Raman Garimella thesis - Final Draft

Estimation of Power and Energy Expenditure from Sensor Data
in Road Biking
Master Thesis presented
by
Garimella, Raman
Matriculation Number: 01/928574
MSc Sports Science
raman.garimella@uni-konstanz.de / garimella.raman@gmail.com
at the
University of Konstanz
Department of Sports Science
Evaluated by
1. Prof. Dr. Dietmar Saupe
2. Prof. Dr. Markus Gruber
Constance, 2016

ESTIMATING POWER FROM SENSOR DATA IN ROAD BIKING 2
Acknowledgements
This thesis has my name on it but it is hardly an individual effort. I thank:
- My supervisor Prof. Dr. Dietmar Saupe – for his hand-holding whenever I needed it.
He made time in every stage of the thesis. I admire his attention to detail, sharp
memory, desire to get to the root of problems, and immense experience in cycling.
- His research group (Powerbike Lab) – they opened doors for me to use their facilities
and knowledge freely. They laid down the project in the first place and I am happy
to finish it for them. I specifically thank Stefan Wolf and Alexander Artiga Gonzalez
for their informal and insightful chats and tips over the last few months about this
topic.
- The Sports Science department – Prof. Dr. Markus Gruber for his timely green
signals as co-supervisor of the thesis. Apart from superior knowledge in his area of
study, his light-hearted humour and warmth over the last two years will be
remembered. My friend and colleague Marcello Grassi took a lot of interest in my
work and lent an ear and a hand whenever I needed.
- John Hamann of Velocomp LLC, USA – for letting me in on the inner workings of
the PowerPod device.
This thesis is the final leg of the MSc course. There were challenges inside and outside the
university, but I thoroughly enjoyed my time in Constance, Germany, and Europe. It was
the first time that I lived away from my home country (India). It is not an exaggeration to
say that the last two years have changed me as a person as well as enhanced my skills as a
professional. For this to happen in the first place, the people to thank are my family: mother,
sister, and brother-in-law. They have been nothing but kind and their support means
everything to me.

Contents
Estimation of Power and Energy Expenditure from Sensor Data in Road Biking................6
Background..........................................................................................................................10
Power in Training ............................................................................................................10
Power Zones.................................................................................................................13
Power Meters ...................................................................................................................13
Direct Force Power Meters (DFPMs) ..........................................................................14
Opposing Force Power Meters (OFPMs).....................................................................15
Modelling Power..............................................................................................................16
The Equation ................................................................................................................17
Estimating Parameters..................................................................................................24
Methods...............................................................................................................................28
Shortlisted PMs................................................................................................................28
SRM .............................................................................................................................28
Powercal.......................................................................................................................29
PowerPod .....................................................................................................................30
Sigma............................................................................................................................31
Velocomputer...............................................................................................................32
Routes ..............................................................................................................................33
Subject and Setup.............................................................................................................34
Experiment.......................................................................................................................35
Analysis ...............................................................................................................................36
Metrics .............................................................................................................................37
Average Power and Relative Error...............................................................................37
Normalized Power........................................................................................................37
Root Mean Square Error ..............................................................................................38
Relative RMSE.............................................................................................................38
Peak Signal-to-Noise-Ratio..........................................................................................39
Energy ..........................................................................................................................39
Estimating Parameters .....................................................................................................39
Results .................................................................................................................................42
Part 1................................................................................................................................42
Full Ride.......................................................................................................................42
Training Zones .............................................................................................................42
Climbing Section..........................................................................................................42

Flat Section...................................................................................................................43
Normalizing..................................................................................................................43
Smoothing ....................................................................................................................43
Sprints...........................................................................................................................44
Part 2................................................................................................................................44
Full Ride.......................................................................................................................45
Climbing Section..........................................................................................................45
Smoothing ....................................................................................................................46
Discussion............................................................................................................................47
Part 1................................................................................................................................47
Powercal.......................................................................................................................47
PowerPod .....................................................................................................................47
Sigma............................................................................................................................49
Notes.............................................................................................................................50
Part 2................................................................................................................................52
Exclusion Criterion ......................................................................................................52
Sensor Data ..................................................................................................................52
CdA...............................................................................................................................54
Crr .................................................................................................................................55
λ....................................................................................................................................57
Predicted Power............................................................................................................58
Conclusion...........................................................................................................................59
Part 1................................................................................................................................59
Part 2................................................................................................................................59
References ...........................................................................................................................60
Tables ..................................................................................................................................65
Figures .................................................................................................................................77

Abstract
Along with scientists and professional cyclists, a number of amateur athletes and hobby
cyclists have started using portable/mobile power meters (PMs). “Direct force” power
meters (DFPMs) are devices that calculate power based on the deformation in bike
components such as pedals, cranks, crank-web, etc. caused by the pedaling forces of the
cyclist. These PMs tend to be expensive. “Opposing force” power meters (OFPMs)
estimate power from data such as speed, road gradient, heart rate (HR), anthropometric
and bike data, etc. These, though not as accurate as DFPMs, are cheaper and hence
attractive options for non-professionals to use. This study is divided into two parts. Part 1
compares three OFPMs for their accuracy against an industry standard DFPM. We field-
tested them under different conditions – submaximal endurance ride, efforts while
climbing, efforts on a flat section, and sprint efforts. PowerPod was the most accurate
OFPM with a root mean square error (RMSE) of 47 W and relative RMSE of 44% for a
75-minute field test. Part 2 aims to estimate parameters for the power modelling equation
from data collected in Part 1. Using those parameters, we wanted to predict power for a
new ride by the same subject. Our estimated parameters agreed with some of those found
in literature. The RMSE of the power predicted by our equation was 46 W and the relative
RMSE was 41%.
Keywords: road cycling, power, power meters, modelling, parameter estimation

Estimation of Power and Energy Expenditure from Sensor Data in Road Biking
Power is a metric in cycling that is increasingly being followed not just by
scientists and elite athletes but also by hobby cyclists and beginners. A sensor that
measures and outputs power is called a power meter (PM). At first, PMs were used for
scientific purposes, and mostly on indoor bicycle ergometers, as they were the only ones
equipped with PMs. But, cycling indoors on an ergometer is different from cycling
outdoors in many ways – unreasonably high heat and dehydration, the cardiovascular drift
phenomenon, use of only certain muscles, etc. – and hence not realistic. With the advent of
mobile PMs, scientists could measure power output in field tests as well (Gardner et al.,
2004). In the early 2000s, professional cyclists started using PMs in their training and
racing. The first time PMs were adopted by a professional bike team was in 1991.
("History,")
PMs have come a long way since then. The PM market has exploded, facilitated by
the entry of the first PMs for the consumer market in 2005 ("History,"). PMs have become
attractive to the general public mainly because of an interest in training and performance
improvement. PMs have become more mobile, they come in all sizes, and can be installed
on most parts of the drivetrain – for instance on cranks, pedals, wheel hub, and even in-
soles ("Power meters: Everything you need to know," 2016).
Advancements in technology, higher scales of production, a competitive market,
high demand and more spending power among people are some reasons that made PMs
affordable for the average consumer. As of mid-2016, the price of a PM ranged from USD
299 to USD 1,500 ("Spring 2016 Power Meter Pricing Wars Update," 2016).
PMs can be divided into two broad categories. The first includes those that directly
measure force applied by the cyclist while pedalling. These are called “direct force power

meters” or DFPMs. The second category includes those that do not measure leg force but
estimate the power output of the cyclist using indirect methods. These are called “opposing
force power meters” or OFPMs.
In the past, indoor cycle ergometers were compared to each other to validate for
accuracy (Abbiss, Quod, Levin, Martin, & Laursen, 2009; W. Bertucci, Duc, Villerius, &
Grappe, 2005; Novak, Stevens, & Dascombe, 2015). Tests were also conducted to
compare portable DFPMs both indoors as well as outdoors (W. Bertucci, Duc, Villerius,
Pernin, & Grappe, 2005; Bouillod, Pinot, Soto-Romero, & Grappe, 2016). It is very rare to
find in the scientific community studies that compare OFPMs. There was one paper that
way back in 2003 that tested an OFPM (G. Millet, Tronche, Fuster, Bentley, & Candau,
2003). There is anecdotal evidence, user ratings, manufacturer claims, blogs, and
magazines online that report on the testing of OFPMs, based on first-hand tests but none
are conducted scientifically. Most of them do not quantify accuracy of instantaneous
power values – the common method is to simply compare average values for long rides or
some intervals, at best ("PowerPod In-Depth Review," 2016; "PowerTap PowerCal In-
Depth Review," 2012; "Reviews," 2016).
We understand that OFPMs tend to lack accuracy; and in the scientific community,
there is a high stress on accuracy (Gardner et al., 2004). This could be a reason why there
has not been much investigation of OFPMs. But, from the point of view of a consumer,
there is a lot of interest. Hence, we wanted to compare OFPMs in the context of a master
thesis backed by a research group. This is Part 1 of the thesis: we shortlisted three OFPMs
to test them against “actual” power from an industry standard DFPM. We conducted three
trials (Rides 1, 2 and 3) but will present one representative trial.

