All things equal does 200 watts produce the same forward motion no matter how you create it?

Taking variables like road surface and grade out of the equation. With the understanding power in watts is produced by force and pedal speed. So if I spin 100 rpms with the appropriate force to create 200 watts or 65 rpm with appropriate force for 200 watts will my bike move forward at the same speed? If not, which one is faster? Assuming I’d have to shift gears.

This is what happens when you get mindless time on a fat bike in the woods.

100rpm vs 65rpm would produce different drag. If you’re in a different gear, same deal. Different drag. It’d be very small. I’m sure it could be calculated or measured.

If grade and surface are the same, and gearing is adjusted to account for 65 vs 100 rpm, then yes, forward speed is pretty much the same. Other than maybe higher drivetrain losses at higher cadence, which would be small.

200 Watts is a unit of power, which is derived from work/time. Work is basically how much force is required for you to move an object (mass) a specific distance. Hence, the heavier the object, the more force will be required to move the mass some distance.

All things equal, the heavier the object, the more work will be needed to move the object. So for a lighter rider, the 200Watts will mean a faster rider when compared to 200Watts from a heavier rider. I assume this answers your question?

To the second point, if you move 200 watts at 65 rpm vs 200 watts at 100 rpm, the question is where is the watts measured from? If from the hub, drivetrain losses are considered already. However, if its 200 watts from the pedal/crank, drivetrain losses still apply. Therefore, your gearing and optimized chain line would be the determining factor. Hence, the 200 watts at the hub would actually mean maybe 220 watts at the pedal with a poor gear ratio, vs 215 watts with a more optimized chain ratio. Depending on the gear selection (big ring/small cog vs cross chaining) you will see a differential between the two and one will be faster than the other. If 200 watts is read at the hub, it will not matter which RPM you are pushing as the 200 watts is absolute at the hubs, so both move at the same speed. Therefore it depends on where you read the power and your losses between the rider and where the power is measured.

Hope this helps. Also I do not classify myself as “smart” so not sure if you can trust my explanation.

Assuming all variables are the same, then 200 watts is 200 watts regardless of your cadence.The only thing that might come in play is how much force is taking you to produce 200 watts at at 100 vs 60. Is one causing your body to rock side to side more than the other? So mainly which one is causing more drag. But most likely you will gain more speed shaving your legs than than fast or slow cadence