Power Measurement

Recently I decided to have a look at other methods of measuring power - specifically the Velocomp Newton and Powerpod, as opposed to the "traditional" strain-gauge systems that an increasing number of cyclists are using. I hope to write more on the Velocomp system, but the thought inspired me to have a look at a variety of ways (both realistic and less-so) of measuring power in cycling.

Input/Physiology

Diet

Definitely on the less-realistic side, this one. As all energy expended on the bike must come from energy input; in theory if you kept track of energy input, removed expenditure due to non-cycling activity, and reduced the remainder to account for the body's efficiency at converting food energy into cycling output - you could have a sort of terrible power meter. You'd also have to account for storage in fat, but you couldn't just use weight change as hydration status would change things too much. In short, not a great idea unless you're only after the average power in a several-week-long race where the cyclist is either cycling, eating, or sitting quietly/sleeping.

VO₂

More plausible here, and something we actually use to an extent. We can measure oxygen use (or CO₂ production) using a face-mask with a rapid gas analyser. As the final endpoint for all "fuel" burning in the body relies on oxygen, we can use a figure of approximately 20J for every ml of oxygen consumed. A 90kg triathlete working (hard!) at a VO2 of 60ml/kg/min therefore produces 1800W. Unfortunately, the proportion of this which hits the pedals is somewhere between 10 and 25% depending on the effort, and how well-trained the individual is. The rest is lost as heat. In short, it's a bit like measuring a car's engine power by how much petrol it uses - there's definitely a link, but it's by no means clear.

Additionally, we know that an athlete can produce power above their pVO2max for short periods - using the phosphocreatine or glycolytic systems. Eventually oxygen will be required (the "oxygen debt"), so averages should work out, but instantaneous power will be lacking.
In some ways, though, this may be more useful than knowing what power is coming out through the legs - as it reflects the metabolic cost of cycling, which might be handy for people using power-based training load. However, it's not easy to measure - requiring expensive kit and uncomfortable masks - so its use will probably remain confined to labs for now.

Heart Rate

Loads of people train with heart rate (even those who aren't using it as an intensity guide), and over a reasonable range the relationship between power and heart rate is a straight line. In theory, your MaxHR represents your VO2max and your resting HR represents your basal metabolic rate (1 MET is conventionally 3.5ml/kg/min). Obviously this then suffers from the same issues as trying to use VO2 above, and additionally the issues of heart rate "lag" (where it takes a while for the heart rate to catch up to where we predict it should be), and "cardiac drift" where dehydration and other forms of fatigue contribute to an increased heart rate at the end of exercise for the same power output.

Powertap have tried to answer some of the issues with their "PowerCal" heart rate monitor. Whilst the algorithm is not public, it presumably uses the rate of change of heart rate (and possibly heart rate variability) to enable a faster response. However, even Powertap only claim it has "varying degrees of accuracy" - which in practice apparently means that it can easily be over 100W out. Unfortunately the relationship between HR and VO2 varies massively between individuals, and as above the relationship between VO2 and power output is also uncertain - it's unlikely that this approach will ever be of real value.

Direct Force

Strain gauges

This is what most people are talking about when they discuss bike power meters. They take various forms, due to varying positions on the bike. I'm aware of:

• Shoe (insole)
• Cleat
• Pedal
• Pedal fixing
• Crank
• Spider
• Chainring
• Bottom bracket
• Hub

Fundamentally all work using the same equation:

Power = Force x Velocity 

Force is measured using a strain gauge - a device which measures how much the crank etc bends, and uses that to work out how much force was applied. Velocity is - when measured around the cranks - calculated by multiplying the cadence and the crank length (and 2π). Simpler systems will assume that the velocity is constant during each pedal stroke, which with a round chainring is usually not a bad approximation. With oval chainrings, the velocity varies and it's necessary to measure the crank rotation much more frequently using accelerometers or similar. Without this, power will tend to be overestimated which may account for some studies showing that oval chainrings improve power!

Measuring at the hub (eg PowerTap) uses strain gauges in a "torque tube" connecting the cassette to the rest of the hub. The power in this case is calculated from the torque and the rotational velocity of the wheel. As all these are round, it doesn't suffer the same issues with oval chainrings.

The main issue with strain gauges is temperature. The gauge uses electrical resistance to measure bending, and temperature can also affect resistance - either directly by changing the resistance of the gauge or connecting wires, or indirectly by causing the crank etc to expand or contract. Various methods exist to overcome this - eg Quarq advertising that they calibrate 10,000 temperature points into their software. Unfortunately, a lot of strain-gauge-based power meters end up prone to some degree of 'drift' as temperature changes.

Another issue with strain-gauge based systems is not so much related to the technology itself, but to attempts to make it cheaper. Rather than trying to measure power in two cranks, or two pedals, some systems will just measure one and double it on the basis that humans are (mostly) symmetrical. Unfortunately true pedal balance is rarely exactly 50/50, and worse it can change as you work harder or tire over a long ride. Obviously hub and chainring-based systems can avoid this by measuring after the two legs' work has been combined.

