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This is a rough first-draft copy of an article subsequently published in "Good Old Boat" magazine.
“Ohm’s Law & Boats”
There are a few fundamentals that must be considered, prior to undertaking any electrical
installations. Anyone, not prepared to understand and apply these principles, should not perform any permanent wiring
. Unfortunately, many Marine
Electricians, and some Boat
Builders, ignore the implications of Ohm’s Law. Fortunately, the concepts are simple, and the equations easy.
A little time spent understanding the relationships will prepare you to do it right - and, after all, if you don’t have the time to do it right; when will you get the time to fix it?
Ohm’s Law provides the fundamental basis for all Electrical
and Electronic circuit design. The Law states: “Current flow is directly proportional to the applied voltage, and inversely proportional to the circuit resistance”. Simply put, in any circuit with a steady applied voltage, such as from a battery
, any increase in resistance will result in a commensurate decrease in current
Every wire, and each termination, has a resistance to current
flow; which causes a voltage to develop across the length of the circuit. This results in a voltage drop between the source (ie: a battery) and the load device (ie: Bilge Pump
It will become apparent that given the low voltages utilized on boats (12VDC
battery), even very small increases in circuit resistance will have major consequences for your boat’s electrical system
. Let’s look at the arithmetic, then address the practical applications.
Ohm’s Law is mathematically expressed:
I = E ÷ R
Where: I = Current in Amps (Amperes) (Current Induces a magnetic force)
E = Potential in Volts (Electromotive Force)
R = Resistance in Ohms
For simplicity’s sake, and clarity, we’ll use the more intuitive colloquial characters:
A = V ÷ R (A =- Amps, V = Volts, R = Ohms)
The formula may be transposed thus:
V = A x R and R = V ÷ A
Resistances in series (one after the other - a daisy chain) are additive, and calculated thus:
RT = R1 + R2 + R3 (& etc.)
Where: RT = Total Circuit Resistance in Ohms
R1 = The 1st Resistance in line (ie: wire)
R2 = the 2nd Resistance in line (ie: terminations)
R3 = the 3rd Resistance in line (ie: the load device ~ Bilge
Electrical Power is measured in Watts, and a Direct Current circuit is calculated thus:
P = Volts x Amps
Where P = Power in Watts
It is useful to note that 746 Watts = 1 Horsepower (HP)
These formulae may be combined and transposed thus:
P = A2 x R
P = V2 ÷ R
A = P ÷ V A = 2√ (P ÷ R)
V = P ÷ A V = 2√ (P x R)
R = P ÷ A2
R = V2 ÷ P
The American Boat
& Yacht Council (ABYC - Section E-22.214.171.124) specifies the maximum voltage drop (ED) permitted on DC circuit as follows:
3% For Panel Feeders, Navigation
Pumps & Blowers, Electronic Equipment
, and other essential equipment
. This category encompasses most situations.
10% For Non-Essential equipment such as Cabin Lighting
The industry standard formula for calculating minimum Wire Size for a given Voltage Drop is:
CM = (K x A x L) ÷ VD
Where: CM = The Circular Mil cross sectional area of the wire
(See Table 1, and ABYC Section E-8, Table III)
K = 10.75 Representing the Mil-Foot Resistance of Copper Wire @ 78o F.
L = The Total Length of the wire in Feet
(This is the ‘Round Trip’ length of both Positive + Negative wires)
VD = Permitted Drop in Volts
(Ie: 3% @ 12.5V = 0.375 ED or 3% @ 25V = 0.750 ED)
This formula does not address the resistance added to a circuit by it’s
terminations (joints & splices). The reality is that each “old’ termination could, after a time in service
, add a resistance of between 0.01 and 0.03 Ohms to the circuit. This additional resistance is, in many installations, greater than that of the wire!
