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article 05, issue 01

Determination of Drag Parameters Utilizing a Bicycle Power Meter 

John Snyder and Theo Schmidt
October 21, 2004


A method is presented for evaluating aerodynamic drag and rolling resistance with a power meter.


Devices are available which measure and record a cyclist's power while cycling.  By observing power occurring at several speeds and applying known characteristics, the following method allows simultaneous determination of a vehicle's coefficient of aerodynamic drag times reference area value (Cd · A) and its coefficient of rolling resistance (Crr).  The method provides an alternative to a wind tunnel allowing acquisition of cost-effective, timely information in actual riding conditions rather than in the laboratory [ref 1, 2 and  3].  Cd · A and Crr are assumed by this model to be speed-independent although in reality both values are influenced by speed [ref 1 and 4] .


Given a power value at a known velocity, the related force is:

   Force = Power / velocity  [equation 1]

In the following, Force total (F total) is the force delivered to the road by the drive wheel.  The force due to acceleration is eliminated by traveling at a constant velocity.  This leaves the sum of forces due to aerodynamic drag, rolling resistance, and the roadbed's slope.

   F total = F aero + F roll + F grav  [equation 2]


   F aero = Cd · A · rho · v ²  · 0.5   [equation 3],

   F roll = m · g · Crr  [equation 4],

   F grav = m · g · sine (angle)   [equation 5]

where m is total vehicle and rider mass, g is local acceleration due to gravity, rho is air density, and angle is the roadbed's slope measured from horizontal.

By observing two power measurements recorded while traveling on a closed circuit such as velodrome or traveling first up-slope and then down-slope over a near-level roadway, the effects of grade variation and any small quantities of wind present can be averaged out as a first approximation.   Such averaging allows equation 2 to be simplified to:

   F total = F aero + F roll   [equation 6].

forcebar graph
[FIGURE 1] change of total force

Two power measurements at two different speeds must be recorded allowing subsequent determination of two different total forces (F' and F") at two associated velocities (v'  and v").  Subtracting one average force value from the other will reflect a specific quantity of change (dF) [fig 1]:  

  dF = F" - F'  [equation 7].

From the definition of efficiency = P out / P in  and equation 1 :

   F total = F observed · eff  [equation 8].

The efficiency of a good drive can be 90-98% and will vary with force [ref 5 and 6]. 

  Rolling resistance is assumed to be speed-independent for this method, so that:

   F" roll = F' roll  [equation 9].


  dF = (F" aero + F" roll) - (F' aero + F' roll)  [equation 10]


 dF = F" aero - F' aero   [equation 11]


  dF = (Cd · A · rho · v" ² · 0.5) - (Cd · A · rho · v' ² · 0.5)   [equation 12]


  2 · dF = Cd · A · rho · ( v" ² - v' ² )  [equation 13],

which permits solving for the final answers:

  Cd · A = (2  · dF) / ( rho · ( v" ² - v' ² ))  [equation 14],

 Crr = [(F' observed · eff ) - (Cd · A  ·  rho ·  v' ² ·  0.5)] / (m · g)  [equation 15].

Two force and speed pairs are needed; F' at  V' and F" at V".  These inputs provide dF from equation 7, Cd · A from equation 14  when rho is known and Crr from equation 15.

The above equations can be used with any consistent set of units.

Measuring Force

The most desirable way to determine force is with a device that senses torque directly at the drive wheel of a known diameter.  For such instruments it is not necessary to determine a drive train efficiency value, e.g., efficiency may be assumed to be 100%, neglecting the very small component of radial tire scrub.  With other instruments which measure force at the pedals, cranks or the chain, the values of drive efficiency and gear ratio must be introduced into the equations. 

Many devices provide speed and power readings rather than torque values.  In this case equation 1 must be applied.

Evidence supporting model:

As reviewed in Human Power, the German periodical Tour, das Radmagazin published a series of wind tunnel Cd · A values obtained from a variety of bicycles [ref 2].  These vehicles' power requirements were subsequently recorded while the same rider employed during the wind tunnel tests rode each bicycle at different constant velocities on a velodrome track.  This previously conducted experiment provides an opportunity to appraise equation 14 by comparing Cd · A values as determined in a wind tunnel and as determined with  power meter data.

