Happy new year guys!! I need to know the exact formula in calculating weight needed for a weight-driven clock. Can you please enlighten me or guide me to a site? Thank you. Le Arsi

I don't know if there is a formula. There are so many variables. The type of escapement, the weight of the pendulum, the size of the pinions/wheels, the run time of the clock, the rate of the pendulum, the length for the run time, the type of pinions, the size of the pivots/bushings and even the width of the wheels. There are a few more that I'm sure I missed. Maybe you could tell us your purpose? Tinker Dwight

A group of graduating students ask my help to guide them how to construct a weight-driven clock as their thesis. This is the only problem that I cannot solve. But doing trial and error we come up with a certain weight that runs the clock. But they need the formula.

Well, you know that how well the clock is constructed has a direct bearing on how much weight is needed. If you could measure the friction from top to bottom, you might be able to measure the required weight. But, the same clock, built well, will need less weight than one poorly constructed. If you substitute ball bearings for bushings, you will greatly increase the efficiency, by reducing friction. But I really don't know how you could possibly put any of this into an efficient formula as there are so many intangibles that are not easily measured.

There is no formula - cannot be one. As others reply: "too many variables" and I won't even extend the loooooong, long list. Well O.K. Can't resist just one more - duration as a function of drum diameter.

Yep trial and error, find the minimum weight the clock will run on then add weight to get a reasonable overswing of the pendulum or balance, you have to allow for when the clock is in new condition to when it's been running for a number of years with some wear and thickening oil.

Clock makers do estimates. They first determine how much energy needs to be added to the pendulum by measuring how long it takes it to decay. You need to know the rotational inertia of the bob and rod to do this. They then assume about a 10% loss at each wheel. Knowing the rate of drop of the weight, and the energy for that much drop, one can calculate the weight. Once you have that, you experiment for an optimum weight to match your clock. There are different percentages for different types of escapements but I don't recall. A deadbeat is more efficient than a recoil as an example. Tinker Dwight

Although only a little bit different than trial and error, one can practically calculate the least amount of energy required to drive a weight driven clock. Fasten one end of a fisherman’s scale (see the link below) to something below the clock. Fasten the other end of the scale to the clock drive (cable/chain/etc). Wind the clock, bringing the clock drive taunt and stretching the spring in the scale. Run the clock, using the stored energy in the scale till the clock stops. The minimum amount of energy required to run the clock will be the value of the weight shown on the scale. http://shop.sportsmansguide.com/net/cb/cb.aspx?a=650058&ci_src=17588969&ci_sku=WX2*0184212000000&pm2d=CSE-SPG-15-PLA&gclid=CJXM_Naw7LsCFY47MgodzWYAJw The same process could be repeated eliminating the first wheel in the train, using the second wheel as the main drive wheel. The clock drive (chain, etc) must play out from the diameter of the second wheel. That value is the minimum amount of energy needed to drive the movement without the first wheel. The test weight value without the first wheel could be subtracted from the test weight value of the clock with the first wheel to determine the amount of energy consumed by the first wheel in the train. In a multi wheeled clock, the process could be repeated with each successive wheel up to the escape wheel. The last test at the escape wheel will be the minimum amount of energy needed to run the escapement. . Best, Dick

In theory you can calculate friction in every bushing, if you know friction factor and normal component of force. However, this force depends on weight so it could be complicated. Escapement friction also could be calculated in the similar way. Basic friction for pendulum is air friction, which also could be calculated. So, you could calculate basic frictions in one movement, and weight needed. These would be only rough approximations, but some sort of formula could be made in my opinion...

I do something similar to Dick Feldman's fish scale as I shy away from formulas and don't fish. Hang an empty coffee can or similar object and fill it with sand until the clock runs efficiently. Weight the filled can for the proper running weight.

Only calculation that's needed is to hang on weight until it runs well. "Runs well" = noticeable over-swing on the pendulum and lively but not to fast strike should start anywhere during the hammer lift. Guess you would have to run it about 10 to 20 years and reassess your weight choice after your clock wears out a bit. My 2, Willie X

Well I don't think fishing scales and a can of sand will get these guys full marks on their thesis. Not sure what course they are taking, but I don't see why they don't start by making some assumptions based on pivot size, bearing type, gear efficiencies. As stated they can start at the bottom and work out the gear separation forces. Once they do all their calculations, then they can compare with the actual weight. Sounds like an interesting project, but they aren't going to be able to look up the machinists handbook and get a formula(e).

There are some rules of thumb. I've seen these on the British clock page ( can't recall the name ). No exact values though. Knowing the amount of power lost on each swing of the pendulum does give you a minimum that can be calculated. Tinker Dwight

Thank you guys for all the answers. Now I know why I too doesn't know the formula. I will let the students read this thread and learn it from the best watch/clockmakers in the world! Regards, Israel