Ride Like the Wind, the Mathematical Version

Wind blown palm trees are always the sign of a hard ride.

My old nemesis, the wind was in true form today, blowing at 16 to 17 mph with gusts in the mid to high 20’s. While riding headlong into the wind, I was wondering just how much more energy was needed to maintain my headway. Sure I was cheating the wind as much as possible, riding in full drops and maintaining an aerodynamic position, but it still felt as if I was riding with my brakes on.

Every cyclist who has ever pedaled into a stiff headwind knows about wind resistance. Needless to say, it’s exhausting! In order to move forward, the cyclist must push through the mass of air in front of him. This takes energy. Aerodynmaic efficiency enables a cyclist to travel much faster, with less effort. But the faster the cyclist goes, the more wind resistance he experiences, and the more energy he must exert to overcome it. When competitive cyclists aim to reach high speeds, they focus not only on greater power, which has its human limitations, but also on greater aerodynamic efficiency.

The energy a cyclists expends is measured in Watts. A Watt is a measure of power similar to horsepower, where 1 Watt=0.00134 horsepower. A completely inexperienced rider, for long periods of time, can output 50 or 100 watts of leg power; whereas a Tour de France racer is said to be able to generate 500 watts or more of continuous power!

Basically there are three forces we have to overcome while cycling. Friction, Air resistance and Gravity.

Friction. At low speeds and on flat surfaces and with no wind, the only resistance that counts comes from friction. Friction goes up proportionally to speed and to total weight. If you have ever ridden on a stationery bicycle that uses a frictional brake, you know that the total effort required goes up proportionally to speed. Of the three forces, friction requires the least amount of energy expenditure.

Air Resistance. Air is a “fluid”, so to speak, though a thin one. When you move through a fluid faster, it puts up much more resistance. For example, while swimming, it requires little effort to move your hand slowly through the water, but when you try to move it quickly, much more force is required. The same is true in the air. At a few miles per hour, (assuming no wind), you barely feel air resistance, but at 15 miles per hour, it pushes strongly against you. The resistance of fluids goes up with the square of the velocity, and the faster one goes the more air resistance one encounters. Thus a 10% increase in speed requires a 33% increase in power, and a 25% increase in speed requires almost a doubling of power.

So, suppose you want to go 25% faster? You need to put out almost double the power! At 12 miles per hour, about half of your total power is used in overcoming friction, and about one-half to air resistance. To go 25% faster you need to increase your power by about 61%. At 20 mph, four-fifths of your total power is already spent overcoming air resistance. To go 25% faster, you need to increase your total power by 83%.

For those number geeks out there, here is the formula: W_to_overcome_air_resistance = Cair x (V + Vwind)^2 x V.

If there is no wind, it is simply: Cair x V^3.

Cair ranges from perhaps 0.8 for a city bike or a hybrid, to 0.7 for a mountain bike, to as low as 0.36 for full racing position on a conventional racing bike.

Thus, a rider using a hybrid or the upright position on a racing bike, traveling at 11 mph, will need to expend 56 watts to overcome air resistance. In racing position on a racing bike (down in the drops), the rider need to expend only 45 watts. A rider using a mountain bike may need to expend almost 90 watts to go the same speed.

Gravity. While climbing steeper hills gravity becomes important, and air resistance becomes unimportant. It is easy to see why: On the way up slopes, gravity greatly reduces speed, and at low speeds, air resistance is insignificant. The faster you go, the more you weigh, and the steeper the slope, the more power is required to take you up the hill. Now being that SW Florida is extremely flat (our only hills are bridges and overpasses), gravity really is not a factor, leaving the wind as our biggest energy consumer.

So as you can see, the wind is our biggest foe when riding here in Florida. There is a wonderful and easy to use online calculator which calculates the extra effort/energy needed to overcome the wind. It really brings what my legs and lungs already know into focus.

Here are todays wind blown numbers.

Route: Treeline
Activity: Cycle
Started: Mar 30, 2011 9:18:47 AM
Ride Time: 1:28:02
Stopped Time: 59:56
Distance: 23.20 miles
Average Speed: 15.81 miles/h
Fastest Speed: 25.03 miles/h
Ascent: 154 feet
Descent: 164 feet
Calories: 1349
Official: No

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