From set of equations with trigonometric functions to one single equation

[David_Rombaut]

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.

[terryhendicott]

Hi,

Here is my engineering accuracy solution.

Cheers

Terry

[David_Rombaut]

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

[Werner_E]

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:

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.

[Werner_E · Accepted solution]

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