jroth@allvax.dec.com (Jim Roth) (08/29/90)
Many of the standard values in electronics and elsewhere follow an
approximate log/exp scale to accomodate a wide range of values.
Examples are resistors, ISO 3'rd octave audio frequencies, etc.
Wire gauges are no exception, but here's an odd thing - virtually
none of the diameters or areas in circular mills are "round numbers".
Yet when we take logs, we find that each jump of 10 wire gauges
increases the cross sectional area of the wire not by a nice round
number like 10, but by about 10**1.007!
Examples:
gauge area log(ratio)
----- ------ ----------
0 105500 1.007055
10 10380 1.006747
20 1022 1.007285
30 100.5 1.007058
40 9.888
Why the brain-damaged exponent?
How on earth was that table created in the first place?
- Jimlarry@kitty.UUCP (Larry Lippman) (08/29/90)
In article <2588@ryn.esg.dec.com>, jroth@allvax.dec.com (Jim Roth) writes: > Many of the standard values in electronics and elsewhere follow an > approximate log/exp scale to accomodate a wide range of values. There were no "electronics" at the time that the American Wire Gage (AWG) was created. The AWG was formerly called the Brown & Sharpe wire gage. Offhand, I cannot give you a precise year of origin, but I would guess around 1875, +/- 10 years. > Wire gauges are no exception, but here's an odd thing - virtually > none of the diameters or areas in circular mills are "round numbers". That's because they are *not* round numbers! The rationale behind AWG is that the ratio between DIAMETERS of succesive gage numbers is 1.123, with the ratio of areas therefore being (1.123)^2, or about 1.26 (remember about 1-1/4). I have no idea why this ratio 1.123 was chosen. > Yet when we take logs, we find that each jump of 10 wire gauges > increases the cross sectional area of the wire not by a nice round > number like 10, but by about 10**1.007! Hey, that's pretty *close* to 10, though. :-) Larry Lippman @ Recognition Research Corp. "Have you hugged your cat today?" VOICE: 716/688-1231 {boulder, rutgers, watmath}!ub!kitty!larry FAX: 716/741-9635 {utzoo, uunet}!/ \aerion!larry
tomb@hplsla.HP.COM (Tom Bruhns) (08/30/90)
Dunno how it all got started, but you should note that a change of 3 in gauge number corresponds exactly to a 2:1 cross-section change.
jeffw@midas.WR.TEK.COM (Jeff Winslow) (08/30/90)
In article <5170088@hplsla.HP.COM> tomb@hplsla.HP.COM (Tom Bruhns) writes: >Dunno how it all got started, but you should note that a change of >3 in gauge number corresponds exactly to a 2:1 cross-section change. Are you sure about that, Tom? According to the tables I have here, it's about half a percent off. I wouldn't even mention it, except that another poster kept coming up with a 1.007 ratio and was wondering why it wasn't exactly 1. I don't know the answer either, but it might have something to do with the fact that 1.007 is just about the ratio of the square root of 10 to pi. Jeff Winslow
whit@milton.u.washington.edu (John Whitmore) (08/31/90)
In article <2588@ryn.esg.dec.com>, jroth@allvax.dec.com (Jim Roth) writes: > Many of the standard values in electronics and elsewhere follow an > approximate log/exp scale to accomodate a wide range of values. > Wire gauges are no exception, but here's an odd thing - virtually > none of the diameters or areas in circular mills are "round numbers". This is an example of functional evolution of a standard. To make wire, a smith starts with a rod; tapers the end (hammer/anvil work) and forces it through successively smaller holes in a 'drawing plate' type of die. The earliest wire-drawing I know of was in France, in 1270. It's still done that way today (but the dies are better material). So, the rod size determines '0' gauge size. Modern wire typically comes from #5 hot-rolled rod; that '0' size could have been the nominal rod diameter at some time in the past. The diminution of diameter on each successive pull through the die determines the successive gauge sizes (and the amount of money it will cost you for a pound of the wire). The gauge/diameter correspondence presumably was standardized (and more than once; there's British and American standards that I know of, with slightly different sizes) by merchants who wanted interchangeable wire from different suppliers. The magic number for the ratio of two successive gauge diameters comes from the need for the drawing operation not to result in terribly many fresh starts (and resultant short pieces of wire to be spliced). The safe stress of the thin wire coming out of the die has to be sufficient to deform the thick wire going into the die; the ratio is not size-dependent, so the gauge table naturally comes out logarithmic in diameter versus gauge number. John Whitmore
greg@bluemtn.uucp (Greg Richter (2XS)) (09/01/90)
In article <3416@wrgate.WR.TEK.COM> jeffw@midas.WR.TEK.COM (Jeff Winslow) writes: >In article <5170088@hplsla.HP.COM> tomb@hplsla.HP.COM (Tom Bruhns) writes: Again, I don't know about why or how, but given a sequence of numbers and some cabalist instinct, you can BS up a storm. Why don't some student type scope out the local library - now you've got ME wondering too. :). -GR -- A fly can't bird but a bird can fly - | Ask me a question and I reply, | Cottleston Cottleston Cottleston Pie! | Greg Richter | {emory,gatech}!bluemtn!greg
tomb@hplsla.HP.COM (Tom Bruhns) (09/12/90)
jeffw@midas.WR.TEK.COM (Jeff Winslow) writes: >In article <5170088@hplsla.HP.COM> tomb@hplsla.HP.COM (Tom Bruhns) writes: >>Dunno how it all got started, but you should note that a change of >>3 in gauge number corresponds exactly to a 2:1 cross-section change. >Are you sure about that, Tom? According to the tables I have here, it's >about half a percent off. >I wouldn't even mention it, except that another poster kept coming up >with a 1.007 ratio and was wondering why it wasn't exactly 1. I don't know >the answer either, but it might have something to do with the fact that >1.007 is just about the ratio of the square root of 10 to pi. > Jeff Winslow >---------- Ooops. Thanks for pointing it out, Jeff. That was a rule-of-thumb I had memorized, and remembered incorrectly as _exact_. Should have known better than to post without double-checking it. Actually it's interesting that both rules-of-thumb are quite close, certainly adequate for most applications (and proabaly within the wire-drawing tolerance, at least over 20 or so gauge numbers...) Which brings up another question: What _is_ the tolerance normally maintained on drawn copper wire?
