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 = 1/2rC_{d}AV_{t}^{2}
Where, r is air density, C_{d}A is the product of coefficient of drag and frontal area, V_{t} is air velocity (m/s) in the wind tunnel. If we divide the measured drag force by V_{t}^{2} to get 1/2rC_{d}A, 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 = 1/2rC_{d}AV_{a}^{2}V_{g}
Where, V_{a} is air speed (i.e.; ground velocity + head wind velocity), and V_{g} 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:
Where C_{RR} is the coefficient of rolling resistance (about 0.0024 for clinchers on asphalt) W_{T} is total weight of bike and rider (Newtons), V_{g} is ground velocity, F_{W} 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 = 1/2rC_{d}AV_{a}^{2}V_{g} + C_{RR}W_{T}V_{g} + F_{w}V_{g}^{3} + W_{T}V_{g}Sin(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:
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.