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VFD Frequency and Fan Law Calculator

Run the VFD Frequency and Fan Law Calculator MicroSim Fullscreen

This p5.js sketch is built on the shared FanPedia MicroSim kit. To run it in the p5.js editor, add the kit files (fanpedia-sim.css, fanpedia-core.js, fanpedia-p5.js and fan-models.js from ../shared-libs/, or their published URLs) to the editor's index.html before pasting the sketch.

About This MicroSim

A variable frequency drive (VFD) changes the supply frequency, and with it the motor's synchronous speed and the fan speed. On a fixed system the fan laws then set the new airflow, pressure and power, with the frequency ratio as the speed ratio. This MicroSim uses the base duty of the chapter's worked example (illustrative values): 10,000 CFM at 2.00 in. wg static pressure, 8.0 bhp, on 60 Hz power with a 4-pole motor.

The model, with r = f / 60:

  • Synchronous speed = 120 × f / 4 RPM
  • Airflow = 10,000 × r CFM
  • Static pressure = 2.00 × r² in. wg
  • Brake horsepower = 8.0 × r³ bhp

It ignores motor slip, drive losses and any fixed system pressure. Frequencies above 60 Hz are not offered: running a fan above 60 Hz starts with checking its maximum safe speed in the current catalog.

# Frequency Airflow Static pressure Brake horsepower
1 45 Hz 7,500 CFM 1.13 in. wg 3.38 bhp
2 30 Hz 5,000 CFM 0.50 in. wg 1.00 bhp
3 50 Hz 8,333 CFM 1.39 in. wg 4.63 bhp

For each challenge you type all three values and press Check. All three are checked together, and each must be within ±2% of the unrounded model value. Each box gets ✓ (solid green border) or ✗ (dashed red border). You have two attempts. A wrong first attempt shows the challenge's hint (the ratio and its square and cube); after a second wrong attempt the model values and the worked calculation are shown and the challenge counts as missed. The running line reads "Challenges correct: n of 3"; mastery is all three challenges (all nine values) correct within two attempts.

After challenge 3, Explore mode unlocks the frequency slider (20 to 60 Hz). Every value in the readout updates at once, each with its percent of the 60 Hz value, and a plot shows percent airflow (r), pressure (r²) and power (r³) against frequency. Explore mode is never scored.

How to Use

  1. Read the challenge ("The drive is turned down to 45 Hz. What will the fan deliver, and what will it draw?") and the base duty in the readout.
  2. Type the airflow (CFM), static pressure (in. wg) and brake horsepower (bhp) in the three boxes and press Check (or Enter).
  3. Read the verdict and the marks beside each box. With an attempt left, fix the values marked ✗ and check again.
  4. Press Next challenge (or Enter). After challenge 3, press Start exploring.
  5. In Explore mode, move the frequency slider. At 30 Hz, notice that airflow is still 50% while power is 12.5%.
  6. Start over clears the score and returns to challenge 1.

Keyboard: Tab moves between the boxes and buttons; Enter checks, then goes to the next challenge; in Explore mode the arrow keys move the focused slider one hertz at a time.

Data label: "Illustrative values · Base duty 10,000 CFM, 2.00 in. wg, 8.0 bhp at 60 Hz · 4-pole motor", shown at the bottom left of the drawing.

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

<iframe src="https://moroshek.github.io/FanTASTIC-textbook/sims/ch15-vfd-fan-law-calculator/main.html"
        height="662px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Learning Objective

The learner will calculate the airflow, static pressure and brake horsepower of a belt-driven fan at a reduced VFD frequency, using the fan laws with the frequency ratio as the speed ratio, to within 2% of the model values (Bloom: Apply, verb: calculate).

Audience

Adult professional development: new application engineers, sales staff, representatives and facilities staff.

Duration

10-15 minutes

Prerequisites

  • Synchronous motor speed, poles and frequency (Chapter 15, "Synchronous Motor Speed")
  • Variable frequency drive (Chapter 15, "Variable Frequency Drive")
  • Airflow (CFM), static pressure (in. wg) and brake horsepower
  • The fan laws (Chapter 25)

Activities

  1. Challenges (7 min): Work the three frequencies on paper first, then type and check. Write down r, r² and r³ for each.
  2. Review (2 min): For any miss, compare your numbers with the worked calculation and name the step that went wrong.
  3. Explore (4 min): Move the slider from 60 Hz down to 20 Hz. Find the frequency where power falls to about half (about 48 Hz) and compare the airflow there.

Common Misconceptions Addressed

  • Power falls in the same proportion as frequency. At 45 Hz power is 42% of full, not 75%; the hint after a wrong attempt gives the cube, and the plot shows the r³ curve far below the r line.
  • Pressure is unchanged by a speed change. The pressure box is checked against 2.00 × r², and the plot shows the r² curve.
  • The VFD changes the motor's poles or the sheave ratio. The formula card states that only f changes; the synchronous speed in the readout follows 120 × f / 4 with the same 4 poles.

Assessment

  • The running line reads "Challenges correct: n of 3"; mastery is all three challenges correct within two attempts, and the summary in Explore mode says whether it was reached.
  • Follow-up question: an owner wants to cut a fan's airflow by 20% overnight. What frequency should the drive run at, and what fraction of full power will the fan draw?

References

  1. FanPedia: The Fan & Blower Encyclopedia (PDF) - Twin City Fan & Blower; p. 71 (synchronous speeds by poles and frequency) and p. 170 (the VFD as a way to change fan performance in the field).
  2. FanPedia online - Twin City Fan & Blower's online version of the encyclopedia.
  3. Chapter 15: Motor Ratings, Speed Control and Positioners - the sections "Synchronous Motor Speed" and "Variable Frequency Drive", with the 45 Hz worked example.
  4. Chapter 25: Fan Laws, System Effect and Sound - the fan laws in full.
  5. Variable-frequency drive (Wikipedia) - background on how a VFD sets motor speed.