The Ithaka Prize Winner: 'The Hour Record: An Engineer’s View'

by Matt Bryan

Whenever there is talk of competitive cycling, the go-to event for the mind of the average Joe is the Tour de France, and who can blame them? Climbs up twisting Alpine roads and near A-road speeds sprinting down the Champs-Élysées do have a great deal of shock and awe - a display of raw power, tactics and scenery that anyone can appreciate. Some may wander into the realms of off-road with cross-country or downhill mountain-biking, and even fewer may have the World Unicycle Championships come to mind. But I would argue that one race stands out, a race that does not fight for space amongst other competitors, nor requires technical bike handling, but a race purely against the clock.

Alongside mass-start and track races, time-trials have been at the core of competitive cycling since its inception: a race in which a rider completes a usually flat course in the fastest time. It’s a discipline that requires pacing of the effort and intense mental concentration, and yet the best time-trialist at the Tour de France will likely never win the race. But strip back all the showmanship and corners and the very course itself and you are left with an unadulterated racing experience. The ‘purest race’ as many refer to it is the Hour Record where a rider rides as far as they can in an hour. But how can such a simple concept be considered the most prestigious race in cycling?

The Hour Record stands the test of time; removing the difficulties and uncertainties of road racing and by setting roughly the same parameters means that the cycling greats of the past can be challenged by the greats of the future in what becomes pro-cyclist Top Trumps. It’s like having Pele at his peak playing against Ronaldo - impossible yet still extraordinary. The classification and rules may have changed over time (more on that) but the very heart of the challenge remains the same. In the words of Eddy Merckx, five-time TDF winner, the Hour Record is “the hardest ride I have ever done” and that is why it enjoys such prestige and majesty.

One: A Brief History of the Hour Record

1.1 The Historical Hour

As the humble bicycle became more popular and affordable for the masses in the late 19th century, its sporting aspects were first realised on the track. But in the 1870s, these ‘bicycles’ were in fact “high wheels”, or more commonly, “penny farthings”. With fixed cranks and no gears, one turn of the pedals resulted in one turn of the wheel which was typically 1.2-1.6 metres in diameter led to a large distance per pedal stroke, but on a 1:1 ratio with the legs. These direct driven machines meant that if a rider pedalled at the modern standard of around 95 rpm, their speed would be a rather unextraordinary (1.4π × 95 × 60) 25.1 kmh -1, barely faster than a professional runner. The first recognised attempt at ‘an hour record’ was in the March of 1876 at “Cambridge University Ground”, with a distance of 26,508m, something that the vast majority of people could do nowadays. From averaged data, 26.5 kmh -1 typically requires a power of ≃ 130W, and studies using data from training app Trainer Road suggest that more than 90% of users can achieve that (irrespective of mass). And so came the development of the ‘upright bicycle’ we know today, or the “safety” bicycle
as the two more similarly sized and closer to earth wheels meant a lot less injury when falling off. With the rider’s position radically altered, so too was the drivetrain itself, as the user was no longer sat directly above the driven wheel. Now the cranks were situated between the wheels, with a chain connecting two sprockets from power to the wheels. With this came the opportunity of gearing, and with that more speed, and with that a renewed vigour for the Hour Record. With a large front chainring driving a smaller rear sprocket, one pedal turn could mean three or even more turns of the wheels if you had the legs! Henri Desgrange (the founding father of the Tour de France) set the first recognised record adjudicated by the International Cycling Association in 1893. He rode a more impressive 35,325m at a more impressive ≃ 280W ( more on power modelling later ), something that a modern amateur could achieve.

More attempts came and the fame of the challenge grew; by 1898, the record had broken 40km, and each successful attempt brought another 1000m or so. The gaps between competitor’s had at first been huge as the technology developed, but as the bicycles used were more and more engineered for speed, it became more about the engine when it came to triumphing over the current champion. The jump from the penny-farthing to the slick track bikes used pre-war was huge, but the 1914 record set by Frenchman Oscar Egg would stand for some 20 years. But these early riders were fantastic all-rounders, Tour de France winners and track riders, used to riding some 400km a day and excelled in all disciplines before the sport had really had a chance to diversify - they were good cyclists, not good Hour Record riders. This pattern continued as the record was held by 3-week Grand Tour winners like Fausto Coppi and Anquetil. These men were used to efforts lasting hours, and in many ways,
so were their bikes; using round steel tubing, huge frames and drop bars, the only difference between them and a bike for conquering the Alps was the omission of the brakes and a single fixed gear. The record pinged back and forth between the greats, increasing by a few hundred metres each time until it settled with one man.

1972 saw perhaps the most famous ride of all time: Eddy Merckx’s 49,431 metres in Mexico City. The bike he used was elegant; an orange steel frame with sharp steel drop handlebars and spoked steel rims - rather simple looking nowadays. Merckx’s record was considered unbeatable, considering how unbeatable he was in every other discipline. He won 11 Grand Tours, all five of the demanding Monuments and three World-Championships - if there was a race worth racing, it was likely that “The Cannibal” had won it. But could technology triumph over talent and prestige?

1.2 The ‘Aero’ Years

The Hour Record’s bikes had remained relatively similar; a steel track bike made as light as possible with the finest crafted components - seemingly the best tool for the job. It was more of a battle of rider against rider. The 80s changed that, and the era of technological advancement had begun and sought to put Merckx in his place. In January 1984, Francesco Moser set a new record and then trumped himself four days later with 51,151m, but his bike seemed space-age in comparison to those of the past. He had a company build him a pair of solid, ‘single-spoke’ disc wheels with a smaller one at the front to give a more aggressive position alongside a streamlined silhouette. But the real development was the use of carbon fibre, and so began the bicycling world’s love affair with the wonder material. Moser’s position on bullhorn bars was striking too and he became a quasi-bedroom poster hero - the man who beat Merckx.

But ten years on the throne was bound to inspire competition, and yield foes that would make him seem far from radical. Along came Graham Obree, ‘the Flying Scotsman’, largely derided for his lack of racing pedigree being foremost a bike-shop owner and an engineer. He fabricated his own bike, using bearings from a washing machine and welding a single tubed frame - but the position was what it was all about. The frame had a low Q-factor, meaning his knees were closer together and he sat low down with a very low stack height. Rather than using the drop bars championed for a century, Obree had flat bars with a very short reach, tucking them very close to his chest, leading his position to be nicknamed ‘the Praying Mantis’. The strange position was tested recently at having an even lower drag coefficient than the modern standard. Obree was a decent time-trialist, but his technological
advancements had won him a world record of 51,596m in 1993.

This achievement lasted for six days. Chris Boardman had just won Gold in the 1992 Olympics and brought his form to a triathlon position with quad-spoke wheels. Whether it was technology or fitness, he set a new record of 52,270m. Obree came back the next year and bested Boardman’s time on his ‘Old Faithful’, but then his world came crashing down. Many had claimed that ‘bike racing no longer resembled its old glory - riders were no longer riding bikes’ and this was of course in reference to the advancements in technology being made and many claim a prejudice against an ‘amateur’ like Obree defeating icons like Merckx. And so the UCI (governing body) banned Obree’s position and imposed the first in a long set of rules to keep cycling ‘pure’.

At this point, the dominant time-trialist and consecutive five-time Tour winner Miguel Indurain set a new legal record at 53,040m, restoring order to the sport in the eyes of many. He and Tony Rominger competed for the next two years, bringing the record up to 55,291m, nearly six kilometres more than Merckx had done. But 1996 would be the pinnacle of technology. Boardman was back, and this time backed up by designers at Lotus. Seeing wing designs used in other industries to cut through the air, the 110 frame was moulded from a single piece of carbon fibre rather than tubes, and he used a stretched out ‘Superman’ position pioneered by Obree all to his aerodynamic advantage. He looked fast, and he was. Boardman set a new record of 56,375m which remains the all time record.

1.3 The Modern ‘Unified Record’

1997 saw an even greater change in rules from the UCI: the ‘Hour Record’ would now be split into two new categories. The current record holders and those previously banned would be moved to ‘UCI Best Human Effort’ where the rules on equipment were far less strict. The new ‘UCI Hour Record’ would have severe equipment regulations, meaning riders would have to use bikes like Eddy Merckx had - tubed frames, shallow spoked wheels and drop bars in a real step back from technology. The UCI wanted to preserve what they saw as the sanctity of the record, and as a result, Merckx became the new record holder. Somewhat angered by the decision, Boardman decided to silence his critics by attempting the record on a ‘traditional’ track bike, which utilised carbon fibre tubes and lugs for its frame rather than a single piece. In 2000, he beat Merckx’s record by just ten metres, and so the Hour Record was once again below 50km at 49,441m.

Few would now attempt the result, and Boardman was only topped by 300m in 2005, but by a Czech cyclist who then failed doping control. The excitement of the record had, in a sense, dried up. There was no push from manufacturers and designers to show off their latest gear and few wanted to test themselves against a high bar. Because of this overregulation, the record became a relic, and it faded away in an era of doping and controversy. Becoming thoroughly modern (by their standards), the UCI reunited the categories in 2014 to create the ‘UCI Unified Hour Record’ and riders were able to use any bike that was ‘UCI-legal’ for standard endurance track events. But the Hour is no standard event, so the bikes had to be a bit more unique than just the common-or-garden track bike found on the World Cup circuit. Disc wheels were back, but now had to be the same size; frames were once again
carbon monocoques (single piece) and the triathlon bar extension was the position of choice. The record was reinvigorated.

Recently-retired Jens Voigt was the first holder of the new record in September 2014, riding 51,110m at the age of 43. Renewed interest meant frequent attempts: 2015 saw Rohan Dennis ride 52,491m as well as four attempts between. The UK benefited from Alex Dowsett in May 2015 before Bradley Wiggins set a huge benchmark of 54,526m in June. Wiggins took on the record as a warm up before his final Olympics and he showed what could be done with development on the humble TT position, especially when a talented rider is on the saddle. Wiggins infamously rode at 440W, a huge power output that went unmatched for almost four years. 10 attempts later, Victor Campenaerts, European Time-Trial Champion, set the current record of 55,089m in April 2019. What was unique was his attempt at altitude, a technique not used widely since Merckx’s era. The competition continues and is exciting as ever.

Two: A Model for Power

Bikes don’t move on their own, especially at the kind of speeds seen on an Hour Record velodrome. The energy required is kinetic, transferred by the rider as they apply a force to the pedals, which in turn turns the rear wheel. In this case, we will focus on the mechanical aspects of the system, rather than the biological aspects. Some 60% or more of a rider’s power is thermally dissipated rather than making it to the pedals, in the same way that a car’s wheel horsepower figure differs from its engine horsepower - the body is not 100% efficient when it comes to aerobic respiration (an even less if a rider goes anaerobic). Therefore, the terminology of power output refers to the energy per second that a rider transfers into the circular motion of the pedals.

Nowadays, power is usually tracked by a power meter: a crank-mounted device which measures the force exerted upon it, then calculates the figure in watts (more on that later). These range in accuracy between 1-5%, but are considered to be a good reflection of effort.

2.1 Is it all About the Rider?

Yes and no. It’s safe to say that an amateur (myself included) breaking the Hour Record anytime soon is unlikely. As much as there is a large emphasis on the engineering of the bicycle used, it's more critical that the legs powering it can use its technology to its full advantage. On a flat road, the average person would struggle to propel a bike at 50kmh -1 (or just over 30mph if you are still imperially inclined) - but this kind of effort would be considered a ‘sprint’, usually defined as the anaerobic or 6-second max. This refers to the maximum power than a rider can attain in a short space of time. A track-sprinter like Chris Hoy is reputed to have a max of 2500W, whereas a road racer might be more like 1500W and someone untrained c. 500W. But for the record, this close-to-sprint speed must be maintained for a whole hour, which really puts the numbers of the pros into perspective. But this doesn’t tell the full story, so what’s usually given is a “four-dimensional” profile, typically figures for the best 6 second, 1 minute, 5 minute and 20 minute powers of a rider.
FTP or one-hour power is usually calculated as 95% of the 20 minute effort, as statistics
have shown a high correlation between figures. Efforts above 20 minutes largely follow a
trend rather than being unique efforts.