The attempt to understand forces acting on a cyclist and model cycling
performance goes a long way back (Nonweiler, 1956). In 1998, a landmark study (Martin,
Milliken, Cobb, McFadden, & Coggan, 1998) was published that described all the forces
acting on the bike and cyclist system. The study has been cited more than 200 times. There
have been several studies that use the equation provided by them, or one on similar lines
(W. M. Bertucci, Rogier, & Reiser, 2013; Dahmen, 2012; Dahmen, Wolf, & Saupe, 2012;
G. P. Millet, Tronche, & Grappe, 2014; Peterman, Lim, Ignatz, Edwards, & Byrnes, 2015).
We also use an equation adopted from that of Martin and colleagues. But, their study
measured average power, and we are interested in modelling instantaneous power. By
modelling, we mean predicting power based on sensor data. For this, we used data (actual
power, speed, elevation/gradient, air density) collected in Part 1. On that data, we
performed a multivariate analysis to solve a system of linear equations to estimate certain
constants/parameters. With these parameters, a customized formula to predict
instantaneous power was obtained. This formula was put to test in a field test (Ride 4). We
compared it to actual power as well as to the OFPMs that were used in Part 1. This is Part
2 of the thesis. Understanding the working behind some OFPMs can help in predicting
power better.
There are several methods to estimate parameters (elaborated in Background
chapter) and they have all been found to be valid ways to model performance for a number
of applications. But the ultimate validation is always a field test (Henchoz, Crivelli,
Borrani, & Millet, 2010). We also know that a field test like ours is one of the best ways to
estimate parameters (García-López et al., 2008). The length and conditions of our data
collection rides and validation ride are what makes our project unique. We have been
warned that road cycling is difficult to model as compared to track or other controlled
environments (T. Olds, 2001). But we have assurance from some authors that using an

SRM PM (Schoberer Rad Messtechnik GmbH, Germany) and applying linear regression
methods is a valid way to estimate parameters (Debraux, Grappe, Manolova, & Bertucci,
2011). We expect that our formula will predict power better than some of the commercial
OFPMs that we test in Part 1.
This thesis is a part of the Powerbike Lab at the University of Konstanz. The
research group develops methods for data acquisition, analysis, modelling, optimization
and visualization of performance parameters in endurance sports with emphasis on
competitive cycling ("The Powerbike Project,").

Background
Power is the rate of doing work. The SI unit of power is J/s or, more commonly,
Watt (W), named after the Scottish engineer James Watt.
Cycling is an attractive activity for physiologists and exercise scientists because it
allows to monitor a variety of metrics on an indoor cycling ergometer (Stannard,
Macdermaid, Miller, & Fink, 2015). Of these metrics, power is often used to measure
performance. With portable PMs, it is possible to take this monitoring to more realistic
settings in-field.
Power is of interest to cyclists across the spectrum ranging from professional
athletes to beginner cyclists as it provides an objective method to bring structure to
training and racing. Professional cyclists have sworn by PMs for a long time ("More than
you ever wanted to know about power meters in pro cycling," 2015) and now hobby
cyclists are finding sense in investing in them.
Power in Training
To improve at a particular physical task, it is imperative to have practice in that
task. Repetition would bring improvement. To improve in cycling, the activity that would
bring most benefit to one’s cycling performance is cycling. Playing tennis may or may not
have a substantial “transfer effect” to cycling performance. This is the principle of
specificity in the science of training.
Repetition without a plan may bring improvements to a beginner’s performance. If
he started riding his bike for 60 minutes every day for an extended period, he would surely
improve at the beginning, and rather rapidly. But, eventually, his performance would
“plateau” i.e., not increase anymore. It is important to bring variation in training to
maximise results for the work put in. The “variation” here refers to overloading

(alternating with resting) the body in a planned and controlled manner. This is the
principle of overloading.
To implement these two concepts effectively, it is important to quantify load/effort
in an objective and repeatable manner. The effective way to train is to vary the duration
and intensity of workouts and plan training blocks by manipulating these two factors. A
training block could be as long as a week, a fortnight (called micro-blocks) or in the range
of a few months or seasons (macro-blocks). This is the concept of periodization.
Distance is an indicator of volume but time is better. A cyclist could ride 50 km
downhill for 1 hour but the same 50 km could take more than 3 h if the cyclist rode uphill.
The same distance could take less or more time based on wind conditions, type of bike,
and air pressure in the tires, to name a few factors.
Previous methods of training involved using speed, rate of perceived effort/exertion
(RPE) and heart rate (HR) as indicators of load. None of these are objective ways to
quantify effort. If two cyclists rode 50 km each at speeds of 20 km/h and 30 km/h, it would
be natural to think that the one who rode at 30 km/h trained at a higher intensity. But, this
assumes that all other conditions (distance, weather, bike type and condition, riding
position, fitness level, etc.) were identical.
A less subjective – but flawed, nevertheless – approach to quantifying intensity is
HR. HR patterns vary across individuals. An elite athlete’s heart could be pumping at 110
beats per minute (bpm) without them breaking into a sweat while an unfit 60-year-old
individual could react very differently for the same value. There are inter-individual
differences due to age, fitness, medical conditions, etc. Therefore, it is common practice to
quantify effort using HR values as a percentage of baseline/threshold/maximum values of
HR. So, if two cyclists exercise at 70% of their maximum HR, to some extent, intensity

can be considered equal. But, HR can vary within an individual too – if a person ate or
consumed caffeine or alcohol, or did not sleep enough, or is anxious, his HR values would
be higher for the same intensity.
The RPE scale is a rating between 1 and 10 – 1 being “a very light intensity” and
10 being “maximal effort”. The perception of intensity could vary not just between
individuals but also within the individual as quickly as on consecutive days. The RPE
approach suggests that one use the subjective marker in their mind to rate how hard or easy
an effort is. This depends on mood, mental fatigue, physical tiredness, time of day, and
personal experiences. A rating of 8 today may feel as hard as a rating of 8 on a different
day but in terms of performance output (load on the cardiovascular, neural and musculo-
skeletal system, for example), they could be vastly different.
In an age where people want to work “smarter” i.e., get the job done in as short a
time as possible and not necessarily “harder”, power training is the modern cyclist's most
scientific tool. Power is an objective way to quantify training load. Some have called
training with power “a game changer” ("Power meters: Everything you need to know,"
2016). A PM measures effort from the output generated and not from input parameters like
HR. A PM is “blind” to external conditions like weather, terrain, mood, mental/physical
fatigue, and equipment. If a cyclist rides at a power output of 200 W for 60 minutes today
and 200 W for 60 minutes two weeks from now, the same two rides may have been over
different distances or weather conditions; one day may have felt harder or more
challenging than the other, but the mechanical output is undeniably 200 W.
Hence, power can be used to be scientific in planning workouts and training plans
and effectively follow all the guidelines laid down by the principles of overloading,

specificity (even for specific skills within the sport of cycling), and periodization. Power is
also great as a pacing tool/marker in races.
Power Zones
Just like with HR, the absolute power numbers must be normalized to the
individual’s ability in order to be able to use power as a meaningful training tool or to
compare individuals. A common metric in coaching science is the Functional Threshold
Power (FTP) (Andy R. Coggan, 2016b). FTP is the power output a cyclist can generate at
lactate threshold (LT). There are some short protocols that allow for a good estimate of
FTP. A popular one is the “20-minute FTP test”. In its simplest form, FTP is approximated
as 95% of the average power output during a 20-minute maximal test. Power zones are
then established with this value as the baseline.
Power zones are demarcated based on the energy system demanded and the
physiological/neurological adaptations to those training intensities. Of the many charts
outlining power zones, the one in Table 1 is borrowed from (Andy R. Coggan, 2016a).
Power Meters
The PM market is driven mainly due to the high interest in training and amateur
racing. This, in turn, has created jobs in the coaching industry. Cycling coaches can now –
without ever having to meet the athlete in person – prescribe and monitor training plans of
athletes by looking at a range of metrics, all based on power measured by portable PMs.
This boom also facilitated books such as ("A Power Primer – Cycling with Power 101,"
2009), co-written by the aforementioned author. All these advances have been possible
only because of mass production of portable PMs, pioneered by SRM a couple of decades
ago.

Direct Force Power Meters (DFPMs)
DFPMs usually consist of a set of strain gauges and an accelerometer. The strain
gauges calculate force produced by the cyclist by measuring the deformation caused in the
bike component where the PM is located and transform this mechanical force into an
electrical output. Power is defined as the product of torque and angular velocity. The
accelerometers measure angular velocity. The product of torque and angular velocity is
calculated several times a second and the final output is averaged – usually over one
second – and transmitted wirelessly to a bike computer, mobile phone or monitor where
power is displayed to the user and/or stored. DFPMs have their flaws in terms of variation
in accuracy and sensitivity (Bouillod et al., 2016) but their accuracy is more than sufficient
for the purpose of training. Devices with higher accuracy, reliability, and product life
naturally cost more. Accuracy among DFPMs varies based on number and quality of strain
gauges, quality of wireless transmission, and method of calculation. For instance, the
PowerTap wheel-hub-based system was reported to have accuracy = -1.2 ± 1.3% (Gardner
et al., 2004), the Stages PM, which measures power from the left crank, has an accuracy =
-8 ± 1% (Hurst, Atkins, Sinclair, & Metcalfe, 2015), and the SRM system – our
benchmark – has an accuracy = 2% (Quod, Martin, Martin, & Laursen, 2010).
As of mid-2016, the cheapest DFPM costs USD 399 but they can be as expensive
as 1,500 USD ("Spring 2016 Power Meter Pricing Wars Update," 2016). All DFPMs need
regular calibration. Manufacturers prescribe the calibration frequency and instructions.
Extreme conditions like heat affect the accuracy and life of the strain gauges and other
components of the PM ("From Power Models to Opposing Force Power Meters and the
iBike Newton+,").

