Max Track Bus Length

Question:  How long can I run a track bus wire starting from the booster out to the farthest point and back again can I run?

Wire has 3 electrical properties.   Resistance, Inductance and Capacitance.  Capacitance and Inductance only effect DCC.

Wire resistance is the one hard physical property that cannot be overcome by using "wiring techniques" that reduce the wires inductance and capacitance problems.  Stated another way, even if you had perfectly addresses all the inductance and capacitance issues that effect DCC, the maximum length of wire will ultimately still be limited by the resistance.  This section also applies to DC.


IN THIS SECTION:

1) HOW IS WIRE RATED FOR CURRENT?
2) WHAT IS OUR PERFORMANCE GOAL?
3) HOW DO WE TRANSLATE OUR PERFORMANCE GOAL INTO ELECTRICAL TERMS?
4) WHAT WRONG WITH USING THE NATIONAL ELECTRIC CODE (NEC) STANDARD?
5) IF VOLTAGE DROP IS NOT A CONCERN FOR 120V, WHY SHOULD IT BE IMPORTANT FOR 12V?
6) HOW DOES VOLTAGE DROP EFFECT TRAIN SPEEDS?
7) GIVEN A % VOLTAGE DROP, HOW DO WE CALCULATE TOTAL WIRE RESISTANCE?
8) WHAT ARE STANDARD WIRE RESISTANCE VALUES?
9) HOW DOES THE TRACK BUS "TWO WIRES" FACTOR INTO THE WIRE LENGHT?
10) MAX TRACK BUS LENGTHS 
11) HAZARDOUS TRACK BUS LENGTHS


1) HOW IS WIRE RATED FOR CURRENT?

When current flows in a given wire, the wire will generate heat due to it's resistance.  

The heat generated has destructive effects on the wire's outer insulation.  The more heat, the faster the decay of the insulation.   

The National Electric Code has various wire current ratings for a given wire size that depends on the type of insulation used and the operating environment the wire will be used in.  The rating will vary depending if the wire inside a conduit or out in the open free air.  

The point is there is no single standard current rating for a given wires size.   The current ratings all depends on the restrictions of the environment that the wire will be used in.   

So what does this mean?  To rate the wire for specific use, you must first define a performance goal for the wire.
 

2) WHAT IS OUR PERFORMANCE GOAL?

What are our problem when we run our layout?  Here is list in decreasing performance order.  Bad to Worst.

1) Locomotive speed varies as it goes around the layout.
2) Lamps or lighted devices are dimmer compared to others of the same type as the wire gets longer.
3) Devices work inconsistently.
4) Wire gets warm/hot
5) Wire burns up when there is a short circuit.

Therefore if we address problem #1 and choose a wiring system that allows a locomotive to run at a constant speed around the layout, ALL the other problems in the list will go away.


3) HOW DO WE TRANSLATE OUR PERFORMANCE GOAL INTO ELECTRICAL TERMS?

We use Ohm's Law

Ohms law is:  V= I * R

It says that if there is resistance, then when current is flowing then there is a corresponding voltage loss or drop across that resistance.  Wire has resistance.  So Ohm's law for wires becomes:

V(voltage drop) = I (current) * R (wire)


4) WHAT WRONG WITH USING THE NATIONAL ELECTRIC CODE (NEC) STANDARD?

The National Electrical Code used for AC power wiring in both residential and business districts is based on the temperature rise of the wire.   The goal is to prevent the wire insulation from deteriorating and creating a hazard electrocution problem and/or a fire.  It also takes into account if the wire is exposed to free air or inside a conduit that can trap heat.   Hence the temperature rise within the wire directly relates to the current rating of the wire.   Since wire gauges have standard resistance values, temperature rise can be translated into a set of wire gauge rules for specific installation conditions.   Other issues such as Voltage Losses/Drop in the wire are NOT the driving concern.  Bottom line the goal is reliability and safety.   The Electrical Code does not address our needs.


5) IF VOLTAGE DROP IS NOT A CONCERN FOR 120V, WHY SHOULD IT BE IMPORTANT FOR 12V?

To understand the effect of voltage drop lets compare 120V to 12V operating voltage conditions.  Lets assume the voltage drop in a given wire size/length combination is allowed to be 2.4V.

If the wire that loses 2.4V when operating at 120V, that means the % voltage drop is  2.4V/120V = 2%.
If that same exact wire loses 2.4V when operating at 12V, that means the % voltage drop is 2.4V/12V = 20%

CONCLUSION: The voltage drop problem for 12V is 10 TIMES WORSE than it is for 120V.  

2% is a very small value for voltage drop.  Stated another way, the 2% voltage drop in 120V is not an important criteria for determine the performance requirement of the wire to be used.   HOWEVER with a 20% drop at 12V, the value is very large and presents a very different situation. 


6) HOW DOES VOLTAGE DROP EFFECT TRAIN SPEEDS?

