Arnold introduced invariants J + , J − and St for generic planar curves. It is known that both J + /2 + St and J − /2 + St are invariants for generic spherical curves. Applying these invariants to underlying curves of knot diagrams, we can obtain lower bounds for the number of Reidemeister moves required for unknotting. J − /2 + St works well to count the minimum number of unmatched RII moves. However, it works only up to a factor of two for RI moves. Let w denote the writhe for a knot diagram. We show that J − /2 + St ± w/2 also gives sharp counts for the number of required RI moves, and demonstrate that it gives a precise estimate for a certain family of diagrams of the unknot with the underlying curve r = 2 + cos(nθ/(n + 1)), (0 ≤ θ ≤ 2(n + 1)π).

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