### Garmin Vector released: L-R power balance comparison with Quarq Elsa

The Garmin Vector is clearly the most anticipated power meter to come onto the market. There's a few reasons for this. One is the freedom of choice it affords in selecting components. With a Powertap, you need essentually a new Powertap for every wheel. With crank-based systems, restrictions are more limtited, but swapping pedals is generally considered easier than swapping cranks (this is debatable, however: my Lightning crank is super-easy to take off and on).

But perhaps more than this is the ability to measure independently the left and right pedal. This is power measurement at essentially the point of contact. It's directly measuring the forces applied by the rider. That was the inspiration for the name: "Vector". It's measuring the force vector applied by the rider's feet.

This is somewhat of an academic point in comparison to the crank spider, since it's generally considered to be the case that there is negligible power loss between the pedals and the spider. There's some loss associated with the inelastic component of flex, but the crank-pedal system is designed to be relatively stiff, so these losses are almost certainly well into the sub-watt range.

But where the Vector has an advantage versus spider-based systems is its access to left and right forces separately. Additionally it has direct access to the direction of force application, something systems measuring power further downstream miss. For example, the Rotor Flow and the Pioneer system have independent L-R measurement. But the Pioneer, for example, is relying on measurements of the L and R crank arm flexing. In most modern cranks, the L and R crankarms have substantially different mechanical properties, due to the presence of the drivetrain on the (typically, on a solo bike) the right side. It thus requires independent calibration of somewhat dissimilar systems. In contrast the Vector has the advantage that the L and R pedal spindle are essentially antisymmetric, and have nominally equivalent mechanical properties. Thus even in the presence of errors in power extraction, averaged over several pedal strokes, L-R balance should be relatively less affected, since if the rider has a symmetric pedal stroke then the errors on both sides should be the same.

SRAM's Quarq Elsa, a spider-based system, takes a bold approach to left-right balance. They assume that a full rotation of the spider can be divided into two segments: one dominated by the left foot, one dominated by the right foot. A super-naive approach would be to assume all work done during the foot on the downstroke. I doubt they do this. Another approach would be to assume during the application of peak torque on each half-stroke, the downward foot is dominant. Perhaps this is what they do. In any case, since a perfectly L-R symmetric pedal stroke would result in equivalent half-strokes, they view deviation from symmetry to be an indication of L-R asymmetry.

Now this reverse assertion obviously isn't the case. I could construct a machine which would apply force to a single pedal and yet deliver a nearly equivalent pair of half-pedal strokes. This would fool the Quarq into thinking I had perfect L-R balance, while in reality L-R balance would be 100:0. Nevertheless, the human body is not such a machine, and it seems conceivable the Quarq approach is good enough in practice with real human riders.

Similarly, just because the pattern of force application is asymmetric, the total power applied need not be asymmetric. For example, suppose my left foot delivers a smoother force pattern than my right. In this case L-R power may be perfectly matched, yet peak torque, or work doing during the L-foot downstroke, may differ. In this case, unlike the previous, Quarq may claim an asymmetry while Vector reports perfect power balance.

So what Quarq describes is an asymmetry of some sort. Vector describes a different asymmetry. Of course, Vector could report a metric associated with peak torque, as well. It has access to more detail then Quarq. By the time Quarq observes torque (and therefore power) the L and R pedals have been combined.

Now, for the first time, the public has access to real data from the Vector. By far the best widely available source is DC Rainmaker's. He rode a bike outfitted with an impressive 4 independent power meters: Quark Elsa, Stages, Powertap, and Garmin Vector. He did multiple rides, carefully correcting installation errors from his first, and combing the data streams synchronously with a WASP ANT+ wireless bridge. Then he posted his data online.

There's a lot to go through, and with my injury I don't have as much time or energy as I used to for this sort of thing. But here's an example of a piece of low-hanging fruit from that data set. I plotted the L-R balance of the Garmin Vector versus the Quarq Elsa. This is from Rainmaker's climbing ride he did towards the end of his test day, after he'd gotten installation dialed in:

The agreement is far from impressive.

