An Engineer on a Bike - Aerodynamics


Armed with my Aero-Mechanical Engineering degree this series of blog posts takes a deep dive into some engineering aspects of road cycling. Given that ten years have passed since graduating I had to dust off the old textbooks and refresh my memory on some of these topics but I hope that they are educational, entertaining and ultimately helpful when you are out on the road.

I cried at the birth of my sons. I cried watching The Green Mile. I cried once cycling home into a block headwind. Every cyclist out there will have a similar experience of helplessly watching the average speed tumble as you struggle through a wind that you swear is treacle and not just air. These moments provide an abject lesson in aerodynamics or the lack thereof.

Up until a few years ago, road bikes were solely judging on their weight thanks to the holy grail of the ideal power-to-weight ratio when tackling climbs. Recently, there has been a huge shift towards aero road bikes that are also lightweight. The fact is that once you go above a modest speed on the bike, aerodynamics is hugely influential.

Professional cycling teams devote huge resources to studying and conquering something known as drag. When a body is immersed in a fluid (air is a fluid in fluid mechanics) and it is in relative motion with respect to the fluid then the drag is defined as the component of the resultant force acting on the body which is in the direction of the relative motion. Put simply, drag is what slows you down.

In terms of cycling, the total drag (also known as the Profile Drag) is made up of two components; the Pressure Drag and the Skin Friction Drag. Let’s look at these two in more detail.

Pressure Drag (Form Drag)

As the fluid flows over a body due to the relative motion there comes a point where, due to the adverse pressure gradient and viscous forces on the surface of the body, we get flow reversal and the fluid flow detaches itself from the surface of the body. This flow reversal produces a vortex which is highly turbulent and consists of large-scale eddies. A high rate of dissipation takes place within this flow regime and as such we have a reduction in the pressure. Because of all of this we have a situation where the pressure acting on the front of the body, say a cyclist, is greater than the pressure acting on the rear of the body and this creates resultant force acting on the body in the direction of the relative fluid motion.

To overcome this pressure drag and to increase the pressure recovery (i.e. to have the same pressure and the front and rear of the body as you would in an ideal flow with no viscous effects) the wake at the rear of the body has to be minimised as far as possible. This is done by streamlining the body so at separation of the flow is eliminated.

Because of this separation in the flow regimes, cyclists can be thought of as bluff bodies (aerodynamically) despite the impressive lengths they go to become more streamlined.

Skin Friction Drag

When a body is moving in a fluid, at the surface of the body there is a shear force at the surface of the body that opposes the fluid movement such that the fluid close to the surface is decelerated.

We could get into topics around the laminar and turbulent boundary layer and the relation of this stress force to the Reynold’s Number but ultimately because cyclists can be considered bluff bodies (as opposed to streamlined bodies) the largest contributor to the overall drag in a fluid is the aforementioned pressure drag.

We could theoretically calculate the contributions to the total drag from the pressure drag and the skin friction drag but to do that you would need to have information on the pressure profile around the cyclist as well as the shear stress distribution on the surface of the cyclist. This would be incredibly onerous therefore the profile drag is typically measured experimentally as a force component in a wind tunnel.

We can then relate the measured drag to the projected area of the cyclist, the fluid density (air in this case) and the free stream velocity as shown in the equation blow:

The linear relationship between profile drag and the air density is why cyclists attempting the hour record do so at high altitude in Mexico where the air in thinner (less dense).

The equation also shows the drag force increases with the square of the velocity and highlights that aerodynamics are dominant at high speeds. The power that a cyclist must output to overcome the aerodynamic forces increases with the cube of the velocity.

So the cyclist has two options; increase their power or decrease their air resistance.

Studies have shown that on a flat road the aerodynamic resistance accounts for over 90% of the resistance a cyclist encounters (other resistive forces include the rolling resistance, the wheel bearing friction losses, potential energy relating to changes in the gradient and the kinetic energy). This figure shows why professional cycling teams devote so much time in the wind tunnel.

Sometimes you might catch yourself in the reflection of a building and think that you look sleek and aero on the bike. The truth is you have a drag coefficient (Cd) greater than a lorry. The figure below shows a comparison of drag coefficients and it makes for depressing reading as a cyclist.

Improving Aerodynamics

Body Position

Before you are tempted to spend a lot of money on a new aero frame, it has to be said that the rider accounts for approximately 80% of the total aerodynamic resistance. Optimising your aerodynamics will offer cheap and immediate benefits.

Looking back at the equation for the aerodynamic drag force, an obvious way to reduce the aerodynamic drag is to reduce your frontal area. Getting down on the drops can offer a 15% to 20% reduction in the drag compared to an upright position. Getting into a time trial position can reduce this by 30% to 35%. Obviously not pedalling is not really option if you are interested in getting places but pedalling does increase the aerodynamic drag by around 6% compared to a static crank.

Keeping the arms bent at the elbow as opposed to straight also lead to aerodynamic efficiencies by reducing the frontal area.

