Equal-load chiller staging crossover calculator

Compare one machine carrying all load with two identical machines sharing it equally, within the observed curve range. The second fixed input is offset by smaller combined quadratic loading.

Units

L_{\text{cross}} = \sqrt{\frac{2 \times b}{a}}

Calculator

Enter the values you know and leave one box empty. Calculate finds the empty one, the result or any input.

Worked example

Given

$b$ = 22 kW
$a$ = 0.00055 kW/ton²

L_{\text{cross}} = \sqrt{\frac{2 \times 22}{0.00055}} \approx 282.8

Symbols and units

Symbol	Meaning	Unit
$L_{\text{cross}}$	total cooling load at equal input	ton
$b$	fixed input of each operating chiller	kW
$a$	quadratic part-load coefficient	kW/ton²

Symbol	Meaning	Unit
$L_{\text{cross}}$	total cooling load at equal input	kW cooling
$b$	fixed input of each operating chiller	kW
$a$	quadratic part-load coefficient	kW/(kW cooling)²

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Results are estimates for study and screening. Check the inputs, units and assumptions before you use them for design, billing or contract decisions.