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Least-Squares fitting of King's Equation

  1. Oct 2, 2007 #1
    1. The problem statement, all variables and given/known data
    A hot wire is placed in a region of mass air flow. There is a current on the wire causing it (wire) to heat up. The current is regulated such that the wire temperature is constant.

    Measurement of current on the wire is related to the mass airflow by King's Equation.

    The goal is to perform a least-squares solution of measured data in order to determine coefficients of Kings equation.

    2. Relevant equations

    King's Equation: output = a + b * flow ^c

    with a, b, and c coefficients to be determined.

    3. The attempt at a solution

    Solve equation using linear least-squares. Problem is the flow raised to the "c" coefficient. Linearization of the equation *may* be the answer? Otherwise using something like Levenberg-Marquardt's non-linear method?
  2. jcsd
  3. Oct 4, 2007 #2


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    Homework Helper

    Yep, it's a non-linear problem. Solution method depends on how many data points you have. If it is 3, then you could solve using linearization (Newton Raphson perhaps, see link in my footer). But if you have a least squares situation (i.e n > 3), then non-linear least squares using Levenberg-Marquardt would be perfectly applicable (also see link in my footer).:smile:
  4. Oct 4, 2007 #3
    Thanks for the feedback and confirmation!

    BTW - what software package did you use to generate the 2-page tutorials? They look excellent!!!

    - Bruce
  5. Oct 4, 2007 #4


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    Homework Helper

    Thanks! I used Excel, Powerpoint, and a bit-map capture utility.
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