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1992 was the year I started racing my bike. During my failed attempts at living the awe-inspiring and lucrative dream of a domestic US professional bike racer, I had a few good rides – well, maybe only two, but who’s counting. There were some key things which allowed the achievement of most of my modest goals along the way - the most important of which, was simply having the discipline and desire to ride my bike - a lot. The second ingredient was having a good coach to nudge me in the right direction and tailor my training program specifically to my needs. It didn’t hurt that my coach was also my brother (former Prime Alliance Director Sportif, Kirk Willett) and wintertime training partner for the better part of the 90’s. There was no motivation like having your coach call you up to schedule the daily ride when there’s twelve inches of snow on the ground and the mercury is hovering below zero.
The final key to my meager cycling accomplishments was using the most economical training technology at the time, a heart rate monitor (HRM). This device was one of the easiest ways to provide training feedback and act as a backbone to my training program. Training with a HRM is still probably the most economical way to structure a training plan, but with the entry of several different manufacturers into the power-measuring arena, training with power is becoming a tempting alternative.
There exists some uncertainty and confusion for consumers when it comes to picking which power meter to use. For a few weeks in early 2003, I had the opportunity to simultaneously equip my ride with three power measuring systems: SRM, Power Tap (PT), and Polar. I will review these systems using the three fundamental design variables of price, performance, and durability - but first, let’s cover some power basics.
Power
What is power? Power is defined as the amount of work done during a given period of time and has the metric units of watts (horsepower in English units).
For cycling, power data is fundamental in determining trends in overall performance due to changes in equipment, positioning, and more importantly training methods. The power produced by a cyclist is used to overcome aerodynamic, inertial, rolling resistance, gravitational, and miscellaneous drivetrain/bearing forces. Cycling speed is fundamentally bound by how much power one can produce.
Work isn’t necessarily sitting at your desk, slamming down a couple cups of coffee and making yourself look busy while mumbling about red Swingline staplers. Work in this context is a force applied over a distance and has the units of energy (Newton-meter or Joules). Everyone does work when they lift a box, lift up their kids, or pedal their bike.
For rotating systems, power can be derived by multiplying torque (force applied at a distance) by the angular velocity (rpm or radians/sec). A torque applied without any resulting motion means that no work has been done, thus, zero power is produced. This means that if you are stomping on the pedals but you are not moving, you will get real tired, won’t go anywhere, and subsequently will be putting out zero watts. There needs to be motion of the system in order for work to be done – remember, a force needs to act over, or through, a distance (the foot needs to sweep out an arc).
There are many parts that rotate on a bicycle due to an external torque (e.g, pedals, crank, bottom bracket, chain, and rear hub). These spots are prime locations for measuring power on a bicycle system.
Measuring Power
The three power systems evaluated all measure the same fundamental parameters of interest (torque and angular velocity) but they use different methods. The primary reason for this can probably be attributed to different design goals, or just plain wanting to do things a bit differently. SRM was the first of the three systems to enter the portable cycling power measurement business, distantly followed by Tune/Graber and its Power Tap product. The Power Tap folks decided to measure power a bit differently than SRM and acquired a US patent in the process. Polar followed a similar path, in terms of measuring power in an alternative method, but the system had its own unique design goal. According to one of the Polar power product developers, Alan Cote, the system looks like it does today because they wanted to be able to measure power without removing or replacing any components on the bicycle. Cote achieved this objective and in the process named Polar as the assignee of the U.S. patent rights. The latest entrant into the power market is the Ergomo system that measures power at the bottom bracket. This system is not included in this review.
Each company achieves power measurement through different methods. SRM uses strain gage technology in a crank based application. Power Tap uses strain gage technology in a hub based application. Polar uses magnetic induction in a chain based application.
SRM
Instrumenting a mechanical structure allows one to convert the phenomenon of interest into an electrical signal that can be subsequently analyzed, mathematically manipulated, and then displayed to the user. Strain gages do just that in the SRM power measuring device.
