temperature rise in wire due to power absorption?

[astroboy]

Is there an easy way to figure out how many degrees a length of wire is going to heat up because its resistance? If a motor's wire were of such a size and length as to cause a .1V drop, a current of 10 amps would mean--I think--that the wire is absorbing 1 watt of power. Is there a formula, something like the definition of a calorie(heat required to raise a gram of water 1 degree C.) that will allow me to determine if the motor wires are going to overheat?

Thanks,
Jeff

[Regecide]

Well you can figure out the power lost using:

P=I^2R

Then you would have to know the specific heat of the metal you're talking about.

And you should be able to figure it out from there.
Alex

[vintage1]

specific heat will tell you how fast it gets hot, not how hot it gets.

No way to tell how hot it will get. Example, there is something called a 'hot wire anemometer' which meausures wind speed by how much it cools an electrically heated hot wire.

They used one in a race car engine management system once - to measure inlet airflow.

It was brilliant. Until it rained. That caused the wire to cool, and the system to calculate it needed about 10 times as much fuel...and the engine flooded shortly after the track did :(

[escapee]

Astroboy

If you concern is just wires overheating - it is extremely unlikely. Without computations, just consider that house wiring is around #14 and runs all over, enclosed, carrying lots of amps often continuously. Much R/C power wiring is around #14 & often use silicone insulation which withstands higher temps.
The ESC that you'll probably be using, should have wiring which is reasonable for comparison. Generally, the ESC & other components would need attention before the wires do.

[astroboy]

Thanks to you folks, too--I see a couple of the same names from my parallel thread on steel wire. From my latest post on that one:


I did a crude test. I hooked up a foot of it between a pack and my homemade discharger. After several minutes of 5.2 amps, it was still cool to the touch. Unless heating varies logrithmically with current, it seems I might be okay with 10 amps.


--So I'm inclined to agree with escapee. It still would be nice to know just the what the resistance is, though, so I could calculate if the weight loss is greater than the power loss of using heavier wire. Since it's a (sport) scale model, getting the stall speed down is more important to me than power output.

Jeff

[Mr.RC-CAM]

It still would be nice to know just the what the resistance is...Measure the voltage drop across the wire segment. Divide that by the current (amps). Divide the result by the wire's length, in feet. Result is ohms/ft.

Using long lengths of wire for this test will yield more accurate results. A 100 feet spool would be nice.

Or, you can look it up. Nominal Wire Gauge Resistance is shown here:

AWG Ohms/ft
------ ----------
4 .000292
6 .000465
8 .000739
10 .00118
12 .00187
14 .00297
16 .00473
18 .00751
20 .0119
22 .0190
24 .0302
26 .0480
28 .0764

A change of ~3 AWG numbers equals a doubling or halving of the wire's cross sectional area. Therefore, if 10 AWG is safe for 30 amps (just for example's sake), then 13 AWG is ok for 15 amps and 16 AWG is good for 7.5 amps.


RC-CAM

[Bruce Abbott]

Originally posted by astroboy
Unless heating varies logrithmically with current....

Power loss is proportional to current squared. It will heat up four times faster at only twice the current!

Calculating power loss is easy, but temperature is much harder to predict. It is affected by numerous factors such as surface area, thermal properties of the insulation, and external environment. The most accurate way to determine temperature rise is simply measure it in your application.

To save weight you could use aluminium wire, which has half the resistance of copper for the same mass. However, it is harder to join, so unless you have long wiring runs it probably isn't worth the hassle.