From Power Models to Opposing Force Power Meters and the iBike Newton+
At Cycling Power Lab we spend a lot of time applying models to answer questions about cycling performance – the
biggest one being “if I want to travel at speed X on course Y, how much power do I need”? It’s essentially a
question of calculating the forces opposing a rider – aerodynamic drag, gravity, rolling resistance, friction –
based on known knowns describing the properties of the rider, bike, course, and weather. The theory says that
if we had completely accurate data describing, for example, the rider’s weight and the makeup of the course, then
our power estimates – consistent with the laws of physics – would be spot on, in fact more real than the numbers
coming from a rider’s power meter.
Now imagine if we took all of this to the Nth degree to develop a power meter with a collection of sophisticated
sensors. Let’s call it an “opposing force power meter” (OFPM) and contrast it with a more conventional
“direct force power meters” (DFPMs). How good could it be in relative terms? It so happens that this question
has been largely answered for us by Velocomp LLC – makers of the iBike – which is the only power meter on the
market to take the opposing force approach.
We recently had the pleasure of discussing the flagship iBike Newton+
in some detail with Velocomp’s
CEO and Chief Physics Officer (that’s right – perhaps uniquely Velocomp have a guy with a PhD in physics responsible
for the products on board “physics engine” among other things). The conclusions should be of interest to anybody
in the market for a power meter.
Setting The Scene - Direct Force Power Meters
Part of the reason DFPM’s such as the SRM are so expensive is that they rely on a collection of strain gauges
retro-fitted into a crank spider (or hub or pedals) to develop an electrical signal which can be translated i
nto torque readings. Fitting those gauges well is somewhat time consuming and, though it may not be one of
Newton’s laws, time = money. They also rely on accurate measurements of the angular velocity of the component
hosting those gauges since power is resolved as “Torque X Angular Velocity”. It follows that the accuracy of
DFPMs depends on 3 things:
1) Consistency of Strain Gauge Response.
Changes in temperature will affect strain gauge response, not just day on day but throughout the duration of a ride.
Ride for a long time or climb a mountain and ambient temperature can change dramatically. Depending on the way
those strain gauges are hosted in a crank spider the choice of chain ring and even bolt tension may also affect
gauge response. There is a reason some Quarqs for example are calibrated using both chain rings.
2) Translation of Gauge Response to Torque (Zero Offset & Calibration)
The basic process of calibrating a DFPM with strain gauges involves reading the frequency response from the strain
gauge under zero torque (the zero offset), applying a known weight to the pedals while reading that frequency response
again, and then running a simple calculation to specify the “frequency response per unit of torque” AKA “slope”
for on-going use by the device.
Now consider for a moment what happens if we apply two or more different known weights to the pedals such as
20 and 40 kilos. If the frequency response (over zero offset) at 40 kilos is not twice that at 20 kilos then we
have a problem - torque response is non-linear. We have to resort to a “line of best fit” (the slope of a regression line)
to specify the slope of the device. Lines of best fit imply error. In fact, when a manufacturer claims “accuracy +/- 2%”
this is the most likely source of error they are expressing.
3) Good Measurement of Angular Velocity
How well a power meter determines angular velocity (i.e. cadence or RPM of the rear wheel) depends on two things –
how often the meter takes a reading and how quickly that reading changes. Stop pedalling abruptly and a DFPM assumes
your cadence remains unchanged until the moment it gets around to re-sampling. This will limit its ability to deliver
unconditionally accurate power numbers in non-steady state cycling.
Is the direct force power measuring approach flawed then? The widespread adoption of DFPM’s suggests otherwise. But it
would not have been prudent to consider the challenges of opposing force power measurement without first reviewing
the challenges of the direct force approach.
Opposing Force Measurement
An OFPM depends on none of the three factors above to deliver power numbers. Instead it depends on accurate specification
and sensing of all opposing forces, preferably at a high sampling rate. The most important question to ask of the opposing
force approach then is just how good can all of these specifications and sensors be? We ask these questions through the
example of the iBike.
The iBike employs a digital tilt sensor to detect road gradient. The technology involved functions similarly to a digital
spirit level with one exception – it can be calibrated much more accurately. You calibrate by going for a five minute
out-and-back ride finishing exactly where you set out. This guarantees good gradient sensing and accounts for the impact
of weight distribution on the bike. An added bonus of this sensor is that it delivers a real time view of road gradient
to the rider. Conclusion – High confidence.
Air density is key to calculating aerodynamic drag related power requirements. The standard formulas required to calculate
it involve static air pressure, temperature and humidity inputs. The iBike senses static pressure and temperature.