Helmets

Unless decapitated, the head of the cyclist represents a significant effect on the drag force due to its relative size and position on the flow stream. For this reason there is a lot of focus on helmet aerodynamics especially when it comes to time-trialling. Some studies have shown that the effect of a good aerodynamic helmet compared to a standard helmet is greater than the difference between fast and slow wheels.

It is common to see long-tailed, tear drop style helmets during time trials since studies have shown that they offer a 10% reduction in aerodynamic drag compared to poorly performing helmets.

Whilst this is all well and good on a mannequin in a wind tunnel, in real life with real cyclists such helmets rarely achieve these results because the cyclists move their heads to relieve the discomfort in a time trial position. That is why some cyclists now opt for a less extreme aero helmet that offers compromise between aerodynamics in more head positions and comfort.

Wheels

Studies have shown that the disc wheels favoured in time trials reduce the aerodynamic drag by up to 70% compared to conventional, spoked wheels. In a controlled lab environment this seems impressive but on the road and in a crosswind then these deep section wheels act as a sail top propel you into the ditch.

Skin Suits

The skin suits that cyclists wear during time trials (and even sometimes in standard road stages in the pursuit of marginal gains) are not just tight to make the cyclist more streamlined. In fact there is a lot more going on below the surface or should that be on the surface.

The skin suits are textured to delay the separation point of the air flow towards the back of the body. Thinking back to the discussion on pressure drag, by reducing the size of the wake we can increase the wake pressure and therefore reduce the resultant pressure drag. Modern textured skin suits even incorporate different textures and patterns on different parts of the body depending on the predominant flow regimes.

To understand textured skin suits one has to know about the Reynolds Number which essentially governs whether a flow around a body is laminar or turbulent i.e. is the flow smooth or does it consist of lots of random eddies. Fundamentally, a turbulent boundary layer is less susceptible to flow separation around a curved body. The small pimples that team Sky incorporated into their recent time trial skin suits are for this very reason.

Nothing illustrates this point perhaps better than a golf ball. If you took a golf ball out of your bag and polished it so that it was completely smooth and then placed it on the tee you would only have to walk half as far along the fairway to play your next shot. Those dimples on the golf ball create a thin turbulent boundary layer that helps the air cling to the ball as it flies towards the green. It clings further to the back of the ball, reducing the size of the wake and allowing the ball to travel further.

Waking up to Drag

The last section has shown the lengths that cyclist can and do go to in order to reduce the aerodynamic drag and common to all these methods is attempting to reduce the influence of the wake pressure. By preventing a pressure drop at the rear of the cyclist and therefore reducing the difference in pressure between the front and rear then significant aerodynamic gains can be achieved.

This pressure difference is everything. We can also think about the problem from another perspective and decrease the pressure in front of the cyclist. By doing this the pressure difference between the front and rear is reduced which as we now know is fundamental to decreasing the aerodynamic pressure drag.

This is why we have a peloton of riders, all conserving energy until the real action at the end of the stage.

Let’s start by looking at just two riders.

If you manage to get within touching distance of the rider in front of you the drag reduction is typically in the range of 15 to 50%. At a bike lengths distance the reduction in drag is typically 10 to30%. In general the relationship between linear distance and an increase in the drag coefficient of the trailing rider is linear.

From the studies, another interesting finding was that during an overtaking manoeuvre, both riders suffer an increase in aerodynamic drag of approximately 6%.

A recent controversy during individual time trials has been the theory that a close moto behind the rider can in fact decrease the riders overall aerodynamic drag and thus gain a competitive advantage in a discipline where the winning margins are small.

We have to think about pressure regions for this to make sense. In front of the trailing moto has a high pressure region at the front that essentially increases the pressure in the wake of the cyclist in front. The moto has therefore reduced the differential pressure between the front and back of the cyclist and thus reduced the pressure drag.

At minimal separation this effect can account for between 1 and 3% drag reduction for the cyclist so it is obvious why it is a hot topic particularly regarding consistency. Replace the moto with a car and the reduction in the lead cyclists drag is greater than 10% at 2m distance. Even as the distance increases to 10m there is still a measurable reduction in drag, enough certainly to qualify as a marginal gain.

Think Like a Fish to Survive

A study of fish in a school showed that those swimming at the rear of the formation beat their tails with a frequency of around 10% less than the fish at the front of the school suggesting that they are using less energy.

Think of the peloton as a school of fish.

Riders in the centre of the peloton can have a drag as low as 5% of an isolated rider meaning that half of the peloton travels through the stage with a very low energy expenditure.

I remember one wet morning cycling to work when I found myself behind a lorry coming off a junction and I was able to accelerate with it up to a speed of around 37mph on the flat with little effort. In fact I ran out of gears and my legs were spinning out of control. This showed the awesome power of aerodynamics on cycling and the constant battle that we are fighting.

#cycling #aerodynamics #drag #drafting #peloton

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