### The Rear Wheel and Cycling Speed

Given that the front wheel is just “along for the ride,” cycling speed is ultimately determined by how fast the rear wheel is spinning. We know that gearing relates the rear wheel rotation to pedal rotation or equivalently to Cadence. From that, we can compute speed by using the rear tire circumference to tells us the distance covered per minute.  From all of this, we can characterize the possible speeds for each of the possible twenty or thirty gearing configurations.

### Computing Cycle Velocity

We know GearRatio relates rear wheel rotation to pedal cycle. Adding in tire circumference in feet  and cadence, we can get the velocity in mph as follows:

V = GR* Cadence * TireCircumference* 60 minutes * miles/ft

### Triple Chainwheel Cycling Speeds

You have just bought your first road bike. It has three front chainwheels and you are bragging you have thirty different possible speeds. But is that really the case? Does one of my front chainwheels provide my low speeds, another for intermediate, and one for high?

Let’s complete the analysis for a standard road bike with three front chainwheels, 27 inch tires, and a cadence of 75. The diagram below shows clearly we have significant overlap in speeds between the three front chainwheels.

### What you see is not what you get

You clearly get thirty different possible speeds, but a significant number of these speeds are approximately possible on multiple chainwheels. Taking the middle ring, we ask what additional speeds are possible with the other two rings. We see three lower and five higher speeds are possible.

The additional gears extend the speeds possible with the middle chainwheel, but significant overlap, 7 speeds on the small chainwheel and 5 on the large chainwheel.

You still can argue you have thirty speeds, but in terms of range, you only have eighteen.

### Compact Chainwheel Cycling Speeds

So what about a dual chainwheel configuration, also called compact?

Here are the speeds again at a 75 rpm cadence. you see they nearly cover the full range of speeds that a Triple Chainwheel does.

### So which is the right choice?

As you can see from the chainwheel captions, many consider the Triple Chainset a dinosaur. The arguments are the compact provides nearly the same range of speeds and at a lighter weight. They also point out the Compact has fewer duplicated speeds or ones that produce chain rub/cross chaining.

The Triple does have some advantages when climbing but not for Elite cyclists. If a rider is “climbing challenged,” the triple may make sense and the additional weight can be compensated by losing a couple of cyclist pounds.

Of course, the Compact is considered the in-look, and some may choose simply to not advertise they are not an Elite Cyclist.  But as for competitive cyclists where they have already shaved the pounds off , that extra weight is an advantage over long races.

### Understanding Multiple Front Chainwheels

Triple and Compact chainwheels provide a range of speeds but with significant overlapping. So we cannot view them as a continuous stream of speeds from low to a high. Given we tend to shift between them less frequently, another way to view them as three separate cycles, one for climbing, another for flats, and still another for downhills.

### The elephant in the room

You might feel something is missing from here. It is nice to talk about spinning your rear wheel multiple times per pedal cycle, but we have said nothing about the effort required to do so. Clearly, the more times you turn the rear wheel, all other things being constant, the more effort and power expenditure is required. At this point, we will say “hold that thought.”

Next Topic:   Cycle Drivetrains