A Lesson in Aerodynamics

In this post, we are going to talk about one of the primary principles of physics that governs how people ride their bicycles on planet earth. If you have a strong aversion to simple math, then you might consider skipping this section. But if you want to know more about the main strategy behind smart biking, or even how to improve the gas mileage of your car, then read on.

Let’s start with the topic of racing. If you know anything about bike racing, you know that big races, like the Tour de France, are a team sport. Most of the time, the team rallies behind one racer (their strongest) and they all work together to help that racer win. How do they do this? Well, there is a lot of strategy involved, almost like a chess match, but there is also one basic physics principle that makes teamwork preferable to racing as an individual. Nick, the physics major that he is, insists on explaining this to you. Hope it makes sense.

Wind: What a Drag!

The reason, in a word, is wind. We have both touted and complained about wind to you on this trip, and it turns out that wind is paramount in the world of biking. Specifically, we are talking about wind resistance, or drag, as it is called in physics. This is the force of wind that pushes against you as you move, and it can happen in two ways: the wind is blowing naturally, or you start moving yourself and create your own wind. In the latter case, it is important to point out, the wind you create always blows against you, and it gets stronger that faster you go. (Boo.)

So drag gets stronger when the wind gets stronger. That seems obvious, so what’s the big deal? If you just bike harder, you’ll go faster and get there quicker, so doesn’t it all just even out? Unfortunately, the answer is no. Drag does depend on your velocity (speed), but not in the way you might think. It turns out that the force of drag increases as the square of your velocity. Let’s freak you out a little more by throwing in the formula, and then we’ll break it down.

F = (k) x (v^2)

F is the force of drag.
K is a just a number and it changes depending on things like your shape, size, the fluid you are flowing in (in our case, the fluid is air), etc.
V stands for velocity
^2 means squared, normally a little number 2 up above, but we couldn’t type that (v^2 = v x v, just like 2^2 = 2 x 2)

It is exactly that square that causes all the trouble. That means at lower velocities, the drag isn’t so bad, but at higher velocities, the force against you starts getting huge, and making headway becomes more and more difficult. Let’s calculate F with some easy numbers to make it real.

Ok, easy numbers…for all of these examples, let’s say k = 1.

Now let’s do a low velocity example. Let’s say your velocity is 3, v = 3. Plugging in the numbers,

F = 1 x 3^2 = 1 x 3 x 3 = 9.

We’re leaving units (like mph, for example) aside right now, but the number 9 is a measure of how hard the force of wind resistance is pushing against you. Savvy?

Now let’s say you want to increase your velocity by 2 units, from 3 to 5. What do you think will happen to the force? Will it increase by 2 also? Let’s plug in and see.

F = 1 x 5^2 = 1 x 5 x 5 = 25.

An increase of 2 in velocity made for an increase of 16 in force. Bummer dude! But if that’s not bad enough, let’s try an example at a slightly higher velocity. Let’s say you want to increase your velocity by 2 again, this time from 10 to 12. Plugging in 10,

F = 1 x 10^2 = 1 x 10 x 10 = 100.

Plugging in 12,

F = 1 x 12^2 = 1 x 12 x 12 = 144.

At this speed, increasing your velocity by 2 means the drag increases by 44. Major bummer!

What are the real world implications of this? Well, the first one you’ll find relevant has to do with driving your car. Did your parents ever tell you that driving at 55 mph gets you better gas mileage than driving 80 mph? Did you think that maybe it was just a self-serving ploy to get you to slow down? Well, for you speed demons out there, sad to say it’s true. The amount of extra energy you expend with that 25 mph increase is huge.

The real world implications for us bikers are significant too. The obvious one is that fighting the wind is a pain, and if the wind isn’t going your way, it can mean the difference between 1 day to get somewhere and 3. This makes planning almost impossible for the cycling tourist.

Fighting Your Own Wind

But even on a windless day, bikers routinely move fast enough to create their own wind, so there are lessons to be learned.

