Inertia-How to make a clock that just won't work.
Force = Mass x Acceleration
From Isaac Newton:
A body in motion will tend to stay in motion unless a force is applied to either speed it up or slow it down.
Recapping: It takes force to accelerate an object.
The force to accelerate an object varies directly with its mass.
The force varies directly with the acceleration.
an example:
It takes much more gas (force) to accelerate a heavy truck than it does a small compact car.
It takes more gas to go from 0 to 60 in 9 seconds than it does to accelerate from 0 to 60 in 22 seconds.
What is a clock?
A clock has a falling weight that accelerates a series of gears until the escape wheel crashes into the tick tock lever.
At this point the weights and gears come to a complete stop.
A sudden deceleration.
Tick
The pendulum reverses direction.
Once the tick tock lever passes a certain point the weight continues its eventual journey to the floor and begins to accelerate the gear train once again.
The escapement wheel gives a little push to the pendulum from the tick tock lever.
At least we hope that the escape wheel gives a little push to the lever. We will see later that this is not always the case.
The gear train continues to accelerate until the escape wheel once again crashes into the tick tock lever.
Tock
The whole thing starts over again and continues until the weights reach the floor.
OK. So what's this all about making clocks that don't work?
I made the assumption that all I had to do was increase the weights that drive the gear train to get my clock to work.
A little sloppy with the scrollsaw work and a few teeth bind ever so slightly.
The pendulum isn't getting a big enough push to keep going.
Everyone knows what happens when you make ASSuMEptions.
It takes force to accelerate the gears.
Heavy gears take more force to accelerate.
The gears that move the fastest take more force than those that move slowly.
And here's the kicker
Gears that are larger in diameter have more inertia (or resistance to moving) and also take more force to accelerate.
Another inertia comparison
Same torque applied to each. That is the length of the arm and the weight at the end is the same for both examples.
The wheels are made of the same material, have the same thickness but have different diameters.
The difference is astounding.
Working Model
Have this neat program called Working Model 2D that can simulate forces in machines and generate animations to see the effects.
Can vary:
Compare 2 escape wheel inertias
This is truly amazing.
This next animation compares two pendulums with just about everything the same.
The difference is obvious:
A torque is applied to the escape wheel in order to give the pendulum a little push to get back the energy it lost to friction on every stroke.
Here are the gory details:
Variable | Small Escape | Large Escape |
Pendulum Length | 20in | 20in |
Pendulum Weight | 5 lb | 5 lb |
Escape wheel Diam | 10.6 in | 21 in |
escape wheel weight | .046 lb | .365 lb |
Escape wheel inertia | .648 lb-in^2 | 20.7 lb-in^2 |
Torque applied to the escape wheel | . 02 in-lb | . 45 in-lb |
Some big gains to made by paying attention to inertia.
The larger torque was needed for the big escape wheel just to keep it going.
The larger torque also makes your clock make a lot more noise.
TICK TOCK rather than tick tock.
This animation shows the little escape wheel working properly.
The large wheel is so heavy that it doesn't speed up fast enough and skips the pendulum altogether.
It would be tempting to simply add extra weight to get the big escape wheel to work properly in this example. It might even work. The problem with wheels with lots of inertia is that it is not only hard to get them going it is also hard to get them to stop.
If your clock is keeping you up late at night with a really loud tick tock you most likely have an inertia problem.
Next time you are in a place that sells grandfather clocks, check out the size of the escape wheel. Should be about the size of a Canadian toonie.
Look at that little guy go.