Fan Laws Reference
The three fan affinity laws — the physics that ties a fan’s speed to its airflow, static pressure, and horsepower. Change the speed and airflow follows in direct proportion, pressure by the square, and power by the cube. They hold for a fixed fan at constant air density, and they explain why VFDs save so dramatically on fan energy.
The three fan laws
| Quantity | Relation to speed | Example |
|---|---|---|
| Airflow (CFM) | CFM₂ / CFM₁ = RPM₂ / RPM₁ | −10% RPM → −10% CFM |
| Static pressure (SP) | SP₂ / SP₁ = (RPM₂ / RPM₁)² | −10% RPM → ~−19% SP |
| Brake horsepower (BHP) | BHP₂ / BHP₁ = (RPM₂ / RPM₁)³ | +10% RPM → ~+33% BHP |
Why the exponents matter
The three laws share one input — the ratio of new speed to old — raised to the first, second, and third power. That escalation is the whole story. Airflow tracks speed one-for-one, so if you need 10% more air you turn the fan up 10%. But static pressure rises with the square, so that same 10% costs you about 21% more pressure — which the ductwork and the motor have to absorb. And horsepower rises with the cube, so the motor draws about 33% more power. Speeding a fan up is never "free air"; it is bought with disproportionately more pressure and power.
Run the same logic in reverse and you get the energy-savings case for variable speed. Trimming a fan to 80% speed gives 80% of the air for barely half the power — the reason a CFM reduction via a VFD pays back so quickly, and why oversized constant-speed fans throttled with dampers waste so much. Check the static pressure against the new operating point whenever you change speed.
Common questions
What are the three fan laws?
They relate a fan’s speed to its performance. Law 1: airflow (CFM) is directly proportional to speed — raise the RPM 10% and airflow rises 10%. Law 2: static pressure is proportional to speed squared — 10% more RPM is about 21% more pressure. Law 3: brake horsepower is proportional to speed cubed — 10% more RPM is about 33% more power. They apply to a fixed fan at constant air density.
Why does slowing a fan save so much energy?
Because power follows the cube of speed. Slowing a fan to 80% of its speed cuts airflow to 80% but drops the power draw to 0.8³ = 51% — roughly half the energy for 80% of the air. That cubic relationship is the entire reason variable-frequency drives (VFDs) save so much on fan and pump motors: a small speed reduction yields an outsized power saving. For example, a 5 BHP fan slowed to 80% speed draws about 2.6 BHP.
How do I find the new airflow after a pulley or speed change?
Use the ratio of the new speed to the old. A fan moving 4,000 CFM at 900 RPM, sped up to 1,000 RPM, moves 4,000 × (1000/900) = 4444 CFM — but the static pressure jumps to the square of that ratio and the horsepower to the cube, so always check that the motor and ductwork can handle the new pressure and power before increasing speed.
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