Fan laws and how to apply them

The fan laws, also called fan affinity laws, describe how a fan's airflow, pressure and power change when its speed, size or the density of the air changes. They are among the most used tools in HVAC: for predicting the effect of a sheave change, estimating savings from a variable frequency drive, correcting for altitude or adjusting a system during balancing.

They are also frequently misapplied. The laws are exact only for geometrically similar fans operating at the same point of rating on a fixed system curve. Real systems often violate those conditions. This guide explains the laws, shows how to use them and highlights where they break down.

The basic fan laws

For a given fan operating on a fixed system (same ductwork, same damper positions), with constant air density:

In words:

• Airflow varies directly with speed.
• Pressure varies with the square of speed.
• Power varies with the cube of speed.

A 20% speed reduction gives 80% of the airflow, 64% of the pressure and about 51% of the power. That cube relationship is why variable speed fans save so much energy.

Applying the laws: worked examples

Example 1: increasing airflow during balancing

A supply fan delivers 4,000 L/s (about 8,480 cfm) at 900 rpm, against 500 Pa (2.0 in. w.c.) of total static pressure, using 3.0 kW at the shaft. The balancer finds the system needs 4,400 L/s, a 10% increase.

1. New speed: 900 x (4,400 / 4,000) = 990 rpm.
2. New pressure: 500 x (990 / 900)^2 = about 605 Pa.
3. New power: 3.0 x (990 / 900)^3 = about 4.0 kW.

A 10% airflow increase requires about 33% more power. Before changing sheaves, check that the motor has enough capacity, that the fan is within its maximum safe speed, and that the new operating point is in a stable region of the fan curve.

Example 2: estimating VFD savings

A fan runs at reduced speed for much of the year. At 70% speed, ideal power is 0.7^3, or about 34% of full-speed power. In practice, VAV systems maintain a minimum duct static pressure, so the system curve does not pass through zero, and savings are smaller than this ideal figure. Motor and drive efficiencies also fall at low loads.

Example 3: density correction

A fan selected at standard air density is installed in Calgary, where density is about 88% of sea level. At the same speed, it moves the same volume of air, develops about 88% of the static pressure and uses about 88% of the power. See air density, altitude and HVAC design in Calgary and the Rockies.

The system curve

The fan laws assume the fan stays at the same relative point on its curve as speed changes. That is true when the system curve follows the square law: pressure proportional to airflow squared, passing through zero pressure at zero flow. Fixed ductwork with no control devices behaves this way.

The operating point is where the fan curve crosses the system curve. Changing speed shifts the fan curve; changing dampers or filters shifts the system curve. See fan selection, curves, efficiency and system effect.

Where the fan laws break down

Systems with a fixed pressure component

VAV systems control the fan to hold a duct static pressure setpoint. The system curve therefore has a fixed pressure offset: even at low flow, the fan must produce at least the setpoint pressure. As speed falls, the fan moves along a different path from the simple square-law curve, and actual power savings are less than the cube law predicts.

The lower the static pressure setpoint, the closer the system gets to cube-law savings. That is the reason static pressure reset is so valuable; see static pressure reset with trim and respond.

Changing system resistance

Filters load up, dampers move and coils foul. Each changes the system curve. The fan laws predict performance on one curve only, so field measurements are needed after significant changes.

Fan efficiency changes

The power law assumes fan efficiency is constant. When the operating point moves away from the fan's peak efficiency, actual power differs from predictions.

Motor and drive efficiency

Motors and VFDs lose efficiency at low loads. Shaft power may follow the cube law approximately, but electrical input power falls more slowly.

Diameter laws need similar fans

The diameter laws apply only to geometrically similar fans, such as the same model family scaled up or down. They do not apply to trimming a wheel or comparing different fan designs.

Using the fan laws in the field

The fan laws are essential during testing, adjusting and balancing:

1. Measure actual airflow, fan speed, static pressures and motor current or power.
2. Compare actual airflow with design.
3. Use the speed law to calculate the speed needed to reach design airflow.
4. Use the pressure and power laws to check that the new point is within motor and fan limits.
5. Change speed by VFD setting or sheave change.
6. Re-measure and confirm, since the laws are a prediction, not a guarantee.

Recording these steps in the TAB report gives owners a clear record of fan capability and margin. See air balancing procedures and instruments.

Fan laws and energy strategy

The cube relationship drives much of HVAC energy strategy:

• Reducing airflow, even slightly, saves disproportionate fan energy.
• Lowering system pressure drop through larger ducts, cleaner filters and fewer fittings reduces required fan speed.
• Variable speed operation outperforms damper or inlet vane control, which reduce flow by adding resistance.
• Oversized fans throttled by dampers waste energy that a properly sized or speed-controlled fan would save.

For more on these strategies, see reducing fan energy.

Frequently asked questions

Does halving fan speed cut power by 87.5%?

Ideally, power falls to one-eighth, a reduction of 87.5%. In real VAV systems with a minimum static pressure and declining motor and drive efficiencies, the actual reduction is smaller.

Do the fan laws apply to pumps?

Yes. The pump affinity laws have the same form: flow with speed, head with speed squared and power with speed cubed. The same limitations apply when systems have a fixed pressure component.

Can I use the fan laws to compare two different fans?

Only if they are geometrically similar. For different designs, compare manufacturer performance data at the actual operating point.

Key takeaways

• Airflow varies with speed, pressure with speed squared and power with speed cubed.
• Small airflow changes cause large power changes.
• Air density affects pressure and power but not volumetric flow at a given speed.
• Real VAV systems save less than the cube law predicts because of fixed pressure setpoints.
• Use the laws to predict, then measure to confirm.