# Voltage Drop for DC Motor

#### fifty60_4802GND

##### Member
Hello Everyone. If I have an air compressor that runs off of 14VDC, and it is located around 150FT away, should I size my wire for the voltage drop steady state of the air compressor, or for the initial inrush current.

For example, the inrush is 35A, and I decide to use 16AWG copper conductors. Would the compressor be completely starved by the voltage drop across the cable during startup, and not start? Or, is the voltage drop not instantaneous? 14VDC is not much to play with, so I be voltage drop can really be an issue with these if ran over any kind of distance.

#### xptpcrewx

##### Power System Engineer
Steady state unless you need the motor to accelerate and develop torque quickly with minimal impact to system voltage. You could use capacitors near the motor to supply some charge. Voltage drop would be instantaneous. 150-ft seems very far for 14VDC.

#### LarryFine

##### Master Electrician Electric Contractor Richmond VA
The lower the system voltage, the more detrimental the voltage drop.

I doubt that your compressor would even start on that much 16ga wire.

#### gar

##### Senior Member
211011-2101 EDT

Some basics. From your information the motor has an internal DC resistance of about 14/35 = 0.4 ohms. By the way motors do not have inrush current, but rather have starting current.

What is the resistance of 300 ft ( 2*150) of #16 copper wire? At 20 C 1000 ft is 4.02 ohms. So at start up what is the voltage across the motor? 14 * 0.4 / ( (0.3*4.02) + 0.4) = 14 * 0.4 / 1.61 = 3.48 V.

At 3.48 V and 35 * 3.48/14 = 8.7 A will the motor start to rotate? Possibly, but that depends upon residual motor and pump torque and pump load.

Suppose that the balance after running stabilizes at 6 A. Then the voltage across the motor is 14 - 6 * ( 0.3*4.02) = 14 -7.24 = 6.76 V, and pump will run at 6.76/14 times its speed at 14 V.

LarryFine's suggestion is good with the capacitor near the motor, and the power switch between the capacitor and motor. If the pump has a fairly low duty cycle, then a storage battery in place of the capacitor might be better solution.

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#### gar

##### Senior Member
211011-2206 EDT

In my previous post I failed to include the motor internal resistance drop in the speed calculation.

So 0.4 * 6 = 2.4 V, the motor internal drop at load, needs to be subtracted from 6.76 - 2.4 = 4.36 V to get the voltage at stabilization to calculate output speed. Thus, output speed is 4.36/14 = 0.31 times its speed at 14 V.

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#### fifty60_4802GND

##### Member
Thanks for all the feedback. Not my design, just evaluating a situation.

The drop is probably not instantaneous because of the leading lagging properties of the capacitance and inductance of the wire, though relatively small. Could be significant in some reference frames.. Would probably need to break the problem out into state space just to see exactly what is happening at any given point in time.

But as a general statement, ohms law should hold up well for each of the 60 cycles per second.

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#### fifty60_4802GND

##### Member
But if course its DC and not AC so there are no cycles. That is my main hesitation as I do not have a ton of experience with low voltage DC motors.

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#### Besoeker3

##### Senior Member
But if course its DC and not AC so there are no cycles. That is my main hesitation as I do not have a ton of experience with low voltage DC motors.

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Well, I have had a lot of industrial experience with DC motors. But mostly these were variable speed systems. In your case your motor would having a starting current of more than ten times. For that we used starting resistors. You have to consider something similar.

#### drcampbell

##### Senior Member
One thing in your favor is that DC motors are not harmed by low voltage with way fixed-speed induction motors are. They just slow down.*

You might want to evaluate the whole situation. If it's not starting reliably, an unloader valve might remedy that by enabling to the motor to start under no load. A (larger) air-storage tank might remedy it by enabling it to start less frequently and cool down more thoroughly between starts.

The inductance/capacitance/transmission-line effects of 150 feet of cable are probably in the sub-microsecond realm while the motor starting event is in the tens or hundreds of milliseconds. (assuming the cable has a velocity factor of 0.5, one microsecond is 150 meters)

* within reason -- this doesn't hold true all the way down to zero rev/min and they might still fail if used at a low speed/high power for long periods of time and rely on a shaft-mounted fan for cooling.

#### petersonra

##### Senior Member
Hello Everyone. If I have an air compressor that runs off of 14VDC, and it is located around 150FT away, should I size my wire for the voltage drop steady state of the air compressor, or for the initial inrush current.

For example, the inrush is 35A, and I decide to use 16AWG copper conductors. Would the compressor be completely starved by the voltage drop across the cable during startup, and not start? Or, is the voltage drop not instantaneous? 14VDC is not much to play with, so I be voltage drop can really be an issue with these if ran over any kind of distance.
You would not "decide" to use a specific conductor size. You would calculate what size the conductors need to be for the motor to work correctly.