Kolmogorov vs RH40 spending rule

I think I might've done this before but since I spent the last week going overboard looking at the Kolmogorov equation I thought I'd go retro and look at RH40 again and put it up against a "solve for withdrawal rate given a fixed risk" version of the K equation.

In one corner: RH40 = withdrawal rate at age n = [age / (40 - age/3)]  (black)

In the other corner: Kolmogorov partial differential equation. Age varies per chart, wealth = $1, mode = 90, dispersion around mode = 9,  m = .04, s = .10, spend rate is solved for fail probability = .05.[1]  (red)

Some minor difference but otherwise this lines up pretty well.  The biggest divergence is at ages where it may not really matter.  For a dumb rule of thumb RH40 works ok. This mainly shows that: 1) using age to drive expectations about longevity probability (whether explicitly in equations or simulation or by proxy in a rule of thumb) as well as to adjust spending can be a pretty powerful part of the analysis and is also why the 4% rule always tripped on its own simplicity, 2) the RH40 formula is very conservative, which was the point when I created it in the first place, and 3) if you can't do a finite-differences-approximation solution to a differential equation in your head, having a simple rule of thumb doesn't hurt...if you need it, which is the other reason I created it.  

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[1] return and standard deviation are basically from a 60/40 allocation mutual fund with mean arithmetic return of around .08 but then ding-ed for inflation, fees etc.  The mode and dispersion are conservative and more or less comport with the Society of Actuaries table for annuitants for a certain age...though not exactly.