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My only trackday experience has been on bikes, but the bikes I rode tended to be fairly softly sprung and underdamped until very recently.

Even at my weight (130 lbs), I could bottom the forks out easily under braking on both my EX500 and SV650. The spring rates in the forks were 0.55 and 0.67 kg/mm, respectively. I was not able to bottom the forks in a corner, but I came pretty close, maybe 2 inches away. The proper spring rate for my weight is 0.85 for race use, which gives a frequency of about 2 Hz.