Let’s now apply these formulae to some real-life marine
Assume a 2000 GPH Bilge Pump Installation
Rated 110 Watts @ 12VDC (Nominal)
Wired with 20 Feet of 2-conductor boat cable (40 Cct. Ft - Pos+Neg)
Assuming a moderately well-charged Battery
applying 12.5 V
Current (I) in Amps:
A = P ÷ V = 110W ÷ 12.5V = 8.8 Amps
Calculate Permitted Drop (ED) in Volts:
VD = % Drop x VApplied = 3% x 12.5V = 0.375 Volts
Calculate Wire Size Required for Maximum 3% Drop:
CM = (10.75 x 8.8A x 40Ft) ÷ 0.375V = 3,784 / 0.375
= 10,090 CM Required
Select #10 AWG wire from Table 1 (#10 = 10,380CM)
Calculate Actual Voltage Drop (ED) using #10 Wire:
VD = A x R = 8.8A x (40Ft x 0.00102 Ohms/Ft*) (From Table 1)
= 8.8 x 0.0408 = 0.359 Volts (0.359 ÷ 12.5 = 2.87%)
Now Let’s calculate the Voltage Drop (ED) if we used smaller #12 Wire:
VD = A x R = 8.8A x (40Ft x 0.00162 Ohms/Ft)
= 8.8 x 0.0648 = 0.570 Volts (0.570 ÷ 12.5 = 4.56% ~ Unacceptable)
The above calculations prove that by slightly undersizing the wire(#12 in lieu of #10 required in this example), we will be providing a mere 11.93 Volts to the Pump
(12.5VApplied - 0.57VDrop), wasting 5 Watts (8.8A x 0.57V) of precious battery power, and severely reducing the output of the pump - way below it’s rated 2000 GPH.
It gets worse! The formula did not include any Termination Resistance. If we assume only 6 ‘old’ splices in our circuit (2 @ Panel + 2 @ Switch + 2 @ Pump), we will have added as much as 0.12 Ohms to our circuit (6 x .03 Ohms ea).
Lets recalculate VD, to include Termination Resistance:
V = A x R = 8.8A (0.0648 Ohms for Wire + 0.12 Ohms for Splices)
= 8.8 x 0.1848 = 1.626 Volts (1.626 ÷ 12.5 = 13% - WOW!)
This Pump will actually only get about 10.87 Volts (12.5 - 1.626) - approaching its minimum operating voltage. Any further deterioration (Ie: low battery or corroded terminal etc), and this pump is unlikely to even operate at all!
Now that we understand the implications of Ohm’s Law, and how it effects our electrical system
, let’s summarize our conclusions, and then look at some practical solutions to the problem of resistance.
Summary of Conclusions:
Resistance is the enemy!
The major causes of electrical failure (or poor performance) are:
a) High resistance due to loose terminals and/or corrosion
caused by moisture penetration. Too many joints!
b) Undersized wire, often factory installed.
c) Vibration and mechanical damage to wires.
Every effort must be made to reduce circuit resistance, including:
a) Plan your wiring
so as to eliminate all unnecessary joints & splices (terminations).
b) Perform high quality terminations that are clean, tight, and water/moisture resistant. (See ‘Anatomy of a Termination’)
c) Install wiring and terminations in “high & dry” locations.
d) Use high quality marine-rated materials, including Type III Tinned Copper Marine Wire (UL Standard 1426 - Type BC-5W2).
e) Calculate and select an adequate wire size. Bigger is better!
The Anatomy of a Quality Termination:
1. Calculate and select adequate wire size (CM = (10.75 x I x R) / E) , and use color-coded conductors where possible. You can code the wire yourself, by adding a band of colored tape near the termination.
(See ABYC Section E-9, Tables XI and XII).
2. Leave a loop of extra wire at each end. This acts as a strain-relief, , provides a drip point for moisture, and provides for a future repair.
