Don Klipstein wrote:
In , E Z Peaces wrote in part:

Don's data shows current at various voltages, from which the changing
resistance could be calculated.

Saying power is proportional to voltage^1.6 implies that resistance is
proportional to voltage^0.4 (unless I've jumbled the math). I don't
know how accurate the formula is over a wide voltage range.

It says service life is proportional to voltage^(-16).
http://en.wikipedia.org/wiki/Incandescent_light_bulb

Power being proportional to voltage to the 1.6 power is something I
remember (I hope accurately) from something from GE on "miniature lamps",
and I found it largely accurate for vacuum-containing incandescent lamps,
at least ones of higher design voltage (14 volts and up maybe?).

This would mean current being proportional to voltage to the .6 power,
and resistance being proportional to the .4 power. It appears to me that
you did not jumble your math.

Meanwhile, I publish the "current exponent" for 3 specific incandescent
lamps, for application to a large number of voltage ranges where one end
of the range is 120 volts. I refer to this as log(i/I)/log(v/120) in
http://members.misty.com/don/incchart.html

For the vacuum one that I mention there, this figure is .58 to .61 for
all voltage ranges (effective average over the range) where one end is
120 volts and the other is anywhere from .5 to 144 volts.

For gas filled ones, this figure is lower. For 100 watt 120V 750 hour
lamps rated 1670-1750 lumens, this figure tends to be about .54. For
lower wattage 120V gas-filled lamps and 120V gas-filled lamps with
multisupported filaments, this figure will be lower. I seem to think that
a "1-size-fits-all" figure for household 120V gas-filled lamps is .53.
(Current is proportional to voltage to the .53 power, and power is
proportional to voltage to the 1.53 power.)

As for light output: There is not that good a "one size fits all"
exponent to describe what power of input voltage that light output is
proportional to. I have seen 3.4 and 3.5 published, and find that to be
reasonable. I have known this figure to be as low as 3.2, as high as
6-plus for extreme dimming, though it appears to me to usually be
between 3.3 and 4.

As for life expectancy: That exponent of -16 appears to me to be on
the extreme side. I usually figure life expectancy being inversely
proportional to voltage to the 12th power, although I find 13th fairly
credible. At one time I mathematicaly worked out -11 from relationship
of filament temperature with voltage and life expectancy of lamps with
different color temperatures, but I seem to think the truth is slightly
more extreme than -11.

I take a page or two of screen space below with cites for this exponent
being anywhere from -10.43 to -14.55.

A Google search has its description of one hit as a result of my
chosen search terms showing 12.86 power for this, not visible in the
link itself (describing a PDF that has to be paid for),

"Physics of Incandescent Lamp Burnout",
The Physics Teacher -- January 2008 -- Volume 46, Issue 1, pp. 29-35

Another statement repeated a bit is that voltage 10% above design
voltage will reduce life to 30% of that expected at design voltage.
I work out the exponent from this to be -12.6.

Two places saying this a

http://www.candelacorp.com/products/lamps/miniatures/
http://www.sunraylighting.com/technicalinfo.shtm

These also say that life will be multiplied by approx. 3 by use of
90% of rated voltage. From that, I work out the exponent to be -10.43.

Although I saw a statement of reduction of life to 25% by use of 110% of
design voltage, in:

http://www.trft.org/b3/B3Pix/CHRSDialLamps.pdf

I work out an exponent of -14.55 from that statement.

In that document is also a statement that use of 90% of design voltage
results in life expectancy 400% of original. From that I work out the
exponent to be -13.2.

As far as I remember, I hope accurately, packages of 130V lightbulbs
with statements of life expectancy at both 130 and 120 volts have the 120V
life being about 2.5 times the 130V life. I work out the exponent from
this to be -11.45.

I also expect this exponent to vary somewhat with filament temperature,
presence/absence of gas fill and with percentage of input power becoming
heat conducted by the fill gas (which varies widely with design current
and filament style).

- Don Klipstein )

Wow! Thanks. Wikipedia was a starting point to help me comprehend your
stuff. Yesterday when I looked at your charts, I didn't make sense of
your logs involving current.