We cannot list all kinds of DFPMs as it is out of the scope of the thesis but there
are very popular guides where thousands of consumers (including us) flock to get their
information on PMs. ("The Power Meters Buyer’s Guide–2015 Edition," 2015)
("Reviews," 2016).
Opposing Force Power Meters (OFPMs)
OFPMs take data such as HR, elevation, gradient, pressure, speed, cadence, etc. as
well as anthropometric data such as height, weight, age, sex, shoulder width, etc. to
estimate the mechanical power output of a cyclist. These are all cheaper than DFPMs – the
most expensive OFPM is comparable to the cheapest DFPM ("Power Meter Pricing Wars:
Let The Games Begin,"). They start as low as USD 49 or can even be in the form of a free
mobile application ("How Strava measures Power," 2016). That is why these are popular
and have a huge commercial potential in the entry-level cyclist market.
The greatest compromise for buying this kind of PM is accuracy. Other
disadvantages include the fact that they are not always “plug and play” i.e., not intuitive to
setup/use and the calibration can be tedious. The installation of some OFPMs can be
cumbersome and may sometimes need an experienced hand. Since the formulae and
algorithms (which are most often a secret) depend heavily on the input of anthropometric
and bike/ride data by the user, extreme care must be taken while inputting as well as
monitoring these data over time.
OFPMs are often the target of harsh criticism from reviewers, bloggers and
magazines that test them. It is understandable, but they must be judged in their context.
They do not compete with DFPMs directly and in that sense, they must be seen as
commodities belonging to a different segment. But the truth is that most OFPMs do work
well under certain conditions. For example, a heart rate based OFPM reportedly works

well when output is relatively steady ("PowerTap PowerCal In-Depth Review," 2012).
Strava – a free mobile application – supposedly has a reliable method to estimate power
accurately during climbing ("How Strava measures Power," 2016).
However flawed and criticized, from time to time, the OFPM industry comes up
with innovative ways to do the guesswork. Polar S710, a PM now out of production
generated interest even in the scientific community (G. Millet et al., 2003). The concept
was that the device would get bike speed from monitoring chain speed and would estimate
force only from chain vibrations.
We will elaborate on three OFPMs that we felt were the best of all the products out
there in the Methods chapter.
Modelling Power
Modelling helps in predicting performance, planning races and training, testing out
strategies, gearing options, etc. This concept is very much in line with the same “train
smart, not hard” philosophy we addressed earlier. The attempt of modelling performance
has been done many times (both in-lab and -field) in the past. Most of the initial studies
were highly simplified and/or their validity can be questioned because they are too old and
we now have better ways to measure as well as estimate power. We will go over these
studies in the course of this report.
Modelling has made it possible to estimate power and/or parameters for historic
rides, when PMs did not exist. One study modelled power for the hour record rides and
compared riders of difference eras. It is a very detailed and interesting read, especially for
cycling fans (Bassett Jr, Kyle, Passfield, Broker, & Burke, 1999). One landmark study
(cited more than 200 times) by Di Prampero & colleagues estimated parameters in the

equation for retardation force for a cyclist and bike system (Di Prampero, Cortili,
Mognoni, & Saibene, 1979).
Knowledge from studies such as the ones above that set guidelines for modelling
performance has carried over to simple calculators on the internet ("Analytic Cycling
Home Page," ; "Interactive cycling power and speed calculator," ; "Speed & Power
Calculator,"). These calculators are generally good starting points for people outside the
scientific community, presented in a user-friendly way with options to play around with
and model performance. CyclingPowerLab has one of the most exhaustive simulators.
They also offer simulating services at a cost for athletes and coaches ("Power & Speed
Models,").
We, in Part 2, will model power from the “demand side” (T. Olds, 2001) i.e., we
use the biomechanical equation proposed by Martin & colleagues. But it needs to be
mentioned that modelling also helps in understanding and linking the “supply side” i.e.
metabolic energetics with the demand side (e.g. linking oxygen consumption with speed,
oxygen consumption with air resistance, etc.) (Capelli et al., 1993; Davies, 1980; Di
Prampero et al., 1979; T. Olds, 2001; T. S. Olds, Norton, & Craig, 1993).
The Equation
We use the following equation borrowed from an unpublished work of a colleague
in the Powerbike Lab (Thorsten Dahmen’s doctoral dissertation, soon to be published on
KOPS, Uni Konstanz) which was originally inspired from the one proposed by (Martin et
al., 1998) – a study still considered the guiding light of all state of the art publications
(Dahmen, Byshko, Saupe, Röder, & Mantler, 2011). Some OFPMs and online services like
Strava also use a simplified form of this equation in their algorithm to predict power
("How Strava measures Power," 2016).

If the cyclist + bike system is taken as an isolated object and a “free-body diagram”
is drawn, the forces would look like this (Figure 1). When the balance of forces is written
in an equation, it would look be written like this:
𝐹𝑡𝑜𝑡𝑎𝑙 = 𝐹𝐾𝐸 + 𝐹𝑃𝐸 + 𝐹𝑟𝑜𝑙𝑙 + 𝐹𝑎𝑒𝑟𝑜 + 𝐹𝑏𝑒𝑎𝑟𝑖𝑛𝑔
Equation 1
where FKE is the force linked to the change in velocity (kinetic energy); FPE is the
force of gravity; Froll is the frictional losses mainly between the bike and road surface and,
to some extent, between the inner tube and tire; Faero is the aerodynamic drag force; Fbearing
is frictional losses in the bearings of the wheels of the bike.
Since power is the product of force and velocity, for a bike travelling at vG (ground
velocity i.e., bike speed), Equation 1, when multiplied by vG on both sides would result in
the “power equation”:
𝑣 𝐺 𝐹𝑡𝑜𝑡𝑎𝑙 = (𝐹 𝐾𝐸 + 𝐹𝑃𝐸 + 𝐹𝑟𝑜𝑙𝑙 + 𝐹𝑎𝑒𝑟𝑜 + 𝐹𝑏𝑒𝑎𝑟𝑖𝑛𝑔)𝑣 𝐺
Equation 2
Bicycles are human powered machines, and no machine is 100% efficient in
reality. So, to account for losses, we introduce the λ term here on the left-hand-side of
Equation 2. This gives us:
𝜆𝑃𝑡𝑜𝑡𝑎𝑙 = 𝑃 𝐾𝐸 + 𝑃𝑃𝐸 + 𝑃𝑟𝑜𝑙𝑙 + 𝑃𝑎𝑒𝑟𝑜 + 𝑃𝑏𝑒𝑎𝑟𝑖𝑛𝑔
Equation 3
The terms in Equation 3 are explained in the sections below.

Potential Energy
𝑃𝑃𝐸 = 𝑚𝑔𝑣 𝐺 𝑐𝑜𝑠𝜃
Equation 4
𝜃 = 𝑡𝑎𝑛−1(𝑆)
Equation 5
𝑆 =
ℎ2 − ℎ1
𝑑2 − 𝑑1
Equation 6
The PE term in Equation 3 refers to the rate of work done against the force of
gravity. Force due to gravity of an object of mass m is mg. Work done against gravity to
lift that object to a height h is mgh. Rate of work done against gravity is mgv, where v is
the velocity with which the object moves in the direction perpendicular to the ground. In
our case, that is given by vG cos θ, where θ is the angle of inclination of the road (Figure
16).
Kinetic Energy
𝑃 𝐾𝐸 = 𝑚′
𝑎𝑣 𝐺
Equation 7
where
𝑚′
= 𝑚 (1 +
𝐼 𝑊
𝑟2
)
Equation 8

If vG is constant, the kinetic energy (KE) is constant and hence work done to
increase the KE is 0. Everything else being constant and steady, if the velocity of the bike
needs to be decreased, negative work needs to be done in the form of braking or natural
declaration. The braking would “absorb” the KE. This component of the power equation is
given by PKE. a is the acceleration at the instant. m' is the effective mass because “there is
additional KE stored in the rotating wheels (KE = ½Iw2
), where I is the moment of inertia
of the wheels and w is the angular velocity of the wheels. The angular velocity of the
wheels is proportional to VG as w = vG/r, where r is the outside radius of the tire.
Therefore, the KE stored in the wheels can be expressed as KE = ½VG
2
/r2
” (Martin et al.,
1998). Moment of Inertia of the wheels Iw can be measured or assumed. If it cannot be
measured, m' can be taken as the total mass (rider mass + bike mass) + the tire mass + rim
mass + 1/3 spokes’ mass (Wilson & Papadopoulos, 2004).
Rolling Resistance
𝑃𝑟𝑜𝑙𝑙 = 𝐶𝑟𝑟 𝑚𝑔𝑣 𝐺 𝑐𝑜𝑠𝜃
Equation 9
Frictional force of an object at rest is proportional to the force normal to the
surfaces in contact i.e., on level ground, the weight of the object. Hence, this force can be
expressed as µmg for an object of mass m. The “coefficient of friction” µ depends on the
properties of the two surfaces.
In the same way, rolling resistance in cycling has been proven to be proportional to
the weight of the bike and rider system (Di Prampero et al., 1979). Rolling resistance is the
biggest of all resistive forces for speeds < 3 m/s (Wilson & Papadopoulos, 2004) in still air
on level ground. Proll also depends on the ground velocity of the bike, tire pressure, width

of tires, size of wheels, type of road surface, tread count, rubber type, etc. All of this is
represented in the Crr term named coefficient of rolling resistance.
“Tyre width, tread pattern, tread count and tyre inflation pressure influence
performance. Tyre pressure affects the contact surface between the tyre and the ground.
When the tyre is under inflated, the rolling resistance increases (Grappe et al., 1999)”
(Steyn & Warnich, 2014). Hence, high pressure reduces Crr. Mass does not affect it as
much as pressure does, according to the same authors.
But where does Proll go? “The main cause of this loss of energy is the deformation
of the tyre, the deformation of the terrain surface and the movement below the surface”
(Karlsson, Hammarström, Sörensen, & Eriksson, 2011).
Rolling resistance is a bigger issue in mountain terrain bikes (MTBs) because of
larger area in contact with the road, lower wheel diameter and rubber thickness. In road
bikes, this force is 2-3 times lower (W. M. Bertucci et al., 2013). Also, since speeds are
faster in road cycling, rolling resistance is not the main focus – aerodynamic drag is.
Schwalbe, a leading manufacturer of tires and tubes, summarizes this force: “1. the
higher the inflation pressure, the lower the tire deformation and thus rolling resistance; 2.
tires with a smaller diameter have a higher rolling resistance, because a small diameter tire
is flattened more and is ‘less round’; 3. a narrower tire deflects more and so deforms more;
4. tire construction: by using less material, less material can be deformed. The more
flexible the material is, the less energy is lost through deformation. " ("Rolling
Resistance,")

