For instance, if there are three stacked timers, each with a base rate of one revolution in one hour, then the bottom one went once around in that hour. But the one on top of that went around once with respect to the lower timer while that lower timer also went around once, so the second timer must have gone around twice on the one hour. Then what must have happened to the top time of the three?

And so forth....