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Fan laws: the math behind every VFD energy savings claim
The fan affinity laws are not estimates or approximations — they are derived from fluid mechanics and are accurate for centrifugal fans operating within their normal performance range. The cube relationship between speed and power is the entire basis for variable frequency drive energy savings in HVAC. A commercial air handling unit fan running at 75% of design speed uses only 42% of full-load power (0.75³ = 0.422). Scaled up to a 30 HP fan running 6,000 hours per year in Toronto at $0.13/kWh, this saves $6,400 per year compared to running at full speed with a damper.
When the fan laws apply
The fan affinity laws apply to centrifugal fans (forward-curved, backward-curved, and airfoil blade types) operating on the same duct system with no changes to air density. They do not apply to axial fans at high speed ratios, or to any fan system where the duct system resistance changes significantly. In a VAV system where duct pressure is controlled, the fan does not operate on a fixed system curve — a more complex analysis using the fan's actual performance curve is needed. Use the static pressure calculator to characterize your system curve before applying fan laws.
Impeller trim vs. speed change
Trimming the impeller diameter (cutting the fan wheel to a smaller diameter) permanently reduces fan performance — useful when an installed fan is over-sized and noisy at full speed. The same affinity laws apply with diameter ratio replacing speed ratio. A 5% impeller trim reduces power by 14% and CFM by 5%. Unlike VFD speed reduction, impeller trim is irreversible, so always calculate first before cutting.
Frequently Asked Questions
The fan laws predict that halving speed gives exactly half the CFM — that is the Law 1 relationship. The reason you might observe a different result in practice is that the fan is now operating at a different point on its performance curve. If the system pressure curve is steep (high friction), the fan at half speed may be delivering significantly less than half the design CFM because the system resistance at that lower flow point is a larger fraction of the available pressure. In a real VAV system, the controller compensates by maintaining duct static pressure setpoint, which means speed doesn't follow a simple 1:1 relationship with airflow. The fan laws give accurate predictions only when the system resistance curve remains unchanged.
Yes, with caution. If you know the existing fan's performance and want to predict what a fan with a different impeller size or different speed motor will deliver, the fan laws give a good first approximation. However, fan performance also depends on blade geometry, inlet conditions, and volute design. Two fans from different manufacturers with the same impeller diameter and speed will not necessarily deliver identical performance. Use the fan laws to narrow your selection, then verify against the replacement fan's published performance curve at your operating point. The available static pressure calculator gives you the operating point to match.