|Cycling Power Meter Review|
|Power Meter Review pg 2|
|Power Meter Review pt 3|
2011 Cycling Power Meter Review
words and images by: Kraig Willett
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 race results – well, maybe only two, but who’s counting! There were some key things, for me, which allowed the achievement of most of my modest goals along the way. The most important key 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’s 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 real-time (and later, with a downloadable polar HRM post-ride analysis) training feedback and the associated HRM vocabulary acted as a backbone to my training program. Cycling training with a HRM is still probably the most economical way to structure a gadget-based training plan, but with the entry of several different manufacturers into the power-measuring arena, training with a power meter (PM) on your bike is becoming a tempting alternative.
The Power of Power?
Should you train with a power meter bolted into place? After having trained with a stopwatch, perceived exertion, heart rate and most recently with all of the above in addition to a PM for the better part of 10 years, I think power simply adds a different perspective to the mix.
Power does have the potential to be a game-changer in one’s general approach to training by cutting through the noise associated with one’s day to day performance. These types of training philosophy paradigm shifts and gains are front-loaded, however, so the long term impact of continued use of power measuring devices can be debated. I haven’t taken my power meter off my bike, yet, though! But, I can say the same thing about my HRM and stopwatch, too.
At the end of the day, power is simply an objective measure that doesn’t really make one faster. Rather, I think the Power of Power is that it is an enabling technological platform that opens up the adjacent possible. For me, the adjacent possible was achieving the level of performance I am capable of in less time. For others, the adjacent possible may simply be a different language that allows for better communication with their coach. And, yet others will see the adjacent possible as the ability to make better equipment or positioning decisions by analyzing power meter files to determine their CxA and Crr.
In short, a power meter can allow individuals to more quickly identify and focus on the training stimuli that are ultimately responsible for race-day performance.
Given these potential benefits and a more mature PM market, many people are making the decision to purchase a power meter these days. Unfortunately, there exists some uncertainty and confusion for consumers when it comes to picking which power meter is the best one. Over the years, I have had the opportunity to ride and experiment with a variety of power measuring systems: SRM, Power Tap (PT), Polar, and most recently the ibike (unfortunately, I don’t have any personal experience with the new quarq power meter, so it has been omitted). I will review these bicycle power meter systems using the three fundamental design variables of price, performance, and durability - but first, let’s cover some power basics.
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. However, ibike takes an alternate approach and doesn’t measure anything that is rotating; instead, it reports power by quantifying resistive forces and then multiplying this value by road speed.
The systems being reviewed take a variety of different approaches to determining power. SRM, PT, and Polar measure the same fundamental parameters of interest (torque and angular velocity) but they use different methods. The ibike measures all the variables on the right hand side of the power equation shown previously. The primary reason for these different approaches can probably be attributed to different design goals, or just plain wanting to do things a bit differently.
SRM was the first of the reviewed systems to enter the portable cycling power measurement business, distantly followed by Tune/Graber/Saris 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 chain based 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.
Ibike, with its novel approach also has some intellectually property in place to protect its product embodiment.
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. Ibike uses an accelerometer, wind speed sensor, barometric pressure sensor, and wheel speed/cadence sensors to calculate and report power.
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 used for this review is hard wired to a CPU (Central Processing Unit, or on board computer) mounted on the handlebar (note, the latest products from SRM are wireless).
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.
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 (more recent versions of the PT are completely wireless).
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 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 some of the other reviewed 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.
Capitalizing on the fact that:
…the folks at ibike set out to develop a product that measured all the stuff on the right hand side of the equation above. That’s a tricky bit of business! Through a variety of sensors contained in a single bar mounted head unit (and subsequent on board data processing), they were able to put a number on aero forces, rolling resistance forces, and acceleration based forces (the net of both translational acceleration and acceleration relative to gravity).
All of the sensors (with the exception of the wireless cadence/speed sensors) are housed in the head unit that is mounted on the handlebars or stem.
Aerodynamic forces are a function of the size and shape of the object, the air density, and the relative speed/direction of the wind.
Where CxA = axial force coefficient area (can be a function of wind direction)
The ibike unit uses temperature and pressure sensors to calculate air density and uses another differential pressure sensor (pitot-static tube) to measure the relative wind speed. The CxA term in the aerodynamic force equation is either calculated based on height/weight, or is empirically derived during a series of coast-down trials. It should be noted that no attempt is made by the ibike protocol to account for the possible wind direction dependence of the CxA term (nor to measure off-axis components of wind), and that this fact may contribute to an error in reported power.
Main sources of error in ibike aerodynamic force measurement:
· No measurement of/accounting for wind direction dependence
· Assumes rider does not change position/CxA during ride
· Pitot calibration is dependent on rider position
Acceleration can occur both translationally (i.e, accelerating from a stop sign) or relative to the earth’s gravity (i.e, climbing/descending mountains). Ibike uses a two-axis accelerometer (though, it apparently only uses one component in its current embodiment) and cleverly lumps both of these accelerations into a single term:
…where the acceleration is the total acceleration in both axial and vertical directions. As a result of this lumped approach, the ibike does not really directly measure the road gradient/slope, and instead uses the bike’s speed measurement to back out the road slope:
Faccel=mass *( gravity*sin(slope) – dv/dt )
…where dv/dt is the speedometer based acceleration. Does this really matter when it comes to measuring power? The short answer is, No, it doesn’t. But, if you want a clean road gradient/slope measurement, this approach is not so great. It was continually mentioned to me by ibike that “the reported slope value when the bike is at rest is meaningless”.
Since the ibike measures total acceleration to compute power with a single axis of acceleration data, it is subject to some errors. For example, turning a corner quickly will create centripetal acceleration, which the ibike sees as a reduction in acceleration and will thus cause a reported decrease in power (even though power is being held constant).
Furthermore, since the accelerometer is mounted on the handlebars and is initially statically calibrated, any time-dependent change in bar orientation relative to the earth’s gravity vector will be picked up by the sensor and will affect the reported power. This is a factor to consider primarily during out of the saddle efforts, shifts in weight distribution that affect the pitch of the bike, or deflection of the stem/bar assembly do to external forces (i.e – reefing on the bars during hard efforts).
Main sources of error in ibike acceleration force measurement
· Dynamic changes in bike orientation
· Dynamic overranging of the accelerometer on non-smooth pavement
Rolling resistance Force
Rolling resistance can be a multifactorial can of worms. Most equations of motion for a cyclist attribute rolling resistance solely to the tires and make it a linear function of road speed:
…where Crr is the coefficient of rolling resistance.
However, it is possible that Crr is a function of road speed and ambient/road temperature. Most certainly, though, Crr is a function of tire pressure (with the lower psi leading to a generally higher Crr value) and road surface condition (rougher roads generally increase Crr). The ibike assumes that Crr remains the same as it was empirically derived during the initial calibration coast downs, or it is simply entered as a user defined value.
Main sources of error in ibike rolling resistance force measurement
· Crr changes due to tire pressure, road surface condition, temperature
· Calibration errors resulting from coast-down trials
Of note, ibike does not theoretically need a cadence measurement to report power (cadence isn’t in any of the formulas above), but, if cadence is installed and you are coasting, the power reported will be zero independent of what the other sensors are reporting. This makes sense, in that, if you aren’t pedaling, you aren’t making power!
In summary, the ibike measures or derives all the variables that contribute to the resistive forces encountered by a cyclist and then multiplies this total resistive force by road speed to determine power.