Humidity is neglected but this has an almost trivial impact on air density. As an indication the difference in the density
of typical sea level air at 0% and 100% relative humidity is less than 1%. Conclusion – High confidence.
Wind (Air Speed)
When we calculate power demands arising from aerodynamic concerns one of the numbers that matters is a product of
air density and velocity in the bike axis. As it happens, air velocity can be calculated using inputs of static air
pressure, dynamic air pressure (effectively the number of air molecules hitting a sensor) and air density. Every
commercial airplane you ever flew on used the same physics to give the pilot an accurate indication of airspeed.
The iBike incorporates a dynamic pressure port on the front of the device which works in conjunction with the
static and temperature sensors mentioned above.
As with gradient data from the tilt sensor this technology facilitates a real time reading of headwind, including
or excluding bike speed, to the rider. Conclusion – High confidence.
The iBike offers real time display of Environmental, Slope & Wind Speed variables - the latter faciliated by it's dynamic pressure port
Speed (Ground Speed)
As with many bike computers the iBike relies on a remote sensor and wheel magnet configuration to maintain a constant
awareness of ground speed. It’s a simple principle but “as good as it gets” and somewhat better than GPS based
speed measurement. Conclusion – High confidence.
Changes in speed that do not result from changes in elevation impact the level of power required from a rider and hold
equal relevance in the calculation of “opposing force” power demands. The iBike uses accelerometers similar to those
employed in motorsport (telemetry) and aviation (flight recorder) applications to detect these forces with a
sensitivity of +/- 0.004g, sampling 800 times a second!
Remember what was said above about the limitations of DFPMs in terms of cadence sampling? Well in certain non-steady
state riding situations you may be able to expect better numbers from an iBike. Conclusion – High confidence.
Rider & Bike Parameters (Weight, Cm, Crr, CdA)
The iBike system requires the user to maintain a “rider and bike” profile such that the physics engine has some
good measurements of combined rider and bike weight, drivetrain efficiency (Cm), aerodynamic drag coefficient (CdA),
and coefficient of rolling resistance (Crr). This profile can be maintained on the device itself or using the
accompanying analysis software.
Consider weight. A “known weight” is used to calibrate direct force power meters. A known weight is also used to
calibrate digital bathroom scales before they leave the factory. With some care and forethought the combined weight
of a rider, bike, clothing and on-board equipment can be established with good accuracy.
Consider drivetrain efficiency. In fact drivetrain efficiency has no impact on the forces opposing the forward motion
of a bike, it only adds to the forces required from the rider. Power Tap users study their power at the rear hub with
no knowledge of how drivetrain efficiency scales that to the power demanded at the pedals. Meanwhile users of crank
or pedal based DFPMs have no knowledge of just how much of their metered power reaches the road.
An estimate of “2% difference” is common. The iBike software simply allows you to specify a difference parameter,
known as Cm. You set it to 1.0 if you prefer to think in terms of power at the hub and yet set it to 1.02 if you
prefer to think in terms of power at the crank.
Now consider Crr & CdA. Here is, in our opinion, the most significant limitation of the opposing force approach.
The physics engine needs good measurements of both parameters to deliver real power numbers. There are a couple
of possible approaches here. You can use the software to establish empirical estimates of these parameters based
on road surface, tyre type, inflation, and riding positions – at Cycling Power Lab we rely on such approaches
frequently for modelling purposes. Or you can execute a roll down test protocol to try and derive better estimates.
We’ve not had great results from roll down tests but then we haven’t tried them with the wind sensing and accelerometer
support built into the iBike. What we can say is that even somewhat erroneous inputs can still provide consistency
in power measurement. Conclusion – Conditional Confidence.
Should I be using an Opposing Force Power Meter?
Lately we’ve had a few emails from people asking us “which power meter should I buy?” Sometimes it’s a little
surprising that people want to delegate that sort of decision but at the same time it’s nice to be trusted.
Our answer is generally that “it depends what’s important to you”.
Certainly no power meter delivers the last word in accuracy; all accuracy is relative to the extent that the prominent
goal is often consistency. And certainly all power meters are absolutely dependent on good calibration. It’s fair
to say that the opposing force approach does require more and continuous attention to certain calibration inputs
to deliver good and consistent numbers so if that makes you nervous then it’s probably not for you. On the other hand
opposing force power measurement requires just one bike-portable device which avoids the expense of strain guage configurations
such that, in the case of the iBike, you're getting a very cost effective power meter with the serious bonus of real time
environmental, gradient and wind data. Having dealt with these issues then it’s really down to how you interpret the
potential limitations of each device, the characteristics you value and how much money you want to spend. Over to you…
You can further investigate the iBike Newton+ and opposing force power measurement at the website