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Chung method errors: what skews road-measured CdA and how to avoid it

Aerodynamics7 min readBorja Alfaraz

Undetected wind

+17 %

That is how much CdA comes out inflated if a 1 m/s headwind blows that the test does not account for.

Model calculation at 43 km/h with a real CdA of 0.24 m². A 1 m/s wind is a barely noticeable breeze.

Summary. Chung’s virtual elevation method1 estimates CdA and Crr with a power meter, but it inherits the errors of every input. Using the power equation2, we calculate how far CdA drifts with each typical error: wind, speed sensor, power meter, mass and air density. We close with a protocol to minimise them, in line with the literature on field measurement3,4.

The CdA from a virtual elevation test is only as good as its inputs. The biggest error is usually wind: an unaccounted 1 m/s headwind inflates CdA by 17 % at 43 km/h. Speed, power and air density follow, each with 2 to 3 % errors.

How much does each error skew the result?

Input errorEffect on CdA
Undetected 1 m/s headwind+17 %
Speed sensor 1 % high (wheel circumference)−3 %
Air density 3 % low (wrong temperature or pressure)+3 %
Power meter 2 % high+2 %
Mass 2 kg high−0.4 %

Table 1. Deviation of the estimated CdA from each input error at 43 km/h. Model calculation [2].

Speed weighs so much because aerodynamic power grows with its cube: a 1 % speed error is almost 3 % in CdA. Mass matters little for CdA, but a lot for Crr, which shares the rolling term with it.

The most common errors in practice

  • Wind: even on what looks like a calm day, the near-ground breeze changes from one pass to the next. It is the main reason two tests on the same day disagree.
  • Power meter calibration: without a zero offset before the test, power can be shifted. A single-sided meter adds the error of leg asymmetry.
  • GPS speed instead of a sensor: GPS smooths and delays speed, and that shows in the virtual profile during pace changes.
  • Braking and traffic: a brake the model cannot see shows up as a false “descent” in the virtual profile.
  • Position changes: sitting up on a section means that section’s CdA is not the position you meant to measure.

How to run a reliable test

  1. Choose a short closed loop or an out-and-back stretch, so wind and elevation errors cancel on each lap.
  2. Test early in the day, with as little wind as possible, and repeat several laps in the same position.
  3. Zero the power meter, check the wheel circumference and use a speed sensor.
  4. Record temperature and pressure at the time of the test to calculate density.
  5. Include low-speed sections if you also want to estimate Crr.
  6. Always compare within the same day: to choose between two positions or two helmets, alternate the setups in the same test.
Rule of thumb: a CdA change is only real if it repeats over several laps and exceeds the lap-to-lap spread of the same setup.

What is known and what is not

Field methods with power meters detect small CdA changes when conditions are well controlled3, and reviews agree that their main limitation is wind4. Reference values in professionals help judge whether a result is plausible5. What no field method fully solves is gusty wind on the day, which is why repetition is the best defence.

Frequently asked questions

Why do I get different CdA values every day?

Mostly because of wind and air density. An undetected 1 m/s wind is enough to change the result by 17 %.

How accurate is the Chung method?

With a good protocol, accurate enough to compare positions and equipment within the same test. Absolute values between different days are less reliable.

The step-by-step method is in how to measure CdA without a wind tunnel.

References

  1. Chung R. Estimating Crr and CdA from power meter data. Documento técnico. 2003. anonymous.coward.free.fr/wattage/cda/indirect-cda.pdf
  2. Martin JC, Milliken DL, Cobb JE, McFadden KL, Coggan AR. Validation of a mathematical model for road cycling power. J Appl Biomech. 1998;14(3):276-91. doi:10.1123/jab.14.3.276
  3. Lim AC, Homestead EP, Edwards AG, Carver TC, Kram R, Byrnes WC. Measuring changes in aerodynamic/rolling resistances by cycle-mounted power meters. Med Sci Sports Exerc. 2011;43(5):853-60. doi:10.1249/MSS.0b013e3181fcb140
  4. Debraux P, Grappe F, Manolova AV, Bertucci W. Aerodynamic drag in cycling: methods of assessment. Sports Biomech. 2011;10(3):197-218. doi:10.1080/14763141.2011.592209
  5. García-López J, Rodríguez-Marroyo JA, Juneau CE, Peleteiro J, Martínez AC, Villa JG. Reference values and improvement of aerodynamic drag in professional cyclists. J Sports Sci. 2008;26(3):277-86. doi:10.1080/02640410701501697

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