**By Jon Johnson**

“*The Force is strong with this one*.” — Darth Vader

Unless you’ve died and gone to bike heaven–where all the rides are downhill, the wind is always at your back, and beer is a high performance sports drink–the Force is decidedly *not *with you. On a bike, the only force that is with you is *you*. All other forces are against you.

To use the term of art, they are “opposing forces.” The term comes from the world of bicycle science—there is, in fact, such a world, the bible of which is aptly titled “Bicycle Science”—and it refers to a model that bike geeks have built and improved over the years. The model describes those forces acting on a bike that suck up the power we generate. There aren’t that many of them, and most will be familiar to anyone has spent any time on two wheels thinking about such things, specifically:

- Aerodynamic drag
- Potential energy—essentially climbing and descending
- Kinetic energy—most pertinent to acceleration and deceleration
- Rolling resistance—tires against pavement
- Drive train friction—chain, bottom bracket, pedal spindles, etc.
- Wheel bearing friction

How much, and when, each of these opposing forces matter depends on a several variables, including obvious things like how fast you’re going, rider and bike weight, climbing grade, position on the bike, and the like.

In fact, the mathematical model has 18 variables, which when combined make for an impressively long and daunting equation. Because this is a family friendly blog, I’ve promised Rob I’d keep the hard core geek stuff—equations and tables and graphs and suchlike—to a minimum, but for those adults who are interested, you can see the full model at **http://ovto.net**. (Fair warning, there is a little math, but it’s pretty soft core—multiplication with a few exponents and little trig thrown in. No differential equations.)

Playing with the model a little reveals that for most road bikes, three of the forces dominate the others: aerodynamic drag, potential energy, and kinetic energy. While rolling resistance and drive train friction aren’t trivial, they don’t play a particularly large role, and beyond oiling your chain and riding on good tires, there’s not much you can do about them anyway. When functioning properly, wheel bearing friction is truly trivial.

There is a lot to say about each of the remaining forces, so much so that we’ll focus in on each separately in future posts. Of these, acceleration is the least intuitive. You probably can’t easily describe how quickly you can accelerate. Before writing this, I couldn’t. (Turns out when starting at 25 miles/hour, I can accelerate about 1.5 miles/hour/second, which is confusing in its own right.) It’s also more complex to model than the other forces, so I’m just going to punt on the details to a future post. Let’s just say that acceleration is what happens when all of the other forces are accounted for—excess energy makes the bike go faster—and that it is expensive to generate meaningful differences in speed. It takes a lot more energy, usually generated anaerobically, to get just a little farther up the road in the same time. It therefore makes sense to spend it wisely. More on this later.

How important is aerodynamic drag? It depends on how fast you’re going, as the graph below demonstrates. (Sorry, couldn’t resist.) The graph shows how much power, measured in watts, is required to overcome the different opposing forces to maintain different speeds. When riding on flats at a steady speed—when potential and kinetic energy are zero—aerodynamic resistance is huge, or at least it quickly becomes so. For example, to maintain a steady 25 mph, you need to work against about 2 watts of wheel bearing friction (it’s barely visible in the graph), 7 watts of drive train friction, 28 watts worth of rolling resistance, and 269 watts of aerodynamic drag. And it gets worse as you go faster: It takes about seven times more power to go 30 mph than to go 15 mph, mostly due to aerodynamic drag.

The single best thing you can do to reduce aerodynamic drag is to go slow, but since this is pretty much exactly *not *the point, racers look for other ways to reduce this resistance. Drafting is the most obvious—it can reduce total resistance up to 30% or more—and it adds many other tactical considerations that we’ll explore later. If you look at the aerodynamic equation over on the ovto site, you’ll see two other variables that everything gets multiplied by: the coefficient of drag (C_{d}, essentially how streamlined you are) and frontal area (A, the size of the hole you’d leave if you rode through a wall in a Bugs Bunny cartoon). Reducing either of these by even a small fraction can pay off big when riding at speed. I’ll have more to say about this soon, but in the meantime it’s worth thinking about ways to get smaller (from the front) and slipperier.

