How long will my clock run ?

The question is fairly easy to answer, but normally it is asked with the expectation of finding a way to increase the running time.
There are a couple of basic factors that govern the length of time that the clock will run, the first is how far can the weight fall before it hits the ground, as it is shown below the higher you hang the clock on the wall the further the weight has to fall and the longer the clock will run. Obviously there is a limit to high how you can comfortably hang the clock so a reasonable expectation for the weights travel is about 1300 mm. This is assuming that the centre of the dial is set to about 1600 mm. There are some detail consideration that could increase this, first arranging things so that the weight starts off from a higher position and secondly making the weight itself shorter, but 1600 mm is a good starting point.

The second major factor to govern the running time is the diameter of the drum around which the cord supporting the weight is wound, the drawing below is a section through Clock 1 showing the cord wound around the drum, the drum in this instance is Ø 3.8 cm.

For each hour that the clock is running, this drum turns one complete revolution, so the length of cord unwound is Pi x (Diameter^2)/4 = 3.142 x (3.8^2) / 4 = 11.34 cm.

This will give us a total running time of 130.0/11.34 = 11.5 hours.

This is annoyingly shy of 12 hours so lets start looking at how to increase this. I have already mentioned mounting the clock a little higher or optimising the size of the weight itself by making it bit shorter, and perhaps a little fatter. The next simple thing to do is to decrease the diameter of the drum so that it unwinds less cord for each revolution. Although this is easy to do, it has a cost, and that is you will need to increase the weight proportional to the change in diameter. Using the same calculation as before, if we reduce the diameter of the drum to Ø3.2 cm, then the running time will be increased to 16 hours.

There is one other thing that we can do to extend the weights travel and that is to take the cord over a guide pulley as shown below so that the travel can be increased significantly if the guide pulley is fixed much higher up the wall. No increase in weight is involved with this change, but you do have to ensure the clock is is well attached to the wall as the pull of the weight is now going to be upwards instead of down.

The mention of pulley's brings us to the final section that shows how the running time can be increased 2,3 and 4 times by using a pulley arrangement shown below. 

The simple arrangement on the left with the weight hanging directly on the Drum gives us the basic run time. The second arrangement has a pulley added above the weight around which the cord passes to an anchor point on the clock frame. Now as the drum rotates there are two cords supporting the weight so for a given movement of the drum the weight will only move half as far so the running time is doubled.. In the third arrangement 3 cords share the movement, so the running time is tripled , and the final arrangement has 4 cords so the running time is quadrupled

You do however have to remember that the weight has to be increased in proportion the running time gained, so double the running time, double the weight.

You also have to remember that as the weight increase its physical size also increases so any increase in length has to be taken off the running time.

Now finally a drawing showing how a simple 2 fall pulley was incorporated into Clock 22.

For further reading on the subject of Pulley's and weights .

Weight Lines, Snatchblocks, and Flight Paths.