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 from the original German language article at:

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

The most well known way to measure air resistance, and above all from 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 the measurements in the wind tunnel. Naturally this causes errors. It is also problematic that many of the wind tunnels used probably have enclosed measuring sections. This requires corrections to the results, in order to adjust them 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 between the individual "test riders" are not sufficient to cause this difference under any circumstances. Some researchers seem to be aware that this problem exists - although it is never openly addressed. They 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 different methods for the determination of the air resistance of a bicycle. These are usually considerably less expensive. Often the rollout method is used. The bicycle rolls without pedaling over a measuring section with as smooth a surface and as still a wind as possible. The drop in velocity 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 were obtained with this method are difficult to rank with confidence since 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 places, 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 the terminal velocity rollout is relatively popular. The vehicle rolls down a constant, precisely known downward gradient; the terminal velocity it finally achieves is recorded. After accounting for rolling friction, the effective frontal area can be determined from the terminal velocity, downward gradient, mass and atmospheric pressure. The measuring method is not exact, but but it is very close to reality.

Heart Rate Measurements

For the individual who wants to experiment with aerodynamic modifications, there is still another another quite inexpensive method that gives rankings, though no absolute values (9). With constant boundary conditions, heart rate is a very good approximation of the rider's applied power. Some modern heart rate monitors with chest electrodes can measure with an accuracy of one heart beat 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.

ATB versus Aero Racing Bicycle

The Bicycle Research Group at the University of Oldenburg determined two bicycles' drag values for "Radfahren" magazine. The measurement took place using the rollout method. For measuring velocity over the measuring section a pocket computer was carried on the items under examination, which served as a time meter, storing the duration of the wheel revolutions for the measurement (2). In the worst case (unimpaired incident flow) the measuring apparatus increases the effective frontal area cwA by 0.005 m2. An appropriate correction of the result of measurement is not intended. The analysis works with corrections to the balance of irregularities in the measuring section.

The measuring section is part of a level corridor in the building of the university about 30 m long. The surface consists of a PVC covering on heavy-duty concrete. The cross section of the course (width x height) amounts to 4.8 m2.

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

ATB, front view  ATB, side view

The ATB we measured came from VSF Bicycle Manufacturer, Bremen. Tyres were Vredestein Snow + Rain 37-622. It was measured with a tire pressure of 350 kPa (50 psi) in front and 400 kPa (58 psi) in back. Further details as well as the position and clothes of the test rider are recognizable in the photos.

Aero bike, front view  Aero bike, side view

The time trial machine made available to us was from Lutz, Boeblingen, a production racing cycle made available by the specialized trade. The frame consisted of elliptical Vitus steel tubes. The cables were internally routed. The bicycle had a plunging handle bar. The back wheel was a flat Ambrosio disk with a Vittoira Formula 1 tubular tire (measured width 23 mm), installed with tape, at 700 kPa (102 psi). In front was an aero spoked wheel. It has a Wolber TX Profil aero rim, 36 triple crossed conventional spokes - a strange (and unreasonable) combination to us - 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 out-deseamed [herausgeputzt]: Bell Stratos helmet over his Wuschel [?] head and tights (instead of a leg shave). The jersey was unfortunately not optimum, as it was somewhat too large. And also the shoes did not match the bicycle so well. The rider's position was not optimal for a time trial: the seat post was too short and the stem too high.

Air Resistance of the ATB About Twice as High

Analyzing the 500 plus data points using the method of least squares yeilds 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 velocity.

Widerstand is the resistance.

Zeitfahrmaschine = time trial bike
Aero bike data points plotted

For the ATB an effective frontal area cwA was determined on our measuring section to be 0.79 m2. The time trial machine came to a value of 0.39 m2. The measuring error amounted to about 1 or 2%. The air resistance of the ATB is thus about twice as high as that of the time trial machine.

These values strictly apply only to our measuring section; they are not directly tranferrable to reality outside. The bicycle with rider blocks the cross section of the measuring section. Thus it leads to a higher value for air resistance than in a free field - just as measurements in wind tunnels with enclosed measuring sections do. Since so far no direct comparative measurements were made with the same bicycle between the measuring section in the building and outside with absolute zero wind, no correction value for the above results, founded on measurements, can be indicated. It can be measured at present only on the basis of other published measured values; for example from wind tunnel measurements or rollout measurements.

Therefore the correction factor necessary to transfer our results to the road might amount to about 0.9. Thus the ATB has an effective frontal area of 0.71 m2 and the time trial machine 0.35 m2. For comparison, a middle class passenger car has a value of approximately 0.6 m2. The bicycle industry is not ashamed there...

Tubular Tires do not Always Bring Advantages

On the corridor floor, the coefficient of rolling resistance cr for the ATB surprisingly amounted to only 0.0032 despite the low tire pressure. The coefficient of rolling resistance for the time trial machine was situated at 0.0035, slightly worse. The measuring error did not amount to as much as 4%. The bad value for the time trial machine was not so surprising for us, since Kyle's measurements (12) show that the assembly status of tubulars greatly affects their rolling resistance. Tubular tires bring advantages only if they are perfectly glued with cement to a precisely fitting rim. Heavy cotton tubular tires do not show advantages compared to modern high pressure clinchers.

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

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by Rainer Pivit, 03/2000

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