Track & Wire Resistance
The following is a discussion on wire and track resistance and the
skin effect for the technically curious. It is not necessary that you
understand this information to benefit from this page. By all means,
read along and learn all you can.
The following measurements of wire and track were made with an LCR
meter. This instrument can measure tiny fractions of resistance, inductance,
and capacitance and uses various AC frequencies. The later allows us
to see the infamous skin effect in action.
I have tabulated the resistance for wire and track at three frequencies.
100 Hz because it's as close to DC this instrument will get, 10 kHz
because it's the closest to DCC frequencies that it gets and is adequate
for our discussion here, 100kHz just to show off the skin effect or
those electrical engineers who wish to consider Fourier analysis -
a way of representing things like DCC square waves with sine waves
that the LCR meter produces. You definitely don't need to understand
Fourier analysis to use this information and will not be discussed
further.
Measurements of this precision are difficult to make. In principle,
all I have to do is connect up the LCR meter. If any connection
is less than perfect, the result could be way off.
I have shown resolution to 4 digits after the
decimal to show trends in the skin effect. The accuracy of
the LCR meter at these resistances is about 0.001 ohms. If you
are wondering what is the difference between accuracy and resolution,
round off the
4th digit and don't worry about it. I could tell you, but if
you don't need to use it in your daily job, you probably won't remember. All
you will get in the short term is a headache!
I then estimated the voltage drop per foot of track or for a pair
of parallel wires a foot long representing buses and feeders. To
get the voltage drop for a single wire, divide by two.
Stranded Wire
| Wire
A.W.G. |
Ohms
@ 100 Hz |
Ohms
@ 10 kHz |
Ohms
@ 100 kHz |
Voltage Drop
@ 0.5 A |
Voltage Drop
@ 1 A |
Voltage Drop
@ 2 A |
Voltage Drop
@ 3 A |
Voltage Drop
@ 4 A |
| #14 |
0.0025 |
0.0027 |
0.0058 |
0.003 |
0.005 |
0.011 |
0.016 |
0.021 |
| #16 * |
0.0056 |
0.0060 |
0.0091 |
0.006 |
0.012 |
0.024 |
0.036 |
0.048 |
| #18 |
0.0045 |
0.0048 |
0.0093 |
0.005 |
0.010 |
0.019 |
0.029 |
0.039 |
| #20 |
0.0101 |
0.0106 |
0.0155 |
0.011 |
0.021 |
0.043 |
0.064 |
0.085 |
| #22 |
0.0160** |
.0.0173** |
0.0371** |
0.016 |
0.032 |
0.064 |
0.096 |
0.128 |
| #24 |
0.0255** |
.0.0276** |
.0.0592** |
0.026 |
0.051 |
0.102 |
0.153 |
0.204 |
* A note about alloys: Frequently, stranded wire #16
and higher is not pure copper. None of those listed above were
pure copper as evidenced by the silver color. Pure copper wire
would have a somewhat lower resistance - unless you were lucky enough
to
have silver plated wire! In the case of my sample of
#16, it would appear that it's copper content compared to #18 is poor. If
copper content was the same percentage in all wire sizes shown, then
#16 would happily fall between #18 and #14 as you would be expect. I'm
sure I could find a sample of #16 stranded from somewhere else that
would perform as expected. I don't believe I made a hook-up error
during the measurement because the 100kHz reading is in line. The
issue of alloy and copper content, shows up again elsewhere in these
tables.
**
These values were not measured. They were calculated using data from the Internet.
Solid or stranded? The skin effect gives the solid, for a given size,
a slightly higher voltage drop. But it's so little, you can relax.
You probably have known that the skin effect was nothing to worry about
at DCC frequencies. Now you have evidence to support that knowledge.
Solid and stranded perform so nearly the same that the difference
is too small to notice. Solid household wire is cheaper than stranded
and solid makes a nice bus - it stays where you put it, stays straight,
and is slightly easier to cut into the "middle" and attach to.
In the garden,
solid will take longer to corrode to the point of being a problem than
stranded. Of course, do what you can to keep moisture
out!
Solid Wire
| Wire
A.W.G. |
Ohms
@ 100 Hz |
Ohms
@ 10 kHz |
Ohms
@ 100 kHz |
Voltage Drop
@ 0.5 A |
Voltage Drop
@ 1 A |
Voltage Drop
@ 2 A |
Voltage Drop
@ 3 A |
Voltage Drop
@ 4 A |
| #10 |
0.0010 |
0.0013 |
0.0035 |
0.001 |
0.003 |
0.005 |
0.008 |
0.010 |
| #12 |
0.0016 |
0.0019 |
0.0047 |
0.002 |
0.004 |
0.007 |
0.011 |
0.015 |
| #14 |
0.0026 |
0.0028 |
0.0073 |
0.003 |
0.006 |
0.011 |
0.017 |
0.023 |
Note: I estimated the voltage drop per foot of track or for
a pair of parallel wires a foot long representing buses and feeders.
To get the voltage drop for a single wire, divide by two.
As you can see, the voltage drop through copper wire #14 or bigger
is very small. Based on this information, it is hard to justify #10
for all except the largest HO layouts.
