The key concept of the so-called “gridiron pendulum” is that such a pendulum contains lengths (rods) of at least two different materials (metals) that behave oppositely in response to being heated (or cooled). Unless I’ve misunderstood the generic description, the idea is that the pendulum length stays constant, independent of temperature, because the expansion of one rod is exactly counterbalanced by the contraction of another rod (sometimes, the description implies that one rod’s expansion is balanced not by the contraction of another rod, but by the fact that the other rod expands in the opposite direction).
Depending on which explanation is used, I am confused buy two things.
how can expansion occur in only one direction?
don’t metals always expand when heated? can a metal contract when heated?
The leftmost photo (of a gridiron pendulum) on this page is extremely helpful in understanding what I’m asking.
If you look carefully at the pendulum’s construction, it’s very clever - the bob is attached to a slider with is free to move up and down. This slider is attached to the bottom of the pendulum’s frame. So, as the outside frame expands, the inside slider expands also, but in the opposite direction, keeping the total length the same.
Invar is a metal alloy that can exhibit negative (albeit small) thermal expansion.
It hadn’t occurred to me that even a precision pendulum clock could be that sensitive to temperature changes, but I guess it was so.
FWIW my brother-in-law recommended a book to me some time ago: Longitude, which tells the story of the development, a few centuries ago, of very accurate clocks to enable useful determinations of longitude while navigating at sea. I haven’t read it yet, but I imagine this issue was covered there.
The steel rods on the outside are connected to the crossbar at the top and the crossbar at the bottom. When they expand, the lower crossbar goes down.
The next inner set of brass rods are connected to the bottom crossbar, but not the top crossbar. Instead, there is a second upper crossbar. Thus as they expand, that second crossbar goes up.
That crossbar has steel rods connected to a second lower crossbar, not connected to the outer brass bars. Thus, they expand downward, and lower the second bottom crossbar.
That one has more brass bars going up to a third upper crossbar, not either of the previous two upper crossbars. That crossbar is where the pendulum weight attaches.
All of which is a fancy way to keep the overall pendulum length the same.
I had assumed that when a rod expands, it would do so at both ends. Now I see (at least I think I see) that expansion at one of the ends is prevented by the attachment of the fixed cross bar. Given that, it’s then easy to understand the whole set-up.
As an aside, I imagine that the fixed cross bars must be very strongly attached, no? Otherwise, the force of the expanding rod would blow it right off. Indeed, I am surprised that still doesn’t happen, i.e. isn’t there a huge force created when a metal is heated?
And, Joe Frickin Friday, great call! I’m actually in the middle of “Longitude” right now! (in fact, as you might suspect, that’s where my question came from)
I think you are misunderstanding how this works.
The inner bars are free to expand - but they only move UP - because they are fixed at the bottom (the top is free to slide up and down). The outer bars also expand, but they only move DOWN, because the fulcrum is at the top. The bob is attached to the TOP of the inner bars, hence the net result is zero length change with temperature (assuming very carefully calculated materials and lengths).