The effect of tire pressure and total mass on Crr is a nonlinear relationship (Grappe
et al., 1999). These authors also claim that Crr diminishes performance up to as much as
11.4% for an increase of 15 kg in mass of the system.
Bearing Losses
𝑃𝑏𝑒𝑎𝑟𝑖𝑛𝑔 = (𝛽0 + 𝛽1 𝑣 𝐺) 𝑣 𝐺 = 𝛽0 𝑣 𝐺+𝛽1 𝑣 𝐺
2
Equation 10
where β0 and β1 are constants.
Losses in the form of rotation and friction of the bearings in the wheels and other
components is proportional to the speed of the bike. The corresponding power, then, is
proportional to the square of the velocity. But this forms a negligible part of the equation
and several studies neglect this (Di Prampero et al., 1979; Meyer, Kloss, & Senner, 2016;
Wilson & Papadopoulos, 2004). We will also neglect these losses in our study. There are
tests online on bearing losses as well as losses in the rest of the drivetrain. Some
companies also sell the findings of these tests for a price ("Friction Facts,").
Aerodynamic Drag Force
𝑃𝑎𝑒𝑟𝑜 =
1
2
𝜌𝐶 𝑑 𝐴𝑣 𝑊
2
𝑣 𝐺
Equation 11
where vW is the speed of the bike relative to wind. The rest of the terms are
explained shortly:
In the field of modelling, in pro cycling, in product development, and so on,
aerodynamic drag force is the most studied and scrutinized topic. This is natural because

drag force accounts for 50-90% of the forces that a cyclist overcomes depending on speed
and position (for MTBs it is less) (Chowdhury & Alam, 2012) (Peterman et al., 2015).
Drag force in fluid dynamics is directly proportional to density of the medium ρ (in
our case, density of air), area A of the object (frontal area of cyclist in head-wind
condition), geometry and properties of the surface of the object represented by ‘drag
coefficient’ Cd, and square of the relative velocity between the object and the fluid vW
(speed of bike relative to wind). This force is given by:
𝐹𝑑𝑟𝑎𝑔 =
1
2
𝜌𝐶 𝑑 𝐴𝑣 𝑊
2
Cd and A, when taken separately, are completely independent quantities. A refers to
the size of rider, and Cd depends on geometric shape of rider (and clothes) (Grappe,
Candau, Belli, & Rouillon, 1998). Cd depends on Reynolds number but in the range of
speeds applicable to road cycling, it can be taken as a constant. (Di Prampero et al., 1979).
But, for simplicity’s sake, we take them to be one constant CdA, commonly referred to as
“drag area”.
Air resistance is of two forms: bluff body (normal to the surface of the rider’s body)
and skin friction (tangential to surface) (Wilson & Papadopoulos, 2004). Some authors call
it “viscous drag” and “form drag”. The former is reduced by lowering surface roughness
(Cd component), and the latter by position (A component) (Defraeye, Blocken, Koninckx,
Hespel, & Carmeliet, 2010a). Area is the most important factor against drag (Debraux et
al., 2011).
Majority of drag force is attributed to the cyclist and not the bike (Barry, Burton,
Sheridan, Thompson, & Brown, 2014). So, where does the Paero go? Much of air resistance
goes into the eddies in the wake (behind the rider) i.e., the KE of air molecules. Beyond a

vG of 7 m/s, aerodynamic drag force is almost 100% of the forces that the cyclist has to
overcome (Wilson & Papadopoulos, 2004).
Drivetrain Efficiency
No bike is 100% efficient. Apart from the bearing losses, we also know that some
energy from the cyclist’s legs also goes into hysteresis losses in the drivetrain (chain,
jockey wheels, other components) as well as bike frame itself. This phenomenon would be
factored-in in the efficiency constant λ. We will assume that this value is constant
throughout the ranges of velocity and power of our experiments. Naturally, λ is a positive
quantity, and cannot be greater than 1. Quoting from Martin & colleagues, “Frictional
losses occur in the drive chain and are related to the power transmitted. Since this loss
occurs between the crank and the rear wheel, it can be viewed as a chain efficiency factor.
Therefore, the net estimated power must be divided by the chain efficiency.” (Martin et al.,
1998).
Estimating Parameters.
Although we have to estimate three parameters for our simplified equation, we will
focus on two: drag area (CdA) and coefficient of rolling resistance (Crr). Drivetrain
efficiency does not account for much of the cyclist’s power in comparison to these two
components.
Drag Area (CdA)
One method of calculating area is weighing photographs of a cyclist by a sensitive
scale. The photographs would have to be taken without parallax error and there would
have to be a reference object with known area in the photograph for equating the weight of
the pictures to frontal area (de Groot, Sargeant, & Geysel, 1995). Once digital cameras
came into the fray, this technique was emulated on computers. Instead of weighing

pictures in grams, the pixel count of the images was taken as the measure. Naturally, this
was a much less labour intensive method. (Chowdhury & Alam, 2012) (Debraux et al.,
2011) (Peterman et al., 2015).
Cd according to one author is given by the expression: 4.45 x m-0.45
where m is the
mass of the subject (Heil, 2002). Some authors have used this equation as well as similar
ones linking surface area and height and mass (Bassett Jr et al., 1999). These approaches,
obviously, cannot be relied on because of the large variation in individuals, types of
jerseys, types of cycling positions and not to mention, the sensitivity of the terms. A study
in 2008 warns that arriving at surface area from body mass is wrong (García-López et al.,
2008).
“Towing tests” are a valid way to estimate aero-parameters in the field (Capelli et
al., 1993). The concept is that a cyclist is towed by a car or motorbike joined by a rope and
a force transducer in series. Usually this is done when wind conditions are relatively still
and the ground is level. An indoor velodrome or hallway is an ideal location for these tests.
Density is calculated from barometric pressure readings at the location. Aerodynamic
forces can be calculated after removing rolling resistance and other components of the
force from the force transducer. To simulate actual riding conditions, cyclists may “soft-
pedal” without actually applying force on the a transmission chain “to reproduce air
turbulence induced by moving legs during actual cycling” (Capelli et al., 1993).
A purely lab-based method is Computational Fluid Dynamics (CFD). CFD is used
to estimate aerodynamic properties and forces. This, though inexpensive, may be
inaccurate (Defraeye et al., 2010a). But, opinion on this is divided. Some say that CFD
allows researchers to validate as well as improve results from wind tunnel tests. “CFD will
provide the ability to compute many output forces and identify exact components which

cause the most drag, a result which is extremely hard to achieve in wind tunnel testing. It
will however be a number of years before CFD can be used to solve accurately flow
around complex moving geometries, such as a pedalling rider.” (Lukes, Chin, & Haake,
2005)
Wind tunnels are a semi-lab/semi-field test. Bikes and cyclists are “mounted” on a
platform in a tunnel with wind blowing from turbines simulating outdoor conditions. They
are used widely for aerospace applications and automobile industry and now in several
other fields including cycling. Though impressive and seemingly state-of-the-art (perhaps
due to the costs associated), wind tunnels have also been criticized: discrepancies were
reported (Grappe et al., 1998); they overestimate Cd (Defraeye et al., 2010a); wind tunnel
tests do not put cyclists under stress because of soft-pedalling i.e., some resistance should
be there to make it realistic (García-López et al., 2008); the lateral movements we see
outdoors are not present indoors while soft-pedalling (Candau et al., 1999); the continuous
variation of wind speed and wind direction is not accounted for; turbulence level is usually
very low compared to outdoor environment, mostly “static” cyclists are considered, i.e.
without pedalling and rotating wheels; the boundary layer on the wind-tunnel floor is not
present in reality (Defraeye et al., 2010a). An alternative option is to go for a scale model
in a smaller wind tunnel, saving costs (Defraeye, Blocken, Koninckx, Hespel, &
Carmeliet, 2010b).
Coefficient of Rolling Resistance (Crr)
Towing tests are also used to estimate Crr. These tests are conducted outdoors (Di
Prampero et al., 1979). They are conducted in exactly the same way as explained above for
CdA estimation.

Another method similar to towing tests is the coasting/deceleration tests (Grappe et
al., 1999). In the simplest example, if a bike (with the same rider, same posture, same
clothes, same tire pressure) with two different tires is released from the top of an incline
and “coasts” down the incline, the distance covered or the time taken can be measured in
order to find out which tire “rolls” better i.e., we can get a ratio of the Crrs of both tires.
A lab test which has been found online is done by
www.bicyclerollingresistance.com ("Tire Test - Continental Grand Prix," 2014). The
website publishes results of tires pumped to different pressures and tested on their
indigenously made rig. It consists of a drum on which the tire rolls – the drum’s surface is
made to resemble the road surface. The speed and power provided to the drum are known
and the power lost in tire deformation can be found out from the number of revolutions
completed by the tire. The load on one tire corresponds to 42.5 kg, which means that for
two tires, the total load would be ~85 kg, which is a realistic “typical” was of a rider and
cyclist system.

Methods
We shortlisted four OFPMs based on reviews and customer ratings from popular
websites ("CycleOps PowerCal review," 2013; "First Ride with new $299 PowerPod
Power Meter," 2015; "Hands on with a $200 Bluetooth Smart power meter and precision
distance/speed sensor," 2012; "PowerPod In-Depth Review," 2016; "PowerTap PowerCal
In-Depth Review," 2012; "Sigma Introduces the ROX 10.0 Ant+-Enabled GPS Cycling
Computer," 2013): PowerPod (Velocomp LLC, USA), Powercal (Powertap, USA), Sigma
Rox 10.0 (Sigma Sport GmbH, Germany) and Velocomputer (Velocomputer, Canada). Of
these, Velocomputer was excluded for reasons explained in the next section.
Shortlisted PMs
SRM
The benchmark PM we used is the SRM device (SRM Science Power Meter,
Schoberer Rad Messtechnik GmbH, Germany). The specific model (called “Science”)
consists of a series of 16 strain gauges with an advertised accuracy of ±0.5% ("SRM
Store,"). But according to literature, the accuracy is around 2% (Quod et al., 2010). In
general, though, SRM is widely accepted as the benchmark and gold standard for portable
PMs, which was validated using the benchmark Monark ergometers (Jones & Passfield,
1998)
The PM is in the crank-web i.e., between the bottom bracket and the crank (Figure
3). It was calibrated as directed by the manufacturer before start of each ride. Here,
calibration means eliminating the zero offset and must not be confused for a longer
calibration process that involves “recalibrating” the PM in rigs with known weights across
force and angular velocity ranges. We are only referring to the simple process of

unclipping from the pedals while the bike computer resets the offset for an unloaded-crank
condition. We assume that this is enough to retain validity of the SRM.
SRM is used for validating indoor ergometers as well, replacing the Monark
ergometers. It can be used in parallel with any ergometer since it is mounted on the
crankset. For example, the result of this study: (W. Bertucci, Duc, Villerius, & Grappe,
2005) states that a certain ergometer should not be used for scientific purposes. SRM has
that level of authority in the academic circles now. It was also used to test an indigenously-
made pedal force measurement system (Bini, Hume, & Cerviri, 2011). It is also the
benchmark for other PM manufacturers.
But the SRM PMs are not without flaws: One paper in recent years reports that the
PM cannot record power < 25 W accurately (Abbiss et al., 2009). Another is that it is not
easily portable between bikes. It needs to be compatible with the bottom bracket of the
bike, and removing and installing the PM is a long process.
Powercal
Powercal uses HR values to guess power. It is simply an HR strap (Figure 4) with
an internal algorithm that somehow converts HR data into watts. It does not have a
calibration or baseline measurement process. Calibration used to exist in an earlier version
of the product, but not anymore, as the manufacturers felt that this extra step did not add
value in terms of outputting accurate results. ("PowerTap PowerCal In-Depth Review,"
2012). The device does not take the input of any anthropometric parameters either. It
wirelessly transmits heart rate as well as power numbers to a bike computer or a mobile
phone that must be within the range of communication of the computer/mobile phone at all
times. The manufacturer offers two models that differ in the way they transmit data –
either via Bluetooth Light Energy (BLE) or ANT+ protocol. We chose the BLE version