So I think the conclusion here is, if you believe the Vector numbers, that the Quarq method fails to reproduce L-R power asymmetry.

This begs the question, however, as to whether the Vector numbers should be believed. Garmin claims 2% accuracy for the Vector. This is for total power. Errors in total power consist of correlated and uncorrelated errors from the individual pedals. If errors from the pedals are uncorrelated, this corresponds to a 2.8% accuracy for each pedal, with the accuracy improved by adding the two together by a factor square root of 2. If the errors from the pedals are correlated, then each pedal has 2% accuracy, and the errors on the two pedals are the same.

Correlated errors might include effects of temperature (since the two pedals are exposed to the same temperature), errors in cadence (assuming each pedal uses the same cadence numbers), and errors associated with symmetric aspects of the way the rider is applying force to the pedals (for example, pushing more on the outside of the pedal than the middle of the pedal), and deviations in pedal characteristics from assumptions in the modeling (for example, assuming some effect is linear when it is not perfectly linear, or assuming a force is parallel to a direction of motion when flex causes it to be not perfectly parallel, etc). Since riders tend to apply fairly symmetric power to the pedals it can perhaps be assumed that most of the error associated with specific ways in which the rider applies power are correlated. These correlated errors will affect the L and R pedals the same, and therefore will not affect L-R balance appreciably. Of course if each pedal were to determine its own cadence, cadence errors would be uncorrelated, which would be unfortunate unless you're riding Power Cranks where the two cranks can turn independently.

Uncorrelated errors include errors in calibrating the pedal, errors associated with uncorrelated aspects of the rider's pedal style, and variation in residual strain from the value extracted during the zeroing process (which involves keeping the pedals stationary without applied force, then backpedaling when the shoes are clipped in). It is the uncorrelated error sources which leads to errors in L-R balance.

So I need to partition the error budget into a correlated and uncorrelated component. Looking at these components, I think it's safe to say a significant fraction of the 2% error budge is correlated. I'll arbitrarily assume half of it. That leaves 1% uncorrelated error. This corresponds to each pedal yielding a 1.4% power error, considering only the uncorrelated component of the power error.

Pedal balance is, for example, right pedal power divided by the sum of the left and right pedal power. It's close to 50%. Consider the case where the right pedal measures 1% high. Then instead of 1.00 / (1.00 + 1.00) = 50%, I get 1.01 / (1.00 + 1.01) = 50.25%.

So the error in L-R pedal balance is approximately a 1/4 of the error in the difference of L and R power, to first order. The error in the difference of L and R power is the square root of 2 times the individual pedal errors, which is the square root of 2 times the total uncorrelated error, which I am assuming is 1%. So the error in the difference is on order 2% of each pedal's individual power. I therefore conclude the net error in L-R balance is around 0.5%. So if it says 50.0%, the reality could be between 49.5% and 50.5%.

Given these error bars, it seems the difference between the Vector and the Quarq is quite significant. It also suggests that DC Rainmaker's asymmetry is real: he's pedaling slightly left-dominant. But it's fairly close. I can't have enormous confidence that DCR's not perfectly symmetric. I can conclude the asymmetry reported by Quarq is not a power asymmetry.

## Comments

I suspect with me that my right up is stronger than my left up, so it is showing a power imbalance to the left. The steeper the climb the more I seem to engage the upward side of the pedal stroke. The Vector may show this same pattern as 50-50, but frankly I'm not sure either is right.

In short, I have no idea what to do with the data. Even if I thought 50-50 was the goal, its possible on the Quark I would end up with a stronger right up and right down and weaker left up/down and be showing 50-50. On the Vector you could have a stronger right up/weaker right down and balanced on the left and get 50-50. Really the 2 measurements tell you very different things and neither tells the whole story.

I guess a true L/R balance measurement could be used to figure out how different fits affect not just power output but also pedalling smoothness.