3. Select the proper size and type of termination device for your application.
a) The smaller terminals are sized to each fit two sizes of wire:
Red fits #18 - #22AWG, Blue fits #14 & #16AWG, and
Yellow fits #10 & #12AWG. I prefer to utilize the larger size of wire in each case (ie: calculate #12 required - use #10. It will give a tighter fit in the terminal; cause less VD, and is mechanically stronger).
b) Match the ‘stud’ size of the terminal to the mounting screw, when using ‘Ring’ or ‘Locking Fork’ terminals. Never use ‘Open Fork’
c) Use high quality tinned or plated terminals.
4. Strip the wire, taking care to not nick any strands. The exposed conductor should only be long enough to fit the barrel of the termination. A high quality ‘automatic’ wire stripper is useful.
5. Apply a permanent identification tag & color code, near the end of the wire (± 6" back). This will identify the load and source of the circuit.
(I use appropriately typed mailing labels, & colored tape - ie: “Cct. 3 - 12v Bilge Pump #1”, c/w a Brown band of tape ~ see ABYC section E-9 Table XII for color codes).
Slide on a Clear Heat Shrink Tube, long enough to cover the label.
Shrink the tubing in place over the label, using a hot air gun (± 400oF).
6. Slide on another Heat Shrink Tube (Adhesive Lined), about 3 times as long as the terminal barrel. This ‘Shrink’ must be sized so as to fit very tightly, when finished.* DO NOT SHRINK YET! (Note: see ‘Products’ appendix). Battery cables
require ‘Insulating Boots’ (ABYC Section E10.6.1) are installed here.
7. Coat the stripped conductor with an anti-oxidant compound
(see “products” appendix)
8. Insert the stripped conductor into the terminator barrel. The wire insulation
should be butted against the barrel edge, with the conductor extending slightly through the barrel (if using ‘Open End’ terminal).
9. Slide the terminator on to the bare wire & crimp, using a quality, size matched, crimper. If the terminal is “seamed’ type, ensure that the seam is laying on the crimper’s ‘flat’. An ‘automatic’ ratcheting crimper will ensure that the proper crimping force is applied - (otherwise squeeze hard). A good tool will provide a double crimp in a single
action (the 2nd crimp being a strain relief near the barrel end).
10. Apply a thin coating of silicone sealant
to the termination, slide the Shrink back down the wire (covering the termination), and shrink, ensuring a tight and water-tight fit.
12. Secure the cable(s) (‘high & dry’) with Tie-Wraps etc. Ensure that the finished termination is not under strain.
13. If using screw terminals (terminal strip, breakers, etc.), cover the finished assembly with anti-oxidant compound, and install ‘dead-front’ barrier.
The above procedure will provide a tight, water/moisture-resistant (corrosion-free) termination - ensuring minimal resistance and long life.
Table 1 - Did Not Copy - Email
me for a FAXED copy.
1. Cross Sectional Area in Circular Mils for American Wire Gauge (‘AWG’) Only. Do not use ‘SAE’! (ABYC Section E-8 Table III)
2. Size (Diameter) designation of wire/cable.
3. Resistance of Copper ‘AWG’ wire PER FOOT @ 77o F. Resistance increases with temperature increase.
4. Minimum tensile force required to pull wire out of termination.
(ABYC Section E-8 Table IV). Note: 1 Lb. ≃444 Newtons
5. Circular Mil area of ‘Automotive’ (‘SAE’) Wire. Do not use, except in emergency
. Note that ‘SAE’ wire is SMALLER than the same gauge of ‘AWG’ wire - they cannot be substituted - If ‘SAE’ must be used, select 1 size larger for temporary fix.
6. Wire smaller than #16 not normally permitted.
1. Soldered Joints:
ABYC does not permit
soldered-only joints (Section E-126.96.36.199). Where crimped joints are also soldered, adequate support must be provided, so as to minimize flexing. The solder causes a ‘hard spot’ in the wire, which is subject to breaking.
