Measuring Aerodynamic Drag

by Rainer Pivit

published in Radfahren 2/1990, pp. 47 - 49

(Numbers in parentheses refer to the pertinent bibliography)

Translated by Damon Rinard and John Allen from the original German language article at:
http://www.lustaufzukunft.de/pivit/aero/messung.html.

Other articles by Rainer Pivit published in "Radfahren" magazine:

The most well known way to measure air resistance -- as used above all in automotive engineering -- is in the wind tunnel. Bicycles also have been measured in the wind tunnel, usually in connection with a record attempt or Olympics project. The extremely high cost of a good wind tunnel and its instrumentation makes its use expensive. Up to now, almost exclusively racing cycles, not everyday cycles, have been measured in the wind tunnel. The measurements are not much fun for the test rider: he is blasted with hot air at 50 km/h and the noise is over 100 dB(A). The energy consumption of a wind tunnel is enormous and is absurd in relation to the small power requirements of a bicycle.

With very few exceptions (4), the wheels do not turn during measurement in the wind tunnel. Naturally, this causes errors. It is also problematic that many of the wind tunnels used probably have enclosed measuring sections, requiring corrections to adjust the results to the reality of the cyclist on the road or the track. As the results for very similar bicycles (conventional racing cycles) vary by approximately 20% among the different wind tunnels' measurements, an absolute specification of the effective frontal area cwA is largely avoided in reviews of the literature.

The differences among individual test riders are not sufficient to cause these differences. Some researchers seem to be aware that this problem exists -- although it is never openly addressed. The researchers do not specify a value of cwA, but instead instead give only the aerodynamic drag force (in lbf or "grams"). Without specifying speed and atmospheric pressure, only data taken using the exact same measuring method can be compared.

The Rollout Method

There are other, usually less expensive methods to determine the air resistance of a bicycle. Often the rollout method is used. The bicycle rolls without pedaling over a measuring section with as smooth a surface and as little wind as possible. The drop in speed over the measuring section is measured. Data measured at widely varying speeds allows the rolling friction and air resistance to be calculated.

There are many possibilities for unrecognized errors with this method. Some of the published measurements which have been obtained with this method are difficult to rank with confidence, as they do not indicate how clean the work was. The rollout method simulates the real bicycle almost perfectly, but because of the absolute prerequisite of zero wind, measurements are usually taken in enclosed spaces, and are valid only for each particular space. The floor can be much more favorable than normal road surfaces, and also the walls of the measuring section can result in large differences from reality outdoors. Among the methods used (20, 21, 24) only terminal-velocity rollout is relatively popular. The vehicle rolls down a constant, precisely known downslope; the terminal velocity it finally achieves is recorded. After accounting for rolling friction, the effective frontal area can be determined from the terminal speed, slope, mass and atmospheric pressure. The measuring method is not exact, but but it reflects reality very well.

Heart-Rate Measurements

For the individual cyclist who wants to experiment with aerodynamic modifications, there is yet another another rather inexpensive method which gives rankings, though no absolute values (9). With constant time-boundary conditions, heart rate accurately reflects the rider's applied power. Some modern heart-rate monitors with chest electrodes can measure with an accuracy of one heartbeat per minute.

With the heart-rate monitor, the rider can keep his power nearly constant and repeat a time trial with different equipment, thus detecting possible differences from the different elapsed times. The method with the heart rate monitor is suitable even for the evaluation of different drive systems (e.g. round vs non-round chainrings).

This method can be simplified somewhat by using rear-wheel hubs which measure drive torque - like the ones by Look and the one (the Power Pacer) to be introduced soon by Balboa Instruments.

Hybrid Bike versus Aero Racing Bicycle

The Bicycle Research Group at the University of Oldenburg determined two bicycles' drag values for "Radfahren" magazine, using the rollout method. A small computer, carried on the bicycle, measuring speed through the measuring section. The computer stored the timing of wheel rotations (2). In the worst case (unimpaired incident flow) the measuring apparatus increased the effective frontal area cwA by 0.005 m2. A correction for this is not anticipated. The analysis did correct for unevenness in the measuring section.

The measuring section was part of a level corridor, about 30 m long, in a university building. The surface was PVC on top of a stiff concrete slab. The cross-sectional area of the course (width x height) was 4.8 m2.