It's worth mentioning that the version 1 of the Kickr turbo trainer uses strain gauges as part of a feedback loop to measure and control power. Unfortunately though, they put them in the small part driven by the flywheel, which makes the velocity very high and the forces very low - and can lead to inaccuracy. Version 2, and a recent firmware update for version 1, uses other methods discussed later to estimate power, as (they claim) the strain gauges turned out to be unnecessary and simply caused problems for some users. Interestingly, in my own testing of the strain gauge versus alternative estimates on a Kickr 1, I found that the alternative was very temperature-dependent in a cold garage - but appeared quite accurate once sufficient warm-up time had been given.

Piezoelectric effect

When a crystal is compressed it can generate charge, known as the piezoelectric effect - and used in reverse in some speakers and buzzers. It is rumoured that some power meters use this rather than traditional "bend" strain gauges as depicted above - particularly it would be suitable for pedal/cleat based systems. I can't find clear data on which devices use piezoelectric sensors - they have a few advantages and disadvantages compared with traditional gauges; most notably they apparently have a bad tendency to drift which must be accounted for.

Other torque methods

In industrial applications where torque (turning force) is transmitted, torque sensors can be used. These rely on a shaft connecting "input" to "output" with a set of teeth at either ends. As the teeth move, the timing of their passage must be read very precisely using electrical coils (induction sensor) or blockage of light (optical sensor). If the shaft is spinning with no force on it then both sets of teeth will be perfectly synchronised. With force, the shaft will twist very slightly and one set of teeth will be delayed a tiny amount compared with the other. This delay tells us the torque in the shaft, and multiplying it by the rotation speed of the teeth (angular velocity) gives us power.
This technique is used in the Elite Drivo turbo trainer, which Elite claim to be the most accurate of turbo trainers and devoid of the temperature drift problems which can occur with others. Certainly as it avoids using resistance, the main reason for temperature drift in strain gauges is simply not an issue, and reported temperature drift for similar industrial sensors is tiny (of the order of 0.05% for a 10 degree change).

I'm not aware of anyone who has managed to get this technology onto a bike yet, despite what Wikipedia says about bottom brackets - in theory it should be possible at the bottom bracket or rear hub. The "torque tube" in a PowerTap wheel uses strain gauges as mentioned above, as does the Rotor InPower.

Chain tension

I think this is a fascinating idea, but I gather it didn't work very well. It was used by Polar some years ago. Using the idea that power is equal to force multiplied by velocity; the theory was to estimate the chain tension (force) and speed while the cyclist was pedalling. Measurement of the chain tension was based on the fact that an object under tension vibrates at higher frequencies (like twanging a stretched elastic band), so a microphone (guitar-pickup style) was used next to the chain to see what pitch it was at. Unfortunately a lot of other things affect the pitch such as the makeup of the chain, the length of chain free to move (which changes with gear changes), and the tension in the "slack" side caused by the rear derailleur spring. But a lovely idea nonetheless!

Opposing Force

Outdoors

If we're not measuring the input to the system via the pedals, cranks, chain or hub, then an alternative is to measure the output - ie the "opposing forces" that in general slow down a cyclist (the exception being downhill). This is the approach taken by Velocomp/iBike/PowerPod Sports in their PowerPod and Newton devices.

The basic list of forces that should be accounted for are:

• Wind resistance
• Rolling resistance
• Slope (altitude loss or gain)
• Acceleration
• (Optionally) Drivetrain losses

Wind resistance is the main force acting against you on a bike moving more than a few mph. It's hideously complicated to predict accurately even in perfect airflow (hence the existence of wind tunnels and massive supercomputers for CFD), and worse when you try to consider gusts and hedges etc. However, in cycling we normally simplify things as much as possible to talk about "CdA" and use a formula which considers the action of wind resistance from the front. Ignoring the component of the wind which comes from the side isn't as bad as it sounds, because whilst irritating it shouldn't really be affecting speed so much except in the phenomenon of disc wheels acting as sails.

P_wind = ρ × v_bike × Cd × A × v_wind²/2

Where ρ is the density of air, v_bike is the speed of the bike, Cd is the drag coefficient of the bike and rider, A is the cross-sectional area of the bike and rider as viewed from the front, and v_wind is the speed of the part of the wind blowing into the face of the rider (negative if there's one of those never-existent tailwinds!).

Measurements can in theory be made of everything except CdA which must be estimated from the rider's body position, or can be calculated from cycling with a known power input (either using a different power meter, or doing "roll downs" where the rider does not pedal and power is therefore zero) - search for the "Chung Method", or play with GoldenCheetah, for more information.

Because this largest component is so potentially difficult to estimate, and can change as a rider changes position, this is probably the main weakness of opposing-force systems. However, with constant rider position the numbers should at least rise and fall consistently relative to each other. And when paired with another method of measuring power (eg a traditional strain-gauge device) the equations can be run in reverse to give a live readout of CdA and allow optimisation of aero position without use of an expensive wind tunnel, which is potentially very useful!

