Fan Sheave Change for a Target CFM
The inverse fan-affinity-laws cannot do - it needs both speeds. Target airflow sets the ratio, and with the fan sheave fixed the required DRIVE sheave scales the same way. The point is the cube law landing on the motor: 8,000 to 9,600 cfm is a 4.0-in sheave going to 4.8 in, 700 rpm to 840 - and 3.0 bhp to 5.18, which OVERLOADS a 5 hp motor at only 20% more air. That is the most common way a well-meant airflow fix cooks a motor.
Formula and source
ratio = target CFM / current CFM; required fan rpm = current rpm x ratio; on a belt drive fan rpm = motor rpm x (drive sheave / driven sheave), so with the fan sheave fixed the new drive sheave = current drive sheave x ratio; SP scales with ratio^2 and BHP with ratio^3.
Fan affinity laws (AMCA / ASHRAE Handbook - Fundamentals) solved for the drive sheave rather than for a known speed, combined with the belt-drive speed ratio.
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