When it comes to attempting the record itself, power meters are banned, which means that a
good rider should be able to determine their power ‘by feel’. This makes the ability to pace
oneself highly important, as going too hard at first will lead to a slowing down later on and
going too slowly will lower the overall distance. Gauging power off ‘feel’ is a real skill that
takes years to get to grips with, so once a rider has decided on a power to sustain for the
hour, they will know exactly how it feels in their legs and heart.

The areas in which a rider excels can be used to show what kind of racing they would be best at, and this kind of analysis is vital for the kind of rider who wants to break the Hour Record. The following values come from a range of reliable sources, eg. coaches, power data etc.

Name Matt Bryan Matt Houlberg Dan Lloyd Bradley Wiggins Peter Sagan
Weight 61 kg 50 kg 69 kg c. 78 kg 73 kg
Class Amateur Category 2 Ex-Pro Ex-Pro Pro
6 second 1320W 1000W 1180W c. 1500W c. 1800W
1 minute 480W 497W 773W c. 800W c. 1000W
5 minute 315W 338W 485W c. 580W c. 600W
20 minute 250W 264W 396W 490W c. 420W
FTP 238W 251W 376W c. 465W c. 400W

Rider Type Sprinter Climber Rouleur Time-Trialist Sprinter/Rouleur

Sprinters are good at all-out, short duration, high power efforts and typically win flat stages where there are bunch sprints (ie. Mark Cavendish, Mario Cipollini etc.) Climbers excel in having a high power to weight ratio which typically means a high figure for the longer efforts combined with a lower weight (ie. Nairo Quintana, Egan Bernal etc.) Rouleurs are all-rounders who do well in rolling terrain where breaking away on smaller climbs and holding on gives them a victory (ie. Phillippe Gilbert, Julian Alaphilippe etc.) Time-Trialists are those who can hold on to a high power for a long effort and do well in longer races across the board, usually serving as part of a team. The very best Time-Trialists are those suited to Hour Record fame as the excel best in the constant one-hour effort that it requires. A good all-rounder could do a similar job, but a TT-specialist is far and away the
most prepared for an attempt at the record. (ie. Rohan Denis, Miguel Indurain) When it comes to a flat course, a power to weight figure matters less as it only affects the friction felt as the lack of hills means little gravitational force to contend with. As a result, Hour Record contenders can be heavier than the average welterweight cyclist, and this allows them to put out more power due to increased muscle size. What’s more important is their frontal area and power to weight. A greater mass typically leads to a higher power in professionals, which comes in turn with a higher area exposed to the wind. Power is proportional to the cube of velocity, whereas frontal area is to the square, so typically, outright power has a greater effect than the size of the rider themselves. Modern commentators have estimated that Eddy Merckx would have had an FTP in the region of 450W, although these figures are backed up by estimated calculations based on his hour record performance and the equipment he was using, it is hard to say considering the lack of power measuring technology in his era.

2.2 Forces at Play

The energy transferred or mechanical work done is the product of the force and the distance it acts over and so it follows that: E = F • d

Dividing this by time gives us power on the left hand side: P = t
F •d

And putting this in terms of fundamental units gives: kgm2s−3

So it follows that: power = kgms−2 • ms−1

More simply for a bike application: power = resistive force • velocity

But the force of a rider on the pedals aren’t the only forces acting on a bike. Although there are numerous resistive forces, these can be simplified to four major forces:

Aerodynamic Drag: Kinetic energy of the bicycle system istransferred to air molecules as the two
collide, applying a force opposite to the direction of motion.

Friction: Tyres in contact with the track have their motion opposed by frictional forces proportional to the normal reaction force exerted on them.

Gravity: Some of the power supplied must go into overcoming the pull of gravity, so less makes it into horizontal motion when it comes to going up a gradient.

Mechanical Resistance: The drivetrain and moving parts of the bike experience their own friction and so are not 100% efficient, meaning power is dissipated as heat, deformation, or sound.

Each of these components can be modelled mathematically, and then combined to create a
model that gives a good estimate of the velocity achieved for a certain power taking into
account a select set of conditions. From the power, a figure for an hour can be obtained.

2.2.1 Friction

Frictional forces oppose the forward motion of the tyres by converting a portion of their kinetic energy into friction. For static objects, like a chair on a hard floor, the forces can be modelled by Coulomb’s law, which states that the frictional force is always less than or equal to the normal force exerted on the surface multiplied by a dimensionless constant, typically given the letter mu (μ) and called the coefficient of friction. A simplistic model would be as follows:

Ffriction ≤ μ ・Fnormal reaction

The issue is that the static coefficient of friction, μ s , is independent of the ‘kinetic’ coefficient of friction, μ k . μ s can be determined easily experimentally: an object is placed on a surface, a force is applied at a set angle, and that angle moved closer to the horizontal until it moves. At that point, the horizontal component of the velocity is equal to the frictional force (or just slightly more than), and then the reaction force can be calculated. This is done by taking the weight of the object in Newtons and subtracting the vertical component of the force applied that was ‘lifting it off of the surface’. A rough, grippy material will have a μ s of close to one, whereas a slippery, low-friction material like glass, will be closer to zero.

In the realms of cycling, the rubber compounds in tyres are designed to a compromise: they should be low friction to increase the efficiency of the rider’s power transfer into forward motion, but on the other hand must have enough available friction to allow them to corner at fast speeds without risk of sliding out. But on the track, the needs of cornering are far less important because the conditions are highly predictable - the bike will steer one way and in shallow bends, and braking is not an issue. So a tyre designed for pure track racing will have an extremely low rolling resistance and be made of a ‘fast compound’ with a slick tread. Currently, the tyre of choice is the Vittoria ‘Pista’ specially designed with asymmetric tread so it grips better when turning left.

But how difficult is it to determine frictional forces in a moving model? What’s helpful is that the two surfaces in question remain identical (enough) throughout, as the tyre is always in contact with a section of an identical track. To calculate an accurate value for μ k is difficult but possible. Using a flat piece of the surface, a wheel with the tyre in question can be attached to a rig that applies a constant force to it through the axle. After accelerating, the wheel should reach a constant velocity, at the point where the frictional force is equal to that applied giving a resultant force of zero. At this point, the force can be divided by the weight in Newtons to give a value for μ k .

However, this method introduces a lot of variables that are hard to control, such as any lateral motion on the rig, the consistency of the materials, among introducing other forces like drag, however minute. A paper from the University of Pretoria carried out its own research into the matter, taking into account these other factors in addition to using a variety of scenarios and found standard values for μ k with a low variance. Their value for the coefficient was 0.002 and other sources put the value between 0.001 and 0.005 with some accuracy, tending towards the lower end of the scale for a good tyre on a wooden track. For those purposes, my model will use a value of 0.0015 ∓ 0.0005, but the uncertainty in this figure is unlikely to have a large effect, considering the low value of the force as compared to the entirety of the resistance.

Coulomb’s Law of Friction states that kinetic friction is independent of the sliding velocity, so
the velocity of the tyre is not taken into account, only the fact that it is in motion. Amontons’ Second Law also states that the area or contact patch has no effect, although tyres widths are another discussion point. (note: ‘g’ is taken to 3 s.f.) Therefore: Ffriction = μ • g • m or Ffriction = 0.014715 m

2.2.2 Gravity

Gravitational force has a huge effect when it comes to climbs, as riders must expend precious power to overcome the force of it pulling them back down the hill, but this in turn allows the conversion of gravitational potential energy gained back into kinetic energy on the descents for blistering speed. But a track is flat, and when riding solo, a track rider stays on the lower line. In team events like the team pursuit, a rider will swing off the front and up the track after a turn on the front. But this manoeuver is bound by the laws of thermodynamics and is not a form of ‘perpetual motion’ as the rider will do more work going up the track than is gained by coming down it. This move is used to put a rider at the back whilst still conserving speed and prevents a gruelling acceleration to keep up with the pack.
In essence, gravity can be ignored when talking about the Hour Record, although there is one caveat. Many riders are now choosing to make their attempts at altitude, and although this is for barometric reasons (see later), moving further from the centre of the Earth does reduce the gravitational force exerted on the rider, reducing their weight and therefore friction.

But before this is labelled as ‘cheating’, the difference is extraordinarily minute as shown here:

Using Newton’s law of universal gravitation: F gravity = r2
Gm1m2

The radius of the Earth (on average) is 6,371,000m. For a rider and bike of 80kg on a track at
sea-level, the force experienced is:

85.56N g 0 .81 r2
Gm1m2 =
6.371×1062
6.674×10−11•80•5.972×1024 = 7 ≈ m = 8 • 9

Increasing the altitude to that of Aguascalientes, Mexico at 1887m changes that force and
the radius to 6,372,887m.
85.10N ∴ Δ% .0586% r2
Gm1m2 =
6.372887×1062
6.674×10−11•80•5.972×1024 = 7 = 785.56
785.56−785.10 = 0

Most would call that level of change negligible, and considering so many other factors, for example temperature, have such a large effect, a small reduction in friction due to gravity can safely go unnoticed. This does of course model the Earth as a perfect sphere too, and so in reality, the localised gravity may not be as close to this figure. A higher altitude changes a great number of properties in an attempt and the reduction in gravity is marginal.

2.2.3 Air Resistance

By far the greatest force slowing down a cyclist is aerodynamic drag, and with most sources suggesting that it accounts for upwards of 70% of resistance at higher velocities, you can see why the pro-cycling world is so obsessive about ‘aero’. The resistive force comes from friction, or impacts with molecules in the air; in recent years, much of cycling’s development budget has gone into making the humble bike as streamlined as possible, reducing the factors that contribute to the magnitude of the force felt by a rider (within the UCI’s guideline). Ironically, the largest force on a moving object is the one that most A-Level Physics textbooks tend to omit, but likely due to the more complex nature of its modelling.

There are a number of quantitative properties that determine how aerodynamic an object is. A standard wind tunnel works by directing a flow of air towards a static object like a bike, which is connected to force sensors that monitor the force it applies as a result of the air ‘pushing’ it backwards. To reduce this force and therefore reduce the drag felt by an object, both the frontal area of the object and its drag coefficient must be optimised.

The most effective way of doing this is by changing the rider’s position, especially considering that around 2/3s of drag is caused by the body rather than the bike. A lower and more tucked in position towards the front of the bike reduces the frontal area that is in contact with the air molecules. But a narrower position with the shoulders as close as possible is again lesser in area and is the major difference between the style of Merckx and Obree (and the racers of today). By comfortably achieving a lower and narrower profile on the bike, the frontal area can be greatly reduced.

But much like friction, the interaction between the air and the rider has its own coefficient - the more aerodynamic a surface, the lower the coefficient and lesser the force felt. To this effect, riders now choose to wear skinsuits, a lycra based one-piece that covers as much skin as possible. With the material being extremely close-knit and uniform across the body, a skinsuit does a much better job of cutting through the air than even bare skin.

A simple model for air resistance is: Fdrag = 2
1 • Cdrag • A • ρ • v2

In this case, the product of C drag and Area is calculated rather than the two separately, as this
can be done experimentally by rearranging to divide the double force measured in the wind
tunnel by the known air density and air velocity squared.

Cdrag • A = ρ•v2
2F drag

The issue is that any change to conditions, including minute adjustments to rider position, materials used etc. means that the value must be recalculated. It is also difficult to determine the frontal area independently for a complex shape such as a bike and rider. Values for C d A are commonly calculated by industry researchers and manufacturers at present, but they do vary from rider to rider, and are highly dependent on the equipment used and the unique behaviour of airflow around the shape in question. There are however benchmarks that the Hour Record contenders of today strive to achieve.

Position Source C drag A value (m 2 )
1993 UCI Standard Endura-Obree 2018 0.204
Modern UCI Standard Endura-Obree 2018 0.185
Obree ‘Praying Mantis’ Endura-Obree 2018 0.172
Obree/Boardman ‘Superman’ Endura-Obree 2018 0.200
Amateur on TT bars A. Jeukendrup 2002 0.2680
TT Bike and Bars w/Helmet Bikeradar 2008 0.2323
Road Bike and Drops Bikeradar 2008 0.3019
‘Comfortable’ Position ‘Bicycling Science’ Wilson 0.7268
Flat Plate - [Bike Sized Estimate] Using NASA GRC values 1.165
Eddy Merckx - Complex Estimate Padilla et al. 2000 0.2618
Graeme Obree - Complex Estimate Padilla et al. 2000 0.1720
Miguel Indurain - Complex Estimate Padilla et al. 2000 0.2441

All of the values given, except those in yellow, have been determined experimentally in a wind-tunnel, the others have been calculated either by using an area multiplied by a known drag coefficient, or by combining a number of factors to come to a conclusion. In the case of Padilla et al.’s estimate from their 2000 publication ‘ Scientific approach to the 1-h cycling world record: a case study’ , they compiled data from numerous riders that allowed them to use a model that could determine the Frontal Area of a rider by their body type, mass and height, and then express that as a percentage of their base surface area. This then combined with testing on track and in a tunnel and backdating from records gave them values for each athlete for their C d A. Their value for Obree matched the recent experimental value from Endura to three significant figures, showing that modelling can be consistent even in the real world.