The strain gages that SRM uses are nothing more than a piece of foil embedded in a plastic carrier. The resistance of the foil element changes depending on how much it is stretched/strained. The strain gages unique characteristic of changing resistance under strain is what allows the mechanical deflections that naturally occur in the structure to be converted into an electrical voltage signal.
Voltage = Current x Resistance or V = I x R
SRM has designed a flexure system (purposely micro-flexible elements) in the spider of the crank that will deflect/stretch as a result of a load applied at the pedal. With the strain gages applied to the surface of these flexures, the small deflections can be converted into a voltage. Through careful calibration (applying known loads in a known orientation and in a controlled environment while monitoring the resulting voltage) it is possible to convert the measured strain into a torque value. It is also interesting to note that SRM does a dynamic calibration at the factory at a variety of torques and cadences to ensure linearity across the entire usage spectrum.
There are several fundamental sources of error that must be mentioned when using strain gages. These include temperature effects, strain field assumptions, and orientation of the gages/transverse sensitivity. Since the underlying structure will deform with a change in temperature, the strain gages will also sense these changes. Therefore, there may be a drift in the zero torque point depending on how warm or cool it is outside. Through clever design and increasing the total number of gages, it is possible to auto-correct these effects and minimize their impact on the final magnitude of the measured value. No system is perfect at accomplishing zero temperature sensitivity and this is perhaps one of the reasons why SRM recommends that the zero point be determined prior to every ride.
Strain gages occupy space on the flexible element being measured and will, therefore, reflect an average strain over the occupied area. If the strain field being measured is constant over the area covered by the gage, or if the gage is infinitesimally small (not likely!) there is no error associated with the measurement. These type of errors can be addressed by clever gage design (smaller gages that occupy less space), or clever flexure design (making sure that strain field is constant where the gage is placed – this is done by manipulating flexure geometry). Typically, the errors associated with non-linearity in the strain field are small and are, more than likely, not fully addressed by any of the SRM units.
Individual strain gage elements are designed to be sensitive in only one direction. Transverse sensitivity is affected by how the gages are oriented and the inherent properties of the gage itself. Ideally, the gages should be oriented along the same direction as a known principle strain axis. Any deviation from this orientation will mean that loads applied in an off-axis direction (for a crank arm this off-axis direction would be any component of the pedal force applied in a direction parallel to the bottom bracket axis – these off axis loads are common and significant when riding out of the saddle) will cause a change in voltage by the strain gage. The off-axis loads should not be included in the power calculation since they do not produce any work (there is no associated motion with this force – i.e, no work is done). Improper installation, poor gage layout design, or poor gage selection will increase the error associated with transverse sensitivity. A perfect transducer would have zero transverse sensitivity, but this is not practically achievable. Typical load transducers can routinely achieve fractions of a percent of error in this category.
The positioning and number of strain gages used to measure the applied torque will affect the accuracy of the measurement. Additional gages will boost the signal to noise ratio, lower the transverse sensitivity and allow for automatic temperature compensation. This is the fundamental reasoning behind the different price points of the SRM offerings – the higher priced models use more gages and have better accuracy. For example, the SRM amateur model uses 2 strain gages and has a quoted accuracy of +/- 5%. The Pro Model, which was used for this review, uses 4 gages and has a quoted accuracy of +/- 2%. The Science version of the SRM uses 8 gages and claims to have +/- 0.5% accuracy.
Strain gages allow the torque applied at the crank to be measured; therefore, one need only monitor angular velocity to be able to calculate power. Crank angular velocity can be determined using cadence (revolutions per minute, or radians per second, where one revolution is equal to 360 degrees or 2*pi radians).
The SRM unit uses magnetic induction to transmit the information acquired in the crank to a receiver mounted on the chainstay. The receiver is hard wired to a CPU (Central Processing Unit, or on board computer) mounted on the handlebar.
The cadence sensor embedded in the crank spider generates an electrical pulse-train signal. For the cadence calculation, the amount of time between the selected peaks in the pulse train is a direct measure of how long it took to complete one crank revolution. This information is converted to an angular velocity by dividing 2*pi by the time period measured.
