Things That Don't Scale: ScopeRoller Manufacturing Experiments

You are probably aware (or at least, should be aware), that lots of objects don't scale up or down the way that you expect. There's a reason that eight foot long ants that can pick up automobiles (as you might expect, if ants were eight feet long) don't exist. It is this amazing thing called the square-cube law.

If you double the length of an object, and change no other design characteristics, its surface area quadruples, and its volume (and therefore its weight) octuples. That ant's muscle attachments have gone up with the square of its increase in linear dimension--but the amount of mass involved in moving those muscles has gone up with the cube of the increase in linear dimension--so it is no longer so amazingly strong for its size as the ant you can step on. If you have any question as to whether this is a good thing or not, go watch the 1950s science fiction classic Them.

This is also why the smaller and less oxygen-demanding insects can get by with surprisingly unsophisticated systems for distributing oxygen through their bodies--the surface area of the breathing tubes in the thorax is, relative to the total number of cells, huge. An eight-foot long ant couldn't get enough oxygen distributed to all of its cells without the complex system of lungs and blood that us larger creatures use, or a vastly more complex breathing tube system.

This square-cube law applies in all sorts of unexpected ways. Mars has a much smaller diameter than the Earth--about 45% of Earth's diameter. This means that Mars has about quite a bit less material inside it, relative to its surface area than the Earth--and is probably why Mars is a dead planet--there's more surface area relative to the contents to let heat leak out.

I've been selling this clever (if I do so say myself, as do my customers) Quick Release Toe Saver gadget for Losmandy mounts. I'm starting to look at making versions of it for other equatorial telescope mounts, and my first experimental victim was a Celestron CG-4. The same design doesn't work here, partly because the diameter of the plastic component that holds the quick release pin is much smaller, and so there's a bit less rigidity to the part. The other problem is that instead of a 3/8"-16 threaded stud, I have to use an M6-1.0 threaded stud, which has much smaller threads relative to the diameter of the stud. The total surface area grabbing onto plastic is quite a bit smaller.

The "let the counterweight slam down the shaft under gravity" test caused the plastic carrier to separate from the threaded stud--not because it stripped the stud out of the plastic, but because the plastic flexed enough for the threaded stud to slip out--even though it is a tight fit under ordinary conditions.

I may have to go with either a single piece of Delrin for this, or make it out of brass or aluminum, to avoid the problem of flexure under dynamic load.