Aerodynamics of Cycling
by Jim Martin

Introduction
It’s popular these days to use the term ‘aero’ to describe bicycles, wheels, helmets, and handlebars. However, do we really know exactly what ‘aero’ means, and what the consequences of aerodynamics are to you, the rider? To shed some light on this topic, I will explain what aerodynamic drag is and how it is measured. Then I will introduce a mathematical model for predicting cycling power based on aerodynamic drag and velocity. Next, I will give some very rough estimates of the cycling power of four categories of riders. The mathematical model will be used to predict the effects that aerodynamic changes to your body position, wheels, and frame will have on your cycling performance. The model will also be used to predict the effects of climbing, the relative trade off between weight and aerodynamic drag, and at the effects of a 5 and 10 mph wind.

What is Aerodynamic Drag?
Put your hand out the car window and the force you feel is the aerodynamic drag of your hand in the air stream. Aerodynamic drag of bikes and riders is measured in the wind tunnels by mounting the bike on a balance and blowing air over it, typically at 30 mph, and results are usually expressed in pounds of drag at 30 mph. The aerodynamic drag is related to the density and velocity of the air and to the frontal area and shape of the object in the wind stream by the following equation:

Drag force = 1/2rCdAVt2

Where, r is air density, CdA is the product of coefficient of drag and frontal area, Vt is air velocity (m/s) in the wind tunnel. If we divide the measured drag force by Vt2 to get 1/2rCdA, we can calculate drag at any speed. Also, we can take it one step farther. Power is force times velocity, so the power to push you and your bike through the air at any given velocity is:

Aerodynamic power = 1/2rCdAVa2Vg

Where, Va is air speed (i.e.; ground velocity + head wind velocity), and Vg is ground velocity.

Mathematical Model for Cycling Power
Aerodynamic drag represents the largest resistance while riding over level ground, however, the total power required to ride a bike is a little more complicated, and can be divided into 5 components:

  1. Aerodynamic power to push you and your bike through air (1/2rCdAVa2Vg) (~85%).
  2. Rolling resistance power (CRRWTVg) (5-15%)
  3. Power to rotate wheels (FwVg3) (~1%)
  4. Power to overcome gravity on a hill (WTVgSin(Arctan(Road Grade)) (varies greatly)
  5. Friction losses in the drive and bearings (small except for chain line cross over) (1-2%)

Where CRR is the coefficient of rolling resistance (about 0.0024 for clinchers on asphalt) WT is total weight of bike and rider (Newtons), Vg is ground velocity, FW is factor related to the power to rotate the wheels (estimates of this number vary widely, I have used 0.0027 for a set of aero wheels, and 0.0044 for regular round-spoked wheels). Additionally, if the power you the produce does not match the power required for a given velocity, you will accelerate or decelerate.

Putting all the factors together yield the equation for cycling power:

Eq 1 Power = 1/2rCdAVa2Vg + CRRWTVg + FwVg3 + WTVgSin(Arctan(Road Grade)

Of course this equation just represents a mathematical model which may or may not represent real world. To test it’s validity I performed a study in which we measured drag in the wind tunnel of several riders, then had them ride at three steady state velocities while we measured power with an SRM crank and wind conditions with an anemometer. The results indicate that our predicted power matched our measured power with a standard error of less than 3 watts, and demonstrate that this is a valid model for power during real world cycling.

Estimated Cycling Power
Earlier, we discussed the advantages of a steep seat tube angle and a short head tube. Now, let's take a look at the rest of the

Knowing the power required for a given riding velocity may be meaningless if you don’t know how much power you can produce. Power is best measured in a physiology lab, however, Table 1 presents the estimated power output for 4 categories of cyclists. These estimated power outputs will be used to illustrate the effects of aerodynamics under a variety of conditions.

Table 1. Estimated cycling power output for 70 kg cyclists in four categories.

  Cat 1 Cat 2 Cat 3 Recreational
Power 350 Watts 300 watts 225 Watts 150 watts

Aerodynamics of Body Position
Although much attention is focused on the aerodynamics of equipment, the most important aerodynamic consideration for a bike and rider combination is the rider. A typical 70 kg rider on a regular bike with standard wheels will have a drag of about 8 lb., a better position will reduce drag to about 7 lb., and an excellent position will yield a drag of 6 lb.. Based on these drag numbers, and the power outputs estimated above, equation 1 can be used to predict the effects of these positions on cycling performance on a flat course with no wind shown in Table 2. The differences in performance with no change in power are remarkable, ranging to about 6 minutes when changing from a typical to an excellent position.

Table 2: Predicted 40k time, flat course, calm conditions, 3 body positions, standard wheels.  Also, time saved by good and excellent positions compared to typical position.

