Originally Posted by
chaadster
I'm not crispy on the physics, but I don't understand how hill climbing cannot be anything but a series of accelerations, when between each stroke, you not only have rolling resistance slowing you, but also gravity working to pull you back downhill?
Nobody rides at a constant speed. There are variations. So, yes, your acceleration is never 0.
That being said, your acceleration when climbing a hill (particularly if you are spinning instead of mashing) is going to be very small, so that the effect of the wheel weight when climbing will be much closer to a factor of 1 (meaning that the weight of the wheel is as important as weight anywhere else on the bike/rider).
As far as whether or not it is inconsequential, even with a factor of two, 200g of extra wheel weight is as bad as 400g of extra weight on your bike (which is just under 1 lbs). In my case, I ought to lose about 15 lbs myself, so I'm not going to do anything extreme to lose 1lbs of my bike.
Added:
Originally Posted by
chaadster
Maybe I'm understanding this all wrong, but any time you need to apply enough force to the pedals to make the wheel spin faster (regardless of road speed, which may be dropping, as on a hill) , a heavier tire will require more force than a lighter one.
A couple important points here:
1) When accelerating a bicycle, you need to not only accelerate the wheels (both linear and rotational sense), but also accelerate the bicycle and the rider. If you compare the mass of the wheels to that of the bike and the rider, you'll see that the wheels are are very small part of a bigger picture. So, yes, it takes more force to accelerate a heavy tire than a light tire, but not (relatively speaking) a lot more force to accelerate a rider, bike, and a
"heavy" tire compared to the same rider, the same bike, and a
"light" tire.
2) When you are moving at a constant speed, you only need to provide enough power to overcome the frictional forces against you. It will take less energy to keep a heavy but low rolling resistance tire moving than a light but high rolling resistance tire.