As we’ve discussed previously, most induction motors rely on ambient air to dissipate those efficiency losses converted to heat. In accordance with NEMA’s MG1 standard, manufacturers typically design their motors assuming air density at or near sea level — enabling successful operation at nominal rating up to 1000 meters (3280 feet).

But, at higher altitudes, the air gets thinner — reducing an air-cooled motor’s ability to dissipate the heat it generates. Depending on your motor’s elevation above sea level, its ambient temperature, and its particular temperature rise characteristics, you may need to derate the motor to prevent it from exceeding the maximum temperature for its insulation class rating.

**Flying high**

A motor’s ability to cool itself varies proportionately with the coolant’s heat-transfer capacity — which, in the case of air-cooled motors, varies proportionately with the density and temperature of the air.

Air density is a function of elevation and air temperature, with density decreasing as elevation and temperature increase:

In the MG1, NEMA offers users a rule-of-thumb: to derate motors by 3% per 500 meters (1640 feet) of elevation above 1000 meters (3280 feet). I’ve also heard a recommendation that motor temperature rise increases 1% per 100 feet. Many manufacturers provide a table like the one below, based upon these rules of thumb, and generally assuming Class F insulation. Note that motors operating in a low-elevation environment below 40°C (105°F) may receive a slight reprieve:

This rule-of-thumb provides a decent approximation of how air density changes compared to an elevation of 1000 meters and ambient temperature of 40°C.

But what happens when your environment falls outside the range offered in this table? For example, let’s say we’re specifying a motor to operate at the visitor’s center at Mauna Kea, Hawaii — 4,210 meters above sea level. The motor is in a conditioned, 22°C (72°F) environment.

To determine whether you need to derate this motor due to elevation, first determine the density of air of at your altitude and temperature; then, divide the air density at your environment by the density of air at NEMA’s reference environment (an elevation of 1000 meters and at a temperature of 40°C) — a process that I’ve reduced to just two variables in Equation 8, below:

From here on out, we’ll call this ratio, “δρ” (delta-rho).

Next, we’ll adjust our known or assumed temperature rise to our elevated environment:

For our Mauna Kea motor, rho equals 0.70. Let’s assume that we’re using the same one-horsepower motor that we previously conducted a heat run test on, which we know it has a 73.8°C temperature rise at 40°C. Applying Equation 4 from last week, we see that if this motor were located at or below 1000 meters, we would expect a temperature rise of 69°C in a 22°C environment. However, applying Equation 9, we determine that this motor will see a (73.8°C / 0.70) 105.4°C temperature rise and thus will operate at 127.5°C in this 4,210-meter-high, 22°C environment — simply because the motor cannot cool itself as well at this altitude.

Finally, we’ll determine whether our expected operating temperature exceeds the maximum for the motor’s insulation class; and, if so, the amount of derating required. An operating temperature of 127.5°C falls well below the 155°C maximum for this Mauna Kea motor’s Class F insulation. So, in this case, we do not need to derate the motor.

But, if the motor had only Class A insulation, with a maximum operating temperature of 105°C, we would need to restrict the motor’s temperature rise to (105°C – 22°C) 83°C. We modify last week’s Equation 3 to account for the motor’s current elevation and ambient temperature by dividing the temperature rise at 40°C by δρ:

For our Hawaiian one-horsepower motor, dividing the temperature rise at 40°C by δρ means that we’re effectively dividing our desired temperature rise in our current environment — 83°C — by our expected temperature rise in our current environ — 105.4°C. In net, this shows our one-horsepower, insulation-class-A motor can provide only (1 Hp × [83°C / 105.4°C]^{2}) 0.62 horsepower on a continuous basis at this elevation and temperature without burning itself up.

Alternately — if you need 100% of your horses — work with a local shop to retrofit an air-cooled motor for high-elevation operation by replacing the factory cooling fan with a higher-volume model. Or, if buying a new motor, go up to a higher insulation class: like the difference between our Class A and Class F Mauna Kea motors, a higher insulation class will enable your motor to operate hotter, offsetting the loss in cooling ability without losing life.

How does the equation change when the motor pumps a hot fluid? To find out, email Nicole at info@motorsatwork.com, or tune in next week.