Computational Fluid Dynamics

But there are many more things to consider when it comes to aerodynamics, and the model above does a good job of combining the behaviours of air molecules into a single value. In the situation of the Hour Record, where being indoors, the molecules are relatively stationary (there is no wind), meaning that the bicycle always ‘cuts’ straight through the air. However, in reality, the molecules do not simply slide over a bike and rider, so when it comes to designing a bike that is aerodynamic, it isn’t simply a case of reducing the frontal area to a minimum, the drag coefficient is heavily dependent on the shape of the object as a whole.

Consider a bullet, a spherical leading face followed by a flat planed base. This has a C drag of around 0.295 ( NASA GRC ). On the other hand, an aerofoil with a similar leading face but a long shallow tail gives a C drag of closer to 0.045 - the reason: turbulent flow. Normal airflow can be described as ‘laminar’, in smooth, straight(ish) layers, but when particles interact with edges, vertices or other shapes, the flow can be disrupted and become turbulent. Something like the perpendicular edge at the rear of a bullet can stimulate turbulent flow, which causes more interactions between the particle and object, resulting in a larger drag and C drag.

So when it comes to designing a ‘fast’ bike or component, the shape as a whole must be considered. For example, wheel manufacturer Zipp has introduced dimpled, ‘saw-tooth’ shaped rims that utilise small turbulent flow to aid aerodynamics by reducing pressure differentials and therefore drag. Designing like this is only possible with software that can simulate the flow of the fluid around the object in different scenarios, hence the increased use and benefits of computational fluid dynamics.

Models can provide a visualisation of the areas that cause the most drag and how a change in design can increase the efficiency of the object. Endura’s SST (Surface Silicone Topography) Skin Suit has been used in three Hour Record successes and has features on the surface that significantly reduce drag, having been developed in a computer operated wind tunnel that measured more than just the resistive force. But on the whole, the C drag A serves as an effective enough estimate for the drag force.

Air Density and Altitude

The drag experienced by an object also depends heavily on how many air molecules there are for it to interact with in a given space or time, so the mass of air per unit volume is used, which is why the density of air or ⍴ is required. At sea level, this is around 1.225 kgm -3 , but as altitude increases, the density of air decreases, which can have a moderate effect on the power required. There are multiple ways of modelling air density, but when the temperature lapse rate is assumed to be zero (that temperature is constant no matter altitude):

ρ = ρ0 • exp( ) R•T
−g•M•h or ρ = 1.225 • exp(− 1.1585 × 10−4h)

Having substituted in the values for gravitational acceleration, the molar mass of dry air, the universal gas constant and taken temperature to be 23 o C (295K) the formula is simplified to an exponential model. Therefore, the higher up you ride, the lower the force of drag felt, but this comes with its own physiological issues which will be discussed later.

2.2.4 Mechanical Resistance

In order to transfer the kinetic energy of a rider’s legs turning the pedals into the motion of the wheels, a bike must have a drivetrain, which like all mechanical systems, is not 100% efficient. Whilst most of the power supplied by the rider is transferred to the bike, some of the energy is lost via friction or deformation. A chain connecting two fixed gears has been the drivetrain of choice for track riding since its inception, likely due to its simplicity and ease of use when it comes to changing over ratios for individual events - in addition to the fact that it is highly efficient. The average bicycle drivetrain has a loss of around five-percent, and with optimisation, this can be close to 2%; compare that to the 70-80% loss of a petrol engine and you can see why fractions of a percentage point really make a difference.

The friction largely comes from the interaction between the chain and the chainring/cog, but this is already quite low as the two are made from similar alloys. Nonetheless, the chain must still slot between the teeth, and at Hour Record pace (say 95rpm on a 56 front-ring), this interaction happens over 300,000 times in the hour, each time losing a small amount of energy. To limit this loss, drivetrains are fabricated from lighter alloys and metals like titanium and their volume also restricted to reduce weight, and therefore the magnitude of force in each interaction. Specially formulated lubricants also contribute to a slicker action and more efficient tooth-profiles with lower tolerances are used.

But making things as light and frictionless as possible isn’t the only thing in mind when designing record-winning drivetrains; they must be stiff enough to cope with the power transfer. Energy is also lost in deforming elements of the drivetrain, and so a thinner and lighter chain will stretch and bend more, which can be worse than a higher friction drivetrain.

For that reason, track-chains are of a higher gauge than road-chains to withstand the constant force in a single direction (whilst a geared bike will have lateral force from a derailleur) as well as provide a solid platform when the chain picks up and drops teeth.

As each interaction of the drivetrain is minute, and the resistive force that it provides is not localised and its magnitude is proportional to the input power, it is much easier to model it as a percentage efficiency. World-class equipment typically allows a 98% efficiency in power transfer, but new technology seeks to further reduce this.

2.3 The Model as a Whole

Combining the three main sources of resistance gives a model that takes an average velocity from the rider for a whole hour and gives the power that it should require, (ignoring the initial acceleration) hopefully as close to ‘real-world values’ as possible. Further modelling can find any of these values from a set of other measurements (see Chapter 5).

As Before: ower esistive p = r force • velocity
Therefore: P = (Ffriction + Fdrag) • v
Introducing Mechanical Efficiency: P • 0.98 = (Ffriction + Fdrag) • v
Substituting in models for air resistance and friction:
Fdrag = 2
1 • Cdrag • A • ρ • v2 and F .014715 m friction = 0
P = 0.98
v(0.014715 m + • C • A • ρ • v ) 2
1
drag
2

Using velocity in metres per second (ms -1 ), this calculates the power required. Taking the
real world situation of Bradley Wiggins, we can test the accuracy of the model:
Wiggins 2015 Hour Record: Known Power = 440w Power using model =
0.98
15.146(0.014715•80+0.5•0.195•1.225•15.1462)
= 441.65 W (5 s.f.)
Δ% = 0.412%
Average Velocity 54.526 kmh -1 = 15.146 ms -1
C d A [estimate] 0.195 m 2
ρ or air density [sea level] 1.225 kgm -3
Mass [w/bike] 80 kg

The C d A estimate comes from the modern benchmark of 0.185, but slightly increasing it due
to Wiggins’s above average height of 1.9m (6ft3), considering he wore a skinsuit, aero
helmet and rode a Pinarello Bolide (all cutting edge). Substituting in these figures gives a
power very close to his actual output. Using the slightly smaller Alex Dowsett’s attempt a
month prior:

15 The Hour Record: An Engineer’s View - Matt Bryan
Dowsett 2015 Hour Record: Known Power = 395w Power using model =
0.98
14.705(0.014715•83+0.5•0.190•1.225•14.7052)
= 395.92 W (5 s.f.)
Δ% = 0.237%
Average Velocity 52.937 kmh -1 = 14.705 ms -1
C d A [estimate] 0.190 m 2
ρ or air density [sea level] 1.225 kgm -3
Mass [w/bike] 83 kg

Therefore, the model is relatively accurate, but it does miss some key details of the Hour
Record, like acceleration and weather conditions. But what would make the model more useful is the ability to take an average power value and calculate the corresponding hour distance. From the current formula:
P • 0.98 = (Ffriction + Fdrag) • v or 0.98P = v(0.014715 m + C Aρv ) 2
1
d
2
Expanding gives: 0.98P = 0.014715 mv + C Aρv 2
1
d
3

This cannot be easily rearranged for v as it is a third-degree polynomial (the other values
being constants in each case of the function).

f(v) = 0.5CdAρv .014715 mv .98P
3 + 0 − 0 = 0

The function has three roots, one real and a pair of complex conjugates, the real one being
the velocity for the set of input values (as the remaining discriminant is negative). Since a
real-world velocity cannot be expressed as a complex number, the function maps values one
to one, giving one real root when set equal to zero. This can be calculated in a number of
ways:

1) NUMERICAL CALCULUS: Newton-Raphson Method

This method relies on graphically solving for the root via iteration - a tangent to the curve is
calculated before its intersect is used at the next value, substituting back into the formula
and then eventually converging to the root.

vn+1 = vn − f(vn)
f′(vn)
f(v) = 0.5CdAρv .014715 mv .98P
3 + 0 − 0
f′(v) = 1.5CdAρv .014715 m
2 + 0

Therefore, using Wiggins’ values and a starting v of 15 ms -1 :
v1 = 15 − 5.128 1.5•0.195•1.225•152+0.014715•80
0.5•0.195•1.225•153+0.014715•80•15−0.98•440 = 1

The value eventually converges to 15.127 ms -1 (5 s.f.), which is 54.456km, just 70 metres
from the actual distance he covered, but the iterative method is a bit clumsy and requires
computer calculation or a lot of arithmetic, in addition to having to completely restart if a
value is to be altered. ( below showing initial value of v=10, and then closer from v=18)
For myself, assuming an average power of 238W, a slightly greater C d A of 0.22 (due to my
lack of professional training and flexibility) and a mass of 68kg with a bike, what would my
attempt at the Hour Record yield on a good day?

v1 = 13 − 1.906 1.5•0.22•1.225•132+0.014715•68
0.5•0.22•1.225•133+0.014715•68•13−0.98•238 = 1

Repeated iteration converges quickly and gives a value of 11.801 ms -1 (5 s.f.) which is
42.482km, giving me the Hour Record if I was in 1912. This seems about right from
experience, considering extended periods at 38kmh -1 is hard work on less aero-optimised
equipment.

17 The Hour Record: An Engineer’s View - Matt Bryan
2) PURE ALGEBRA: The Cubic Formula

Just as quadratic or second-degree polynomials can be solved by a formula, so can cubic
equation, albeit the formula is a little more complicated.

Considering:
(f v) = 0.5CdAρv .014715 mv .98P
3 + 0 − 0 = 0
a = 0.5C d Aρ c = 0.014715m
b = 0 d = -0.98P

Cardano’s Method allows the roots of a cubic to be found, first by creating a ‘depressed
cubic’ via substitution and eventually coming to this conclusion:

Although it consists of many terms, in the case of our formula, b is zero, thus cancelling out
11 terms of 17. The remaining six are actually only two unique terms, which can be further
substituted for ease of use.

2a
−d = C Aρ d
0.98P = α & c
3a = 1.5CdAρ
0.014715m = β

Now using alpha and beta, the formula becomes:

v =√ 3
α +√α2 + β3 +√3
α −√α2 + β3
In the case of Wiggins,
α = 2a
−d = 0.98•440
0.195•1.225 = 39
70400
β = c
3a = 0.014715•80
1.5•0.195•1.225 = 3185
10464

Substituting these values into the compressed version of the formula gives a value of 15.12658 ms -1 (7 s.f.) or 54.457 km, 69m less than Wiggins actually achieved. The same exact answer is given for myself, at 11.80060 ms -1 (7 s.f.). The method has its issues in the possibility of complex answers, but gives exact numbers unlike the estimates of the iteration. Also, the high accuracy in the answers are let down by the lower accuracy of the numbers used in the calculation, for example C d A is only two significant figures etc.

Plotting the model in Cartesian form gives a graph that can be used to estimate the velocity for a certain power based on the input values. Shown here is a 70kg bike and rider with a C d A of 0.2 at sea level. (blue is in ms -1 , red is in kmh -1)

However, in all, a simple model and some calculations does quite an effective job of estimating the distances possible in the Hour Record, typically to less than half a percent of the practical figures. Such a tool is invaluable in calculating the effects that changes in design will have on the distance covered, and so should be used by an Engineer with any hope of breaking the record.

Three: Designing vs. the UCI

For a sport such as cycling which has wholly embraced technology and actively strives to increase performance to that only imaginable years before, you would assume that its regulatory body would have also wholeheartedly embraced cutting-edge tech.