(Figure 14) and used a mobile phone (Apple iPhone 5, Apple Inc., USA) to record data.
The BLE version works in conjunction with a mobile application (“PowerTap Mobile”)
that is available to use only on Apple Inc. products. The mobile application takes the input
of age, sex, weight and type of bike but this is only to estimate caloric energy expenditure.
For calculating the actual power numbers, there is no input taken. The mobile phone was
placed in the bag mounted on the top tube of the bike (Figure 11).
Users on online forums criticize this product. It must be noted that the
manufacturer of this product makes the more famous and successful PowerTap DFPMs.
For them, Powercal is the lowest-priced product, understandably aimed at beginners. They
present this as just a rough way to quantify training effort, and nothing more ("FAQs,").
From one review, we learned that Powercal fails in sprints, and that is expected. HR values
react with a lag when it comes to short, maximal efforts. But the review points that
Powercal performs well in long, steady efforts and that the average values are close to
actual power data. For indoor rides, though, it is reported to not be as accurate. This makes
sense because cardiovascular drift i.e., an increase in heart rate values over time is a
common phenomenon when the body is not cooled quick enough. Some reviews were
even more critical and rated it 1 on a scale of 5, saying “the Powercal isn’t a power meter,
and shouldn’t be presented as one.” ("CycleOps PowerCal review," 2013)
PowerPod
“PowerPod uses a combination of an accelerometer, air pressure, and barometric
sensors to measure the total forces opposing your motion on the bike to provide pro-level
accuracy,” claim the manufacturers. ("PowerPod power meter for cycling fitness," 2015).
The manufacturer of this device claims to be in business for 12 years.

It must be used with wireless speed and cadence sensors. It weighs 32 g (Figure 5).
It must be mounted firmly on the handlebar of the bike (Figure 12), with the pressure
sensor facing forward. PowerPod does not have a display unit of its own, but can be paired
wirelessly with a computer to display and/or store data. We did not use a monitor to view
the power numbers of the PowerPod during the experiment. PowerPod has a simple
calibration process that lasts around five minutes. The user is instructed to ride at any
speed while the device records inclination from pressure sensors and accelerometers and
synchronizes these two sensors.
Only one blogger by alias “DCRainmaker” talked about PowerPod in detail, with
glowing reviews, recommending it to beginners of the sport ("PowerTap PowerCal In-
Depth Review," 2012). There appears to be a conflict of interest here, though, but it is
declared. He is one of the backers of the project, getting a discount in exchange for
investing in the product. The author does not report accuracy figures for instantaneous
power – only focusing on average values. Instead, graphs are presented for visual
inspection. The same author also claims that it has become more popular ("PowerPod rolls
out ANT+/Bluetooth Smart version, improved road surface algorithms," 2016).
Sigma
Sigma Sport makes bike computers, among other cycling accessories. In their most
expensive bike computer (as of April 2016), the Sigma Sport ROX 10.0 (Figure 6), there is
a formula for power based on speed, elevation, and anthropometric data. The bike
computer can display power in case a PM is present, is GPS-enabled and contains a
barometric altimeter. In the absence of a PM, the computer uses its own formula to
estimate it. The formula is not revealed. “A calculated power estimation is based on factors
like bike weight, rider height and weight, shoulder width, speed, cadence, and incline, but

it can’t calculate external factors like headwinds—or motor-pacing! For this reason,
calculated power data becomes more accurate when there’s less wind and when terrain is
steeper,” reports one review ("Sigma Introduces the ROX 10.0 Ant+-Enabled GPS Cycling
Computer," 2013).
The anthropometric and bike data that this device asked for can be seen in Table 2.
This computer was also mounted on the handlebars of the bike, with live feedback to the
rider (Figure 11). The same ANT+ speed and cadence sensors (Garmin Ltd., USA) as for
PowerPod were also paired with this device (Figure 13). The computer estimated speed
from GPS data when the sensors were not available. There was no calibration process.
Velocomputer
Velocomputer was a PM introduced four years ago ("Hands on with a $200
Bluetooth Smart power meter and precision distance/speed sensor," 2012) with the claim
that it could estimate power from bike speed and accelerometer data. The product was a
magnet-based speed and cadence sensor with a built-in accelerometer to detect road
inclination. The device could only be used with a mobile phone application (called
“Velocomputer”). The production and support of the device was discontinued, as we
learned just before the start of the experiment. It supposedly made use of mass,
acceleration, a constant CdA, Crr and used vG as vW in the power equation.
This device was discontinued and, in its place came a magnet-less speed and
cadence sensor set that could pair with any number of computers or mobile phones via
Bluetooth and/or ANT+ protocols, including the proprietary mobile application
Velocomputer. We purchased this as well. We faced the following issue: power values
were clearly wrong or sometimes even negative. We guess that this is because the formula

for power was designed for an earlier version of the PM where elevation data was also
taken into account. There were more issues:
 the mobile phone would lose connection with the speed and cadence
sensors multiple times and, hence, continuous data could not be recorded
 the new version of the mobile application would not sync with the old
product, and the old version of the application was no longer available
 there was no support offered from the manufacturers even after repeated
efforts to contact them. The last update to their mobile application was on
5th
January, 2016 ("Velocomputer,")
The company has moved on from being a self-proclaimed PM to being a
manufacturer of speed and cadence sensors. They received several poor reviews from
consumers ("Velocomputer,"). This reinforced our belief that the product was unreliable.
Attempts to understand the reasons behind these issues by way of reaching out to
consumers on online forums also yielded no results either.
Routes
For Part 1, we chose a 33-km round-trip route in the Thurgau canton of
Switzerland (Figure 7). This stretch of road had hardly any traffic in the evenings. This
helped in maintaining a near-non-stop ride. Being a round-trip, the ride started and ended
at the same point, with a net elevation gain and loss of 333 m. It fulfilled our conditions of
having a climb section (5.9 km long) and a flat section (3.6 km long). The surface was
asphalt and uniform for the most part. The ride took roughly 75 minutes. We recorded
three rides on this track for Part 1.
For Part 2, we chose a shorter (15.5 km) but similar track to the one in Part 1
(Figure 8). It was in the outskirts of the German town of Constance. It was also a round-

trip, had a climbing section and was on near-uniform asphalt roads. The total elevation
gained and lost was 148 m.
Subject and Setup
The subject (Figure 9) was the author himself – a 27-year-old moderately-trained
male (1.72 m, 68 kg – mass includes clothes and accessories just before the start of the
rides of the experiment) cyclist with more than 5 years of experience in road cycling, with
an average of 5 h of cycling per week in the last 2 years. From experience, the subject
knew that weight loss through dehydration is at a rate of 0.5 kg/hour for summer
conditions for a submaximal ride. Hence, the mass of the system was deducted at the rate
of 1 kg/h Part 2. Other anthropometric data can be found in Table 2.
Clipless pedals (Shimano PD-R540 SPD SL Sport Pedals, Shimano Inc., Japan)
and cleated shoes (Shimano RP2 SPD-SL, Shimano Inc., Japan) were used. The PMs were
mounted on the road racing bike of the lab (Radon GmbH, Germany). The bike frame
material was an aluminium alloy. The bike was one size larger (56 cm) than the subject
was used to but was comfortable to ride. The tires used on the bike were standard road
bike training tires (Continental Grand Prix, Continental AG, Germany) and were used at a
tire pressure of 110 psi (7.58 bar or 758 kPa). They were pumped using a manual floor
pump and by visual inspection of a dial gauge (LifeLine pumps, Wiggle Ltd., UK). The
weight of the bike – including bottles, water, and accessories – was 13 kg for all rides of
the experiment (Figure 15).
The computers and mobile phones were all charged fully and calibrated if, and
when required before the start of every ride. The 3 rides on the longer track were
conducted within 11 days of each other. The bike set up was not changed in all this time.

Experiment
Part 1: The constraint for the subject was to ride in the hoods position so as to
maintain a constant frontal area (Figure 10). Hoods are not a racer/professional type of
position – it is a position that most beginners adopt. No other conditions of choice of
gearing, or cadence were imposed. The next instruction was to ride in a range of power
(~200 W) – not a constant effort, but a steady effort – for the climbing and flat sections.
The value of 200 W is well below the FTP of 240 W of the subject. At all other times, the
instruction was to ride “normally”, with no regard to the constant pedalling, breaks,
braking, and so on. Except for three sprints in the end, the effort was submaximal
throughout.
Part 2: This ride (Ride 4) was seven weeks after Ride 1 of Part 1. The same
instructions as for Part 1 applied for this ride.
The SRM PM was paired with a bike computer (Garmin Edge 510, Garmin Ltd.,
USA). This computer was mounted on the handlebars to always have visual feedback of
power. The computer stored the power averaged over one second.
We think that this duration and style of both parts best mimics amateur riders – the
target consumers of the OFPM companies. The clothes and shoes used for the study were
similar for all four rides – each piece of garment was of the same level of tightness – but
not identical.

