Trains4Africa
Because all Boys (and some girls) love Trains

TRACK & WIRE RESISTANCE

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

 

CREDIT:    http://www.wiringfordcc.com