You’d unfortunately be very wrong (but perhaps they are getting better). Being so steeped in history, the UCI is often reluctant to allow new technology into the sport, especially when it seems to take away some of the prestige of years gone by. If the UCI had its own way, I wouldn’t be surprised if the entire peloton was forced to ride single-geared steel bikes from the early 1900s again. Take the Col du Tourmalet, a climb first ridden on the Tour in 1910, and 86 times since. Back then, only the best riders would make it to the top, often having to walk sections - now, riders race up matching the speeds of cars. In the eyes of the UCI, technology dilutes the challenge and heritage of the sport. To that effect, they impose a number of guidelines on all the races they manage.

When it comes to designing and riding a bike for the Hour Record, it must be compliant with the UCI’s guidelines for track pursuit bikes (since 2014). These are subtly different to the standard track bike rules in that a TT handlebar is permitted and the saddle must be positioned slightly further back. A good 35 pages of the 50 page document are concerned with the shape and design of bicycle frames and handlebars that are competition legal. These range from the sensible to the weird and oddly specific.

A Selection of the UCI’s Technical Regulations:

ARTICLE 1.3.001

“Each licence holder shall ensure that his equipment (bicycle with accessories and other devices fitted, headgear, clothing, etc.) does not, by virtue of its quality, materials or design, constitute any danger to himself or to others.”

In essence, any bike used for any competition must be safe and not likely to cause danger to the rider or others. This rule has been used to ‘ban’ certain types of wheel that were prone to shattering during competition in the 90s.

ARTICLE 1.3.004

“No technical innovation regarding anything used, worn or carried by any rider or license holder during a competition may be used until approved by the UCI.” All equipment used for the Hour Record or similar must be pre-approved by the UCI, which introduces a deadline some weeks before an attempt. Oddly enough, this rule doesn’t apply to mountain-biking, suggesting that it is just a case of bureaucracy.

ARTICLE 1.3.006
“Equipment shall be of a type that is sold for use by anyone practising cycling as a sport. Any equipment in the development phase and not yet available for sale (prototype) must be the subject of an authorization request to the UCI Equipment Unit before its use.”

Much like homologation in motorsport, parts used must be available to the general public, except in special circumstances. However, Wiggins used custom-printed titanium handlebars, a product still not
available to the public, bringing into question the validity of the rule.

ARTICLE 1.3.007

“The bicycle is a vehicle with two wheels of equal diameter. The front wheel shall be steerable; the rear wheel shall be driven through a system comprising pedals and a chain.” This seems sensible enough, but is a rule to keep bicycles as ‘bicycles’. Moser’s famously huge rear wheel was ‘banned’
under this rule, and so would any form of more efficient drivetrain or a bike with rear-steering etc.

ARTICLE 1.3.008

“The rider shall normally assume a sitting position on the bicycle. This position requires that the only points of support are the following: the feet on the pedals, the hands on the handlebars and the seat on
the saddle.” Again, another rule which seems to define a bicycle. This outlaws the use of recumbents, which being more aerodynamic, would go far further in an hour, but only a traditional bike is valid. In
this case, alternative, faster body positions are also out of the question.

ARTICLE 1.3.010

“The bicycle shall be propelled solely through a chainset, by the legs (inferior muscular chain) moving in a circular movement, without electric or other assistance.” This was introduced after a spell of ‘motor-doping’ to reaffirm that the bike must be solely human-powered. E-bike racing is another discipline that might gain traction in the future.

ARTICLE 1.3.014
“The plane passing through the highest points at the front and rear of the saddle can have a maximum angle of nine degrees from horizontal. The length of the saddle shall be 24 cm minimum and 30 cm
maximum. A tolerance of 5mm is allowed.” This rule sets out the guidelines for saddle positions, as most riders tilt theirs slightly down as it puts less pressure on the body and allows them to put out more power. But the UCI restricts this to 9 o , having previously been much less lenient. They have
specialised measuring devices to perform checks on rider’s bikes.

ARTICLE 1.3.015
“The distance between the bottom bracket spindle and the ground shall be between 24 cm minimum and maximum 30 cm.” A rule from the road prevents track bikes from achieving lower stack heights by shifting the BB lower. With 170mm cranks on a slightly banked track, 20cm height would be safe and more aerodynamic.

ARTICLE 1.3.019
“The weight of the bicycle cannot be less than 6.8 kilograms.” Heralding from an era of questionable
carbon fibre for safety reasons, bikes must meet the weight limit, despite the ability to make them as light as 4kg, and therefore able to accelerate much quicker. This is more of a hindrance on the road not track.

ARTICLE 1.3.020
“The elements of the frame shall be laid out such that the joining points shall follow the following pattern: the top tube (1) connects the top of the head tube… etc.” From the fallout of the Obree years came enforcement that frames must be in the traditional shape, and those more aero like Boardman’s Lotus were outlawed for being ‘too unlike a bicycle’, and that it would ‘change the existing disciplines’. The rest of the article sets out min. measurements.

ARTICLE 1.3.023
“a fixed additional handlebar may be added to the steering system; for track and road competitions, the maximum distance of 75 cm may be increased to 80 cm to the extent that this is required for morphological reasons; for riders that are 190 cm tall or taller the extremity of the handlebar
extensions may be extended to 85 cm.” The UCI sets out the maximum length of TT handlebar extension based on the height of a rider and subject to review, ie. how aero you can get and how close you may get to the ‘Superman’ depends if you exceed an arbitrary height limit. Wiggins was able to,
but Dowsett was not.

ARTICLE 1.3.024
“A fuselage form shall be defined as an extension or streamlining of a section. This shall be tolerated as long as the ratio between the length L and the diameter D does not exceed 3.” The infamous 3 to 1 rule is the bane of designers, meaning that frame cross sections cannot be made to be perfect aerofoils as this shape would be too long and illegal, despite being much more aerodynamic.

ARTICLE 1.3.033
“Items of clothing may not modify the morphology of the rider, of which the purpose is not exclusively that of clothing or protection. Modifications to the surface roughness of clothing are authorised but may only be the result of threading, weaving or assembling of the fabric. Surface
roughness modifications shall be limited to a profile difference of 1mm at most.” Under this rule, some of the most aerodynamic skinsuits used for the Hour Record are now banned (as of March 2019) as the silicon structures on the surface exceed 1mm. For the same reason, aerodynamic fairings on shoes are banned and the benefits of clothing technology negated. Gloves must also be 5-fingered,
and so most now opt to ride without them.

ARTICLE 1.3.033 BIS
“Socks and overshoes used in competition may not rise above the height defined by half the distance between the middle of the lateral malleolus and the middle of the fibula head.” Finally, the ‘sock-doping’ rule. As shorts must be worn, having a longer sock is more aerodynamic, but must not exceed the halfway point between ankle and knee as this would be ‘too advantageous’. This is
perhaps the finest example of the UCI. So, with so many regulations to follow that are actively enforced before the start of all UCI events, bike engineers have a difficult task on their hands - designing a bike that is faster than the competition whilst still being restricted to the guidelines of the past. It’s like telling an architect to build a skyscraper from wattle and daub. It must be so frustrating to know how to make a bike that is faster, whether it be using a non-traditional shape or uniquely
shaped tubing or an altered position, but having those developments declared illegal. Retroactive rule changes must be even more frustrating, as a technology developed by an engineer is no longer allowed to be used for competition, although you do get the coveted ‘banned by the UCI’ tag-line. One man who knows these frustrations more than anyone is Graeme Obree, an engineer and rider labelled as a cheat for developing a far faster bike himself. In the 90s ‘transition period’ between tech and tradition, he and the UCI were constantly at war, with him describing them as ‘autocratic’. Whatever your opinions, if you want to take the Hour Record, you have to play by the rules, but where do you start?

Four: The Leading Edge
In the modern era, it’s far rarer for the sport to happen across an exceptional rider - with modern training and understanding of how the body works and how best to utilise it, the gap between rider’s skill and strength has narrowed considerably. To that effect, any other advantage has a much greater effect and that’s why the equipment used really matters, especially for something as performance-focused as the Hour Record. In a normal road race, whilst aerodynamic advantage amongst other benefits have some role, these can equally be thrown away in seconds if a group gets split, if there is a crash or dependent on the terrain. On a track, where the conditions are as predictable and controlled as possible, the Hour Record is a race for one rider against the clock, and so maximising the performance of their bike to aid them is on par with training. Jens Voigt’s Trek Speed Concept, the first bike legal under the new 2014 regulations.

4.1 The Heart of a Bicycle
Any bicycle requires one essential element - a frame. It not only holds everything together, but also provides much of the characteristics for how the bike will handle, perform, and most importantly feel. The UCI dictates that the frame must follow the traditional ‘double triangle’ shape that is instantly recognisable as a bike, but even with this considered, there is still plenty of room to innovate. The three most important aspects of an Hour Record frame are its materials, aerodynamics and its geometry.

Frame Material
Ever since Boardman, carbon fibre has been the material of choice for all professional cyclists, loved for its high strength to weight ratio, extreme stiffness and workability when it comes to complex shapes. The first carbon frames were much like the steel ones that the superceded; using carbon fibre tubes with steel lugs (connecting pieces between the frame tubes that are typically brazed to complete it), the frames still looked traditional, but utilised the lower weight that the new material allowed. However, they still had the same issues of flex that had plagued bikes since their inception. When a powerful rider transfers a good deal of power through the pedals, some of this energy goes into deforming the frame, and with steel bikes this was an issue. Despite its relatively high tensile and compressive strength, lugged steel frames experienced flex around the joints - the weak spots of the frame, where the tubes could move and rotate a small amount around each join.

For the average cyclist, this wasn’t an issue, but with those at the top of the sport putting the power they did through the pedals, they turned to renowned frame builders to alleviate the issue. Merckx had a working relationship with the master Italian frame-builder Ernesto Colnago, who fabricated him an extremely light frame for his 1972 Record, and who would continue to experiment with finer steels and ovular tubing to increase the stiffness of his frames. Nowadays, steel is still preferred by some endurance riders, and some high-quality steels like Reynolds’ 953 stainless can cost more than £2000 a frame.

But new techniques using carbon would allow even stiffer bikes. Being supplied as a pliable cloth which is then hardened with a resin under pressure and temperature, the carbon could be moulded into any shape. Monocoque frames are made by layering sheets of carbon in a frame mould, before being set in a specialist oven. These single-piece frames were far lighter and the technique is dominant in the market today. Seeing as carbon fibre is available in a number of different grades and blends, and that its lateral strength is highly directional, the properties of the composite can be exploited for a number of benefits.

