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5 inches MINIMUM.
With the RAA Ch85 750 Cruzer we simulated the worst case scenario as flat tire and 2 big guys setting in the plane. We are using the Viking spring. Really worst case would let the suspension collapse to the stop ring. We are flying off a grass strip and are using tundra tires so actual clearance is not relevant to your case. I believe FAA/CARS (in Canada) has some sort of minimum.
Confirmed that we had 11” of clearance A/C empty, inflated front tire, normal compression on spring w 0200
This is from the FARs:
14 CFR 23.925 - Propeller clearance. (a)Ground clearance. There must be a clearance of at least seven inches (for each airplane with nose wheel landing gear) or nine inches (for each airplane with tail wheel landing gear) between each propeller and the ground with the landing gear statically deflected and in the level, normal takeoff, or taxing attitude, whichever is most critical.