The first is that pedaling your heart out to get from 25 to 27 mph is a waste of energy! You are better off pedaling your heart out up the hills, where the wind you are facing is less, and then coasting down them. Dominic’s grandfather was a strong believer in this strategy, and won the Classics Division of the Tour of the Gila (a 4-day stage race in our homebase of Silver City, NM) doing just that. Pedal up, coast down.

Lance Armstrong may or may not like the wind, but it is the reason he routinely won the Tour de France and other stage races that involve many days of racing. In racing, there are two types of racers—climbers and sprinters. They use different sets of muscles that work at the expense of each other. So good climbers make poor sprinters and vice-versa. On the flat stages, the riders stay in a pack, and then at the end, the sprinters make a break and pedal like the dickens. This is where you see those dramatic finishes where bikes are flailing all over the place and they lunge forward at the last second to best their opponent by a few milliseconds.

The mountains are where the climbers shine, albeit at a slower speed. As we now know, slower means less wind resistance. So with little wind resistance, the strong climbers maintain a small advantage in speed, and after several hours it begins to add up. The racers who fell behind try to make it up on the downhills or the flat ground, but alas! As we have already seen, fighting the wind for an extra 2 mph at high speeds is a lost cause, even if you are a superb sprinter. The sprinter may have bested the climber by a few seconds in the flat stage the day before, but in the mountains, multiple-minute or even multiple-hour leads are established, and it’s the overall time that wins the race. Any guesses what kind of racer Lance Armstrong is? That’s right, he’s a climber.

So why do sprinters even bother racing? Well, there is some chance for glory. Each day (or stage) is a mini race unto itself, and on days when the course is mostly flat, sprinters get a chance to show their prowess for speed and win that day’s race. There’s glory in that alone, but if you’re really good, you might just win more stages than the overall winner. Ironically, it is actually possible for a cyclist to win the entire race without winning the most stages, or even one stage, for that matter. Seems unfair, but not any more so than the electoral college.

Wiiiiiiiiind, Keep Us Together

The other reason that cyclists other than climbers still participate in the race has to do with another physics principle—drafting. This is where you hug tight to the rider in front of you and use him or her as a wind block. This makes riding a lot easier for the rider behind. Oftentimes, racers will work together and rotate out, each taking a turn fighting the wind at a hard pace while the other one hangs on behind and rests. This eventually turned into a team game, so that nowadays teams will work together to help “pull” their strongest rider along on flat ground and downhill (where wind is the strongest). When all the teams are racing, they hoard together in what’s called a peloton (French for “pack”). This is the big group of riders you see in photos, and riders take turns pushing the pace at the front and then dropping back when they get tired to let someone else take over. It’s hard to quantify just how much faster or more efficient this technique is, but let’s just say that pro riders often average 30 mph or above, while on our best day, we averaged 18 or 19. It’s an all-out blitz all day and they friggin’ fly!

The strategy for racing gets complicated from here on out, but usually a group of riders will make a break and try to leave the peloton behind. If you do it right, your rider or your team will be in this breakaway, and if your timing is just right, you might just make it all the way before you get caught. Easier said than done, for the peloton is a force to be reckoned with.

Our Wind Strategy

We are a far cry from elite racers, but we too have been trying to use physics to our advantage. On the uphills, we ride however we like. But on downhills, flats (few of those so far), and windy days, we form a line and take turns pulling each other along.

You’d be surprised, but this makes a huge difference. On hills, we form a tight line and the person in front pedals hard, “pulling” the other two along. With this windbreak, the riders in back end up braking more than they do pedaling. They focus on staying tight (sometimes within a few inches of the wheel in front) and watching and listening for visual and verbal commands from the leader, swerving around potholes and feathering the brakes just the right amount. The front rider does this till he or she gets tired, falls off the side, and the other two bump up in the rotation. Onward we go!

We are generally pretty low key about our riding, but on days when we face an onslaught of wind or need to cover a lot of ground, this strategy is critical, and it saves us lots of energy.

We’ll do a post later about riding as a team, but for now, hope you enjoyed the physics lesson!