In areas where a bike should be as stiff as possible to make pedalling efficient (like the bottom bracket), the lay-up of the carbon fibre sheets can be altered by placing them in alternate directions, giving increased stiffness in all directions and a rigid pedalling platform. The remainder of the bike can be completed as usual, but with greater strength fibres in areas of high stress, like the headtube and joining pieces. On the other hand, areas like the chainstays can be made extremely stiff horizontally to ensure a steady and planted rear wheel, but then made to be more flexible vertically (sometimes called ‘compliance’) which gives a more comfortable ride in rougher terrain. When it comes to the Hour Record, weight
isn’t as much of a concern as it only really affects the brief acceleration period and has a
small frictional penalty, but the frames are built to be as stiff as possible to maximise the
efficiency of pedalling on the track.
Carbon fibre technology is constantly being improved, largely thanks to the large budgets of
the aerospace and automotive sectors which trickle down to the bike industry. And so stiffer
and lighter varieties of carbon are being developed that will further increase the efficiency of
a frame, even if they are already very efficient at this moment in time.
24 The Hour Record: An Engineer’s View - Matt Bryan
Frame Aerodynamics
Although the rider typically counts for a large percentage of the frontal area and therefore
the drag experienced, the frame still has an effect, and this can be lessened with careful
design. The UCI does make things difficult, considering the restrictions on the shape of the
frame and its minimum measurements. In an ideal world, the main tubes of the frame itself
would be aerofoils, rounded at the front (the leading edge into the wind) before gently
sloping back to a point. But a full aerofoil would firstly breach the ‘3 to 1’ rule on
aerodynamic fairings, but also be detrimental in other conditions.
When turning into a corner, even one as shallow as the velodrome, the shape designed for
maximum forward efficiency can increase drag at different degrees of yaw. A long tail
greatly increases the surface area of the frame, and so when not directly in the wind, the
drag force can increase. Designing the ideal tube shape for the Hour Record is difficult as it
must balance the straight line efficiency, paired with the minute difference in angle that each
of the corners on the track brings. An asymmetric design might help, but would require
extreme rider precision to fully utilise. Currently, the frames are constructed to be as
aerodynamic as allowed, with specific focus on the seat tube, forks and down tube which
have the biggest effect on the drag of the frame itself.
Working around the ‘3 to 1’ rule led engineers at Trek to develop an optimised tube shape
called the ‘Kammtail Virtual Foil’, a tradeoff between a typical round tube cross section and a
full blown aerofoil, which gives a high aerodynamic advantage whilst keeping UCI legal.
The truncated tail ensures a low surface area
and reduces weight whilst also retaining
most of the aero advantage of the full shape.
The model for the airflow around each shape
is remarkably similar, and a good example of
pushing design to the limits of what is
allowed.
Recently companies have started to experiment with aerodynamic paints for their frames,
coatings that reduce drag as opposed to a raw carbon fibre finish. Whilst the benefits are
marginal at the moment, surface designs that disrupt airflow or simply those that reduce the
energy of each collision could really help in transforming already fast frames into bikes that
seems to repel the air they travel through.
Frame Geometry
A bike’s ‘geometry’ refers to its frame measurements, of which there are many of importance
when it comes to dictating the characteristics of a bike. Typically, the length of the individual
frame ‘tubes’ is what is changed by a scalar factor when a bike is tailored to different rider
sizes - ie. a taller rider might have his seat tube increased by 30mm and his top tube
lengthened by 40mm to suit his larger profile. But there are other key measurements that are
important when it comes to making a fast Hour Record bike.
25 The Hour Record: An Engineer’s View - Matt Bryan
The most crucial of these is the ‘stack height’ of a frame, which refers to the absolute
vertical distance between the horizontal plane of the bottom bracket and the top of the
headtube, where the handlebars are mounted. A racing frame with a low stack height will
allow a rider to get as low as possible as the front end of the bike is shorter and unobtrusive
of the rider’s upper body. In times gone by, extreme frames with aggressive, downward
sloping top tubes were used, even sometimes with the handlebars mounted beneath the
headtube to get them as low as possible, (as the saddle to handlebar drop is increased) but
further research into the aerodynamics and physiology of positions has pointed to a happier
medium.
This is in turn relates to ‘BB drop’, the height of the bottom bracket in relation to both the
axles. The centre of the cranks is the defining position that the bike is built around; saddle
height is set per rider, so putting the bottom bracket as low as possible shifts the entire
position lower, thus creating a position with less surface area. A lower BB gives a lower
centre of mass too, making a bike handle more predictably and with greater stability. As long
as the pedals are not in danger of scraping the track, a BB should be placed as low as
possible. Most track riders tend to use shorter cranks, not only as these aid pedalling motion
at high cadences, but also as it allows a more aggressive position.
As handling isn’t a high priority in the Hour, most of the angles that dictate the steering of a
bike can be ignored in favour of a longer ‘reach’ - that is the horizontal distance between the
BB and headtube, or how ‘long’ the bike is. A long reach allows riders to “stretch out” and get
a lower and flatter position, ideally with the back parallel to the track. With the current UCI
position, reach is important, but Obree’s ‘Praying Mantis’ used a frame with a shorter reach
to allow him to get his arms underneath him, so it might be perhaps that the optimal position
isn’t reach dependent.
Current developments are largely concerned with increasing the aerodynamic efficiency of a
bike as the ‘perfect’ or close to best geometry sanctioned by the UCI seems to have been
found. But still, minute changes in measurements can have a huge impact on the qualities of
a frame, and perhaps in the future we will see extended wheelbases to control turbulence
between the two wheels or even fully customised frames to the micrometre measurement of
their rider so that they ‘fit like a glove’ even more so.
4.2 Position is Everything
Closely related to and hand in hand with the geometry of a bike is the riding position of its
pilot. The measurements of the frame allow a whole range of positions, and considering the
majority of drag experienced is due to the body, optimising the frontal area and shape
presented by the rider is vitally important to going fast. Contorting the body into shapes
required for the Hour Record requires a great deal of flexibility and core strength, especially
when this must be maintained for the best part of an hour. The aerodynamic advantage of a
position must be balanced with its comfort, and it is quite possible that a low position will
have an impact on the ability to pedal and put out the maximum possible power.
26 The Hour Record: An Engineer’s View - Matt Bryan
With the rules of today, the Hour Record position is universally the same as that seen in road
time trials: the rider rests their elbows on a set of pads perpendicular to the body, before
resting their forearms out front on a set of extensions. Consensus is that achieving right
angles (or close to them) is fastest, but with body shapes differing greatly from person to
person as well as their biomechanics, tweaking positions is far more of an experimental
science than a ‘de jure’ science. Innovation comes in the form of adjusting the angles of the
extensions, their height and reach until a low C drag A and stress on the body is reached, these
values measured in a wind tunnel testing session. Although counterintuitive, a higher
position sometimes yields a lower drag than one in which the rider is as low as possible, as it
isn’t just a case of lowering the frontal area, but influencing the airflow behind it to be as
smooth as possible.
Image of Wiggins mid-Record, showing his body position and angles .
But the UCI standard is far from the fastest, with a typical C d A of 0.185 - Obree’s tuck with
his arms in yielded a value of 0.172, but it’s difficult to determine why without the
intervention of computer simulation. However, all of these are made to look very
un-aerodynamic when compared to recumbent, where a rider sits far lower and more
horizontally giving a value usually five or more times lower. With UCI-illegal fairings on a
specially designed bike, the C d A can be reduced so much that the current Hour Record for
human powered vehicles stands at more than 92km, riding at a speed that is humanly
impossible on an upright bike, that would require a power of more than 2000W sustained in
ideal conditions.
So, until the UCI allows the return of the ‘super-positions’ of the 90s and encourages their
further development, it appears as if the position for riders is reaching its limit. The most
recent attempts have used custom printed handlebar extensions to mould to the shape of
the rider’s arms. Campanaerts also used base-handlebars as narrow as 330mm for his initial
acceleration, trading off initial stability for aero advantage in the longer term.
27 The Hour Record: An Engineer’s View - Matt Bryan
4.3 The Humble Wheel
The very items which facilitate the movement of a bike have gone through numerous design
iterations in their millenia lifespan. Following a brief wooden period, the standard was
quickly set as an alloy rim laced with steel spokes to a central hub with a pair of bearings.
With the lack of brakes on track bikes, the braking track could be omitted, leading to less
material being used and thus an even lighter wheel. Wheel-building was an art and creating a
strong, well-riding wheel took time and effort. The box-section wheel remained in use for the
Hour Record until the 80s, until deeper-section wheels were trialled for their aerodynamic
benefits.
‘Box-section’ refers to the cross-sectional shape of the rim, deriving from the narrow square
used at first, but developments in technology led to these being extended outwards towards
the hub, giving a ‘deep-section’ wheel. The large gap occupied by spokes in a traditional box
wheel is a minefield when it comes to airflow: molecules of air flowing in the direction of
motion interact with the spokes, which rapidly change position and impact the linear flow.
Causing even more drag is the fact that the rotating spokes also create their own areas of
turbulence from rotation, creating constantly changing areas of high and low pressure, which
contribute to a wheel that is far from aerodynamically ideal. Bladed or flat spokes alleviate
this somewhat, but do not solve the problem.
Francesco Moser introduced the disc wheel to the Hour Record scene in the early 80s.
Carbon fibre proved an ideal material to construct a spokeless wheel from, as it could be
moulded easily and retained its shape well, unlike traditional alloys under compression. With
a smooth outer surface that was identical throughout, the disc wheel was far more
aerodynamic than the spoked wheels it superseded. Despite being heavier, they were ideal
for the track as worries over crosswind performance were not an issue, as the linear airflow
in the direction of motion would flow more effectively over the flat plane.
Diagram from Zipp showing airflow over a deep-section and disc wheel.
With disc wheels now the standard, and seemingly much more effective than the
alternatives, attention can now be shifted onto the other aspects of the wheel that contribute
to its overall performance. The hub houses the bearings that are essential for a smooth
rotation, but new technology aims to make them even more efficient. Over the last few years,
28 The Hour Record: An Engineer’s View - Matt Bryan
ceramic bearings have gained popularity - the regular crystalline structure of the silicon
nitride creates spherical shapes that are much more uniform than stainless steel bearings,
which combined with a lower frictional force between the material and itself, gives a bearing
which reputably less drag than normal. For a normal rider, the three-figure cost of upgrading
for what is a small reduction in drag seems uneconomical, but for the Hour Record, every
saving counts, so ceramic bearings with specialist low-friction lubricants are employed in
their hubs.
Whilst the flat surface of a disc is far more advantageous than a box-section, research is
going into developing surface patterns that can further reduce drag, much like the dimples
on a golf ball. By influencing small pockets of airflow, beneficial turbulence can be created
that allows smoother airflow over the top of it, especially in situations where the plane meets
a junction. Wheel rims are getting wider for this very reason too - some drag is created by the
gap between the wheel and the tyre seated on it, and by making the angle between the tyre
bead and rim much shallower, the size of this gap is further reduced. The standard tubular
tyre which is glued to the rim itself is likely to be succeeded by the tubeless tyre, which hugs
the wheel tighter as the space between the tyre and rim is pressurised, rather than a
separate sealed chamber.
4.4 Fast Fashion
Not only do riders want to look fast, they want to feel fast too, and by having clothing which
