First of all, I would like to argue that bent arrows look better, also in the original plot. But since the curve becomes singular at 0, this does not immediately work because of dimension too large errors. However, it does once we approximate the inner-most stretch by an arc.
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,bending}
\begin{document}
\begin{tikzpicture}[scale=2]
\pgfmathsetmacro{\myt}{pi}
\draw[{Latex[bend,length=2pt]}-]
(0: {0.002*\myt*\myt})
arc({0}:{180}:{0.002*\myt*\myt});
\draw plot[domain=pi:25.1327,variable=\t,samples=75,smooth]
({\t r}: {0.002*\t*\t});
\end{tikzpicture}
\end{document}

And here is the original pic with a bent arrow.
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,bending}
\begin{document}
\begin{tikzpicture}
\draw [domain=0:25.1327,variable=\t,smooth,samples=75, -{Latex[bend]}]
plot ({\t r}: {0.002*\t*\t});
\end{tikzpicture}
\end{document}

Note that one should always load bending when one attaches arrows to curved paths, regardless of whether or not one bends the arrows, since otherwise the paths get distorted. Bending cures the distortion even when not explicitly used.
-LatexuseLatex-? however, the result be ugly .... – Zarko Mar 30 '19 at 23:29Latex--and then you will need to have a look at: https://tex.stackexchange.com/questions/176779/how-can-i-improve-the-look-of-an-arrowhead-at-the-end-of-a-small-radius-arc/176781#176781 – hpekristiansen Mar 30 '19 at 23:29