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How to Use the Bilinear Interpolation Calculator

This article demonstrates the Bilinear Interpolation Calculator. Click here to learn more about our methodology.


You can access all calculators on the HVAC Calculators page or the ^^ drop-down menu above. The calculators are listed alphabetically by category.


Most of our calculators give the option to select metric or English units. For this calculator, as long as you stay consistent with units, you can use any units.


Example: 

Suppose you want to calculate the Total Cooling Capacity of a 5-ton Bryant® package unit. A snippet of the equipment's performance data table at design conditions is provided.  For our scenario, the design conditions are: 

  • Condenser Entering Air Temperature:  79oF

  • Evaporator Entering Wet Bulb Temperature: 65oF

Solution:

This problem will be solved three times.  Solution 1 will be to perform linear interpolation three times using Steps 1, 2, and 3 as described in the methodology sectionSolution 2 will use the combined bilinear interpolation equation shown in Step 4 of the methodology section. Solution 3 will show how to use the calculator to quickly and accurately obtain the results.

For all solutions, the following inputs are below as provided in the table or given values:

P11 = 55.04 MBtuh

P12 = 59.00 MBtuh

P21 = 52.59 MBtuh

P22 = 56.34 MBtuh

x1 = 75oF

x2 = 85oF

y1 = 63oF

y2 = 67oF

x = 79oF

y = 65oF

Solution 1: 

Step 1: Interpolate  around point (x,y1)

R(x,y1)  = P11(x2-x)/(x2-x1) + P21(x-x1)/(x2-x1)

= 55.04 (85-79)/(85-75) + 52.59 (79-75)/(85-75)

= 54.06 MBtuh

Step 2: Interpolate around point (x,y2)

R(x,y2)  = P12(x2-x)/(x2-x1) + P22(x-x1)/(x2-x1)

= 59.00(85-79)/(85-75) + 56.34(79-75)/(85-75)

=57.936 MBtuh

Step 3 Perform a linear interpolation at point (x,y) using the results from Step 1 and Step 2:

R(x,y) = R(x,y1)(y2-y)/(y2-y1) + R(x,y2)(y-y1)/(y2-y1)

= 54.06(67-65)/(67-63) + 57.936(65-63)/(67-63)

=55.998 MBtuh

Solution 2:

The bilinear interpolation as a single equation as shown above: 

R(x,y) =  P11(x2-x)(y2-y)/((x2-x1)(y2-y1)) + P21(x-x1)(y2-y)/((x2-x1)(y2-y1)) +  P12(x2-x)(y-y1)/((x2-x1)(y2-y1)) + P22(x-x1)(y-y1)/((x2-x1)(y2-y1)) 

R(x,y)=55.04(85-79)(67-65)/((85-75)(67-63))+52.59(79-75)(67-65)/((85-75)(67-63))+59.00(85-79)(65-63)/((85-75)(67-63))+56.34(79-75)(65-63)/((85-75)(67-63)) 

    =55.998 MBtuh

 

Solution 3: To Solve using the calculator, enter the inputs in the same order they appear in the table.  Below is a table showing the inputs.  The result is shown in red in the middle of the table as 55.998MBtuh.

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