The September issue of the Journal of Financial Planning has an article on how market cycles influence the SWR.
Market Cycles and Safe Withdrawal Rates
The article talks about secular bull & bear cycles that typically last around 30 years. He goes on to show that the returns during these cycles deviate significantly from the mean. He also says that it is impossible to correctly state where we are currently in a secular cycle, but points to metrics like P/E to give us clues.
Finally, he uses a 100% S&P portfolio to illustrate the different SWRs that a bear-bull-bear sequence, a bull-bear-bull, and a start midway in a sequence would produce.
I found most of it pretty obvious and would prefer to use FireCalc or the studies by the likes of Bengen than try to finesse an SWR based on a guess of where we are in a secular market cycle.
Please note that he uses "capital" returns of the S&P 500 for a lot of his calculations. That is, he does not include dividends in the return numbers. I didn't catch that at first and couldn't quite understand why he was using a 4.8% cumulative return for the S&P from 1881 to 2000.