elec140@canterbury.ac.nz (09/13/90)
In article <5170089@hplsla.HP.COM>, tomb@hplsla.HP.COM (Tom Bruhns) writes: > jeffw@midas.WR.TEK.COM (Jeff Winslow) writes: >>In article <5170088@hplsla.HP.COM> tomb@hplsla.HP.COM (Tom Bruhns) writes: >>>Dunno how it all got started, but you should note that a change of >>>3 in gauge number corresponds exactly to a 2:1 cross-section change. > >>Are you sure about that, Tom? According to the tables I have here, it's >>about half a percent off. > >>I wouldn't even mention it, except that another poster kept coming up >>with a 1.007 ratio and was wondering why it wasn't exactly 1. I don't know >>the answer either, but it might have something to do with the fact that >>1.007 is just about the ratio of the square root of 10 to pi. > >> Jeff Winslow >>---------- Just to add more fuel to the fire, if you use decibels (defined as 10log(x), where the log is base 10 and the x is a ratio) then a ratio of 2 is 3.01dB. Decibels are a common engineering unit (at least in Electrical Engineering), so perhaps the gauges sizes are based on this. -- ********************************************************* Chris Kaiser Postgrad - Elec Eng Dept Canterbury University Christchurch, NEW ZEALAND E.MAIL: c.kaiser@elec.canterbury.ac.nz ********************************************************* "When you're fresh out of lawyers You don't know how good it's gonna feel" - Al Stewart, 1988 *********************************************************
josip@ra.src.umd.edu (Josip Loncaric) (09/14/90)
In article <1990Sep13.173238.9156@canterbury.ac.nz> elec140@canterbury.ac.nz writes: >In article <5170089@hplsla.HP.COM>, tomb@hplsla.HP.COM (Tom Bruhns) writes: >> jeffw@midas.WR.TEK.COM (Jeff Winslow) writes: >>>In article <5170088@hplsla.HP.COM> tomb@hplsla.HP.COM (Tom Bruhns) writes: >>>>Dunno how it all got started, but you should note that a change of >>>>3 in gauge number corresponds exactly to a 2:1 cross-section change. >> >>>Are you sure about that, Tom? According to the tables I have here, it's >>>about half a percent off. > >Just to add more fuel to the fire, if you use decibels (defined as 10log(x), >where the log is base 10 and the x is a ratio) then a ratio of 2 is 3.01dB. >Decibels are a common engineering unit (at least in Electrical Engineering), so >perhaps the gauges sizes are based on this. > I tried that... B&S wire gauge seems to be roughly equal to -20 * log10 (wire circumference in inches) or, alternatively, wire diameter in inches is just 1 / (pi * 10^(gauge/20)) which seems to fit my B&S wire gauge table reasonably well... I'll be very pleased if this is actually THE formula... -- Josip Loncaric / SRC / U. of Maryland / <josip@ra.src.umd.edu> -------------------------------------------------------------- ! Today's Special: Opinions....$0.02 each ! --------------------------------------------------------------
tomb@hplsla.HP.COM (Tom Bruhns) (09/14/90)
>Just to add more fuel to the fire, if you use decibels (defined as 10log(x), >where the log is base 10 and the x is a ratio) then a ratio of 2 is 3.01dB. >Decibels are a common engineering unit (at least in Electrical Engineering), so >perhaps the gauges sizes are based on this. ...but _if_ a ratio of 2 in x-section was a 3.01 change in gauge number, then a ratio of 10 in x-section would be exactly a 10 gauge number change. ..."Which it ain't." So who has looked this up in an engineering/ technology history? (Besides, I _suspect_ wire gauges were settling down before common use of dB.)