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Amplifing Torque and Horsepower

If “Man” can outrun any race horse and can out distance any race horse on a bicycle, is he amplyfing his “manpower” with leverage or “cheating”, since most horses can’t ride bikes, yet?

Man can’t outrun a race horse on level ground or going up a hill- bicycle or not.

A bicycle is simply converting how energy is used and leverage is of course involved when you have gears and levers. If a horse could ride a bike he’d be much faster than a human through sheer “horsepower”.

Not amplifying. More accurately, the bike’s gearing acts like an impedence matching transformer allowing man to actually deliver the power his muscles can make to the load.
For example, If a team of two horses can pull your chariot at 20 mph, how fast can your chariot go if you hitch 100 horses to it? Probably no faster than the slowest horse on the team can run.