Attention "Ohm Counters"*: You would be horrified to find out
how much resistance is in a junction. If you are not soldering
your feeders to your buses and are using terminal blocks for easier
troubleshooting, you will want to make sure your connections are "gas
tight." This means air cannot get into the junctions and
oxidize it over time. One of the easiest ways to achieve this
is to use a star washer. It pierces the surface of the wire and
the terminal block, which may have minute layers of oxidation on them,
and gets clean metal-to-metal contact. Since the deformation
of the wire and the terminal block is in the exact shape of the star
points, air cannot get into these surfaces. If you should loosen
the screw, you may loose your gas tight connection. Be sure to
retighten snuggly when done.
If you use new terminal blocks, spade lugs, and shiny wire, you will
probably be fine. However, if many years down the road you loosen
the connection, you will definitely add possibly significant resistance
no matter how much you tighten. The problem is that the wire
probably will not contact the screw in exactly the same place it did
before. The part of the screw it is now touching is probably
oxidized. If it doesn't have that new luster look to it
, it is definitely oxidized. You would be smart to add a star
washer at this time.
*"If you are a rivet counter, you just might be an ohm counter."
Nickel-Silver Track
| Track
Code |
Ohms
@ 100 Hz |
Ohms
@ 10 kHz |
Ohms
@ 100 kHz |
Voltage Drop
@ 0.5 A |
Voltage Drop
@ 1 A |
Voltage Drop
@ 2 A |
Voltage Drop
@ 3 A |
Voltage Drop
@ 4 A |
| 250 |
0.0042 |
0.0049 |
0.0167 |
0.005 |
0.010 |
0.020 |
0.029 |
0.039 |
| 100 |
0.0275 |
0.0275 |
0.0286 |
0.028 |
0.055 |
0.110 |
0.165 |
0.220 |
| 83 |
0.0424 |
0.0424 |
0.0434 |
0.042 |
0.085 |
0.170 |
0.255 |
0.340 |
| 70 |
0.0757 |
0.0757 |
0.0767 |
0.076 |
0.151 |
0.303 |
0.454* |
0.605* |
| 55 |
0.1107 |
0.1107 |
0.1110 |
0.111 |
0.222 |
0.443* |
0.664* |
0.886* |
| Marklin Z |
0.0676 |
0.0681 |
0.0778 |
0.017 |
0.034 |
0.068 |
0.102 |
0.136 |
| Track
Code |
Voltage Drop
@ 5 A |
Voltage Drop
@ 6 A |
Voltage Drop
@ 7 A |
Voltage Drop
@ 8 A |
Voltage Drop
@ 9 A |
Voltage Drop
@ 10 A |
| 250 |
0.049 |
0.059 |
0.069 |
0.079 |
0.088 |
0.098 |
Note: I estimated the voltage drop per foot of track
Nickel-Silver is an alloy. The values may vary
between manufacturers of nickel-silver track.
The nickel-silver was interesting. As you can see, it
conducts rather poorly. This is the reason you need frequent feeders.
Notice the skin
effect is less pronounced in nickel silver than it is in copper. Too
bad copper isn't like nickel-silver in this respect.
*Don't panic! Yes
these voltage drops look ugly. But
how many of you are going to have enough diesels lashed up running
on code 55 to draw 4 amps? Likewise for the other occurrences"starred" above. Consider
how you will use your track.
Brass Track
| Track
Code |
Ohms
@ 100 Hz |
Ohms
@ 10 kHz |
Ohms
@ 100 kHz |
Voltage Drop
@ 0.5 A |
Voltage Drop
@ 1 A |
Voltage Drop
@ 2 A |
Voltage Drop
@ 3 A |
Voltage Drop
@ 4 A |
| 332 |
0.0007 |
0.0016 |
0.0110 |
0.002 |
0.003 |
0.006 |
0.010 |
0.013 |
| 100 |
0.0036 |
0.0041 |
0.0154 |
. |
. |
. |
. |
. |
| Track
Code |
Voltage Drop
@ 5 A |
Voltage Drop
@ 6 A |
Voltage Drop
@ 7 A |
Voltage Drop
@ 8 A |
Voltage Drop
@ 9 A |
Voltage Drop
@ 10 A |
| 332 |
0.016 |
0.019 |
0.022 |
0.026 |
0.029 |
0.032 |
I have included code 100 brass track for comparison purposes only. If
you are new to model railroading, you should know that nickel-silver
track is much, much easier to keep clean than brass. So
I'm
not going to bother to estimate the voltage drop for it. Give the brass
track that came with your starter set to the obnoxious kid down the street. All
that track cleaning will keep them out of your hair for a while. Mr. Wilson! Mr.
Wilson! (I really dated myself with that
one, didn't I?)
Fortunately for those into G-scale and Gauge-1, brass track is practical. As
all know, 332 is seriously out of scale. On the plus side, besides
keeping flanges a little further away from outdoor ballast that is
out of place, it also conducts electricity very well.
A Non-Illuminated (Cold) #1156 Car Taillight Bulb
| Ohms
@ 100 Hz |
Ohms
@ 10 kHz |
Ohms
@ 100 kHz |
| 0.4345 |
0.4356 |
0.4560 |