Rolling resistance is mainly due to the deformation of the tyres and inner tubes as the flat contact patch moves around the tyre (there is some contribution from bearings, but hopefully little!). Rubber exhibits "hysteresis" where not all the energy used to squash the tyre comes back when it rolls on, and as a result energy is lost. This can be minimised by using expensive, flexible tyres with latex or no inner tubes - and interestingly width helps too.

P_rr = m × g × C_rr × v_bike

Where m is the mass of the rider and bike, g is gravity, v_bike is the bike speed, and C_rr is the coefficient of rolling resistance - which depends on the choice of tyres, pressure, and road surface.

Slope power is just the power required to move a rider uphill - or gained by going downhill. This could be measured by using altitude changes with a sensitive (eg barometric) altimeter; the iBike system seems to use an inclinometer to measure the angle of the road for even more rapid detection, and the altimeter to calibrate the inclinometer.

P_slope = m × g × slope × v_bike

Where again m is the mass of the rider and bike, g is gravity, v_bike is the bike speed, and slope is the percentage gradient (negative for downhill).

All the above will give a power value for a bike and rider moving at a constant speed, but in reality we slow down and speed up, so the last necessary term is acceleration.

P_accel = m × a × v_bike

Again m is the mass of the rider and bike, and v_bike is the bike speed. a is the rate of change of vbike - positive when the speed is increasing and negative when it is slowing.

Lastly, drivetrain losses (usually only a couple of percent) could be considered - but in practice we tend to ignore these with direct force power meters and just accept that a measurement at the hub (eg PowerTap) will probably read slightly lower than one at the cranks. An opposing force power meter is therefore more similar to a hub value.

The value reported by an opposing-force power meter like the Powerpod will therefore be the sum of these separate values. It looks quite complex and obviously requires accurate measurement or estimation of a number of factors rather than just the force and angular velocity of strain-gauge power meters. But interestingly it appears to work - I'll hopefully put a separate review up later, but in playing with an iBike Newton+ I've had some very plausible-looking numbers despite all the assumptions it's making. I've not tried it on my race bike yet, which has a Power2Max power meter on it - but I'm hoping to play with live CdA analysis, and compare the readings from the two meters - and I genuinely expect to see some correlation there.

Indoors

For all the claims that Opposing Force power measurement is something weird and wonderful, we've been doing it for a while indoors. Obviously it's a lot simpler as there's no wind resistance or slope, and the acceleration is just that of a turbo trainer flywheel.

Many turbo-trainer manufacturers nowadays will publish power curves for their turbo trainers - basically allowing conversion between a wheel speed (must use a rear wheel sensor for obvious reasons!) and a power value. This obviously completely ignores acceleration, and assumes rolling resistance does not vary between setups (the "road surface" is at least the same), but allows a ballpark figure to be produced. Unfortunately, differences in setup are often significant - particularly tyre pressure and pressure of the trainer roller against the tyre - leading to its use in Zwift to be somewhat looked down upon (unnecessarily in my view; I'm happy to race anyone).

Ignoring acceleration is fine for steady-state efforts, but for short intervals and especially for virtual racing on something like Zwift, acceleration power is important. Unfortunately details for calculating this are rarer, but Zwift has a few trainers marked as "ZPower" where it will consider acceleration of the flywheel (confusingly, many people use "ZPower" to mean any power-curve estimation). Having played with a genuine ZPower-supported trainer (Cyclops Fluid2) on Zwift, I found that the numbers seemed vaguely plausible - but far lower than what I'm used to. So ZPower isn't always the fast route to the front of races that people accuse it of!

The above examples make indoor opposing-force measurement sound incredibly inaccurate, which is surprising given that outdoors (which is much harder) the Powerpod seems to make a decent stab at it. I think this is much more an issue with consistency between trainers (especially the ones which leave the wheel on) which weren't really designed for this sort of estimation. In fact, some of the high-end trainers such as the Wahoo Kickr also make use of the opposing-force principle.

As mentioned earlier, the original Wahoo Kickr (V1) used traditional strain gauges to estimate power - in fact, it seemed to use the strain gauges as part of a feedback loop to keep an opposing-force model in check. The opposing-force model uses the electrical requirements of the braking unit, and acceleration of the flywheel, to estimate power from the braking strength required to keep the wheel speed down. With a number of V1 units suffering issues with their strain gauges - apparently because they had located them in a low-force-high-speed area with therefore much greater sensitivity to noise - Wahoo decided to refine their model to the point where they realised it could be used without any strain gauge input at all. This "new model" is what is used on the V2 and subsequent Kickr models, and is available for the V1 as a firmware update - though certainly on the V1 appears to be quite temperature-sensitive and is presumably the reason for additional temperature sensors in the V2 model.

I am confident that other trainers use a similar principle, though I don't have precise details - but it seems likely that the Tacx Neo and Genius use models derived from opposing-force brake current rather than a traditional strain-gauge approach.