Quasi-Logarithmic Kitchen Timer
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With rotary encoders you can also do velocity sensing which could allow convenient coarse/fine adjustment, but for kitchen timer that probably isn't that useful.
I had an old Frigidaire-made range a few years ago with a timer. It was a fairly basic thing; the only fanciful feature it had was a clock with a timer, a knob, and a VFD. No buttons at all; the mode was set by the direction of the initial turn. (The rest of the machine also worked with knobs: Simmerstats for the burners, and mode-select and thermostat knobs for the oven, with no computerization for those bits at all.)
It worked great. The rotary encoder was the most responsive I've ever used and did not appear to miss any steps. The velocity ramps were fantastic, and the knob was small in diameter and thereby easy to turn fast.
I could set a timer approximately with a quick, singular flick of my fingers, which was plenty good enough for most of my cooking. Setting a timer for about 20 or 30 minutes (or an hour, or whatever) was simple.
If I wanted to be precise, that was also simple: Get to the right neighborhood with a clockwise flick, and then just turn the dial a bit slower to work in tighter precision (down to 1 minute per encoder stop).
It takes a lot of words to describe, but it was intuitive AF in use.
The clock didn't drift much over time (it was synchronized to line frequency -- not perfect anymore, but pretty good).
Walltime was easy to set (for DST buggery or power outage), too: Same knob, still no buttons. Same excellent acceleration ramps. Just start with an anticlockwise flick, and it's setting the clock instead of the timer.
(Screw it up by twisting it the wrong way on initial rotation? It didn't matter much because the cost of resetting the clock was very, very low and the action of it felt like a pleasant release from modern human interface chicanery)
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Clock on present-day oven also works, but it's crap. Pick a mode with a button. Set digits by holding or tapping up or down buttons. Accept input digits by pressing another button.
But tapping always only goes in 1-minute steps, which sounds nice except: The debounce is bad and it misses rapid taps. And holding it sounds nice, except: It always overshoots, by a lot -- the acceleration ramps are, to put it as kindly as I can, sadistic.
Setting the clock is miserable. The fastest and least-annoying way to adjust for DST is to mash the button 60 times at the right cadence: Too fast, and it misses inputs.
Too slow and it takes long enough that the motivation is to try the sadistic button-hold acceleration again (which will be uniformly punished by sending it even further away from the target than where it started).
I'd put black tape over the display (like a VCR from the 1980s) and forget about it, but: In a curse of integration-at-every-expense, this display is also used to set the temperature for the oven and I need that function.
The rotation needed to bump up the next timing point is too large, if we want anything more than like 2 minutes (let alone 10) it's just so much slower than punching in time on a number pad.
I've also searched for the perfect kitchen timer, and thought about making my own. I think the mechanical twist UX is great, just one twist and you're done. Or two if you do the recommended full wind up. But precision is not great, and the alarm sound doesn't keep sounding (which is a positive if you know you'll be in the same room — no need to turn it off).
Maybe a digital twist design could work. Something like yours but you actually twist the dial directly, and it starts right away when you let go. That would solve both shortcomings, or all three really if you count the full wind up thing. Then you get accurate timing with a single motion. The only new con is that it needs power, unlike the purely mechanical.
A very carefully designed button-based one could be good too. I use my oven's timer today which is decent: One press to "activate", then a +1 min button that you can also hold. If it had a +10 button too it'd approach very good.
That's fine if you need something to be in the microwave for a few minutes, but it absolutely sucks if you need something to be close to (or much less than) the period time... it's completely random and depending where the prior usage started, how much active time your ingredients experience.
It was programmable, too. 45 seconds on high, then 2 minutes at 50%? 45P5200S (where P is the Power button and S is Start).
I also found that nobody but me cared about any of that at all. Everyone else who ever used it always ran it at 100% power.
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One of these days, I'll get another one that has variable power like this again. But it'll be a "flat bed" Toshiba, since the present lineup from Panasonic all includes spinning glass carousels and those have always been both stupid and unnecessary.
Is it? Or does Toshiba just mitigate the problem on the magnetron side? My impression was always that the spinning is a crude compensation for non-homogenous power density (preventing hot/cold spots), which makes sense to me (except if you're just heating soup or somesuch obviously).
In all cases, the magnetron emits a field that is somewhat akin to a modern flashlight in that it is directed (or a particularly fancy flashlight of yore), and it can be focused with some modicum of precision (or not). The emitted RF also bounces around inside the box like light does, and it therefore features standing wave interference patterns. So something has to move, or we get hot spots and cold spots (or perhaps even cold sides).
Carousels smooth things out by spinning the plate (and ultimately the food) around. It's easy to visualize: Just look through the door of any carousel oven in operation. (Shine a flashlight in there for extra effect.)
But (what are now called) flat bed microwaves achieve the same desirable distribution, and they do this with a rotating microwave stirrer. This spinnamathing also distributes the magnetron's RF output across the food being heated. This can be accomplished by deliberately bouncing the RF around in repeated patterns, or just disturbing the environment enough to mix up standing wave patterns, or both.
They're often shaped like metal fan blades. Sometimes, they're more-alien RF designs with deliberate ridges and/or holes. They're hidden in the top or bottom of the oven[1].
Microwave stirrers work very well. The mechanism is just invisible to the buyer while the carousel is very much visible.
And to be clear: The carousel also works. It just became the clear winner in the marketplace not because it was technologically advanced but because of buyer perception; it was easy to see, and therefore easy to sell. Microwave stirrers were (and are) much more hand-wavey.
But having scorched more than one bag of popcorn when it somehow got wedged and stopped spinning while I wasn't looking, I'd rather avoid spinning the food around. So that's how I endeavor.
[1]: The Kenmore we had when I was a kid had a mechanical timer (with a mechanical bell!) and an electromechanical speed knob (which I've come to understand was just a simmerstat like for an electric range), and the stirrer was at the top. It was metal, and fan shaped. It was hidden behind a plastic panel that was secured with little plastic pushpins fasteners. And that panel was somewhat translucent, so young-me could see that something was moving behind there.
I was little, curious, and unsupervised, so of course I took it apart. At first I was amazed that this microwave oven had metal inside of it and it had not yet caused a nuclear explosion and a black hole that wiped the entire galaxy out of existence. I figured the rest out over time.
Though if you prefer a portable one you can stuff in your pocket they have that too, and it also does just what it says on the tin.
The quasi-logarithmic idea is a good one. I would buy a simple one that just has a dial. No button required. But I agree with the other commenter that the 0-60 part would be quite useless for a kitchen timer. Better to have more resolution in the commonly used 0-30 minute range.