provides them with a performance advantage, they will have a greater chance of breaking
the record. Despite heavy UCI regulation, like the infamous ‘sock-doping’ ruling, there is still
plenty of leeway when it comes to outfitting a rider, the most vital part being the skinsuit that
covers the majority of the body.
In days gone by, attire was a simple affair with a tight fitting woolen jersey and a pair of
shorts, with tough leather shoes strapped onto the pedals. But the era of ‘aero obsession’ led
to a complete redesign of cycling equipment and one that has continued to this day.
Although pioneered in the 50s and 60s as Spandex, elastane or more colloquially ‘Lycra’
wasn’t adopted until the 80s, but its benefits were clear. Being a synthetic fabric,
manufacturing tolerances ensure a largely identical material, which especially when woven
with a high thread count per unit area, gives a light but even sheet of material. Compared to
natural wool, with its chunkier threads, Lycra is much more conducive to aerodynamic
applications.
But perhaps more importantly, the Lycra used widely in the skinsuits of today is extremely
close fitting, hence the term ‘skinsuit’ as if a second skin. With no material acting like a sail
in the wind and increasing drag, tight-fitting clothing is faster and more comfortable - the
benefit can be felt by anyone, even at lower speeds. The one-piece skinsuit is preferred over
a two-piece jersey and shorts when legal for the event as the lack of a seam between the two
is more aerodynamic, as well as it fitting the body better, as the garment is pulled taut across
the whole body rather than in sections. Air-disrupting structures have been trialled in clothing
to great success, but have since been outlawed by the UCI due to their unfair advantage, so
at the moment, the optimal skinsuit covers as much of the body as possible and has a
29 The Hour Record: An Engineer’s View - Matt Bryan
tight-knit, low-friction elastane blend. Lycra is a great innovation from a technical
perspective, as what was a necessity ie. riding in clothes, is now faster than not doing so.
Although aero is highly important, it is also important for a rider to be comfortable, both
physically and with regard to bodily systems regulating temperature effectively. Some
polymers can restrict airflow to such an extent that the rider begins to overheat and their
power output will drop (as seen with Wiggins in 2015), but this is only really an issue in
extreme conditions. The helmet is important too, considering that the head itself represents
a large proportion of frontal area, and such protection must be worn. Development started
with ridiculously long aerofoil shapes that extended halfway down the back, but has since
settled on a shorter, more rounded shape that routes air better over the back. Time-trial
helmets tend to cover more of the face than a typical bike helmet, and include a large visor
as part of the shape to shield the rider’s eyes from the wind. The idea is to make the head as
spherical and wind deflecting as possible.
Alex Dowsett in his Hour Record attire, complete with borderline illegal socks!
Shoes are also critical as they serve as the only connection between the rider and the
drivetrain, much like the tyres of a car being the only contact with the road. Early shoes
functioned with the straps used on pedals, but were made from stiffer leather to reduce flex
and energy loss when force was applied to the pedals. ‘Clipless’ (ironic name seeing as you
‘clip’ in) pedals have their origin in the 80s, and connect the rider directly to the bike, allowing
a far more efficient power transfer by reducing the rotation of the ankle and increasing the
overall stiffness of the system. But early pedals of this sort often went wrong, leading to
Graeme Obree bolting his shoes to the pedals instead so they wouldn’t come undone.
Modern riding shoes are optimised for large area points of contact for high pedalling
efficiency and often use carbon soles to limit flex to a minimum.
Aerodynamic fairings have largely been outlawed, but clothing can still play a huge part in
the C d A value of a rider, as can shaving any skin that remains exposed to limit the turbulent
effect of hairs, especially as the area above the sock-line and the knee remains uncovered.
30 The Hour Record: An Engineer’s View - Matt Bryan
4.5 A Record-Winning Drivetrain
Gears and chains are what makes bikes bikes, but these ‘parts of the furniture’ are not
overlooked when it comes to pushing a bike faster and faster. Even with the widespread
adoption of multiple geared systems some decades ago, track racing has always stuck with
fixed-gears. In this case, the rear sprocket is ‘fixed’ to the rear wheel, screwed tight onto a
threaded hub and secured with a lock ring; this is different to the free-wheel mechanism
present in the vast majority of road going bikes, where the gearing and wheel can move
independently and allow the user to coast, or move without pedalling. But track racing hasn’t
simply stuck with fixed gears as it is ‘part of their heritage’ and as the UCI states that all
track-racers must be fixed. It has its benefits in that specific application.
On a geared bike, the chain is moved between different sized sprockets by a derailleur to
change the ratio, but having different combinations requiring different lengths of chain, the
drivetrain must have a way of making the chain tight again - this is done by a return spring in
the rear mech itself and the chain is fed through two jockey wheels. Whilst this system is
effective in taking up the chain slack and keeping the bike functioning, it introduces some
frictional resistance and additional bearings, something which an Hour Record racer could
do without. For that reason, a single-geared bike is more mechanically efficient than a
geared equivalent.
If the wheel is rotating on a fixed-gear, then the pedals must be too - they only stop when
stationary or skidding. Although often disputed, the prior momentum of the cranks due to the
current motion is said to make subsequent pedalling motion easier, and it makes sense.
Even though the energy required to accelerate the pretty lightweight cranks is miniscule,
riding with a fixed wheel takes this energy away from you when you start to apply the power.
However conversely, the momentum of the system must be conserved, so the rotational
motion of the cranks is, in a sense, fed by the rear wheel and therefore must detract from the
kinetic energy of the bike itself. Either way, from personal and consensus opinion, riding a
fixed gear in a straight line certainly feels like a more fluid motion than a geared bike.
The French have a word, ‘souplesse’, which describes the art of smooth pedalling, and it's
something you begin to notice if you have watched a lot of pros riding. To them, pedalling
seems natural, being a fluid motion with little unnecessary movement that wastes precious
power. After the initial acceleration of the record, a good rider will settle into this kind of
rhythm, typically aiming for cadences upwards of 95rpm, faster than the average rider, but
preferred as it takes stress off certain muscles and limits the fatigue felt. A rider could put
out 500W with a huge gear at 60rpm, but they would soon find their legs feeling heavy, but a
rider spinning much faster will feel more comfortable.
Gearing
The choice of gearing is really important to consider when it comes to an Hour Record
attempt. To achieve a record speed at an achievable cadence for an hour, you must first
work out what is traditionally called ‘Gear Inches’, although the metrr is much preferred.
Firstly the distance travelled in one wheel rotation is found by measuring the absolute
31 The Hour Record: An Engineer’s View - Matt Bryan
diameter of the wheel with tyre, and multiplying by pi. The universal ‘700c’ wheel is (by
ETRTO standards) 622mm across, add to that a 23mm tyre of height ~40mm, giving a
diameter of 662mm and circumference of 0.662π meters. Next, the gear ratio must be
calculated by dividing the number of teeth on the front chainring by the number on the back
chainring. Multiplying the ratio by circumference gives the distance per pedal rotation.
Finally, to calculate velocity, this distance is multiplied by the rider’s cadence. Summed up
(where theta/Θ is rpm):
v = πd • rear teeth
front teeth • θ or in kmh -1 v = πd • .06 rear teeth
front teeth • θ • 0
So, for a common large gear 53/11: v = 0.662π • 5 .06 7.117kmh 11
53 • 9 • 0 = 5
A current attempt would want to look for a gear that gave a velocity of around 55.5kmh -1 in
order to break Campanaerts’ record, accounting for initial acceleration. At 95rpm, this would
require a gear ratio of : ratio = v .6818
0.06πdθ = 55.5
0.06•π•0.662•95 = 4
But there are a large number of combinations that come close to this gear range.
42/9 4.667 51/11 4.636 56/12 4.667 66/14 4.714
47/10 4.7 52/11 4.727 61/13 4.692 108/23 4.696
It all depends on what cadence is preferred by the rider, with some preferring as high as 110
rpm. Wiggins rode on a 58/14, giving him an average cadence of 105.47 rpm (assuming his
wheel diameter etc.) However, there is another factor: efficiency. Even if a 9-tooth cog was
readily available, no discerning rider would use it - being so small in diameter, the chain must
bend more severely each time it passes around the sprocket, and the more a chain has to
bend and move, more energy is wasted. In that case, a setup with a similar ratio but with
increased sized gears both front and rear is preferred as the chain angle is reduced, leading
to a more efficient drivetrain. The difference may only be fractions of degrees, but
considering the some 6328 rotations that Wiggins chainring completed and the 26,217 times
that his rear wheel and gear rotated, the wasted energy counts.
Alongside the gears themselves, the chain is pivotal when it comes to making a fast
drivetrain, and as previously mentioned, interacts with the gear teeth hundreds of thousands
of times. But a number of ways to reduce the energy lost by the chain have been developed.
Chain lubricants have been in use as long as the bicycle, and the formulation of the oil itself
can play a huge part in the overall efficiency of the drivetrain. Chain ‘waxes’ have recently
become available to amateurs after their introduction on the pro-circuit, promising power
saving advantages. Rather than being applied in situ, the chain must be soaked in wax, and it
has been shown to have a 1-5 watt advantage. Specialist chains have been developed by
CeramicSpeed, which incorporate Teflon coatings so that the chain is ‘non-stick’ to the
chainrings, and by Muc-Off, who spent ~£6000 on formulating a new lubricant for Wiggins
(although the details are limited on exactly what was used). But every watt counts against
the clock, and for the peak of the sport, cost isn’t a factor.
32 The Hour Record: An Engineer’s View - Matt Bryan
CeramicSpeed’s DrivEn concept drivetrain in its geared form, a fixed prototype is functional.
Although the UCI states that a bike must have gears and a chain, current research is going
into drivetrain systems that are even more efficient. In the mountain biking world, sealed
gearboxes are being developed in order to limit the wear caused by dirt on a derailleur
system, although these are not in the same league of efficiency as required by the track.
CeramicSpeed recently unveiled their latest concept, DrivEn, a drivetrain system available
with one or multiple gears. Rather than a chain, the perpendicularly mounted teeth drive a
carbon fibre driveshaft running on highly efficient bearings, which in turn turns a sprocket at
the rear wheel. Claims of ‘99% efficiency’ come from the fact that the driveshaft is far stiffer
than a chain, so deforming under load is marginal, and thus more of the rider’s power makes
it to the wheels. Despite being UCI illegal presently, it shows that there is innovation to be
had, and perhaps chance in the future that a bike will be close to 100% efficient, a real
landmark in an era focused on sustainable transportation.
4.6 ‘Marginal Gains’ - advantage by any means.
A phrase now ubiquitous with Team Sky-Ineos does a very good job of summarising the
mindset of the sport over the last few years: any performance gain, however marginal,
counts, especially true when facing the clock itself. Over the years, riders and engineers alike
have done some truly ridiculous things when it comes to the pursuit of speed, and it's a trend
that is seemingly continuing into the modern era.
Leading track tyres now use compounds that incorporate graphene added in small amounts
due to its ‘superlubricity’ which can reduce the overall coefficient of friction. Existing as
hexagonal layers of carbon, and when structurally altered to give even more order to its
structure, the material can be almost frictionless, but its presence in a tyre compound has a
small effect, but a high cost - £260 for a pair of Vittoria Pista Speeds.
33 The Hour Record: An Engineer’s View - Matt Bryan
Less marginal, but still an important decision, is what altitude to attempt the record at. At a
sea level velodrome, a rider can breathe normally and as they would do throughout most of
their racing career - track or time-trial specialists rarely ever race above 500m. Or do you
choose a track high above sea level? Whilst there is an oxygen penalty, with there being a
lower air density, there are less air molecules to cause a drag force on the rider. It is all about
finding the perfect balance between reducing drag but still keeping enough oxygen for the
body to function and maximise the power output.
If the relationship between altitude and power was a simple linear one, or more likely
exponential as with the air density, a differential equation could be set up to determine this
