Wire length tables: Difference between revisions

Introduction

Describe wire length, voltage loss, etc. here.

Tables

The following table shows the American Wire Gauge (AWG) size for several different round trip (RT) wire lengths based on maximum current (A) for a 12V DC system (assuming 3% maximum wire loss):

This table was adapted from Engineering Toolbox [1] .

Calculating Wire Sizes

Assumptions made:

1. copper wire resistivity = 11.2 [2]
2. 3% loss from wires
3. allowable voltage drop = 0.36V
   • 12V system, 3% (0.03) wire loss -> 12V x 0.03 = 0.36V

Variable Declarations:

• A_n: circular mil area
• n: AWG
• m: AWG
• Conductor resistivity: constant, 11.2
• Current: current through wire in Amps, acquired from table
• Roundtrip (RT) wire length: complete length of wire, ft, acquired from table
• Allowable voltage drop: voltage drop through wires, V

Table 2. Calculating Wire Sizes

Eqn. #	Equation	Step/Explanation
#1	${\displaystyle A_{n}=(5*92^{\frac {36-n}{39}})^{2}}$	Eqn. 1 was used, rearranged, and iterated on to produce Table 1. [3].
#2	${\displaystyle n=36-{\frac {39*log{\sqrt {\frac {A_{n}}{5}}}}{log(92)}}}$	Algebraically rearrange Eqn. 1 to solve for n. The resulting equation is Eqn. 2 to the left.
#3	${\displaystyle n=1-m}$	If n<0, replace n with 1-m in Eqn. 1 [4] .
#4	${\displaystyle A_{n}=(5*92^{\frac {36-(1-m)}{39}})^{2}}$	Substituting n equals 1-m into Eqn. 1 yields this equation (Eqn. 3). Use Eqn. 3 if n<0.
#5	${\displaystyle m={\frac {39*log{\frac {\sqrt {A_{n}}}{5}}}{log(92)}}-35}$	Solve Eqn. 3 for m, the resulting equation (Eqn. 4) is to the left.
#6	${\displaystyle A_{n}={\frac {(conductor-resistivity)*(current[A])*)roundtrip-wire-length[ft])}{allowable-voltage-drop[V]}}}$	Eqn. 3 is also a rearrangement of Eqn. 1. Use Eqn. 4 to solve for A_n

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References

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