VFD versus Sheave Change on an Oversized Constant-Volume AHU
AHU-3 serves 30,000 sq ft of open office on a constant-volume system. The supply fan is belt-driven, 30 hp, 460V three-phase, delivering a measured 20,000 cfm against 6.0 in. w.c. total static. The discharge balancing damper is throttled roughly 35% closed because the floor was subdivided after the original design and the space now needs about 16,000 cfm. Measured motor input at the operating point is 23 kW. The unit runs 6,000 hours per year. Electricity costs $0.19/kWh with a demand charge of $18 per kW-month, and the fan runs through all peak periods. A contractor quotes $28,000 installed for a VFD and pressure-sensor control package and promises a three-year simple payback. A second contractor offers to change sheaves to reduce fan speed mechanically for about $4,500.
1. Estimate the achievable flow reduction and annual savings using the fan affinity laws. State the assumption built into the calculation and explain why it overstates the result here.
Read the worked answer
Flow reduction available. Required flow 16,000 cfm against delivered 20,000 cfm: speed ratio = 16,000 ÷ 20,000 = 0.80. Removing the damper throttle and slowing the fan to 80% speed is the whole opportunity.
Affinity laws: flow ∝ N; pressure ∝ N²; power ∝ N³.
- Power ratio = 0.80³ = 0.512
- Ideal power = 23 kW × 0.512 = 11.8 kW
- Add VFD losses and poorer motor efficiency at part load: use 12.8 kW actual.
- Savings = 23 − 12.8 = 10.2 kW
Annual value:
- Energy: 10.2 kW × 6,000 h = 61,200 kWh × $0.19 = $11,628
- Demand: 10.2 kW × $18 × 12 months = $2,203
- Total ≈ $13,830 per year
- Simple payback = $28,000 ÷ $13,830 = 2.0 years
The assumption that breaks. The cube law assumes a system with no static head - that all pressure falls with speed. A real duct system has a fixed component: filter loading, coil pressure drop, terminal minimums. If the control holds a minimum static of, say, 1.5 in. w.c. of the 6.0 in. w.c., the pressure does not fall as N² and the savings are less than predicted. Apply a 70–80% realization factor: at 75%, savings fall to about $10,370 and payback stretches to 2.7 years. Still inside the contractor's claim, but the claim is only right by luck, not by method.
Also verify the 16,000 cfm requirement with a block-load calculation before spending anything.
2. Which option do you recommend - VFD or sheave change - and under what conditions would you change the answer?
Read the worked answer
The sheave change will show a far better payback on paper. Reducing speed 20% mechanically gives the same 11.8 kW fan power: savings about 11.2 kW, roughly $15,200 per year, against $4,500 installed - a payback under four months. Nothing about the cubic math changes.
So why the VFD is still the better recommendation, and why the exam answer is not the cheap option:
- The 16,000 cfm number is an assumption, not a measurement. It comes from a floor plan, not a load calculation. A sheave change hard-codes that guess into steel. If occupancy, plug loads, or partitioning change again, you re-sheave and re-belt a 30 hp machine on a roof.
- Filter loading. A fixed-speed fan delivering 16,000 cfm on day one delivers less as filters load. A VFD with static-pressure control holds flow and reports it.
- Controllability. The VFD supports unoccupied setback, demand-response curtailment, and a future conversion to VAV. The building has a floor that has already been subdivided once; the trajectory is toward variable volume.
- Two-year payback clears any reasonable hurdle. The marginal $23,500 buys options that are expensive to retrofit later.
I would change the recommendation to the sheave change if: the space is genuinely fixed for the foreseeable future (a data hall, a lab with fixed exhaust), the capital budget is constrained in a year with the mandated projects, and the sheave change is used as a deliberate interim step with the VFD designed and specified anyway.
Never do both at once. If a VFD is coming within two years, do not spend $4,500 re-sheaving.
3. Describe the measurement and verification plan you would require, including the parameters to record and the conditions that would void the predicted savings.
Read the worked answer
Baseline (before any change), minimum one week:
- Fan motor kW at 15-minute intervals, logged, not spot-read.
- Fan airflow (duct traverse or hood) and total static at the same time.
- Damper position, VFD/damper control signal, and filter differential pressure.
- Outdoor air temperature so the baseline can be normalized to like conditions.
Requirements for a valid baseline: the unit must be at full required flow with known filter condition, and the log must be long enough to capture a full occupied/unoccupied cycle and at least one weekend. A one-hour spot reading is not a baseline.
Post-installation verification:
- Prove the airflow: confirm the system delivers the calculated 16,000 cfm at design static, not 13,000 cfm with a happy VFD.
- Log kW at several speed points and plot against the affinity prediction. A fan that draws more than roughly 10% above the predicted curve is usually riding a system curve with unexpected static - check for a closed fire damper, a collapsed flex duct, or a fouled coil.
- Confirm the pressure sensor is located two-thirds of the way down the duct run, not at the fan discharge. A sensor at the fan makes the VFD useless.
- Verify the static-pressure setpoint can actually be reset down, and that the setpoint is at minimum during unoccupied hours.
Conditions that void the predicted savings:
- Minimum static setpoint set high "for safety" by the balancer, which pins the fan near full speed.
- Economizer or fire/smoke damper left partly closed, forcing the fan to run faster for the same flow.
- The unit converted back to constant volume by defeating the pressure control.
- Filters changed to a higher-MERV grade without re-checking fan capacity - the flow guarantee quietly fails.
Require a written report with the logged data attached, and hold back final payment until it is delivered.