maximum point where the oxygen density is optimal - but the thin air affects people in
different ways. In recent years, South American riders have dominated in the final few days
of the Tour and Giro, where the relentless mountain stages take their toll on European and
North American riders. Being more acclimatised to altitude, those from the high mountains
themselves have less of a power deficit when the body is starved of oxygen. Other riders
have tried to replicate this, with Merckx reportedly training in a sealed Belgian shipyard, and
riders have been on a quest to increase their blood-oxygen levels ever since.
But does it all work? Well since its construction in 1968, the Agustín Melgar Olympic
Velodrome has hosted at least 11 record breaking attempts, and a nearby velodrome in
Aguascalientes has had even more winning hours, including Campanaerts’ Hour in April
2019. But then again, many Hour Records have been set at sea-level velodromes, including
Boardman’s 56.375km in 1996, still unbroken to this day. So is all the hassle of training in the
mountains and lowering air density worth it? It’s hard to say one way or the other.
Another consideration is the weather. Atmospheric pressure changes daily, and in the case
of Wiggins, he chose a bad day for his record attempt. By manipulating the ideal gas law:
ρ = p
Rair•T
Therefore, air density is proportional to air pressure, so with Wiggins riding on a day of
heightened pressure (reportedly 103.5 KPa as opposed to average 101.325 KPa), the air
density was higher, and therefore his drag force was increased. So to compensate, his team
decided to heat up the velodrome, as density is inversely proportional to temperature,
meaning Wiggins rode at 30 o C, which cancelled out some of the effects of the high pressure.
On the other hand, Wiggins overheated and started to flag much earlier, with some
suggesting he could’ve gone as far as 55km if the conditions were right. Increasing the
temperature caused increased perspiration, but also reduced the rate of energy transfer
between the two thermodynamic systems of Wiggins and the velodrome, but the heat meant
that he was far more fatigued than he expected.
Many have argued that a true Hour Record should be held on the same track, rather than
teams manipulating the effects of weather and temperature to best eachother. But as long
as there is competition, any slight benefit can be manipulated, and will be.
34 The Hour Record: An Engineer’s View - Matt Bryan
Five: A Theoretical Model in the Real World
5.1 First Hand Testing
It’s all well and good reading figures given by manufacturers of ‘10% less drag’ or ‘54% more
lateral stiffness’ - it’s a bike industry staple that numbers seemingly plucked out of thin air
are brought up to help sell a product. The theory behind most of the advantages provided by
the developments in the Hour Record checks out, but I wanted to determine their actual
benefits in the real world. Granted, without access to specialist equipment like wind tunnels
or rolling roads, the degree of accuracy in my testing would be low at best, but with good
technique, I was hopeful that I could draw a meaningful conclusion.
One of the greatest advancements from the last few decades was the use of disc wheels, so
I would find it easiest to measure. Using a flat, straight piece of road, I would measure the
time it took to ride on a fixed gear bike with box-section wheels, also recording the average
wind speed, my average power output and the air density. With this data, a rough value for
the C d A can be achieved, even if some uncontrollable variables had an effect on it. I would
then repeat with a rear disc wheel - except that near £3000 of carbon fibre was out of reach.
CdA = ρv3
2×(0.98P −0.014715mv)
Carefully measuring up my rear wheel, I cut out two circular sections of High Impact
Polystyrene to act as wheel covers - by attaching and sealing with tape, the wheel would act
as a disc wheel analogue, and hopefully retain 90% or more of the benefits of a purpose built
wheel. Disc wheel covers are in fact used by many amateur time-trialists, and are
commercially available, although I was quite pleased with mine.
35 The Hour Record: An Engineer’s View - Matt Bryan
Outline:
Course Mostly flat section of the B2177, with a gradual bend and good tarmac.
Equipment Steel frame fixed gear with 46/18 ratio. Long drop 420mm handlebars and
130mm stem to give semi-aerodynamic position, UCI illegal brakes fitted
to make UK road legal. Slick 28mm standard compound tyres on alloy,
40mm semi-deep section wheels. Track crankset and road-style clipless
pedals.
Independent
Variable
Change from standard wheels to the addition of aerodynamic wheel covers
that act as a ‘disc wheel’
Dependent
Variable
Average speed for a constant power.
Control
Variables
Same road used, same power input from rider, same equipment other than
wheel covers, similar conditions , same rider position, similar mass.
Issues with the Experimental Technique:
● Although the power should be kept the same for each run, I had no access to a power
meter compatible with the bike, so the power output was done on ‘feel’. By riding at
my limit, I tried to ensure that any power above my average was impossible, and
therefore repeatable. I am a reasonably experienced rider, and so using the heart rate
data should assure that the average power between each run was roughly identical,
although this will contribute to the total percentage error in the conclusion.
● It wasn’t possible to complete testing on the same day, partly due to the fact that
fatigued legs would not have been able to output the same power as before. The only
issue would be change in the wind conditions, but this can be taken into account.
● The GPS measuring software I used (Strava) is only accurate to the nearest ten
metres, and thus the timings have a reasonable degree of error present in them.
Although not to the same degree of accuracy as a professional wind tunnel set up, the
testing serves as a good comparison between two types of wheel. As power was kept
roughly the same, position kept the same and mass the same (to the nearest 0.05kg with the
wheel covers), frictional forces and drag not dependent on the rear wheel should both
remain constant, and so can be ignored for comparison.
36 The Hour Record: An Engineer’s View - Matt Bryan
STANDARD WHEEL
Run AVG. Speed
(kmh -1 )
Speed Deviation
(kmh -1 )
AVG. HR
(bpm)
Wind Speed and
Direction (ms -1 )
Effective Speed
(wind adj.) (ms -1 )
N 1 32.6 ∓ 1.6 187 4.5 : 7.1 Eastward 9.05
2 31.8 ∓ 2.1 182 4.5 : 7.1 Eastward 8.83
3 32.7 ∓ 1.1 187 4.5 : 7.1 Eastward 9.08
4 31.5 ∓ 2.2 186 4.5 : 7.1 Eastward 8.75
5 32.9 ∓ 1.5 188 4.5 : 7.1 Eastward 9.14
N Total 32.3 ∓ 1.7 186 P ≈ 350W 8.97 > 9.636
S 1 37.1 ∓ 3.2 189 4.5 : 7.1 Eastward 10.3
2 36.8 ∓ 3.4 185 4.5 : 7.1 Eastward 10.2
3 37.1 ∓ 2.8 187 4.5 : 7.1 Eastward 10.3
4 37.6 ∓ 1.9 186 4.5 : 7.1 Eastward 10.4
5 36.5 ∓ 2.9 187 4.5 : 7.1 Eastward 10.1
S Total 37.0 ∓2.8 187 P ≈ 360W 10.3 > 9.1345
‘DISC’ WHEEL
Run AVG. Speed
(kmh -1 )
Speed Deviation
(kmh -1 )
AVG. HR
(bpm)
Wind Speed and
Direction (ms -1 )
Effective Speed
(wind adj.) (ms -1 )
N 1 32.9 ∓ 2.3 192 5.8 : 8.0 NEwards 9.14
2 32.4 ∓ 1.4 184 5.8 : 8.0 NEwards 9.00
3 32.8 ∓ 1.9 189 5.8 : 8.0 NEwards 9.11
4 32.4 ∓ 1.6 187 5.8 : 8.0 NEwards 9.00
5 32.3 ∓ 1.4 185 5.8 : 8.0 NEwards 8.97
N Total 32.6 ∓ 1.7 187 P ≈ 350W 9.06 > 9.30
S 1 35.0 ∓ 2.9 190 5.8 : 8.0 NEwards 9.72
2 33.9 ∓ 4.1 182 5.8 : 8.0 NEwards 9.42
3 36.5 ∓ 3.5 189 5.8 : 8.0 NEwards 10.1
4 35.7 ∓ 2.8 184 5.8 : 8.0 NEwards 9.92
5 35.9 ∓ 3.9 186 5.8 : 8.0 NEwards 9.97
S Total 35.4 ∓ 3.4 186 P ≈ 360W 9.83 > 9.41
37 The Hour Record: An Engineer’s View - Matt Bryan
Calculation
Average Speed for each attempt was taken from the Strava data file. The Speed Deviation
refers to the averaged difference between the max and min speed for each attempt from the
average in order to give an idea of how constant the effort was for each. Heart Rate was
measured with a wrist LED monitor. Wind Speed and Direction was taken from the Met
Office for that hour and direction confirmed on site.
The Effective Speed (wind adj.) is calculated in an attempt to offset the difference in
conditions between the separate tests and to offset the advantage that a certain distance
might bring. By calculating the wind velocity in the plane of motion, this can be added or
subtracted from the bike velocity to give a more comparable figure. Although this ignores
the effect of crosswinds etc. it removes most of the influence of the controlled variable.
Wind against the rider is added to the velocity as it detracts from the velocity they achieved,
whilst tailwinds are negative. The wind in that direction was calculated using trigonometry
for the average direction of the segment.
eg. Red Arrow shows the direction of motion, whilst blue
arrow shows absolute wind direction. Green arrow shows
component of wind in direction of motion. Angle is change
from horizontal so difference in bearing.
Southbound = 145 o Wind = 5.8 ms -1 at 090 o
wΔθ .8 cos (145 x = = 5 − 90) = 3.33 ms−1 (3s.f.)
This adjustment would treat the bike as if it was travelling faster than it actually was, so is a
bit heavy-handed. It would also suggest that the reference point of the bike being stationary
to be them travelling backwards at a slow speed or forwards when no power is applied.,
which in reality is not the case. The two routes have slightly different wind characteristics,
therefore adjustments must be made, which also reduces the degrees of freedom by one.
Northbound wind adjustments will be multiplied by 0.2 as a factor of correlation with the
bearing line, and Southbound will be multiplied by 0.35. These derive from the closeness of
the overall path to a straight line, and with respect to the wind direction.
Standard Northbound +0.666 ms -1 Disc Northbound +0.24 ms -1
Standard Southbound -1.1655 ms -1 Disc Southbound -0.42 ms -1
The adjustments should hopefully limit the effect of wind on the two cases, although it does
not include the factor of crosswinds which can have an effect of velocity perpendicular to
their motion. The motion of air particles is different to account for, so there is a severe
reduction in accuracy using this method.
38 The Hour Record: An Engineer’s View - Matt Bryan
Therefore, for the data collected:
Statistical Results (ms -1 ) Standard Standard adj. Disc Disc adj.
Northbound Mean μ 8.97 9.64 9.04 9.28
Northbound St.Dev σ 0.152 0.152 0.067 0.067
Southbound Mean μ 10.28 9.1145 9.83 9.41
Southbound St.Dev σ 0.102 0.102 0.247 0.247
Combined Mean μ 9.63 9.378 9.44 9.434
Combined St.Dev σ 0.668 0.291 0.434 0.192
So from the sample of ten observations, the disc wheel appears to be 0.056 ms -1 / 0.2016
kmh -1 faster than its standard counterparts. The disc wheel also has a lower standard
deviation, suggesting it is more predictable, but this holds little weight in a small sample. As
velocity is proportional to the inverse cube root of C d A, an increasing v suggests a lowered
coefficient of drag and frontal area.
v ∝ 1
√3 CdA CdA = ρv3
2×(0.98P −0.014715mv)
Standard Disc
CdA = 1.225×9.378 3
2×(0.98×355−0.014715×75×9.378) C A d = 1.225×9.434 3
2×(0.98×355−0.014715×75×9.434)
C d A ≈ 0.66819 C d A ≈ 0.65624
∴ ΔC d A = 0.01195 = 1.7884%
So it would appear that the disc wheel results in a 1.7884% reduction in the C d A of the bike
and rider. But with a change so small, it is important to check whether it is statistically
significant. Assuming that the times recorded are modelled by a normal distribution, a
hypothesis test can be carried out.
39 The Hour Record: An Engineer’s View - Matt Bryan
Hypothesis Test
H 0 : μ = 9.378 and the mean velocity is identical to that of the standard testing.
H 1 : μ > 9.378 and so the disc wheel increases the value of μ, the average velocity.
α=0.05 ⇒ Testing carried out at a significance level of 5%.
In this case, the mean for the standard wheel is taken to be the population mean, and the
mean for the disc wheel is taken to be the sample mean.
Distribution of sample means: ⊽ ~ N(μ, ) (9.378, ) n
σ2 = N 10
0.2912
⊽ = 9.434 P(⊽ ≥ 9.434) = 1 − Φ( ) 1 (0.6085) 0.291/√10
9.434−9.378 = − Φ
∴ P(⊽ ≥ 9.434) = 0.2714 > 0.05
As, the probability of the sample mean being observed is 0.2714, this is greater than the
significance level of 5%, therefore there is insufficient evidence to reject the null hypothesis.
This suggests that the disc wheel has no or very little effect on the performance of the bike.
Conclusion
Due to the low sample size dictated by the conditions of testing and down to the difficulties
in controlling the control variables, it is difficult to draw a meaningful verdict from the testing
I carried out. The C d A values I calculated from my results were good for comparison, but the
nature of the other variables meant that they were somewhat different from those calculated
in lab conditions or using a purpose built wind tunnel.
Industry figures put the C d A benefits of a disc wheel in the region of 4-5%, reasonably close
to the figure of near 2% that I came to. If professional grade equipment was available, I am
sure that I would have seen more conclusive results, but the techniques that I used were still
somewhat valid in assessing the difference that a disc wheel would make.
In addition, the figure I calculated was deemed statistically insignificant in a 5% test, but this
is again down to the sources of inaccuracy in my testing and shows that the benefits of disc
wheels are not extraordinary. Additional testing too may have shown a greater difference
and so would repeats in identical wind conditions.
So what can be drawn from my manufacturing and testing? Perhaps that there is an
aerodynamic benefit in using disc wheels, but not an enormous benefit. A powerful rider with
box-section wheels will still outride a weaker rider with a disc wheel. The benefit to drag is in
