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The 3 Fan Laws and Fan Curve Charts
This article was written by Tim De Stasio with Southern Comfort Consulting and Service. It was originally published on his blog, which you can access by clicking THIS link, but he permitted us to republish it on HVAC School as well. Thanks, Tim!
It is critical for an HVAC technician to understand airflow and how blowers and fans perform under various conditions. These relationships are expressed in the three fan laws, which are mathematical formulas. While designers must use these laws in a quantitative way when sizing and selecting equipment and ductwork, a service technician should also understand them in a qualitative way—as in how changing fan speed or static pressure affects airflow and horsepower.
Fan Law 1: CFM is directly proportional to RPM.
Formula: CFM2 = CFM1 X (RPM2 ÷ RPM1) or RPM2 = RPM1 X (CFM2 ÷ CFM1)
What it means: As you increase fan RPM, CFM increases at a 1:1 ratio. So if you need to increase CFM by 10%, your RPM has to increase by 10%. Since it is a 1:1 ratio, we can interchange RPM for CFM in Fan Laws 2 and 3. We use Fan Law 1 all the time in the field. If we need to change the airflow, we change fan speed by changing a speed tap, VFD output, pulley diameter, or other means.
Apply it in the field: If your blower is moving 1000 CFM at 1100 RPM, and you need to decrease airflow by 10% to 900 CFM, Fan Law 1 says your RPM must decrease by 10% also. Let’s put that in the formula:
RPM2 = RPM1 X (CFM2 ÷ CFM1)
RPM2 = 1100 X ( 900 ÷ 1000)
RPM2 = 990 This is your new RPM.
We also need to understand that for us to make predictions using this fan law and fan laws 2 and 3, everything else about the air and the system needs to stay the same, including air temperature and density. System friction must also stay constant, so these fan laws cannot be used with automatic dampers that self-adjust to maintain flow.
Fan Law 2: Total Static Pressure changes with the square of CFM (or RPM).
Formula: SP2 = SP1 X (CFM2 ÷ CFM1)² or SP2 = SP1 X (RPM2 ÷ RPM1)²
What it means: A 10% increase in CFM will result in a 21% increase in static pressure. Think about that. A small increase in airflow creates a significant increase in duct pressure. This increased pressure will be evenly distributed across components like coils and filters. So, this fan law can be applied to total static pressure or a static pressure drop across a single component in the system. That matters because some components have static pressure limitations that affect their performance. Air filters work best when they have a low-pressure drop across them. This usually means the air velocity is low enough to allow for “dwell time” through the filter material, catching more particulates. Condensate traps that are already close to their limit may have to be made deeper so that they don’t get overwhelmed. Air proving switches must be adjusted so that they do their job at the new CFM and static pressure.
Apply it in the field: At 1000 CFM, you read a 0.9″w.c. pressure drop across a media filter. You need to increase your airflow to 1200 CFM. What will be the new pressure drop?
SP2 = SP1 X (CFM2 ÷ CFM1)²
SP2 = 0.9 X (1200 ÷ 1000)²
SP2 = 1.3″ w.c.
This new pressure drop will probably be too high, according to most filter manufacturer specs that recommend less than 1″. It will perform like a dirty filter, even when brand new. The filter surface area now has to be increased. Using Fan Law 2 to predict static pressure will prevent you from creating unintended consequences by increasing airflow on a system that is already close to its limit.
Fan Law 3: Horsepower changes with the cube of CFM (or RPM)
Formula: HP2 = HP1 X (CFM2 ÷ CFM1)³
What it means: A 10% increase in airflow results in a 33% increase in horsepower required to do that work. If your motor is already close to its rated HP, a small airflow increase can overload it. Let’s demonstrate that.
Apply it in the field: At 1000 CFM, your blower draws 1.5A. You need to know how much HP it is using now and what your new HP will be when you increase airflow to 1200 CFM. Use an amps-to-hp conversion tool to calculate HP1 in the Fan Law Formula. You’ll have to know—or make an educated guess— what the motor efficiency and power factor are. As you can see below, HP1 is 0.206 HP.
Now, what happens to HP2 when we increase the airflow from 1000 to 1200 CFM?
