The Aerodynamics of Cycling
From: Jim Martin
Newsgroups: rec.sport.triathlon
Subject: Aerodynamics of Cycling
Date: 25 Jan 1996 20:02:20 GMT
Organization: University of Texas at Austin
Hello RSTers
A while back, I solicited your comments for a talk on cycling
aerodynamics. I received many helpful comments for which I am grateful.
Many people asked me to post my speaker notes for the talk I will give at
the SMW TriFed meeting in Dallas (Frost Yer Fanny), and you will find it
below. Of course, the formatting is lost, and I hope the tables remain
reasonably well aligned when it appears in RST.
The examples given in the tables are based on body positions bikes and
wheels I have measured in the GM and Texas A&M wind tunnels. I have
avoided comparison of specific wheels (except the combination I chose to
represent aero vs. standard) and frames because it detracts from the big
picture that I want to present.
Hope this will help you with your racing.
Best regards,
Jim Martin
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Aerodynamics of Cycling
Jim Martin
I. 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 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 = 1/2rhoCdAVT^2
Where, rho is air density, CdA is the product of coefficient of drag and
frontal area, VT is air velocity in the wind tunnel. If we divide the
measured drag force by VT^2 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 = 1/2rhoCdAVA^3
VA is air speed (i.e.; ground velocity + head wind velocity).
II. 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 the air
(1/2rhoCdAVA^3) (70 - 95%).
2. Rolling resistance power (CRRWTVG) (5-15%)
3. Power to rotate wheels (FwVG^3) (~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%)
Additionally, if the power you the produce does not match the power
required you will accelerate or decelerate. Putting all the factors
together yield the equation for cycling power:
Power required = 1/2rhoCdAVA^3 + CRRWTVG + FwVG^3 + WTVGSin(Arctan(Road
Grade)
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, and I have have not
measured them myself. I have used 0.0027 for a set of aero wheels, and
0.0044 for regular round-spoked wheels).
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 seven 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 5 watts, and demonstrate that this is a valid model for power during
real world cycling.
III. Knowing the power required for a given riding velocity may be
meaningless if you don't know how much power you can produce. If you, as
a Triathlete or Duathlete, are equally well trained at cycling and
running, and have average running economy (1.6 kcal/kg/mile) and average
cycling efficiency (19% gross cycling efficiency) your sustainable power
output can be estimated from this simple equation:
Power (watts) = 60 * Body weight (lb.) /10k run time (minutes).
Based on this equation, Table 1 presents the estimated power output for 4
categories of triathletes/duathletes. Keep in mind that if you are
estimating you power in a multi-sport event, you should use your
'multi-sport run' time, whereas if you are estimating your cycling time
trial performance, use your 'run only' time. These estimated power
outputs will be used to illustrate the effects of aerodynamics on a
variety of riders.
Table 1. Estimated cycling power output for a 70 kg person based on 10k
multi-sport running time:
Elite Well Trained Trained Recreational
10k Time 35 min 40 min 48 min 60 min
Power 264 watts 231 watts 192 watts 154 watts
IV. 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 on 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.
Position Drag @30 mph Elite Well Trained Trained Recreational
Typical 8.0 62:49 65:51 70:16 76:01
Good 7.0 60:14 63:07 67:22 72:57
Excellent 6.0 57:23 60:10 64:07 69:47
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 75
degrees). 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 my 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 (or less) to stay adapted to the
position.
2. 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.
3. 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.
V. 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.
VI. 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.
Position Drag @30 mph Elite Well Trained Trained Recreational
Typical 7.6 61:40 64:38 68:54 74:39
Good 6.6 58:58 61:47 65:55 71:23
Excellent 5.6 55:57 58:39 62:35 67:47
The difference made by aero wheels is about a minute and a half to two
minutes. When I was preparing this talk and I got to this part, 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.
VII. Similarly, 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 3.
Table 4: Predicted 40k time, flat course, calm conditions, 3 body
positions, aero wheels, aero frame.
Position Drag @30 mph Elite Well Trained Trained Recreational
Typical 7.3 60:53 63:47 68:04 73:40
Good 6.3 58:05 60:53 64:57 70:20
Excellent 5.3 54:59 57:39 61:30 66:38
The effects of an aero frame result in saving about an additional minute.
VIII. The effects of light weight components seem to be a topic of
interest for many triathletes/duathletes, 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 about 2000 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.
Table 5: Predicted 40k time, 3% grade out and back course, calm
conditions, 2 body positions, aero wheels, 3 bikes.
Drag @30 mph Elite Well Trained Trained Recreational
22 lb. 6.3 65:04 69:38 76:55 87:24
17 lb. 6.3 64:37 69:05 76:12 86:27
17 lb. 6.8 65:52 70:22 77:31 87:47
An extremely light bike on a very tough climbing course will only save
you about 30 seconds to 1:00, but if this lighter bike compromises your
aerodynamics even a little bit, you will be SLOWER.
IX. Till 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, aero wheels, aero frame.
Drag @30 mph Elite Well Trained Trained Recreational
Calm 6.3 58:05 60:53 64:57 70:20
5 mph wind6.3 60:11 63:17 67:51 74:05
10 mph wind6.3 67:30 71:51 78:27 87:56