As stated before, out performance goal is making sure our trains will run at consistent speed as set by the throttle.   The motor is the device that drives the train.  If you every used a DC train before, you know that motor speed is directly proportional to voltage applied to the motor.  The motor voltage comes from the track voltage which comes from the throttle.   

To maintain motor speed, you need to maintain the track voltage at a constant voltage value over the entire layout with no voltage losses or voltage drops in the wire.  Unfortunately a 0V (0%) voltage drop is not possible because there is no such thing a true value of zero ohms in a wire other than in a Science Laboratory.  In other words, it is impossible to maintain a constant motor speed.  We must accept some amount of voltage drop or loss in the wire.

What this means is for a given track voltage drop or loss of X%, the motor speed will drop by X%.

Example: A 20% drop means a train going 100 MPH would drop to 80 MPH.   Likewise a train going 50MPH would drop to 40MPH and so on.   A better performance would be a lower 10% or even a minimal 5% voltage drop maximum in the wire.

The following table show what are the voltage drops allowed in the wire for three different % drop values.

 Voltage20%10%5%
10V
(N scale)
2V1V0.5V
12V2.4V1.2V0.6V
18V 
(G scale)
3.6V1.8V0.9V

To make motor speed variation due to voltage drop have a minimal visual impact on the train speed, we need to reduce the voltage drop to value of 10% or less.


7) GIVEN A % VOLTAGE DROP, HOW DO WE CALCULATE TOTAL WIRE RESISTANCE?

Again we use Ohm's law.  But this time we work backwards and determine the maximum resistance value of the wire. 

So ohms law V = I * R is re-written to solve for R becomes:

V / I = R

But we only know the value V = Voltage drop   But what is I?

That answer is found by the maximum track current specification of the DCC system and/or the DCC booster current rating you have purchased.  Typically maximum track current ratings for most DCC system fall into following ranges:

1A, 3A, 5A, 8A, 10A.

To be clear, it is NOT the motor current rating.  Why?  DCC allows multiple engines of any combination and type to all run at the same time.  Therefore maximum current the DCC system is rated for sets the maximum number of engines you can run.  This represents the worse case track current that will flow in your track wires.

So the equation becomes

V(voltage drop) / I (Max Track Current) =  R (Max Wire Resistance)

Using this equation, we can now calculate the maximum resistance allowed in the wire for various track current ratings.

OHM TABLES

12V: Max Wire Resistance (OHMS)
% DROP1A3A5A8A10A
10%1.20.40.240.150.12
5%0.60.20.120.0750.06


10V: Max Wire Resistance (OHMS)
% DROP1A3A5A
10%1.00.3330.2
5%0.50.1670.1


18V: Max Wire Resistance (OHMS)
% DROP5A8A10A
10%0.360.2250.18
5%0.180.1130.09


8) WHAT ARE STANDARD WIRE RESISTANCE VALUES?

Wire total resistance is proportional to two physical parameters of the wire:

1) The diameter of the copper wire which is defined by a standard such as the American Wire Gauge or "AWG"
2) The LENGTH of the wire.   

For a given wire size (AWG) the wires resistance is specified in Ohms per foot.   Because the ohm values are so small, they often list the same value for large lengths that make the math easy.

The following wire chart gives you an idea of resistance for a given length of a single stranded wire.  It has been restricted to AWG sizes suitable to properly wiring up a layout.

American Wire Gauge
AWG
Ohms/Foot100Ft Ohms1000Ft OhmsApproximate Metric
Equivalent
mm^2 WG
180.0061480.61486.1480.75
160.0039900.39903.9901.5
140.0025080.25082.5082.5
120.0016200.16201.6204

You can find tables of Wire Gauge versus ohm/foot from various wire providers.    For a given wire gauge size, the ohm/foot value may vary slightly depending if it is solid or stranded and if stranded how many strands it has.   But in the end, all the ohm/foot values are pretty close in common value. The above table reflects the average or common ohm values for a given AWG.


9) HOW DOES THE TRACK BUS "TWO WIRES" FACTOR INTO THE WIRE LENGHT?

Track bus wiring involved two wires.  One for each rail.  The current path of a complete circuit starts at the booster or DC throttle, runs out to the farthest point on the layout and connects to rail A.   Then the return wire connects to rail B across from rail A and must make it all the way back to the booster or DC throttle where is all started.  In other words one wire going out and one wire coming back. 

THAT MEANS:

1) THE WIRE LENGTH IN A TRACK BUS CABLE IS 2 TIMES LONGER THAN THE DISTANCE IT NEEDS TO RUN THE TRACK BUS TO REACH THE FARTHEST POINT ON THE LAYOUT.

2) YOU MUST DIVIDE THE MAX WIRE LENGHT BY 2 TO GET THE MAXIMUM TRACK BUS LENGHT.