The editors of "Radfahren" magazine requested measurement of a hybrid bike with 37 mm wide 700c tires, equipped as a city bike, as well as a time trial machine.

ATB, front view  ATB, side view

The hybrid bike we measured came from the bicycle manufacturer VSF, in Bremen. Tyres were Vredestein Snow + Rain 37-622. Tire inflation was 350 kPa (50 psi) in front and 400 kPa (58 psi) in back. Further details as well as the position and clothing of the test rider are recognizable in the photos.

Aero bike, front view  Aero bike, side view

The time trial machine was from Lutz in Boeblingen, a production racing cycle made available by a specialty shop. The frame had elliptical Vitus steel tubes. The cables were internally routed. The bicycle had a cow-horn handlebar. The back wheel was a flat Ambrosio disk with a Vittoria Formula 1 tubular tire (measured width 23 mm), installed with tape, at 700 kPa (102 psi). In front was an aero spoked wheel. It had a Wolber TX Profil aero rim, 36 triple-crossed conventional spokes --- a strange (and unreasonable) combination in our opinion -- and an IRC Roadlite EX 25-622 tire (real width 22 mm) at 700 kPa (102 psi). The rider (1.84 m, 72.0 kg) was also somewhat overdressed: Bell Stratos helmet over his curly hair and tights rather than shaved legs. The jersey was unfortunately not optimumal, as it was somewhat too large. Also, the shoes did not match the bicycle very well. The rider's position was not optimal for a time trial: the saddle was too low and the stem was too tall.

Air Resistance of the Hybrid Bike About Twice as High

Analyzing the 500 plus data points using the method of least squares yields a curve for velocity and retarding force, assuming constant rolling resistance, and air resistance increasing with the square of the velocity.  

28" means 700c
ATB data points plotted
 
 
Laeufe means runs.
g is acceleration due to gravity.
ro is air density (rho).
Umfang means scope.
Masse means mass.
Radzus is the additional mass for the inertia of the wheels
Ergebnis means result.
Cr is the coefficient of rolling resistance.

CwA is the product of the coefficient of drag, Cw, and the area, A.
Streu means standard deviation.
Regrkoef is the regression coefficient.

Geschwindigkeit is the speed.

Widerstand is the resistance.

Zeitfahrmaschine = time trial bike
Aero bike data points plotted

In our measuring section, the effective frontal area cwA of the hybrid bike was determined to be 0.79 m2, and for the time-trial machine, it was 0.39 m2. Statistical error amounted to about 1 or 2%. The air resistance of the hybrid bike is therefore about twice as high as that of the time trial machine.

These values pply only to our measuring section; they are not directly tranferrable to reality out of doors. The bicycle with rider reduces the cross section of the measuring section. Thus it leads to a higher value for air resistance than in a free field -- just as do measurements in wind tunnels with enclosed measuring sections. No direct comparisons have been made as of yet with the same bicycle in the measuring section in the building and outside with absolute zero wind, and so no correction for the above results based on measurements, can be given. A comparison is possible at present only on the basis of other published measured values; for example from wind tunnel measurements or rollout measurements.

The correction factor necessary to transfer our results to the road might amount to about 0.9, giving an effective frontal area of 0.71 m2 for the hybrid bike and 0.35 m2 for the time-trial machine. By way of comparison, a mid-sized passenger car has a frontal area of approximately 0.6 m2. The bicycle industry ought to be ashamed...

Tubular Tires do not Always Bring Advantages

On the corridor floor, the coefficient of rolling resistance cr for the hybrid bike surprisingly amounted to only 0.0032 despite the low tire pressure. The coefficient of rolling resistance for the time trial machine was 0.0035, slightly worse. Statistical error did not amount to as much as 4%. The bad value for the time trial machine did not surprise us, since Kyle's measurements (12) show that the way tubulars are isntalled greatly affects their rolling resistance. Tubular tires bring advantages only if they are perfectly cemented to a precisely fitting rim. Heavy cotton tubular tires do not have advantages compared to modern high-pressure clinchers.

It is often assumed that the rolling friction on rough asphalt paving is about twice as high as on a plastic floor.

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