40k Time
Position Drag @ 30mph Cat 1 Cat 2 Cat 3 Recreational
Typical 8 57:14 60:23 66:49 77:12
Good 7 54:51 57:53 64:04 74:03
Excellent 6 52:14 55:08 61:02 70:35
Time Saved by Positioning
Position Drag @ 30mph Cat 1 Cat 2 Cat 3 Recreational
Good 7 2:23 2:30 2:45 3:09
Excellent 6 5:00 5:15 5:47 6:37

The key elements of a good aero position are:

  1. Horizontal torso. Defined by having your chest, or better yet, your back parallel to the ground, this is absolutely the most important element, as it can result in large magnitude changes in aerodynamic drag. Unfortunately, it may be the most difficult to achieve, because as you approach this position, your thighs start to hit your torso. This interference imposes limits on your body's aerodynamic position, but is due to traditional bike geometry (i.e.; seat tube angles of 73 to 75º ). The way to overcome this limitation is to go to a more forward position, which will allow you to roll your whole body forward. Note of caution: a forward position seat post and long steeply-dropped stem may allow you to assume a good aero position, but will result in a bike that is not well balanced, and may be dangerous to ride. A much better approach is to buy a frame that is designed to be ridden in a forward position. These positions are uncomfortable in two ways. First and foremost, by rotating your hips forward to get your torso horizontal, you are rotating your weight right on to your soft and tender parts. Specifically, riding in this position may exacerbate the condition of prostatitis that is common among cyclists. Extra seat padding helps but does not eliminate the problem. A truly anatomical saddle that distributes your body weight over the whole seat might really help. Some riders try to alleviate this problem by tilting the nose of the saddle down, but this only results in a tendency to slide off the saddle and to strain your shoulder and arm muscles. Secondly, and to a much lesser degree, you tend to get a sore neck the first few times you ride, the discomfort lessens with time and can be minimized with stretching and massage. These draw backs are minimal because you don't have to ride the forward position daily to go fast on it. My experience with Team EDS, as well as my own bike is that you only need to ride it once a week (maybe less) to stay adapted to the position.
  1. Narrowly spaced elbow pads. Narrow elbows are an essential detail of an aero position. However, the magnitude of improvement is much less than what is achieved by adopting a horizontal torso position. Research conducted by Boone Lennon has shown that subtle changes in elbow width and aero bar angle may have significant effects on drag. This research was performed on traditional geometry bikes, with the torso adopting the characteristic cupped shape, and probably illustrates the need to block air flow out of the torso area. More recent data on riders in a horizontal torso position shows much less effect from these variables. I do not believe these two findings are contradictory, rather, they indicate that once the torso is horizontal there is little you can do to improve or impair aerodynamic drag.
  1. Knee width can change aerodynamic drag by up to half a pound. Pedaling with your knees close to the top tube is an essential part of good aerodynamics.
  1. Is there a trade-off between position and power output? If done badly, maybe, but if done well, no. Recently, Heil et al., (MSSE, May 1995) have investigated this question, and the results tend to show that your cardiovascular stress for a given power is increased by decreasing the trunk to femur angle. Therefore, if you lower your elbow position, you may need to move the saddle forward to maintain your trunk to femur angle while getting a lower, more nearly horizontal torso position.

Aerodynamics of Wheels
The effects of aerodynamic wheels can be substantial. They can lower the aerodynamic drag by about 0.4 lb. compared with standard wheels with round-wire spokes and require about half the power to rotate. For the following examples, I will use a Specialized 3 spoke front and a lenticular rear disc. Table 3 shows the predicted effects these wheel will have on 40k time trial performance.

Table 3: Predicted 40k time, flat course, calm conditions, 3 body positions, aero wheels.  Also, time saved in a 40k by using aero wheels compared to standard wheels.

40k Time
Position Drag @ 30mph Cat 1 Cat 2 Cat 3 Recreational
Typcial 7.6 56:08 59:15 65:33 75:46
Good 6.6 53:39 56:38 62:41 72:28
Excellent 5.6 50:55 53:44 59:30 68:50
Time Saved by Aero Wheels
Position Drag @ 30mph Cat 1 Cat 2 Cat 3 Recreational
Typical 7.6 1:06 1:08 1:16 1:26
Good 6.6 1:12 1:15 1:23 1:35
Excellent 5.6 1:19 1:24 1:32 1:45

The difference made by aero wheels is about a one to two minutes. When I was preparing this table, I didn’t believe the model’s prediction. So I recruited a friend and went out to a fairly flat loop and rode at constant power with regular and aero wheels. The results were almost exactly what the model predicts. This study needs to be repeated with better control such as wind and road grade measurement, but it provides anecdotal evidence that the predicted effects of wheels are realistic.

Aerodynamics of Frames
The effects of aerodynamic frames can be substantial. The best frames can reduce drag an additional 0.3 lb. compared with round frame tubes. The critical areas of a frame seem to be the leading edge (fork, head tube, handlebars) and the area between the riders legs. The frames that perform the best tend to have air foil shaped leading edges and seat tubes (or no seat tubes). The effects of an aero frame are estimated in Table 4. The aero frame results is time savings of about 1 minute.