The real difficult part in this whole operation is how this data is processed and recorded. Torque and cadence are constantly varying, yet data is reported at one-second intervals. This means that some sort of averaging scheme is being applied to arrive at the reported power. I have no idea how this is done, and won’t even begin to speculate about it.
In summary, the SRM uses strain gages in the crank spider to measure torque and pedaling cadence to measure angular velocity – the product of these two components will yield power.
Power Tap
The Power Tap system also uses the same fundamental strain gage technology to measure torque – but they measure it at the hub instead of in the crank like SRM. Furthermore, unlike SRM who uses magnetic induction to transmit the data from the rotating piece of equipment to the hard-wired CPU, the PT unit uses a radio frequency signal generated in the hub hardware to transmit the information via a seatstay receiver hardwired to the handlebar mounted CPU.
The Power Tap uses strain gages, and therefore, is susceptible to the same sources of error as the SRM- mainly temperature compensation, strain field assumptions, gage alignment/transverse sensitivity.
The system makes use of eight strain gages in the hub using a special configuration tailored for measuring torque in a shaft. The orientation and the extra gages help make the resulting strain measurements more robust at boosting the signal to noise ratio and rejecting the chain bending moments and shear forces inherent to the geometry of the system.
Furthermore, since PT measures torque at the rear hub, it needs to measure the angular velocity at the same point. This means that instead of monitoring cadence for the angular velocity (like SRM), they measure rear wheel angular velocity. Angular velocity with the PT is measured with a sensor in the hub that marks/transmits each revolution of the hub. This is elegantly done by embedding a magnet in the axle and a reed switch in the hub body. With each revolution the switch is closed and opened creating a pulse train signal similar to the simple cyclometer on most cyclocomputers.
As an aside, it should be mentioned that there is a theoretical difference in the power reported by the SRM and PT systems. This difference is a result of the PT measuring the power at the hub and the SRM measuring power at the crank. The power at the hub is downstream of the system drivetrain losses (frictional losses at the chain/gear interface). Theoretically, the PT should measure around 2% less power than the SRM.
In summary, the PT system uses strain gages in the hub to measure torque and simultaneously tracks rear hub angular velocity in order to calculate power.
Polar
Polar took an interesting path to solve the power measurement problem. Polar uses chain tension and chain speed to calculate power. At the heart of this system is what is essentially an electric guitar pickup mounted to the chainstay.
This sensor allows the frequency of vibration of the chain to be monitored by generating a voltage that is proportional to the up and down velocity of the chain. Position of this sensor is important, since better results will be had when the change in up and down velocity of the chain is the greatest (point of largest deflection or the middle span of the chain). Signal processing of the data collected will allow the frequency of vibration to be determined. Converting this measured chain frequency to the all-important chain tension requires knowing some fundamental vibration theory. Vibration of a flexible, massive, string is described by the equation:
This equation illustrates the reason why users must measure and input the mass per unit length of the chain and the separation distance between centers of the hub and crank. Without this information, the chain tension cannot be determined based on the measured chain frequency. These extra bits of user-measured data add to the uncertainty of the measurement. This is one of the fundamental reasons why the Polar has a lower claimed accuracy on its power measurement device.
Unlike the other two systems, Polar does not measure a torque on the bike system. It turns out that the power being put out by the rider can be determined simply by measuring the chain tension and multiplying it by the chain speed. The small sensor that requires the replacement of one of the rear derailleur pulley screws measures the chain speed.
This method of monitoring chain frequency is not an exact science. Positioning and proximity of the sensor relative to the chain can affect the results. It also requires significant signal processing and filtering in order to reduce the data.
Polar uses cadence to determine sampling periods – the cadence measurement is done via a small magnet attached to the crank. The cadence pickup is located within the chain tension pickup mounted on the chainstay.
In summary, Polar uses chain tension and chain speed to determine power.
