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c grid generation naca aerofoil by fletcher

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Old   September 5, 2016, 06:23
Default c grid generation naca aerofoil by fletcher
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Peter Müller
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I want to implement a code to generate a c-grid around the naca aerofoil. So i read some threads in this forum and found the book computational techniques for fluid dynamics by Fletcher and his FORTRAN code. In principle he describes the procedure in his book.

But there is one initialization I don't understand. He is integrating the integral for arc length

P { margin-bottom: 0.21cm; } RA = ∫0XA √(1+(y')2) dx

numerically using the formula describing the naca profile

P { margin-bottom: 0.21cm; } y = t(a1 x1/2 + a2 x+ a3x2 + a4 x3 + a5 x4)

He starts the code with the initialization

RA(2) = 0.5*PI*XA(2)

This is an initialization so he has to derive this expression by an analytical consideration. How can I manipulate the above formulas to derive this expression? I found no explanation in his book or anywhere else.
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