Been watching some discussions on wire sizes and without
responding to any particular statements . . . .
If the material from which wires are made had zero resistance,
then any size wire could carry any amount of current! Consider
the formula for power where watts = volts x amps. This
relationship works whether the watts are used to do something
useful (light up a bulb) or worthless (warm up a wire). First
a little background:
As a useful rule of thumb, remember that 10AWG wire has a resistance
of 1 ohm per 1000 feet or .001 ohm per foot. Every time you
step three AWG sizes, you double/half the wire's cross section.
So, it follows that 13AWG wire is .002 ohms/foot, #16 is .004 ohms/
foot, #19 is .008 ohms/per foot and 22AWG is .016 ohms per foot.
In the other direction, 7AWG is .0005; 4AWG is .00025 and 1AWG
is .00013 ohms per foot. If you want to get a good estimate
on intermediate sizes, just do a linear interpolation. For
example, 20AWG is about 1/3rd of the way between .008 and .016
ohms per foot. So, 1/3 of .008 ohms is .0026 ohms. Add to .008
yields approx .0106 ohms. A check of a REAL wire table sez
20AWG is .0102 . . . Not bad for a quick approximation.
Now, knowing the resistance, you can calculate the LOSSES in
any particular wire. Suppose we drag a 7 amp load through
a piece of 20AWG in a composite airplane and round trip from
bus bar to load and back to ground is 15 feet. 15 feet times
.0106 ohms is .159 ohms. Ohms law sez Volts = Amps x Ohms
so the voltage drop in this hunk of wire is 7 x .159 or
about 1.113 volts. Hmmmm . . . in a 14 volt system, 8% of
the energy for the device at the other end of the
wire isn't getting there.
Going back to the first equation, 7 amps x 1.113 volts
is 7.8 watts. Where does this power go? Off as HEAT. One
respondent to this thread noted that 20AWG would produce
a 35 degree C temperature rise when loaded with 7 amps.
This is a free-air figure. Suppose the wire is buried in
a wire bundle? THEN 7 amps will undoubtedly cause it to get
much hotter. Okay, let's take the free air rise and say
we're going to run this wire through the tailcone where we
expect to see a hot-day soak up to 65C. With a 35 degree
rise, the wire surface can be expected to top at 100 degrees
C . . . pretty toasty.
The copper isn't in any trouble with this scenario but the
considerations are two fold:
(1) The INSULATION should be rated for operation under these
conditions (mil-w-22759/16 wire is good for much more than
100C . . . don't have the numbers off the top of my head)
-and-
(2) the voltage drop to the powered device needs to be evaluated
for acceptability.
Here is an excerpt on wire data from my book:
AWG Ohms/ 35C Rise 10C Rise Max Path
No. KFeet Amps Amps for .7 volt Loss
at 35C rating.
2 .156 100 54 45 Ft
4 .249 72 40 39 Ft
6 .395 54 30 32 Ft
8 .628 40 20 27 Ft
10 .999 30 15 23 Ft
12 1.59 20 12.5 22 Ft
14 2.53 15 10 18 Ft
16 4.01 12.5 7 14 Ft
18 6.39 10 5 11 Ft
20 10.2 7 10 Ft
22 16.1 5 8 Ft
In the 20AWG, 7-amp, 15-foot scenario I illustrated
above, voltage drop might be the condition I'd
like to correct so going to 18AWG wire would reduce
both voltage drop -and- temperature rise. For those
interested in the math note that from Ohms law,
Ohms = volts/amps. In the example below, the volts
and amps cancel ohms leaving feet:
1000Ft 0.7 volts
------------ x ----------- = 15.6 Path Feet
6.39 Ohms/KFt 7.0 amps
So, 18AWG would do fine in our 7 amp, 15 foot loop.
Now, all this having been said, there are no hard
rules for de-rating a wire If you suspect that voltage
drop might be an issue, do your own analysis like that above
. . . I like to keep wire losses less than 5% but that's
MY rule of thumb.
In some cases, a gross overload of a wire is
an acceptable design parameter. For
example: 250 amps to crank an engine is routinely
handled with 2AWG wire . . a TEMPORARY 250% overload.
Here, voltage drops are very important. I've had a
lot of canard-pusher builders wrestle with starter
performance when their ships were wired with
4AWG and the battery was in the nose. This is about
a 24-foot round trip. Play with the numbers a bit
yourself and see how much of a 12-volt battery (with
it's own internal resistance of say .004 ohms) is going
to get to a starter on the far end of 4AWG wires in a
Long-Eze.
On the other hand, an RV with the battery right behind
the firewall can tolerate 4AWG cranking circuits because
the round trip is only 4 or 5 feet long. For regulators
that use the field supply line to also sense bus voltage,
I'll routinely use 20AWG wire in a 3 amp circuit! This
is a voltage drop consideration. Some regulators become
unstable with mere millivolts of uncertainty about
bus voltage. A 22AWG field supply, 5 feet long inserts
240 millivolts of "rubber band" in the regulator's
sense circuit with a 3 amp load. Dropping to 20AWG
drops the uncertainty to 150 millivolts.
This little mini-seminar on wire is to illustrate the
potential pitfalls of grabbing any wire chart and
hooking things up accordingly. This is where networking
with other builders and individuals willing to share a
career's worth of experience is very much worth your time
and trouble. I hope this effort dispels another myth
surrounding wire selection. We have very few concerns
for "burning up" a copper wire. The major considerations
are insulation ratings -and- making sure the things
you hook up have enough juice to run properly.
When in doubt as to temperature rise (wire passes though
a hot section of the airplane or is buried in a bundle
of wires) pick the next larger AWG number for the circuit.
When in doubt as to voltage drop, calculate it out. For a
continuous running load to lose more than 5% of it's
voltage enroute is another good cause to put in bigger
wire. Finally, if you expect to exceed 150C (rise plus
ambient) on a wire run, consider re-routing the wire,
shielding it from heat sources or put in fatter wire.
Now, here's a brain teaser for you. Why does the
path length for 5% drop get longer as the wire diameter
increases???? You guys who have read the book stand
by here . . . let's see if anyone can deduce the reason
from what's been published above. Hint: What is the
mechanism by which a warm object sheds heat energy into
the surrounding environment?
Regards,
Bob . . .
AeroElectric Connection
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(o o)
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