The article by Tanaka describes a rapid and accurate method for the determination of contact pressure in the Hertz elliptical contact problem, without the need to use tables or graphs such as those given by Harris or Johnson in the original author’s Refs. 2 and 3. Tanaka avoids the elliptic integral and proposes a numerical integration (Eqs. 7 and 8).

Readers may not be aware of another—much earlier—rapid and accurate method which was proposed by the late Alan Dyson. In Dyson’s method the ellipse axial ratio, $a/b$ is determined directly from the integral equation, (Tanaka’s Ref. 3):
$AB=a/b2Ee−KeEe−Ke$
(1)
where $e=1−b2/a21/2$ and E and K are complete elliptic integrals. The other required quantities, such as $p0$ and δ then follow...
1.
Dyson
,
A.
,
Evans
,
H. P.
, and
Snidle
,
R. W.
,
1989
, “
Wildhaber-Novikov Circular Arc Gears: Some Properties of Relevance to Their Design
,”
Proc. R. Soc. London, Ser. A
,
425
, Appendices A2 and A3, pp.
360
361
.