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Figures (1)

Fig. 1
Fig. 1

Determination of the radius of curvature. Note: for O read Θ.

Equations (12)

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tan θ = d / ( R 2 - d 2 ) 1 2
tan 2 θ = A / D 1 ,
R 4 A 2 - 4 R 2 d 2 ( A 2 + d 2 ) + 4 d 4 ( A 2 + D 1 2 ) = 0.
R 2 = 2 d 2 { 1 + ( D 1 + A ) 2 + ( D 1 / A ) 2 [ 1 + ( A / D 1 ) 2 ] 1 2 } .
R 2 = 4 d 2 D 1 2 A 2 ( 1 + 3 A 2 4 D 1 2 - A 4 16 D 1 4 + A 6 32 D 1 6 ) .
R = 2 d D 1 A ( 1 + 3 A 2 8 D 1 2 - 13 A 4 128 D 1 4 + .
R = d / sin θ ,
sin θ = tan θ / ( 1 + tan 2 θ ) 1 2             ident . ,
cos θ = 1 / ( 1 + tan 2 θ ) 1 2             ident . ,
tan θ = ( 1 - cos 2 θ ) / sin 2 θ = [ ( 1 + tan 2 2 θ ) 1 2 - 1 ] / tan 2 θ             ident . ,
tan 2 θ = A / D 1 ,
R = 2 d D 1 A ( 1 + 3 A 2 8 D 1 - 13 A 4 128 D 1 4 + )

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