Curvature is the reciprocal of radius of curvature. Thus, this is a Cesàro equation for the parallel curve of an Euler spiral.
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Expression 7: "k" left parenthesis, "s" , right parenthesis equals StartFraction, 1 Over "r" left parenthesis, "s" , right parenthesis , EndFractionks=1rs
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Here's a simpler formula that's equal to the one given in the Wieleitner paper.
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Expression 9: "k" Subscript, 1 , Baseline left parenthesis, "s" , right parenthesis equals "m" StartFraction, "a" Over StartRoot, 2 "l" cubed , EndRoot , EndFraction StartFraction, 1 Over StartRoot, "s" positive StartNestedFraction, "a" squared NestedOver 2 "l" , EndNestedFraction , EndRoot , EndFraction plus StartFraction, 1 Over "l" , EndFractionk1s=ma2l31s+a22l+1l