Analysis
Sampling Frequency: All power data was stored at a frequency of ~1 data point per
second. The sampling frequency of each PM was higher than 1 Hz, but it is common to get
the averaged power over one second.
Software:
 MS Excel (Microsoft Corporation, USA) was used for organizing data,
simple arithmetic operations and producing graphs.
 MATLAB (MathWorks, USA) was used for the least square analysis of the
parameter estimation of Part 2. We used the lsqlin function. This function
calculates the solution to the set of equations such that the sum of squares
of the estimated power and actual power is the least.
 Golden Cheetah, an open source software, was used to convert file types to
.csv format.
 Sigma Software (Sigma Sport, Germany) was used to export the workout
files stored by the Sigma.
 Isaac Software (Velocomp, USA) was used to view and export the
PowerPod files to .csv format.
 For the Powercal, it was the online software VirtualTraining (PowerTap,
USA).
 Garmin Connect (Garmin Ltd., USA) was used to upload files from the
Garmin device for power data from SRM, elevation and ground speed. We
downloaded the workout file to a personal laptop computer (Lenovo Group,
China).
File types:

1. SRM: Garmin Connect was used to export files to .fit or .tcx file type.
Golden Cheetah was used to convert it to a .csv file
2. Powercal: The HR and power numbers were downloaded in .tcx file format.
Golden Cheetah was used to convert this file to the .csv file format
3. PowerPod: The file format of the recorded workout is .ibr. “Isaac Software”
exports the files to a .csv file format
4. Sigma: The file can be exported to the .tcx file format from Sigma’s
interface. Golden Cheetah was used to convert to a.csv file format
Metrics
Average Power and Relative Error
Average power is the arithmetic mean of all the data points recorded by the
respective PMs. Standard Deviation (SD) is also mentioned. Both are expressed in Watts.
Relative error is given by the formula:
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐸𝑟𝑟𝑜𝑟 (%) = 100 ∗
(𝑃𝑜𝑤𝑒𝑟𝑂𝐹𝑃𝑀
̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ − 𝑃𝑜𝑤𝑒𝑟𝑆𝑅𝑀
̅̅̅̅̅̅̅̅̅̅̅̅̅)
𝑃𝑜𝑤𝑒𝑟𝑆𝑅𝑀
̅̅̅̅̅̅̅̅̅̅̅̅̅
Equation 12
Normalized Power
Normalized Power (NP) is a popular metric in coaching and is described as “In
essence, it is an estimate of the power that you could have maintained for the same
physiological "cost" if your power output had been perfectly constant" (Andy R. Coggan).
NP is calculated as follows: take the 30 second average of power; raise these to the power
of 4; take the average of these values; take the 4th root of this average. It is given by

𝑁𝑃 (𝑊) = √∑ 𝑃𝑜𝑤𝑒𝑟̅̅̅̅̅̅̅̅̅30𝑖
4𝑇
𝑖=30
𝑇
4
Equation 13
Root Mean Square Error
Average power and NP are interesting to note but as sports scientists and athletes, we are
more interested in the accuracy of instantaneous power. Hence, we want to track the Root
Mean Square Error (RMSE), expressed in Watts, which is given by
𝑅𝑀𝑆𝐸 (𝑊) = √
∑ (𝑃𝑜𝑤𝑒𝑟𝑆𝑅𝑀𝑖 − 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑𝑃𝑜𝑤𝑒𝑟𝑖)2𝑇
𝑖=30
𝑇
Equation 14
It is the square root of the average of squares of difference between actual and
estimated power at every second.
Relative RMSE
If we want to quantify the error in instantaneous power relative to actual power, we
introduce relative RMSE, given by
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑅𝑀𝑆𝐸 (%) = 100 ∗
√∑ (
𝑃𝑜𝑤𝑒𝑟𝑆𝑅𝑀𝑖 − 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑃𝑜𝑤𝑒𝑟𝑖
𝑃𝑜𝑤𝑒𝑟𝑆𝑅𝑀𝑖
)
2
𝑇
𝑖=1
𝑇
Equation 15
Naturally, this is valid only for non-zero power. We went a step further and ignored
data where actual power was < 25 W because for small values of power, the above formula
tends to large values. SRM PMs are also known to be inaccurate for power values below
25 W (Abbiss et al., 2009).

Peak Signal-to-Noise-Ratio
Signal-to-noise-ratio (SNR) essentially compares the useful part of a signal with
the noise in a signal. Peak Signal to Noise Ratio (PSNR) has different formulae. This is
one formula, expressed in decibels:
𝑃𝑒𝑎𝑘 𝑆𝑖𝑔𝑛𝑎𝑙 𝑡𝑜 𝑁𝑜𝑖𝑠𝑒 𝑅𝑎𝑡𝑖𝑜 (𝑑𝐵) = 20 𝑙𝑜𝑔10 𝑃𝑒𝑎𝑘𝑃𝑜𝑤𝑒𝑟𝑆𝑅𝑀 − 20𝑙𝑜𝑔10 𝑅𝑀𝑆𝐸
Equation 16
Energy
“The total mechanical energy expenditure is calculated by integrating the power
measurements over the entire training session.” (Vogt et al., 2006). In our case, data was
recorded in intervals of 1 s. So, Energy is the sum of all the data points, expressed in
Joules, given by
𝐸𝑛𝑒𝑟𝑔𝑦 (𝐽) = ∑ 𝑃𝑜𝑤𝑒𝑟𝑖
𝑇
𝑖=1
Equation 17
Estimating Parameters
For estimating power based on our own formula, we first had to calculate the
parameters (λ, CdA and Crr) from the rides in Part 1. In total, we had a total of ~3 x 75 =
225 minutes of power, speed and elevation data. From this, we removed data with power <
25 W and cadence 0 RPM.
Substituting in Equation 3 and rearranging, we get:
𝑃𝑆𝑅𝑀 =
1
𝜆
(𝑚′
𝑎̅𝑣 𝐺 + 𝑚𝑔𝑣 𝐺 𝑠𝑖𝑛𝜃) +
𝐶𝑟𝑟
𝜆
(𝑚𝑔𝑣 𝐺 𝑐𝑜𝑠𝜃) +
𝐶 𝐷 𝐴
2𝜆
(𝜌𝑉𝐺
3
)
Equation 18

Equation 18 now takes the form
𝑦 = 𝑘1 𝑥1 + 𝑘2 𝑥2 + 𝑘3 𝑥3
Equation 19
Where k1, k2, and k3 are three unknowns and yi, x1i, x2i, x3i are the knowns.
𝑦𝑖 = 𝑃𝑆𝑅𝑀𝑖 = 𝑘1 𝑥1𝑖 + 𝑘2 𝑥2𝑖 + 𝑘3 𝑥3𝑖
Equation 20
𝑘1 =
1
𝜆
𝑘2 =
𝐶𝑟𝑟
𝜆
𝑘3 =
𝐶 𝐷 𝐴
2𝜆
Equation 21
𝑥1𝑖 = 𝑚𝑖
′
𝑎̅𝑖 + 𝑚𝑖 𝑔𝑣 𝐺 𝑖
𝑠𝑖𝑛𝜃𝑖 𝑥2𝑖 = 𝑚𝑖 𝑔𝑣 𝐺𝑖 𝑐𝑜𝑠𝜃𝑖 𝑥3𝑖 = 𝜌̅𝑖 𝑣 𝐺𝑖
3
Equation 22
In theory, we only need three equations to find out these unknowns given above.
But we have thousands of data points in order to calculate the “best fit” for these
unknowns.
We measured moment of inertia Iw for our bike another study (unpublished work of
Thorsten Dahmen) and its value is 0.18 kgm2
. That made m’ = 82.6 kg at the start of the
ride. Average density was found to be 1.12 kg/m3
, 1.15 kg/m3
, 1.13 kg/m3
and 1.13 kg/m3
for Rides 1-4, respectively and we used these values in Equation 18. We used 9.81 m/s2
for
the value of g. We do linear regression – reported to be a good way to estimate parameters
to “provide best match of parameters” (Dahmen et al., 2012). We set upper and lower
limits for the values that these parameters can assume, based on physical constraints and
values obtained from literature (Table 3). Since two of the three PMs in Part 1 use bike

speed in their formula (instead of wind speed, which is the correct method), we decided
that to be able to have a fair comparison between our model and those PMs, we must use
bike speed as well.
When we finish the lsqlin algorithm, we get parameters that are put back in the
formula. Note that this formula also returns negative values for power – as that is the
nature of the algorithm. Since it is not possible to have negative power from a cyclist’s
legs, we take these instances as 0 power instances. This mostly happens when the road is
sloping down too much or when there is a sharp deceleration (in the form of braking,
perhaps).

