• Category Archives: Magic Numbers

A Ton of Air

I enjoy playing with numbers to gain insight into things that we often take for granted. There are many ballpark numbers that just about every HVAC tech has memorized, some more accurate than others. One very common ballpark number is airflow of 400 CFM per ton. One problem with this ballpark number is that it does not account for the required specific heat ratio for a particular application. But that is not what I want to talk about today. That airflow rate, 400 CFM per ton, is within the operating parameters of most HVAC equipment, even if it is not the most effective for a particular application.

What I want to show is how much work is involved in moving 400 CFM of air. At the ASHRAE “A” indoor condition of 80°F 50% relative humidity, a pound of air takes up about 13.6 cubic feet. Dividing 400 CFM by 13.6 tells us how many pounds of air the blower is moving each minute: 400/13.6 = 29.4 pounds per minute. Multiplying that times 60 tells us how many pounds of air the blower is moving per hour: 29.4 x 60 = 1764.7 pounds of air per hour. Recalling that a ton of weight is 2000 pounds, an airflow of 400 CFM is nearly a literal ton of air per hour! To get exactly a ton we would need to move 453.3 CFM: 453.3 / 13.6 = 33.3 33.3 x 60 = 2000 pounds per hour. But of course that 400, or 453 is just the airflow per ton of cooling capacity, not the total airflow. So a 2 ton system moving 800 CFM would be moving 3529 pounds per hour. If that same system were moving 906 CFM, it would be moving 4000 pounds of air an hour. That is a lot of weight to push around.

Think of the total external static pressure as the hill up which the blower must move all that weight. It becomes obvious that if the hill is higher, the blower will have to work harder. Think of the external static pressure a blower must operate against as the hill up which it must move all that weight. Forward curved centrifugal blowers lose capacity against higher external static pressures. Just as water pumps move less water if you make them move the water higher, centrifugal blowers move less air against higher static pressure.

In the case of constant airflow ECM motors, the blower motor puts in the work to overcome the loss of blower wheel efficiency to move all that weight up the steeper hill. In the case of constant torque electronic motors, while the motor gives a steady output, the blower wheel still loses efficiency. There is a decrease in the amount of air the blower can move. In the case of PSC motors, not only does the blower wheel lose efficiency, but the motor also loses capacity. The airflow drop can be drastic. So give the poor blower a break. Use air filters with low pressure drop and keep them clean. After all, the blower IS doing a ton of work! Check out my book, Fundamentals of HVACR published by Pearson if you would like to investigate further.

Magic Number 2652 Explained

Testing a capacitor under load means testing it while it is in an operating circuit. To do this you measure the operating capacitor amp draw and voltage and then apply them to the formula

Why does this work and where does the 2652 come from? To answer these questions, we need to understand what a capacitor does in an AC motor circuit.

What Does a Capacitor Do?

A run capacitor’s job is to add enough capacitive reactance to offset the inductive reactance of the winding it is in series with. Current in an inductive (magnetic) load lags the voltage. This means that the current peaks AFTER the voltage. Since the current and voltage are out of phase with each other, they don’t work together, causing inefficiency. Adding a capacitor in series with an inductive (magnetic) load helps correct this because capacitors cause the current to peak BEFORE the voltage. The amount of capacitive reactance needed depends upon the inductive reactance of the motor.

Like resistance, capacitive reactance is measured in ohms. The capacitive reactance produced by a particular capacitor varies with both the frequency of the AC current and the microfarad capacity of the capacitor. Higher frequencies and higher microfarad capacity both decrease capacitive reactance. The formula is

 This means that capacitive reactance is equal to the inverse of the product of 2 x pi x frequency x Farad rating. Through the magic of algebra we know that we can swap the XC (capacitive reactance) and C (capacitance) terms to get our formula for capacitance. That gives us the formula

 This can be rewritten as  

In this formula, 2π is a mathematical expression for a cycle. Recalling that the circumference of a circle is twice the radius times π, the expression 2π represents a complete turn of a circle if we are not concerned with the circle’s radius. Frequency is represented by f, which is always 60 cycles in North America. Together, 1/2πf calculates the effect of frequency on capacitive reactance.

works out to 0.00265258 for 60 cycle power. This would produce an answer in Farads, but we normally work with microfarads. Multiplying this by 1000 to get 2652.58 produces an answer in microfarads. This is usually rounded to 2652.

What about the capacitive reactance, XC? Remember that capacitive reactance is measured in ohms and that ohms can be found by dividing volts by amps. So we can substitute the capacitor voltage divided by the capacitor amps for the capacitive reactance. However, since 1/XC is the inverse of capacitive reactance, the fraction is flipped to perform the multiplication, placing amps on top. Together the two terms become

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