Re: Self-tuning piano

Robert Scott wrote:
> Let me suggest several plausible explanations.
>
> 1. The Mapes coated string was not coated so well that a few copper
> windings didn't manage to bite through the coating as the strings were
> being wound. This could be verified by measuring the resistance
> between the copper and the steel. Therefore you were not comparing
> two different things, but really only the same thing twice.


Well, I oversimplified when I said that I noticed the difference
between coated and uncoated strings. What actually happened was that I
detected continuity between the copper and the steel on the coated
strings and was baffled as to why it still heated the string with
reasonable amounts of current. I got the same results with an ordinary
string.

Since the copper is in intimate contact with the steel along almost the
entire length of the string, the wound string should behave like
resistors in parallel. Resistors in parallel should result in a total
resistance that is less than *either* resistor. In other words, the
string should have less resistance than even the copper alone! No
matter how much resistance may be at the junction between the
materials, it can still only serve to *decrease* the total resistance.


....but it doesn't. It's virtually the same resistance as the unwound
core.

Even if I connected a long copper wire only at the ends of the steel
wire and the copper had the same resistance as the steel, it should
still cut the total resistance in half.


> 2. Even though copper has 1/8 the resistivity of steel, the copper
> windings are more than 8 times longer than the steel core, so they end
> up having even more resistance. The turn-to-turn connections have
> much more contact resistance than a single turn itself, so the current
> would rather go around and around than jump from one winding to the
> next.


There are numerous paths for electricity to take in such a setup.

1. It can pass straight through the steel core.

2. It can pass spirally through the copper winding.

3. It can pass from the steel to the copper anywhere along the spiral
contact line and back again, at will.

4. It can pass between adjacent coils anywhere along the contact line
between windings.

All of these paths working together can only *reduce* the total
resistance. In fact, they should drastically reduce it. Even steel
windings would do so.


> 3. The fact that coated string "perform the same" as uncoated ones
> does not mean they have the same resistance. It is possible that the
> output characteristics of your power drivers are such that they will
> pump about the same amount of heat into a wide range of resistances.
> A constant-voltage output will put more heat into a lower resistance.
> A constant-current output will put more heat into a higher resistance.
> Something that is a blend between constant-voltage and
> constant-current will do something inbetween these extremes, which
> might be a fairly constant heat output, depending only on PWM
> duty-cycle, and independent on on resistance, within a certain
> reasonable range of resistances.


I didn't use any PWM when testing the strings. Since the resistance is
extremely low, it is impractical to measure it with an ohmmeter. I
simply apply a given constant DC voltage and measure how much current
it produces in the string. If the string behaved like calculations
would predict (even with contact only at the ends), it should pull
large amounts of current at very low voltages to produce the same
wattage and the same flattening of pitch...but it doesn't. I have
literally removed the copper and got the same results. It's as if the
copper doesn't exist.

Don
Kansas City

.

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