The 1963 F1 car would beat a 986 Boxster, and probably quite handily. If nothing else, the power to weight ratio overwhelmingly favors the F1 car. F1 - 200 HP, 1000 lbs = 5 lbs per HP. Boxster S - 250 HP, 2855 lbs = 11.4 lbs per HP. The ratio is less than half for the F1 car, so every time the F1 car accelerates, it is going to blow away the Boxster.
If you factor in the braking and cornering advantages of the F1 car (even on old tech tires), then the gap grows even greater.
The only street Porsche that could probably give the F1 car a run for it's money on the track would be the 918. Sorry, but our puny 986's just can't do it.
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