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David_Rombaut8-Gravel
8-Gravel
May 3, 2022
Solved

From set of equations with trigonometric functions to one single equation

  • May 3, 2022
  • 2 replies
  • 2531 views

I have a set of 4 equations which are used to determine the relation between Bèta and Delta_L.

Now I have to generate a list of values for alpha and through x2' and beta + y2' I am able to calculate Delta_L. For any value of Delta_L I then need to interpolate to get to the approximate solution. I would however prefer to have a direct correlation between Delta_L and Bèta without alpha (if possible of course). Thought the symbolic engine might be able to help but to be honest it's been a while since I last used it so I'm stuck.

 

I have attached the formulas in the attached calculation sheet.

 

Any help is kindly appreciated.

 

    Best answer by Werner_E

    So here is the worksheet with the functions made dependable on r and L3 and also using L2=L3+r as you amended

    Werner_E_0-1651655011865.png

     

    2 replies

    T
    21-Topaz II
    terryhendicott21-Topaz II
    21-Topaz II
    May 4, 2022

    Hi,

    Here is my engineering accuracy solution.

    Cheers

    Terry

      D
      David_Rombaut8-GravelAuthor
      8-Gravel
      May 4, 2022

      Hello Terry,

       

      thanks a lot for your solution.

      I did forget to mention that we want to be able to alter "r" as well. Your solution does make it possible to generate a formula for any different value but ideally we would have a plc programmable equation that makes it possible to calculate D_L for any given value of b (within 0 to p/2 range) and r (within 50 to 85 range).

      Like I said before, no idea whether that's even possible or not.

       

      Found out by altering the "r" in your sheet that I had missed another relation: L2=L3+r

      I replaced L2 in all formulas now by L3+r so it's no longer a variable

      W
      Werner_E25-Diamond I
      25-Diamond I
      May 4, 2022

      The symbolic was not of much help in finding a alpha for any given beta.

      Fortunately a  numeric approach using a solve block or the root function is all that is needed.

      Here is DeltaL as a function of beta:

      Werner_E_0-1651653283465.png

      Of course you can make all functions also dependable of the three input values r, L2 and L3 for more flexibility, as Terry had shown in his approach.

       

       

        W
        Werner_E25-Diamond IAnswer
        25-Diamond I
        May 4, 2022

        So here is the worksheet with the functions made dependable on r and L3 and also using L2=L3+r as you amended

        Werner_E_0-1651655011865.png

         

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