Climbing is another obviously important force to anyone who has ever been on a bike. Less obvious is how quickly it becomes important, which is pretty quick. The graph below shows the proportion of power that goes to offsetting that different forces on different grades. On a 0% grade (flats), the vast majority goes to aerodynamic resistance (purple area), but potential energy (orange) grows very quickly as you begin to climb. For instance, for a 150 pound rider putting 300W of power into a bike on just a 2% grade, the power going to offset gravity is roughly equal to aerodynamic drag. The reason is a little complex but goes something like this: as you ride up hill the bike slows, which reduces aerodynamic resistance; as grade increases, the bike eventually slows to a point where aerodynamic drag equals the power required to fight gravity, and as grade gets even steeper, gravity begins to dominate. At 300W, the grade where aerodynamic drag and gravity are equal is about 2%. There is still plenty of aerodynamic drag at 2%, so drafting and aerodynamics still matter, but by the time you get to about 6 or 7%, it’s really mostly about gravity. (Unless you’re riding into the wind. More, later.)

On climbs, everyone knows that weight is also important. To show how important, and on what grades, I get to show one more graph, then I’m done. The graph below charts the power necessary to travel 15 mph for riders from 100 to 220 pounds on nine different grades, from 0% to 16%. To start, look at the bottom line, a 0% grade. It shows that, all other things equal, there is virtually no difference in required power between a 100 pound and a 220 pound rider to go 15 mph on flats. Actually, all things aren’t equal—larger cyclists have larger frontal areas—but because big riders can typically generate considerably more absolute power than small riders, they usually have an advantage over small riders on the flats, even factoring in their larger frontal areas.

This all changes on hills. As the figure shows, by the time you get to a 16% grade, the 220 pounder has to generate almost twice as much power as the 100 pounder to get up the hill at 15 mph, which would be *really fast* on a 16% grade. The steeper it gets, the more relative power the heavier rider needs.

This is obviously good news for lighter riders, right? Only sort of. It is good news *only if* smaller riders can generate more power per pound—or watts/kg in standard bike geek lingo—than larger riders. If a larger rider’s added weight goes to generating proportionally more productive power, he or she can get up a hill just fine. When it comes to fighting gravity, riders with the same watts/kg will get up the hill equally fast, *and* larger riders with their larger absolute power advantage will go faster on the flats. Given this, the focus quickly shifts to “productive mass”—which would not include things like fat, bike and kit, or muscle mass that doesn’t contribute to energy going into the pedals—and the degree to which watts/kg varies with mass. (Again, more on this later.)

The upshot from the opposing forces model? Aerodynamic drag dominates on the flats. Everything else takes a back seat till you start to climb or accelerate. Gravity, or potential energy, quickly takes over on hills, especially as you go beyond about 5%. When climbing, mass matters, but what really matters is the power you can generate in proportion to your weight—it’s all about watts/kg. And finally, acceleration (and deceleration), which is what happens after all the other forces are dealt with, will suck up as much energy as you can create, but it comes at a high cost, and it should be spent wisely.

We’ll explore these topics individually in future posts before looking at them in combination, with an eye to tactical and strategic implications.

For more from Jon please click on this link **http://ovto.net.**

*Jon is utterly fascinated with aerodynamics & racing strategy. He is a billy goat on the bike and a professor at the University of Arkansas off the bike. – OCA *

Very cool post. So, as a lightweight rider, if my biggest weakness seems to be hanging on on the flats (absolute power), then I’m much better off with an aero bike than super light bike (which would only slightly increase my watts/kg)?

Looking forward to the future posts on the individual variables.

You raise a good point. Lately I have really started to buy in on the aero craze. I originally thought it was just the bike industry reinventing itself to sell more stuff. But the numbers don’t lie. When you think about it the climbs we have around here aren’t long enough to justify an ultralight setup. Because on a race course a climb is only a small portion of the course. Unless it’s an uphill finish which is pretty rare around here as well. Keep the aero bike!

Generally speaking, you want to be as aero as possible, especially if you’re light to begin with. This is a long-standing debate, but because we spend relatively little of our time on pitches shallower than 5%, and because aerodynamic drag eats up so much power, it’s usually worth a few ounces to get more aero. (See also http://www.cervelo.com/en/engineering/thinking-and-processes/weight-vs-aero.html.) That said, light and aero is the best of both worlds.

No doubt someone is going to mention the superior handling and responsiveness and other performance characteristics of lighter bikes, to which I have no mathematically grounded response. As a Cannondale Supersix Evo rider myself, I should add that I like the lightness, and other factors matter, too.