Originally Posted by
rpenmanparker
Ignoring minor influences and concentrating only on wind it takes the same force to ride 18 mph into a 10 mph headwind as to ride 28 mph with no headwind. But to keep the same cadence at a slower speed you have to gear down. So as the guy who originally brought this up asked, you have same force, same cadence, different gears and also different power because same force but different velocity. He asked would you notice the differences. The answer is only the speed of scenery passing you by and sensation of speed. What are you arguing about?
Eh? Are you forgetting that the drivetrain is a torque converter? You have same force
at the wheel, same cadence, different gears. Because you have different gears, to have the same force
at the wheels, you necessarily have proportionately different force at the pedals. You know you are going 18mph into a 10mph headwind rather than 28mph into still air because you are pushing the pedals less hard.
FWIW, the speed you'd have to be going into a 10mph headwind to equal the power needed to roll 28mph in still air is ~23.5mph. Bonus points for anyone who manages to verify my calculation. Hint: it involves solving a quadratic equation...
(Double bonus points if you can remember the quadratic equation without looking it up. I didn't get double bonus points...
)
EDIT: okay, I should say my calculation only works if you assume drag force is proportional to velocity. It's not (force is proportional to the square), but at bicycling speeds, the error shouldn't be too bad.
EDIT2: if you believe the online cubic equation solver, the real answer is 21.8mph. About 10% error using a linear assumption rather than the quadratic for the force/velocity relationship.