How this instrument works
This instrument runs the mixed-air blend equation backwards. The ordinary version predicts a mixed-air temperature from a known damper position; here the target mixed-air temperature is the known quantity and the outside-air fraction is what's missing, so the algebra is rearranged to solve for f instead: f = (T_ret − T_target) ⁄ (T_ret − T_out) × 100. A building automation system running an economizer sequence performs this same inversion continuously, because a supply-air setpoint is fixed by the mechanical design while outdoor conditions — and the damper position needed to meet that setpoint — drift all day.
The numerator, T_ret − T_target, measures how far the setpoint sits below the return stream; the denominator, T_ret − T_out, is the full spread available to blend across. Their ratio is simply how far along that spread the target falls, written as a percentage of the total distance from return toward outside. That is also why the two source readings must differ: if T_ret equals T_out there is no spread to divide by, no damper position can move the blended reading at all, and the equation is undefined rather than merely large.
The output only means something physical between 0% and 100%. A figure above 100 says the setpoint is colder than the outside stream itself, a temperature no amount of extra outside air can reach — the cooling coil has to close the remaining gap. A figure below 0 says the setpoint sits above the return reading, which calls for heating rather than blending. Real economizer sequences clamp the computed fraction between a configured minimum, kept open for ventilation, and 100% fully open, handing anything past those limits to the mechanical coil.
- Enter the return-side reading into Return air temperature, °F — air already inside the building, on its way back to the unit.
- Enter the current outdoor reading into Outside air temperature, °F, taken at the intake louver.
- Set Target mixed air temperature, °F to the setpoint you want the blended stream to reach before the coil.
- Read Required outside-air damper fraction, % — the damper opening needed to produce that setpoint from the two source readings.
- A result outside 0–100% means blending alone cannot reach the setpoint; mechanical heating or cooling has to make up the rest.
Worked example — sizing the damper for a 65°F setpoint
A rooftop unit's controller carries a fixed 65°F mixed-air setpoint in its economizer sequence. This morning the return sensor reads 72°F and the outside sensor reads 35°F. Solving f = (72 − 65) ⁄ (72 − 35) × 100 = 7 ⁄ 37 × 100 = 18.9189189189% tells the controller exactly how far to drive the damper: about 18.9% open, letting in just enough of the colder outside stream to pull the warmer return air down to the 65°F the downstream coil is sized around.
That figure is not a one-time answer; the controller re-solves it every scan cycle, since the outdoor reading drifts through the morning while the setpoint stays fixed. If the outdoor sensor later climbs to 40°F, the same algebra gives f = (72 − 65) ⁄ (72 − 40) × 100 ≈ 21.9% — a wider damper opening needed to reach the identical 65°F target from a milder outside stream, exactly the adjustment an economizer loop makes in real time as conditions change.
Questions
Why solve for a percentage instead of the usual mixed-air temperature?
Because in many control sequences the mixed-air setpoint is the fixed design target and the damper position is the unknown a controller has to compute. This instrument inverts the ordinary blend equation — normally solved for temperature given a known damper position — to solve instead for the position given a known temperature target, which is the direction an economizer control loop actually runs.
What does a required percentage above 100% mean?
It means the target mixed-air temperature is colder than the outside stream itself, so no damper position — not even fully open — reaches it. The remaining gap has to be closed by the cooling coil; a result over 100 is a flag that the setpoint sits outside what blending alone can deliver on that day.
Why must the return and outside air readings be different?
Because the denominator, T_ret − T_out, is the entire span the damper has to blend across. If the two readings are equal, that span is zero, the division is undefined, and no damper position changes the outcome at all — mixing a stream with itself never shifts its temperature, regardless of the setting.
Can the required percentage come out negative?
Yes, when the setpoint is placed above the return air reading. Blending in air that is colder than the return stream can only pull the mixture down, never above the return temperature, so a target set higher is unreachable by damper position alone and calls for heating instead — the negative figure flags that mismatch rather than a calculation error.
Who actually runs this calculation in practice?
Controls technicians commissioning a rooftop unit's economizer sequence, checking that the damper actuator drives to the position the building automation system computed for a given setpoint. Engineers writing a sequence of operations for a new install use the same inversion to confirm the damper's mechanical range can reach the design target across the site's expected outdoor swing.
How does this differ from the standard mixed-air temperature calculator?
The standard version takes a known damper position and the two source readings and computes the resulting mixed-air temperature — the forward direction. This one runs the same relationship in reverse: given the mixed-air temperature you want and the two source readings, it solves for the damper position required to produce it, the question a setpoint-driven control loop actually needs answered.