Garmin Vector the Polar Pedal Based Power Meter

These two companies, and several others have claimed to be making a power meter that measures straight from the pedal.  There are some obvious benefits to this, including but not limited to: Power before mechanical drag, and individual leg power.  It isn't that simple though.  Each pedal sees a complex loading which is very hard to reduce.  Sure accounting for the bearings will eliminate the torsion the pedal axle sees, but there is still much more.  Cycleops measures the torsion of the hubshell, and multiplies that with the radial velocity of your pedals (read: Cadence).

Here is what Garmin and the other folks have to take into account:
-Position of the Crank/pedal
-Angle of the Pedal
-Centripital effect of the pedal.  (It should be noted that the effect due to the Coriolis acceleration is reduced to zero)
-Deflection of the pedal axle
-Cadence
-Crank Length
-Speed

Here is what that requires:
-Potentiometer (Easy)
-Multiple Accelerometers
-Multiple Strain Gauges
-A fairly complex computer to make sense of all the data.

Building it is what I am guessing is not going to be a problem.  Validating the equations is where things get messy.  For example, pedaling very fast (over 150 rpm), will make the accelerometers read essentially trash.

The complex computer would require a fast (with respect to other brands running at 2-3 Hz) processor running at around 60Hz, and a large medium for storage, 16gb should do.  It will also have to process all the data.  I am pretty sure that all the companies will be using the dynamic equation of motion (EOM) in conjunction with the Stokes equations of vector calculus. (See: http://en.wikipedia.org/wiki/Stokes%27_theorem#General_formulation for more information).  I am hoping to have the equations written out an simplified over spring break, but to be honest that probably won't happen.  Anyway, I hope this is some insight about how complex these little power meters are.

Cost Analysis of a Cycleops Powertap

Professional cyclists all have very similar equipment.  Their bike is the top of the line in terms of stiffness and weight.  This leads to a bike race being won by the rider, not the bike.  Training is a key aspect in gaining an advantage over the competition.  Many professional cyclists focus on quality of their training, as they often have a second job.  A power meter’s job is to do just that, optimize training.  Using advanced programs such as “Power Agent” one can see a graph of essentially every aspect of his or her ride.  The power outputted is an instantaneous response to any input and is more useful than heart rate.   “Power Agent” can also normalize the outputted power so that it may be compared.  By examining power profile curves a racer can tune his or her race strategy.  Hunter Alan’s “Training and Racing with a Power Meter” shows a chart illustrating a racer’s power to weight from the levels of Untrained to International Professional as well as certain power profiles.

There are several power meters currently on the market.  The main difference is the accuracy, or amount of strain gages, and placement of the gages.  The Powertap is one of the cheapest options, and it comes in the form of a hub.  The main disadvantage is the weight, as well as the reliance on one wheel, when in reality; most racers have a variety of wheels.  A second option, made by both Quark and SRM, is positioned on the crankset to eliminate the stated problem.  These models also have a higher accuracy due to the quantity of strain gauges, and being positioned closer to the input.  The newest style of power meter, yet to be released, is a pedal based system manufactured by both Garmin, and Polar.  By moving the measurement closer to the input, mechanical inefficiencies are neglected.  One of the main concerns with the pedal measurement is the complexity of the input.  The input is essentially a combined loading problem with a rotating reference point.   This new design, once released, will revolutionize the power meters, due to the ability to read both the left and right pedal power independently.

The Cycleops Powertap is the most popular and inexpensive power meter on the market and was further analyzed.  When dealing with torsion, strain is measured as the result of an applied torque to a stationary shaft.  In the Powertap, the stationary shaft is the bike axle.  To most accurately measure torque, strain gages are mounted in pairs.  They are ideally attached at 45 degree angles, with one gage measuring strain from increasing length (tension), and the other measuring decreasing length (compression).  Because there are two strain gages, the sensitivity is effectively doubled.

The Strain Gages in Place (Each gauge costs about 25 cents)

Measuring torque in a stationary torsion shaft has other applications such as power measurement in engines, motors, turbines, and any other system that utilizes dynamic twisting motion.  Stationary torsion shafts can also be used in applications involving torque tool and sensor calibration, spring testing, and friction measurement.

It is important to note that in order to decrease cost of strain gage installation in a cylindrical member, the strain gage needs to be applied to a flat surface.  This can be easily accomplished by machining a flat plane into the shaft.  The installation on a curved surface is a little tricky, and would be expensive.  The strain on the flat surface is also essentially constant throughout, yielding an accurate strain measurement.

The Torsion Bar and Housing (Hub)

The basis of the circuitry revolves around having the four strain gage rosettes located on the torsional bar on the hub. Each strain gage rosette consists of two grids at 45 degree angles. Two sets of strain gage rosettes are connected together and connected into two full Wheatstone bridges. This is beneficial, because full Wheatstone bridges are the most sensitive and allow for excellent temperature compensation. As described in, a Wheatstone bridge with four active gages adds a factor of four to the sensitivity equation, giving it a greater sensitivity, rather than having multiple quarter Wheatstone bridges. The signal from the circuit is transferred to a receiver with the use of induction or ANT+ wireless.

Conclusion:

The Saris powertap is a effective power measuring device; however, the cost is astronomical. The technology used is similar and essentially identical to an electronic bathroom scale. My estimate is that the power tap unit, including circuitry and head unit costs Saris around $50. With new powertap alternitives sprouting up, the cost should hopefully decrease.

--Blaine Benson

*Contributions by Ante Beslic, Jeff Narkis