Results
Part 1
Full Ride
We provide results for Ride 3, which was representative of Rides 1-3 and all the
tests we conducted.
The average power recorded by SRM for the full ride was 156 W, which reflects
that it was a sub-maximal ride. To get a visual idea of the trends of the OFPMs, Figure 17
shows power vs time of each PM averaged over 30s. It is clear that, on average, Powercal
overestimates power, Sigma underestimates it while PowerPod is close to the actual
power. The average power values (Table 5) confirms this suspicion. PowerPod's average is
indeed very close to real values, as foretold by reviews. In all metrics, PowerPod stands
out from the other two. NP is higher for PowerPod, suggesting that there were errors in
estimating low power but it is 10 times more accurate than the other two PMs. While
average values are impressive, the RMSE and relative RMSE and both high in absolute
terms – 47 W and 44%, respectively. Once again, it is better than the other two by a
margin.
Training Zones
We split the based on time spent in power zones described in Background chapter.
Figure 22 shows the histograms for each OFPM. This gives a visual idea of the intensity
of the ride – that it is submaximal. A maximal ride would be between zones 3 and 4.
Climbing Section
In this section, which was 3.6 km long and 13.5 min long with an elevation gain of
147 m, similar trends were observed for PowerPod and Sigma as for the full ride – the
former was close to actual power while the latter was underestimating. Powercal, on the

other hand failed to show any real correlation, at least visually (Figure 18). PowerPod got
slightly worse in terms of average values (Table 5). RMSE and relative RMSE dropped
heavily in this section - probably because of fewer data points. Once again, PowerPod was
most accurate of all.
Flat Section
Flat section was the only time that Sigma was closely correlated to SRM in certain
sections within the flat section (Figure 19). This also happened to be the time that speed
was relatively steady and unchanging (see Discussion). Powercal was overestimating
power once again, and PowerPod looked to be the same. Sigma was better than the other
two in estimating NP, with an error of -5.26% (Table 5). But in the other errors, PowerPod
turned out to be the most accurate.
Normalizing
After noticing a steady trend of over- and under-estimating power by Powercal and
Sigma, it was suggested (by Alexander Artiga Gonzalez) to study the data after subtracting
the respective means from the datasets. Perhaps the power differed by a constant? There
are indeed reductions in the RMSE and PSNR for Powercal and Sigma (Table 6), but still
not enough to be better than the PowerPod. Notice also that the error values for PowerPod
did not change even after this transformation.
Smoothing
To give a benefit of doubt to the OFPMs, we decided to observe the trends in errors
when the data is smoothed i.e., when a moving average of power numbers is taken. We
averaged the data over 3s, 5s and 30s. Beyond 30s, we do not think that athletes,
consumers or scientists would be interested. The expectation was that the errors would

drop with progressive smoothing, and it was true (Figure 20). The PowerPod continued to
be the best of all PMs.
Sprints
Figure 21 shows the unsmoothed curves for the power output of the PMs for the 3
sprints. Each sprint was studied for 30s. If at all, only the PowerPod came close to the
SRM, with Sigma and Powercal not coming close to estimating the max power. We even
allowed for a lag of at least 10s just in case the Powercal decides to react late. This did not
happen. Table 7 summarizes the max power recorded in the 30s window and the PowerPod
did impressively well in one trial with an accuracy of 3%.
Part 2
During Ride 2 of the three rides in Part 1, we noticed that the parameters estimated
were slightly off (Table 4). when investigated, it turned out that the reason this could be is
the weather conditions. When the difference between vW and vG is taken, if it is positive,
we can consider it as headwind i.e., Table 8 shows the duration for which there was
headwind and tailwind. Clearly, Ride 2 was in conditions that were different from the other
rides. This is reflected in the parameters too. Hence, we decided to exclude Ride 2. We
took the average of the parameters obtained from Rides 1 and 3, and substituting for k1, k2
and k3 in equation 19, we get
𝑃𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑𝑖 = 1.0101(𝑚′
𝑎𝑖̅ 𝑣 𝐺𝑖 + 𝑚𝑔𝑣 𝐺𝑖 𝑠𝑖𝑛𝜃𝑖) + 0.0095(𝑚𝑔𝑣 𝐺𝑖 𝑐𝑜𝑠𝜃𝑖) + 0.1429(𝜌𝑉𝐺𝑖
3
)
Equation 23
Hence, our final equation is as follows
𝑃𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑𝑖 = 83.43𝑎𝑖̅ 𝑣 𝐺𝑖 + 802.64𝑣 𝐺𝑖 𝑠𝑖𝑛𝜃𝑖 + 7.55𝑣 𝐺𝑖 𝑐𝑜𝑠𝜃𝑖 + 0.16𝑉𝐺𝑖
3
Equation 24

According to our predicted power formula, 40% of the power went in overcoming
aerodynamic forces, 30% to rolling resistance and the rest to changes in KE, overcoming
gravity, bearing losses and drivetrain losses.
Full Ride
Total distance was 15.5 km, net elevation gain was 148 m and time taken was ~35
min. Figure 23 shows the graph for the smoothed power output vs time (time not indicated
on x-axis). Visually, we can tell that our prediction grossly underestimates power in more
than a couple of sections. Towards the end of the ride, when speed was slightly high and
power output was more than average, our prediction overestimated power. This could be
due to the fact that there was a tailwind, and our formula cannot account for it. The graph
also shows the other OFPMs during the same ride. Our prediction is second best, visually
speaking.
Table 9 shows the summary of the metrics tracked. Predicted power fared well in
the RMSE, with a value of 45.71 W, which is better than that of PowerPod. In most other
metrics, PowerPod fared better but only by a small margin. These are promising results.
The trend was that predicted power underestimated power by a small factor. NP was very
high, suggesting many 0s in our power prediction. This can be attributed to the fact that
when Pprediction was negative, we took it to be 0. This is the result of using the least square
fit algorithm to solve for the system of linear equations.
Climbing Section
Total distance was 1.6 km, time taken was 6.5 min and total elevation gain/loss was
81 m/11 m. Figure 24 shows the graph of smoothed power vs time for the climbing
section. There is an underestimation of power followed by an overestimation, but they
seem to be within acceptable limits because these differences do not show in the numbers,

and in comparison, predicted power is the best. Table 9 shows the summary of metrics.
Predicted power was most accurate in quite a few of the metrics, except of average values
once again. This is again attributed to the fact that we end up with negative power values,
which we truncate to 0.
Smoothing
Figure 25 shows the effect of progressively smoothing data on the RMSE. With a
healthy error for instantaneous power, the error does not reduce at a rate fast enough when
compared to the other OFPMs. But, RMSE for instantaneous power is far better for
predicted power when compared to Powercal and Sigma.

Discussion
Part 1
Powercal
This study (Vogt et al., 2006) found that energy estimated from HR data is over- as
well as under-estimated depending on the power zone. This happens even when adjusted
for individuals. Hence, using HR to estimate power is flawed in the first place. And when
there is no distinction between individuals, it is worse. Such a device can surely be
expected to fail under many conditions: it would fail for sudden changes in speed, for
instance. In downhill periods when HR is still high and the cyclist is not pedalling, it
would output a non-zero power value (since it anyway does not take cadence into account).
The reviews said that in long workouts with a steady output, power numbers are estimated
well, but we did not find this to be true. Powercal presumably takes not just the absolute
value of HR but also the changes in HR. Any such pattern or correlation is very hard to see
in the plot of HR and power over time (Figure 18; Figure 19).
Does Powercal account for cardiovascular drift i.e., the increase in HR over time
for the same power output? Probably not. This is designed as a plug & play device, i.e.
theoretically, a user could be 3 h into their workout and strap this on and still get a power
reading without knowing any history (neither of the workout, nor of the athlete) or asking
for input. Even the calibration process that once existed was done away with (see
Methods) because the manufacturers thought that it was not worth the effort for the user.
PowerPod
The average power readings were excellent and were surely in the advertised range
between -2.89% and +2.77% off actual power for submaximal rides between 2 and 3 hours
("PowerPod power meter for cycling fitness," 2015).

PowerPod takes CdA as a constant value of 0.332 m2
. This value was probably
arrived at from tabulated data from literature based on the anthropometric data of the rider,
bike type and riding position.
Algorithms that want to estimate power based on ground speed go wrong (as we
see with the Sigma) because wind is not accounted for. For modelling in still air, this
approach works. But for real-world tracks, estimating power based on ground speed would
not work. PowerPod passes the first test. The second test, that of yaw angle is still a
challenge to be met. Wind speed also comes with a yaw angle (Figure 26). PowerPod’s
dynamic pressure sensor only measures wind that is in the direction perpendicular to the
sensor i.e., in the direction of the ride. This is a flaw because it neglects cross-winds. In
heavy cross-wind conditions, the PowerPod can be expected to drop in its accuracy
because the high drag forces in the actual direction of the wind would be neglected (C. R.
Kyle & Burke, 1984) and the effective frontal area, that changes with yaw angle, is also
measured wrongly (Bassett Jr et al., 1999).
The device has two pressure sensors – a static pressure sensor and a dynamic
pressure sensor. The dynamic pressure (
1
2
𝜌𝑣 𝑊
2
) is directly plugged into their equation, thus
avoiding errors in measuring density and velocity separately. This is one of the strengths of
the device. The other major strength is the way the device uses accelerometer, discussed in
Part 2.
Data from the static pressure sensor and thermometer is used to measure density,
which is then plugged into dynamic pressure to “back calculate” speed with respect to the
wind, but this is only done to provide this data to the user. The device and algorithm
actually do not need this information to predict power.

Sigma
Sigma generally underestimates power. In the flat sections, it sometimes
overestimated power probably because of the high bike speed (power is proportional to the
cube of speed).
The only consolation for the Sigma was that it worked better than the other two
OFPMs under one special condition: when speed/power was steady and terrain was flat
(Figure 19) with RMSE = 17 W for a 200 W effort over 120 s.
The review, based on which we shortlisted the device also says that “Calculated
power is based on a formula that measures a rider’s progress over time; it’s a best
estimation of power output displayed in watts."("Sigma Introduces the ROX 10.0 Ant+-
Enabled GPS Cycling Computer," 2013). This means that the Sigma device perhaps had an
algorithm that “learns” and adapts to the rider. How it does so is not revealed, and neither
is our study long enough to investigate this aspect of the algorithm. For the record, for the
few rides that we recorded and the several trials that we conducted in preparation for the
experiments, the Sigma did not improve dramatically in its accuracy (we are talking about
a period of three months).
We noticed that when the Sigma Software gave us the file, the time entry was in
increments of 0.9-1.1 seconds and not necessarily in 1 second intervals. When Golden
Cheetah was used to convert it to .csv file type, it shows us data in increments of 1 s. We
suspect that this kind of rounding up/down done by Golden Cheetah could have accounted
for an error. But it is not easy to say to what extent this rounding process affects it.

