My wife and I need our coffee. For years now we’ve used a percolator exclusively, because there isn’t anything to it that could just suddenly fail one day or not work because of a power outage. On numerous occasions we have placed the percolator on the wood stove or on a camp cookstove when the power was out. But a percolator needs looking after. One can’t just set it on the stove and walk away, and come back later when you remember you had coffee started. Our formula looks like this:
- Grind beans, fill filter basket, fill with water
- Bring to near-boil on stove – about ten minutes.
- Turn heat down to simmer for 8 minutes.
A failure in the timing of step two results in coffee boiling over onto the stove top. A failure to observe the timing of step three can make for really strong or burned coffee. But once you know the rules, it’s easy.
However…
We just had a baby five weeks ago. Our first. And in these first weeks we discovered that you have to choose between tending the percolator or tending the baby. Blowing step two or three became an everyday occurrence. While cleaning up the mess for the third time in as many days when I missed the critical step two window, I remembered I had a drip machine that I had saved from the trash pile. It’s a basic model with only an on/off switch and no frills, but works just fine.
One of the missing frills is an auto-shutoff, as most of them have these days, to turn off the burner after a couple of hours to keep from burning the last bit of coffee in the bottom of the pot. It’s easy to forget to turn it off and make a mess out of it, not to mention it sits there using hundreds of watts of power making that mess. I think it needs improving. Let’s add our own shutoff timer!
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There’s no real need to get into calculus for the voltage. The general solution for first-order delays like this is e^-(t/(RC)), which simplifies to 1/e for the case of t=RC.
Even without this equation, you can solve for multiples of RC. Think of the resulting voltage as the new starting point for the next period. Thus for 2RC it’s 1/e divided by e again, or e^-2.