A post appeared on Facebook. The post stipulated the following conditions:

1) Bike A has a total weight of frame and wheels of x (let's say, 15 pounds).

2) Bike B also has the same total weight of frame and wheels of 15 pounds, but the wheel set of bike B has lighter rims, say ½ pound lighter.

Both bikes are being pedaled up a hill. The post claimed that the lighter wheel is easier to pedal up hill. How does the iBike account for that?

The answer is: lighter rims can be beneficial whenever the bike's speed is changing (i.e. the bike is accelerating).

**However, a constant bike speed, whether on the hills or on the flats, bike A and bike B perform identically.**

Power is defined as Force x Speed. From Newton's law, F = m*a, where m is the total mass of bike, rider, wheels, etc, and a is the total acceleration of the bike (includes bike changing its speed, and gravitational acceleration on hills).

The instantaneous power required to

*linearly*accelerate a mass m is p = m*a*v, where "a" is total acceleration (this would be both bike acceleration and acceleration due to hill slope), m is the total mass of the bike (including the wheels), and v is the speed of the bike in the direction of travel.

However, on bikes there is also

*rotational acceleration*of the wheels that enters into things: it also takes power to change the speed (accelerate) the bike's wheels. How much? It depends on starting bike (linear) speed, bike acceleration rate, rim weight, rim size, and more.

Suffice it to say, it's complicated. But whenever the bike is not accelerating, rotational acceleration is zero, so rim weight makes no difference.

In situations where the rider is accelerating rapidly (say, in a crit), then slamming on the brakes to slow down to avoid crashing into the rider ahead, there's no doubt but that lighter rims are better. But on hills? The answer is not obvious...In fact, in an article written by Lennard Zinn in VeloNews, he has this to say about heavy rims on hills:

"The bike always has to accelerate at least once to get up to speed, and that will take more energy to do if the added mass is at the rim than if it has instead been added to the frame. One question is whether the extra energy required for this initial acceleration is trivial and can be ignored or not. After that, even if the rider speeds up and slows down the same way on each bike without using the brakes, it will not matter where the extra weight is located, at least in the “ideal, frictionless universe” used in elementary physics calculations of motion.

**If the rider stops pedaling, even on a climb, he will be carried further up the hill by the flywheel effect of the heavier rims than he will be on the bike with weight added to the frame. Then when he starts pedaling again, he will end up at the same point in the same amount of time on either bike.**

*This is the principle that Ondrej Sosenka depended upon when he set the hour record with heavy rims; he reasoned that the heavy rims would carry him along and keep the speed more constant as he went through periods of weakness and strength. It seemed to work for him; I’m not going to argue with that result*." (Italics added)

Read more at http://velonews.competitor.com/2012/06/ ... UVRB5U8.99