Table 1 depicts selected Cd · A values measured during the wind tunnel experiments at two different air speeds (12.50 m/s and at 16.67 m/s).  Table 1's difference column shows Cd · A may vary with speed.  

Table 2 represents the power data from the same set of vehicles.

12.50 m/s

16.67 m/s


8.34 m/s

12.50 m/s

16.67 m/s

M5 Low racer, full fairing  



6 %

M5 Low racer, full fairing  




Flux low SWB, rear fairing  



0 %

Flux low SWB, rear fairing  




Moser bike



12 %

Moser bike




Cadex road racer



- 4 %

Cadex road racer




Radius 16V



0 %

Radius 16V




[TABLE 1]  Wind Tunnel derived Cd · A (m² )
[TABLE 2] Power (watts)  


Weather conditions and drive train characteristics occurring at the time of testing were not reported in the review.  Therefore, several assumptions have been applied: air density of 1.20 kg/m³, combined rider and vehicle mass of 100 kg, null wind conditions, and drive train efficiency of 95 %.

Table 3 compares Cd · A values determined using equation 14 with inputs from Table 2 to the wind tunnel determined Cd · A values appearing in Table 1.  

Wind Tunnel @ 12.50 m/s    Power Analysis @ 8.34 - 12.50 m/s
M5 Low racer, full fairing 0.044 0.045
Flux ultra-low SWB, rear fairing 0.19 0.18
Moser bike 0.21 0.22
Cadex road racer 0.25 0.24
Radius 16V 0.28 0.27
[TABLE 3]  Wind Tunnel found values compared to power meter derived values of Cd · A (m²) 



As presented in Table 3 the power meter and wind tunnel Cd · A values are similar to a good degree.  

When using a power meter the following concurrent environmental conditions should also be measured: local air temperature (K), local air pressure (hPa), the combined rider and vehicle mass (kg) and if possible the drive train efficiency (percent). Air temperature and local air pressure (also known as station pressure) may be used to determine a reasonable estimation of air density via the ideal gas law for dry air [sup 1] [fig 2].  Humidity or dew point may be accounted for as well.  Air pressure values reported in regional weather observations are usually a sea-level equivalent pressure. Thus they are not suitable for determining actual air density until the local altitude-correction has been removed [ref 1, 7 and 8 ].  

Fully faired streamlined vehicles may exhibit a sailing phenomena in steady cross-winds  [ref 9].  It is recommended that parameter testing, even for unfaired vehicles, be conducted when wind conditions are as close to still as possible. 

Further work:

Here we have used two sets of measurements to determine two unknowns.  The method could be expanded to using many sets of measurements and known simplified models for the speed variation to arrive at meaningful estimates for Cd · A and Crr as a function of speed.  

Ultimately a sophisticated  power and velocity monitoring instrument fitted with an array of environmental sensors including acceleration-slope, temperature and  barometric pressure could display Cd · A and Crr in real time while riding.  

Supplemental File:

1. Excel format  spreadsheet (17 kB)


[FIGURE 2] Screen capture of spreadsheet pwrdrag2.xls 



1.     Wilson, D. G. and Papadopoulus, J. 2004. BICYCLING SCIENCE 3rd edition. The MIT Press. Cambridge, MA.

2.     Wilson, D. G. 1997. Wind-tunnel tests, Review of Tour; das Radmagazin article. Human Power 43 : 7 - 8 (PDF 4.3 MB).

3. Snyder, J. 2000.CdA and Crr measurement. Human Power 51: 9-13 (PDF 4.4 MB).

4. Tamai, G. 1999. The leading edge: Aerodynamic design of ultra-streamlined land vehicles.  Bentley. Cambridge, MA.

5. Cameron, A. 1999. Measuring drive-train efficiency, Human Power 46: 5–7 (PDF 3.8 MB).

6. Spicer, J. and others. 2000. On the efficiency of bicycle chain drives. Human Power 50: 3-9 (PDF 1 MB).

7. Wilson, D. G. 2003. HPV Science, Human Power 54: 4–7 (PDF 2.7 MB).

8. Jones, N. 2003. PowerCalc v2.0.8 (computer program). available from URL:

9. Weaver, M. 1999. Technical notes: Body shapes and the influence of wind. Human Power 49: 21-24 (PDF 2.1 MB).

All hyperlinks were last confirmed active on October 22, 2004.

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