Notes
These OFPMs cannot be used for scientific purposes. As explained in the
Background chapter, accuracies expected for scientific PMs are much higher than what we
found.
In studies comparing PMs, power over a range of different cadences is recorded for
validation. But, for OFPMs, no such thing needs to be considered. In fact, high cadence,
which leads to high HR, will only result in higher power values in Powercal. Other than
that absurdity, both Sigma and PowerPod do not use cadence in their formula, except for
the fact that when cadence is 0, power is automatically taken to be 0. They only use
cadence as a check.
More importantly, most studies comparing PMs verify accuracy of power
measurement across a range of power values. This is one of the limitations of Part 1. We
used only one subject for comparing PMs. It is common practice to recruit only one
subject (Bouillod et al., 2016) (W. Bertucci, Duc, Villerius, Pernin, et al., 2005). Rather
than recruiting more subjects, we should have checked for validity and accuracy of the
PMs across different power brackets, and not just submaximal as we did.
We chose to work on the road bike because: 1. Powerbike lab works with road
bikes, 2. most research is conducted on road bikes (except for some rare cases (W. M.
Bertucci et al., 2013)), 3. It is far less complicated to work with a relatively stiff road bike
frame on a relatively smooth surface, both being near ideal-conditions where modelling is
highly simplified. Perhaps most research is conducted on road bikes because road cycling
is the sport that is very obsessed with getting faster for the same power output, due to the
high aerodynamic resistance (as a percentage of total resistance). In Mountain Biking, it is

less to do with cutting corners in technology or position on the bike and more to do with
skill, technique, experience, etc.
It must be stressed again that the Sigma Rox 10.0 is not the flagship product of the
parent company. Neither was Powercal for their parent company. In some sense, it was
perhaps an unfair comparison to make between Sigma, Powercal and PowerPod because
the parent company of PowerPod does nothing else but make the device, and have been
improving over the last 12 years.
One of the reasons we chose to study OFPMs is because they are affordable for the
beginner. But prices of DFPMs have only been dropping over the last few years ("Power
Meter Pricing Wars: Let The Games Begin,"). In fact, the only company to have ever
hiked the price of a PM was the company that produced the cheapest PM. They hiked their
price from USD 350 to USD 399. Other than this, every single PM has dropped its price
when compared to three years ago. We guess that the reasons for this are the following:
better production techniques, cheaper sourcing of material, economies of scale, highly
competitive market, and a high demand for PMs driving a high supply, and a combination
of these reasons driving each other. Does this mean that eventually we will see a day when
DFPMs become so affordable that the one USP (“Unique Selling Point”) that OFPMs have
i.e., affordability, will be lost? Only time will tell.
As a closing note and as a final word of advice purely from a consumer point of
view, I would like to quote Rob Kitching of CyclingPowerLab: “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...

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.” ("From Power Models
to Opposing Force Power Meters and the iBike Newton+,"). Knowing under what special
conditions an OFPM works well is the recommendation for consumers.
Part 2
Exclusion Criterion
We excluded Ride 2 because it was too windy (Table 8). It is common for scientists
to suspend or exclude data when conditions are windy (W. M. Bertucci et al., 2013;
Peterman et al., 2015). These studies focused on measuring parameters in still air. While
avoiding wind altogether was not our aim, it was physically impossible that parameters
estimated from Ride 2 in the context of the parameters obtained from Rides 1 and 3.
Sensor Data
Ground Speed from ANT+ sensor: The principle of the sensor is as follows: it is
mounted on one of the wheel hubs (front or rear) of the bike. The in-built accelerometer
counts the number of revolutions. For every revolution completed, the sensor transmits the
information to the bike computer. The bike computer, in turn, knows the wheel size (i.e.,
circumference) that was manually input by the user – 2105 mm in our case. This value is
displayed and stored as speed for the user in the workout file. While it is accurate enough
for the needs of a cyclist and/or coach, there may be an issue when we try to use this speed
data to calculate acceleration and use that for modelling power.
Acceleration: We computed the average bike speed over 3 s. Acceleration was
calculated as the rate of change of this average velocity. This provided a smoothing of the
acceleration data, and helped in lessening the erratic nature of predicted power.

Elevation: The products in the earlier generation of PowerPod’s history used
accelerometers with sampling frequency of 800 Hz ("From Power Models to Opposing
Force Power Meters and the iBike Newton+,"). PowerPod’s five minute calibration
process exists to calibrate this same accelerometer to the pressure sensors to get baseline
elevation values and to account for any “out of level mounting issues.” ("PowerPod power
meter for cycling fitness," 2015). This way, gradient and elevation data are calculated far
more accurately than by barometric altimeters that are found in bike computers. For our
tests, we used this accelerometer gradient data for two of the rides (Ride 3 and Ride 4)
when it was available. When it was missing (due to false calibration perhaps), we used
smoothed elevation data from the Garmin device. The illustration and method of
calculating slope is given in Figure 10. We used height and distance difference between
points 15 seconds apart in order to get smoother and realistic slope values. This helped in
reducing the erratic pattern in the predicted power. Using instantaneous elevation data
from the barometric altimeter of the Garmin Edge 510 cycling computer records elevation
data with a lag – slower than what we need for instantaneous power.
Density: A number of authors (Bassett Jr et al., 1999; Martin, Gardner, Barras, &
Martin, 2006; Meyer et al., 2016; T. Olds, 2001; Peterman et al., 2015) did not take the
standard value of density of dry air at sea level as 1.22 kg/m3
. They all stress on the fact
that since aerodynamic drag is usually the most important resistance to overcome in road
cycling, this term in the equation is sensitive and that density must be calculated at the
location for the specific weather conditions (mainly temperature, humidity, pressure). Most
often, they calculated density from peto tube measurements at the spot, or used
information from local weather stations. We also did not use the default value, since we
have density data from the PowerPod device during each ride, which it calculates from the
static pressure port present inside. This is the only information we used to get an

“advantage” over the OFPMs that used a default value of air density. Average density was
found to be 1.12 kg/m3
, 1.15 kg/m3
, 1.13 kg/m3
and 1.13 kg/m3
for Rides 1-4, respectively.
Drag Area (CdA)
All methods - coasting, towing, wind tunnel etc. have all been found to be valid
ways to model power. Table 10 shows results obtained for CdA estimation in literature
from authors in the past few decades using various methods. Of these, only two studies
were within 0.01 m2
of our CdA (0.283 m2
).
There are many reasons for such a wide range of values (0.2-0.4 m2
) as seen in the
table: there is large variation in estimating CdA because of anthropometric differences, bike
type, accessories, static and dynamic conditions (Defraeye et al., 2010a); jersey design
affects aerodynamics in cycling i.e., lose and tight clothing and even choice of fabric plays
a crucial role in CdA (Oggiano, Troynikov, Konopov, Subic, & Alam, 2009); helmet
design also affects drag area (Barry et al., 2014); it is difficult to exactly reproduce
position and obtain same CdA even within individuals (García-López et al., 2008); even for
one position, there are significant differences between individuals in drag area. (Lim et al.,
2011) Hence, mean values like those calculated by some authors listed in the table mean
nothing.
CyclingPowerLab says 0.361 m2
is CdA for a subject of our anthropometric data
and riding style. But we know from all the above evidence that we must be wary of using
empirical data.
For further validation, hiring a much smaller wind tunnel to test scale models
would be one recommendation (Defraeye et al., 2010b). CFD analysis would also be a
recommendation but the accuracy of modelling the shape and surface of human beings in
motion (even a cyclic, so-called “predictable” motion like pedalling) is questionable and

needs to be investigated. The topic is quite vast and the author of this thesis has put
together a proposal for doctoral research on this very topic in recent months.
For some reason, if we want to know Cd for each ride, we could imitate what these
authors did: Step 1: estimate CdA from field test; Step 2: Divide drag area by frontal area
i.e., Cd = CdA/A. They found using this method that there are individual differences in drag
coefficients (Peterman et al., 2015).
PowerPod used CdA as 0.332 m2
for our subject. Isaac Software has a feature to do
CdA using actual power data. We did not go into this feature as the method itself is not new
to us – they would use linear regression as well. Also, the main use of PowerPod was
thought to be limited to Part 1 and not for parameter estimation. The next step and
recommendation would be to use PowerPod (or a similar device) in conjunction with a
DFPM to better estimate parameters. With the resources and powerful tools of the
Powerbike lab, we are certain that much use can be made of this device. The idea and
product are cheap, already available in the lab, do not require much computing time, and
support from the manufacturer is guaranteed.
Coefficient of Rolling Resistance (Crr)
Table 11 shows a snapshot of Crr data recorded by several authors in the past. Of
these, our value of 0.0094 came close to those obtained by four authors. This validation,
based purely on comparison, is more promising than the CdA estimation, which was
comparable to only two studies. Since some of them lump the Crr as a comprehensive
coefficient for other forms of losses, it is hard to compare Crr across studies (Zhan, Chang,
Chen, & Terzis, 2012).
The problem with using results from coasting or towing tests is that the results are
limited to the particular surface in question, for the particular pressure and that particular

mass of the bike and cyclist system. This limitation will always be the problem. This
limitation exists for our findings as well. We determined Crr for only one type of surface
i.e., smooth tarmac. Once again, these experimental conditions are far from real conditions
where riders change and experiment with pressure, tubes, brands, and models all the time.
The testing methodology itself is not flawed, but the approach is impractical.
The issue with using results from lab tests on rollers is that they are not being
tested on a realistic riding surface, so the deformations caused cannot be the same.
In any case, the rolling resistance term in the power equation contributes only 10-
30% of the total resistance. Only at speeds of less than 3 m/s (Wilson & Papadopoulos,
2004) in the conditions of level road and still air is the rolling resistance the highest force
to overcome.
A very interesting concept of using a dynamic i.e., a non-constant Crr has been
introduced by two parties: ("PowerPod rolls out ANT+/Bluetooth Smart version, improved
road surface algorithms," 2016) and (Meyer et al., 2016). The concept uses vibrations
measured at the handlebar level in the z-direction (i.e., perpendicular to the riding surface)
by the PowerPod or by a smartphone, respectively, to come up with an ever-changing Crr.
Using accelerometers of the calibre of 800 Hz sampling frequency once again, the
PowerPod claims improved results from this approach. PowerPod device, which was not
recommended for use on shaky surfaces like cobbled streets can now be used anywhere if
they are to be believed. At the moment, Isaac Software takes a default value of 0.005 based
on the pressure input by the user. But it would be interesting to note how far off this value
the “actual” dynamic Crr is. We could not get into this aspect of the product because the
upgrade in the device came after our experiments had already been conducted: Sep 5,
2016.

Raman Garimella thesis - Final Draft

Raman Garimella thesis - Final Draft

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