While soldering will greatly reduce moisture penetration and joint resistance; it’s is often very difficult to accomplish in the tight quarters encountered. I seldom solder terminations, except for Bilge Pump wiring (where water/moisture is a huge problem), and Battery Lugs (where hydrogen gassing causes corrosion).
2. Bilge Pumps:
Not only do Bilge Pumps reside in a very harsh environment
, but the Manufacturers provide inadequate wire leads on their pumps. They seem to be ignoring the problem of connecting their #16 AWG lead to the much larger (seldom smaller than #12 - often larger yet) branch circuit wires required (due to VD) to feed the pump. Often, the leads could be longer, to allow terminating above the highest likely water
level. And finally, many manufacturers do not use tinned wire.
One solution to the ‘mis-matched’ wire size problem, is to use a ‘Butt Splice” one size larger than the branch circuit (feed) wire, inserting both the feeder wire and the pump lead into the same end and crimping. Install the sealing heat shrink so it extends beyond the (empty) end of the splice about 1". Fill the end with silicone, then shrink the tube, sealing the unused end.
Always use the highest quality materials available! Cheap
products represent a false economy.
• Heat Shrink Tubing:
I like Clear Thin Wall tubing (2:1 Shrink Ratio) for protecting labels, and Adhesive
Lined Thick Wall tubing (3:1 Shrink Ratio) to water-proof terminations. Use flame-retardant tube, where available. Shrink ratio is the difference between it’s original size, and it’s recovered size, after shrinking. Always use the smallest diameter tube possible (ensuring a tight final fit), with the highest available shrink ratio.
Ancor Marine Products, 3M, Panduit, T&B, Burndy, Ideal, etc
• Sealants & Anti-Oxidant Compounds:
There are numerous compounds, suitable for protecting joints,
but ensure that the product is suitable for ‘use on energized circuits’.
- Starbright “Liquid Electrical Tape”
- 3-M “Scotchkote-Electrical Coating” & “#1602/1603 Insulating Sealers”
- “Corrosion X” Penetrant
- Ideal “No-Alox”, Burndy “Penetrox”, GB “Ox-Guard”
- Vaseline (Petroleum Jelly), tho’ it liquefies @ higher temperatures.
• Terminals & Lugs:
I like heat shrink terminals & butt splices, or nylon insulated terminals. Insist upon tin plated terminals, with serrated barrels, and seamless or brazed barrel construction. Larger lugs should be of the closed end & seamless type, and all terminations must be sized to match the wire used.
Ancor Marine, 3-M, T&B, Panduit, etc
• Wire & Cable
Use only , properly sized (bigger is better), new, tin plated marine wire (UL Standard 1426 - BC-5W2). Finely Stranded Type III wire is more flexible than Type II, and is preferred (especially where subject to vibration). When storing wire in ship’s inventory, always seal the ends against moisture penetration (Silicone or Liquid Tape).
E. & O.E.
February 18, 2002
The forgoing is a first-draft copy of an article that, with changes & refinements, was published in the March/April 2003 (Issue 29) edition of “Good Old Boat Magazine”.
The technical editor, Jerry Powlas, also did some real-life testing of terminations, heat rise, and voltage drop. His results are published on-line at:
Gordon A. May is a Master Electrician and Marine technician, specializing in the design & implementation of complete yacht re-fit projects. Gord, and his wife Maggie, spent the 90's living aboard
and cruising their C&C
29 “Southbound”, in Florida
and The Bahamas
. Now living in Thunder Bay, Canada
(Lake Superior), Gord is an Electrical Designer
Coordinator for Cuthbertson Engineering (Mechanical, Plumbing
, & Electrical).
“Ohm’s Law & Boats”
Gordon A. (Gord) May
313 E. Amelia Street
Thunder Bay, ON, P7E 3Z8, Canada
Tel: (807) 622-0770 and (807) 622-3600
Fax: (807) 622-3633
2002 © by Gordon A. May - All Rights Reserved