the region of 2-5%, corroborated by the numbers that I was able to calculate.
40 The Hour Record: An Engineer’s View - Matt Bryan
5.2 Merckx by Modern Standards
Now to validate the ‘estimated’ FTP of Merckx, typically given as 450W. Using the estimated
C d A of 0.2618 and his average velocity as well as his mass (74kg + ‘12lbs’ of bike = 79.4kg).
Considering his altitude was 1,887m, a lower air density would also be a factor, but affect his
power output if he was not fully adapted to the environment. 49,431 kmh -1 is equal to
13.731ms -1 . Therefore:
ρ = 1.225 • e (−1.1585×10−4×1887) .98445 kgm = 0 −3
∴ P = 56.79W 0.98
13.731(0.014715 ×79.4 + 0.5×0.2618×0.98445×13.7312)
= 3
This figure is quite far away from the 450W that many commentators suggest, but this could
be for a number of reasons:
● Merckx’s bike was not as mechanical efficient as those of the present day, so the
98% efficiency may be more like 96% due to inferior bearings, materials, frame
stiffness and down to the strap-style pedals that he used.
● Climate has slightly changed in the last five decades, with some historical
measurements suggesting an air density more like 1.02 kgm -3 , but it is all dependent
on what model is used, and no barometer reading for the day in Mexico can be found.
● Merckx’s tyres were likely not as fast rolling as today’s, so an increased μR of 0.02 is
more likely the case.
∴ P = 82.77W 0.96
13.731(0.016 ×79.4 + 0.5×0.2618×1.02×13.7312)
= 3
Even adjusting for these continuity errors struggles to reach a value as high as the 450W
suggested, but it isn’t surprising. Merckx was riding in an era where there was little in terms
of sports science and understanding of athlete’s physique. Close to 400W is still mighty
impressive, especially when his closest rivals would never be able to perform that well.
Merckx was a standout athlete and is still the idol of many, and although this modelling is by
no means definitive, it seems unlikely that his FTP was that high in comparison to his Hour
performance, but it is hard to draw much that is meaningful without any hard data, and only
from a single performance of his long and successful career.
41 The Hour Record: An Engineer’s View - Matt Bryan
Six: Rules Aside: Maximum Performance
As impressive as the feats of the UCI Hour Record are, achievements in the region of 55
kilometres seem unextraordinary when compared to records for ‘Streamlined Human
Powered Vehicles’. These types of bicycles are unequivocally illegal in the UCI’s eyes,
consisting of a recumbent position and chassis where the rider is fully reclined and then
covered entirely by an aerodynamic shell. The penalty of increased friction due to a higher
mass is more than negated by the aerodynamic advantage gained by the lower profile and
generally more aerodynamic shape.
A human on a traditional bicycle is one of the least aerodynamic shapes imaginable, typically
given a drag coefficient (C d ) of close to one - the best HPVs are closer to 0.1, with some even
less than 0.075. By reducing the drag coefficient by a factor of ten and slightly reducing
frontal area too, the impact of aerodynamic drag on these HPVs is greatly reduced. The best
contenders for the UCI Record look for a C d A in the region of 0.2, whilst the fastest HPVs
achieve a value of around 0.02. The HPV record currently stands at 92,432m, or around 68%
further than the upright record.
So what if the best riders in the world were allowed to use recumbents? Using Wiggins:
Mass ~89 kg
v =√ 3
α +√α2 + β3 +√3
α −√α2 + β3
v = √ 3
17600 + √176002 + 35.643 +√3
17600 − √176002 + 35.643
∴ v = 31.686 ms−1 = 114.07 kmh−1
C d A 0.02 m 2
Friction (μ k g) 0.014715 ms -2
Power 440W
Air Density (ρ) 1.225 kgm -3
α - alpha 17600
Wkg -1 m -1
β - beta 35.64 Nkg -1 m -1
In reality, a rider would struggle to achieve the same power numbers whilst in a completely
different position, so this estimate is likely a bit high. The increased velocity also means that
HPV records have to be attempted on larger outdoor circuits so wind must be factored in.
But without breaking the rules, is there a maximum distance for the Hour Record, a point at
which a bicycle cannot go any faster for an hour?
It’s probably best to assess the constants first; for example, the rough size of a human is
unlikely to change drastically in the next few decades, the average having fluctuated by a few
centimetres over the last millenia. Air density may change too, but keeping the current value
of sea level gives a good reference point, and it again seems unlikely that massive change in
barometric conditions will facilitate record-breaking attempts. In addition, the mass of a
42 The Hour Record: An Engineer’s View - Matt Bryan
bicycle is already relatively low, and is unlikely to be reduced by a significant amount, and the
same goes for the mass of the riders themselves. So that leaves a handful of factors that
could change and affect the performances displayed in the record.
Firstly is advancements in the aerodynamics of the bikes used. As both the rider and bike
contribute towards the C d A value, both position and components matter. Experimentation
with rider position still happens regularly, so perhaps some reduction in drag can be
achieved by further optimising the standard ‘TT’ position. The bikes used do get better and
better with each attempt, but with diminishing returns - like a graph tending to a minimum
value, it's hard to see the upright bicycle improving by a truly significant amount. With newer
technologies, estimates put the value at around 0.16 in the near future, any less than that
would be unrealistic on an upright bicycle.
Friction is another quality subject to change. In an ideal world, the power lost to friction
between the tyre and surface would be negligible, but friction is required to facilitate the
motion of the bike as per Newton’s Third Law. The coefficient between a track and good
quality tyre is already one of the lowest known values in existence, but perhaps optimising
the compound further to give close to the minimum friction required might be possible. In
that case, the value of μ k g may be more like 0.01.
Most importantly is power, and the real question is, how much further can the human body
be pushed? Ignoring the drug-riddled era of recent memory, the FTPs of pro riders have
increased gradually due to better training and understanding of biometrics, and newly
available measurably of these factors. The greatest outright FTPs are currently in the region
of 460+ watts, but it seems that even the fittest riders in the world would struggle to top this
in the near future. At this power, a rider will burn 1656kJ or 396 kcal purely through the
pedals, but taking into account the some 75% of energy lost as heat, a rider can be burning
1584 kcal an hour. Even on a high-energy diet and with the best fitness on the planet, this is
gruelling. If man could push in excess of 500 watts for an hour, it’s unlikely that his body
would be in a fit state at the end of it. To that effect, a talented rider of mass 75kg may reach
a limit of around 480W. Using these estimates to infer a maximum record distance:
Mass 81 kg
v =√ 3
α +√α2 + β3 +√3
α −√α2 + β3
v = √ 3
2400 + √24002 + 2.7553 +√3
2400 − √24002 + 2.7553
∴ v = 16.705 ms−1 = 60.139 kmh−1
C d A 0.16 m 2
Friction (μ k g) 0.01 ms -2
Power 480W
Air Density (ρ) 1.225 kgm -3
α - alpha 2400 Wkg -1 m -1
β - beta 2.755 Nkg -1 m -1
43 The Hour Record: An Engineer’s View - Matt Bryan
6.1 The Future of the Hour Record
So, with some generous estimates based on research and years of previous data, it looks
unlikely that the Hour Record will exceed the 60km mark. Continuous year on year
improvements do follow the law of diminishing returns, and this too is obvious in the margin
by which each new Hour Record holder had beaten the last by. From thousands of metres in
the early 20th Century to just ten metres in 2000, the most recent record bucked a trend with
a 563m increase. In an era of marginal gains, it seems as if the record will continue to creep
up in distance, yet no one has surpassed Chris Boardman’s record of 56,375m.
Cycling continues to be a popular spectator sport, with its followers constantly impressed by
the fortitude and unwavering devotion of its riders. In no other professional sport do athletes
give it their all for hours at a time or judge success by how much pain they endured in order
to achieve it; and the jewel in the crown of ‘the world’s toughest sport’ is the Hour Record.
Very few other events can see months of training result in a rider emptying themselves of all
energy and feeling, only to miss the distance by a few hundred metres and become
consigned to the footnotes of obscure cycling journals.
In the words of Boardman, “There is no second place. You either win or you lose”. The Hour
Record is pure in its premise, just one rider and their bike against the clock, but it is evil in its
execution. And yet, month after month, the best riders in the world attempt to better each
other in any way possible, yet only a handful will ever hold the record itself. So what does the
future hold? Ever better technology that will infiltrate every aspect of the sport - perhaps.
Greater understanding of how the human body copes in an hour of full-out effort - maybe.
There is only one certain in the Hour Record; an endless stream of hopefuls waiting to join
the ranks of Coppi, Merckx, Wiggins et al. But without intelligent engineering, these feats of
human endurance would never materialise. It takes the effort of a rider and a team of
designers, mathematicians and directeur sportifs to orchestrate a new record.
To sum up the Hour Record in one word is difficult, but I think ‘effort’ is apt. A phrase popular
on the British Hill Climb circuit does an even better job.
“If you don’t throw up at the top, then how do you know that you’ve given it your all?”
44 The Hour Record: An Engineer’s View - Matt Bryan
Sources:
Chapter Sources (accessed between 30/7/19 and 22/9/19)
1 https://www.ridley-bikes.com/the-flying-moustache/
https://commons.wikimedia.org/wiki/File:Henri_Desgrange_en_1893.jpg Le Miroir des
sports, 8 juillet 1920, p.2
https://cyclehistory.wordpress.com/2015/03/05/a-history-of-cycling-in-n1-objects-no-
3-merckxs-hour-record-bike-1972/
https://twitter.com/colnagoworld/status/854610672856027138
Power Statistics
https://forum.trainerroad.com/t/the-bell-curve-of-cylists-how-fast-are-the-average-tr-us
ers/5840/5
Historical Data
https://en.wikipedia.org/wiki/Hour_record ,
https://www.cyclingweekly.com/news/latest-news/hour-record-the-tangled-history-ofan-
iconic-feat-166791
2 SufferFest - 4D analysis
https://thesufferfest.com/blogs/training-resources/learn-more-about-rider-profiles ,
https://www.youtube.com/watch?v=YvemLgLpO3c&t=1029s ,
Pro Cycling Power Stats
https://cyclingtips.com/2017/06/just-how-good-are-male-pro-road-cyclists/ ,
http://www.srm.de/news/road-cycling/usa-pro-challenge-stage-6-7/
https://www.reddit.com/r/peloton/comments/2zlcw0/if_eddy_merckx_suddenly_appe
ared_at_the_starting/
Pretoria Paper:
COMPARISON OF TYRE ROLLING RESISTANCE FOR DIFFERENT
MOUNTAIN BIKE TYRE DIAMETERS AND SURFACE CONDITIONS
Wynand J.vdM. STEYN & Janike WARNICH
Department of Civil Engineering, University of Pretoria, Pretoria, Republic of South Africa
https://www.researchgate.net/publication/279323381_Comparison_of_tyre_rolling_re
sistance_for_different_mountain_bike_tyre_diameters_and_surface_conditions
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Exp
eriment%2005web.htm
Aerodynamics:
https://www.youtube.com/watch?v=oJ9H0INZ2_s&list=LLGM-yAkNAeYveTUrcxC3Mu
g&index=4&t=0s
https://stories.endurasport.com/graeme-obree-1
45 The Hour Record: An Engineer’s View - Matt Bryan
https://www.cyclingpowerlab.com/CyclingAerodynamics.aspx
https://www.bikeradar.com/advice/fitness-and-training/how-aero-is-aero/
https://www.physiology.org/doi/full/10.1152/jappl.2000.89.4.1522
https://www.grc.nasa.gov/www/k-12/airplane/shaped.html
http://www.bikeaerodata.com/how-much-does-it-cost-1
Modelling:
https://www.shopforwatts.co.uk/blogs/news/dowsett-hour-record-take-2
https://youtu.be/Wo00qo0oV88
https://www.researchgate.net/publication/51660070_Aerodynamic_drag_in_cycling_
Methods_of_assessment
https://math.vanderbilt.edu/schectex/courses/cubic/
https://www.cyclingpowerlab.com/DrivetrainEfficiency.aspx
3 UCI Document:
https://www.uci.org/docs/default-source/equipment/clarificationguideoftheucitechnic
alregulation-2018-05-02-eng_english.pdf?sfvrsn=fd56e265_70
4 https://commons.wikimedia.org/wiki/File:Jens_Voigt_-_Hour_Record_-_bike.jpg
https://www.trekbikes.com/international/en_IN_TL/inside_trek/kammtail_virtual_foil/
https://www.youtube.com/watch?v=nhv0jrsAW5w (Motherboard video on recumbent
hour)
https://road.cc/content/feature/175644-ceramic-bearings-pros-and-cons
https://www.cyclingweekly.com/fitness/power-vs-aerodynamics-get-balance-right-324
633 Wiggins (credit: Watson)
https://www.zipp.com/wheels/super-9-carbon-clincher-disc/ Zipp Testing
https://www.cyclist.co.uk/in-depth/1932/ride-like-alex-dowsett Dowsett
https://cyclingtips.com/2018/03/fast-chain-lube-that-saves-you-money/
https://cyclingtips.com/2018/07/ceramicspeed-driven-drivetrain/
https://en.wikipedia.org/wiki/Agust%C3%ADn_Melgar_Olympic_Velodrome
http://blog.enduranalytics.com/post/Air-pressure-is-everything
https://thijsvandenbrande.be/2015/06/wiggins-myhour/
5 http://bikeretrogrouch.blogspot.com/2014/05/the-hour-record.html
6 http://www.recumbents.com/wisil/simul/HPV_Simul.asp
https://en.wikipedia.org/wiki/Hour_record_(recumbents)
https://trainright.com/adjusting-cycling-power-ranges-temperature/
https://www.cyclist.co.uk/news/691/chris-froome-s-numbers-what-do-they-really-mean
https://www.pinterest.co.uk/pin/467811480015861032/
http://www.ox.ac.uk/news/2017-04-18-highs-and-lows-englishman%E2%80%99s-average-heig
ht-over-2000-years-0
46 The Hour Record: An Engineer’s View - Matt Bryan