HP2 = HP1 X (CFM2 ÷ CFM1)³
HP2 = 0.206 X (1200 ÷ 1000)³
HP2 = 0.355. This is your new HP requirement. What happens if your motor is only a 1/3 HP (0.333)? Your motor will be overloaded and will not last long. You’ll need to step up to a 1/2 HP motor. Wouldn’t that be good to know before proposing the airflow change?
Fan Curve Charts
Manufacturers test their equipment under a variety of conditions and plot fan performance on a “Fan Curve Chart.” This is useful for predicting how the performance changes as other variables change.
Fan curve charts look different from manufacturer to manufacturer. Most look like a graph shown below. The curve represents a constant RPM for a specific model. Plot a horizontal line starting at the static pressure axis until it intersects with the curve. Then plot another line straight down to the CFM axis. This is the CFM at those conditions.
Some manufacturers add a brake horsepower (BHP) curve to this chart to show how much power is required to do the work we are asking the fan to do at a given RPM and SP. This intersection is called the operating point. When a BHP curve is added, we can determine the horsepower required by plotting a vertical line up from our operating point to intersect with the BHP curve.
Using the 3 Fan Laws with a Fan Curve Chart
The manufacturer will always provide a “system line” representing the path the fan has to stay on as conditions around it change. Any point plotted on the chart must be along the system line. Once an operating point can be plotted on a fan curve chart at a known RPM, we can now use the 3 fan laws to predict what will happen if RPM or SP changes. CFM and horsepower will change with RPM and SP changes.
Refer to the fan curve above; let’s assume the RPM curve is for 1000 RPM. Assume the CFM units are X1000. Let’s also assume that the static pressure units are inches w.c. Let’s pretend, at the given operating point, this fan moves 6500 CFM at 4″ w.c. The required BHP is 6.9. What if we want 6000 CFM instead?
What will our new RPM be?
Fan Law 1: RPM2 = RPM1 X (CFM2 ÷ CFM1)
RPM2 = 1000 X (6000 ÷ 6500)
RPM2 = 923. The fan has to be slowed down to this RPM to get the desired CFM.
What will our new SP be?
Fan Law 2: SP2 = SP1 X (CFM2 ÷ CFM1)²
SP2 = 4 X (6000 ÷ 6500)²
SP2 = 3.4″ w.c.
What is our new HP required?
Fan Law 3: HP2 = HP1 X (CFM2 ÷ CFM1)³
HP2 = 6.9 X (6000 ÷ 6500)³
HP2 = 5.4
Selecting Equipment Using Fan Curve Charts
Manufacturers provide performance specifications to allow designers to select the right fan for their system. In residential design, we size the duct friction based on the fan performance of the air handler we have pre-selected based on the tonnage our load calculation calls for. But in commercial design, we size the fan based on the friction of the duct system we have already designed. In either case, we must consult the manufacturer’s fan performance data to verify the fan is a good match for the load.
Exercise: Select the better exhaust fan for our commercial application. 1000 CFM @0.5″ w.c. We have 2 choices: Greenheck Model SQ-130-B or a smaller model SQ-100-VG.
Both models will do the job. Notice the larger model SQ-130-B operates at a lower RPM (1140) compared to SQ-100-VG (1521). Lower RPM will usually mean quieter operation. If noise is a concern, you may decide to select the larger fan. But the smaller model requires less BHP (less wattage to run) and no doubt costs less. So, if initial cost and operating cost are a priority, you would select the smaller SQ-100-VG.
Notice, also, the shaded grey area. This is the unstable area where the fan does not run fast enough to move the air predictably. This is the stall and surge effect.
Most manufacturers now utilize selection software that automatically plots the design conditions you enter into the fan curve chart, giving more accuracy. But it is still important to be able to read a fan curve chart.
Ultimately, a service technician should understand the three fan laws to be more accurate when making airflow adjustments. Commercial technicians, especially ones that commission and balance equipment, should read fan curve charts so they can take the guesswork out of making adjustments or find potential design flaws. Even if you are not in those sectors of the industry, having this knowledge will always enable you to be a better technician.
—Tim De Stasio
Southern Comfort Consulting and Service