Table 4: Predicted 40k time, flat course, calm conditions, 3 body positions, aero wheels, aero frame.  Also, time saved in a 40k by using an aero frame compared to a standard frame.

40k Time
Position Drag @ 30mph Cat 1 Cat 2 Cat 3 Recreational
Typcial 7.3 55:25 58:29 64:43 74:48
Good 6.3 52:52 55:48 61:46 71:25
Excellent 5.3 50:02 52:49 58:29 67:40
Time Saved by Aero Frame
Position Drag @ 30mph Cat 1 Cat 2 Cat 3 Recreational
Typical 7.3 0:43 0:46 0:50 0:58
Good 6.3 0:47 0:50 0:55 1:03
Excellent 5.3 0:53 0:55 1:01 1:10

Weight
The effects of light weight components seem to be a topic of interest for many cyclists, however the effects of weight on cycling performance may not be as significant as one expects. To illustrate the effects of weight I have modeled a very tough out and back 40k with a constant grade of 3% which results in 600m or about 1970 feet of climbing/descending with aerodynamic bikes that weigh 22 lb. and 17 lb., and a slightly less aero bike/position that weighs 17 lb. The results are shown in Table 5.

Table 5: Predicted 40k time,3% grade out and back course, calm conditions, two aerodynamic drag conditions:

Bike Wt

% Grade Drag @ 30mph Cat 1 Cat 2 Cat 3 Recreational

22 lb

3 6.3 57:32 61:50 71:29 90:11

17 lb

3 6.3 57:14 61:27 70:53 89:06

17 lb

3 6.8 58:26 62:41 72:11 90:26
  Cat 1 Cat 2 Cat 3 Recreational
Time Lost climbing compared to flat 4:40 6:02 9:43 18:46
  Cat 1 Cat 2 Cat 3 Recreational
Time Saved by 5lb Lighter Bike 0:18 0:23 0:36 1:05
  Cat 1 Cat 2 Cat 3 Recreational
Time lost by giving up 0.5lb of
aerodynamics to save 5lb of weight
0:54 0:51 0:42 0:15

The hilly course will cost between 4 and 19 minutes, compared with a flat course. An extremely light bike on a very tough climbing course will only save you about 18 seconds to 1:05, but if this lighter bike compromises your aerodynamics even a little bit, you will be slower by 15 to 54 seconds. Interestingly, lighter weight is more of a help to slower riders.

Headwinds
Until now, I’ve modeled everything in calm conditions, however, I personally have rarely ridden in calm conditions. Wind effects can be remarkable, largely because you spend a longer time in the head wind than you do in the tailwind, and consequently, the slower head wind portion has a greater effect on average velocity. Table 6 demonstrates the effects of 5 and 10 mph winds on an out and back course, direct head wind one way, tail wind the other.

Table 6: Predicted 40k time,flat out and back course, windy conditions, good body position, aerowheels, aero frame:

40k Time

Wind

Drag @ 30mph Cat 1 Cat 2 Cat 3 Recreational

0 mph

6.3 52:52 55:48 61:46 71:25

5 mph

6.3 53:23 56:24 62:34 72:38

10 mph

6.3 54:56 58:14 65:01 76:26
Time Lost on a Windy Day

Wind

Drag @ 30mph Cat 1 Cat 2 Cat 3 Recreational

5 mph

6.3 :31 :36 0:48 1:13

10 mph

6.3 2:04 2:26 3:15 5:01

Headwinds
The cycling power required for any velocity can be predicted based on a mathematical equation. In general, the slower the rider, the more improvement he/she can expect from improved aerodynamics. The main take-home message to be learned from this discussion is that the biggest changes in aerodynamic drag and in cycling performance come from changes in body position, which can improve 40k time by over 6 minutes. An excellent position on a regular bike with regular wheels will allow you to out perform a rider with a typical position on an aero bike with aero wheels by 3 to 4 minutes. Aero wheels can reduce drag by about 0.4 lb. and will reduce your 40k time by about 1 to 2 minutes. An aero frame can reduce drag an additional 0.3 lb. and save you about an additional minute. The effects of bicycle weight, even on a tough climbing course are minimal compared with the effects of aerodynamics. Finally, windy conditions slow you down because you spend more time in the headwind than you do in the tailwind, and consequently, the effects of headwind and tailwind don't ‘average out’.

     Jim Martin is a doctoral candidate in Exercise Science at The University of Texas at Austin, the director of sports science for Team EDS, and has served as a consultant to Project 96. He has authored scientific publications on maximal neuromuscular function, growth development and aging, and cycling aerodynamics and writes a monthly column for Bicyclist Magazine.