10) MAX TRACK BUS LENGTHS 

MAX TRACK BUS LENGTH = 1/2 * (MAX RESISTANCE) / (OHM-PER-FOOT)

DCC only: Any distance over 30ft should consider using twisted pair (paired) wiring and install a RC filter at the far end of the track bus.  The bus lengths over 30FT are shown below in Orange.

Why?  For a laymen's interpretation, go hereTwisted Pair Bus Wiring

Note: If you place the booster in the center of the Track Bus, you can double the Max Track Bus length.  A 30Ft bus can become 60Ft.  (30Ft<-Booster->30Ft)


12V: Max Track bus length (FEET)
American Wire Gauge
AWG
 %
Voltage Drop
1A
Booster
3A
Booster
5A
Booster
8A
Booster
10A
Booster
1810%98Ft33Ft20Ft

185%49Ft16Ft









1610%150Ft50Ft30Ft19Ft
165%75Ft25Ft15Ft








1410%239Ft80Ft48Ft30Ft24Ft
145%120Ft40Ft24Ft








1210%370Ft123Ft74Ft46Ft37Ft
125%185Ft62Ft37Ft23Ft


N Scale 10V: Max Track bus length (FEET)
American Wire Gauge
AWG
%
Voltage Drop
1A
Booster
3A
Booster
5A
Booster
18 10%81Ft27Ft16Ft
18 5%41Ft14Ft
     
16 10%125Ft42Ft25Ft
16 5%63Ft21Ft13Ft
     
1410%309Ft103Ft62Ft
145%154Ft51Ft31Ft


G Scale 18V: Max Track bus length (FEET)
American Wire Gauge
AWG
%
Voltage Drop
5A
Booster
8A
Booster
10A
Booster
1610%45Ft28Ft23Ft
165%23Ft14Ft
     
1410%72Ft45Ft36Ft
145%36Ft22Ft18Ft
     
1210%111Ft69Ft56Ft
125%56Ft35Ft28Ft


11) HAZARDOUS TRACK BUS LENGTHS

The following information is just a FYI.  If you built a layout with anything even half way close to these track bus lengths, the locomotive(s) would still perform so poorly that you would already know right away that you had a problem and would need to fix it.

A Hazardous track bus length is a length of track bus wiring that will not permit the booster or DCC circuit breaker to shutdown when a short is present.  In other words, the Booster or DCC circuit breaker can no longer offer any protection.  

Why?  The total wire resistance of the track bus is higher than the output impedance of the booster/DCC circuit breaker.  In other words, a short circuit will not allow the booster or DCC circuit breaker to shutdown.  Full current (power) will flow allowing damage to occur in any combination of the following:

a) The booster itself which may not be designed for continuos operation at full power all day long.  This assume only a booster is being used without DCC circuit breakers.
b) Any Undersized wiring.  
c) Weak Connection point in the wiring system. 
d) Locomotive or rolling stock causing the short.   (see discussion below the table)

The following table assumes a nominal DCC track voltage of 14.25V

Booster or DCC circuit breaker current rating or setting
(Amps)
Booster/DCC Circuit Breaker Output Impedance
=
Maximum Track Bus wire Resistance
(Ohms)
Maximum 12AWG
Track Bus Length
(Feet)
Maximum 14AWG Track Bus Length
(Feet)
Maximum 16AWG Track Bus Length
(Feet)
Maximum 18AWG Track Bus Length
(Feet)
Power available for damage if not shutdown 
(Watts)
 
101.43441285179116143
81.78549355223145114
52.85880568357232 71
34.751466947595386 43
1.59.5029321894119077321

Notice: 

1) as the wire gauge get smaller, the maximum track bus length gets lower.
2) as the booster current rating or DCC circuit breaker current setting goes higher, the maximum track bus length gets shorter.


Item "d" failure above is true even is your track bus length does not even come close to exceed the length of the table.  There are example of a high resistance short involving locomotives/rolling stock.
The point is that designing a track bus with a performance goal will automatically force you to implementing a very low track bus wiring resistance that will minimize chances of the rolling stock damage.  The high resistance short will still be able to trip the booster or DCC circuit breaker into shutdown.   In other words you build a safety resistance margin to maximum the success of your DCC system protection mechanisms to protect your rolling stock in addition to protecting itself.

Notes:

1) This does not account for the parallel track resistance which would reduce the effective track bus resistance. However there are so many variables in track level electrical continuity that it could be ignored in practice.  Broken/Cold Solder rail joints or small wire gauge track feeders.

2) A short circuit does not mean ZERO OHMS.  There is no such thing a zero ohm short.  A short circuit only means an operating condition where the consequential resistance will draw more current than can be supported by the power source (Booster or DCC circuit breaker).

3) In term of damaging power, it worth to note that a common simple soldering iron is typically 25Watts.  Clearly enough to start a fire if a weak point of high resistance was concentrated in one spot.  There are known examples of terminal connection points burning up due to improper installation.


9/30/17