# Why Does Body Weight Matter in Cycling?

And why are those Tour de France riders so damn skinny? There is a scientific explanation as to why top cyclists are so light and lean, and that’s how we’re going to break it down today.

Let’s start with a question: why can’t a cyclist just get up to speed, say 40 km/hr (25 mph) and coast their way to victory? Well, because they slow down of course, but why do they slow down? Newton’s First Law states that every object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. So, if a cyclist slows down there must be some force acting on them. This force is the force of air pushing back against the rider, air resistance.

If we hang a bike in a bike stand, spin the front wheel, and let go; it will eventually slow down. This is due to internal friction in the bearings, another force slowing riders down. When a cyclist rides over the pavement their tires deform slightly to absorb bumps and the changing force on the tires. This deforming absorbs energy and dissipates it; this is rolling resistance. And the last force slowing us down is gravity.

The most famous equation to come out of Newtonian physics describes how forces act on a body:

\sum F = m*a

The summation symbol here is essential. The SUM of the forces acting on an object equals the mass times the acceleration of the body (cyclist).

The only force pushing a cyclist forward is the force pushed into the pedals and transferred into the rear wheel. As a result, a cyclist is in a dynamic balance between the force they can push into the pedals versus air resistance, internal equipment resistance, rolling resistance and gravity. For a rider to stay at a constant speed (acceleration = 0), the following must be true for any given point in time:

\sum F = m * a\\ F_{human} – F_{air} – F_{internal} – F_{rolling} – F_{gravity} = 0\\ F_{human} = F_{air} + F_{internal} + F_{rolling} + F_{gravity}

This final equation is the plight of the cyclist. How does one get human force to go up and air resistance, internal resistance, rolling resistance, and gravity to go down. Let’s look at each of these forces and see how weight affects them.

## Force of air resistance

Air resistance is the combined force of pushing air molecules out of the cyclist’s way. The sum of these small pushes is the force of drag or force of air resistance a rider feels. Without going too deep into air resistance, the most important equation for determining the force of drag is:

F_{air} = \frac{C_d A \rho V^2}{2} \\ C_d = \text{coefficient of drag}\\ A = \text{frontal area}\\ \rho = \text{air density}\\ V = \text{velocity of the body}

The force of air resistance scales with the coefficient of drag, frontal area, air density, and velocity. Since there is an assumption of constant velocity and a rider cannot control the air density, the two factors to focus on are the coefficient of drag and frontal area.

Drag coefficient is weird and it’s normally determined experimentally. It is essentially a factor applied to an object based on its shape and how that shape moves through air. Airfoil shaped objects allow air to move around them more easily, thus their drag coefficient is significantly lower. Weight doesn’t significantly affect the coefficient of drag of a cyclist, it’s not like shedding a few extra kilos turns a rider’s arms into airfoils.

But an area that is commonly overlooked is the effects of weight loss on frontal area. Frontal area is very simply, the area of the body that is facing the wind. This can be determined by taking a photo of a cyclist from the front and measuring how much space their body and bike take up. If they change positions and another photo is taken from the same perspective, a relative change in frontal area can be determined.

Decreasing adipose tissue in the body through weight loss is an effective way to reduce frontal area. One research paper that I have lost to the search engine (sorry!) claimed a 3% improvement (decrease) in frontal area for each 3kg (6.6lbs) lost by a rider. Another paper comparing riders of differing body mass looked at the disparity in frontal area. They found a relationship between frontal area and body mass such that:

A = m^{0.762}

Using this equation, for a 70kg (154lbs) rider who loses 3kg (6.6lbs):

A_{70kg} = 70^{0.762} = 25.4\\ A_{67kg} = 67^{0.762} = 24.6\\ \text{Difference} = 1 – \frac{24.6}{25.4} = ~3.2\%

So, maybe that old paper was right! One good reason cyclists shirk the extra adipose tissue is because that mass is increasing their frontal area and real gains are possible when it’s lost. On a flat stretch of road, air resistance accounts for 90%+ of the force resisting the rider, a decrease in air resistance of 3% is directly proportional to a 3% increase in speed in those situations.

## Force of Internal Resistance

Internal resistance is resistance internal to the equipment used. There are many bearings in a bicycle; in the crankset, front wheel, rear wheel, headset, freehub body, derailleur pulley wheels and the bushings in the chain have an internal resistance as well. These internal resistances are normally determined by bearing quality and proper lubrication. Overall, internal resistance accounts for a small portion of total resistant force with mechanical efficiency values reported over 95%. That is, 95% of the force put into the pedals is delivered to propel the cyclist forward.

The one small contribution weight makes to internal resistance is the radial load placed on bearings. Bearing efficiency is related to the amount of force pushed into the center of the bearing. Front and rear wheel bearings have significant radial force from the weight of the rider, although the increases in friction are likely nominal, they are still there.

## Force of Rolling Resistance

Rolling resistance comes from the flexion of the rubber tire against the ground. In a simplified way, the force pushing down from the weight of the rider smushes the front of the tire that just touches the ground and after passing along the ground releases that energy as it continues around for another cycle. This pattern can be graphed and is referred to as the hysteresis loop. The smaller the loop, the less rolling resistance. The amount of deformation in the tire is directly proportional to the weight of the cyclist. A 3% lighter cyclist will induce 3% less deformation.

The other area of interest is bumps in the road. For a given bump, for a cyclist to travel over it, their bike must lift up to go over it. It takes energy to lift the bike over the bump directly proportional to the weight of the cyclist. Thus the energy used to overcome bumps is also smaller for a lighter cyclist.

## Force of Gravity

Our time spent riding a bike can be split into three categories: uphill, flat, or downhill. When riding uphill, the main force acting against the rider is gravity. Gravity is really quite simple: the force applies a constant acceleration on all mass. Referencing the Newtonian force equation above, the force of gravity is directly proportional to mass. Not only that, mass is the only factor in the force of gravity on earth. So if a rider wants to go uphill as easily as possible, it might be a good idea to get that mass down!

Another way to look at this is the amount of work done to go up a hill:

\text{Work} = F * d, d = distance\\ F = m * g, g = \text{acceleration due to gravity} (9.8m/s^2)\\ \text{Work to climb a hill} = mgh, h = \text{height of hill}

To go a certain distance vertically, the energy use can be calculated using the final equation above. So work to climb a high is directly proportional to weight and if a rider loses 3% of their body weight, the amount of work to climb that hill goes down by 3%. The resistive force of gravity is the biggest single reason to have a low body weight as a cyclist. Each day spent riding in the Tour de France is somewhere around 5000-6000 calories for a grand total in the range of 105,000 to 126,000 calories over 3 weeks. If these rider’s were 3% lighter their caloric demands would drop similarly to *only* 101,850 to 122,220. This may not seem consequential, but saving 4,000-5,000 calories can be the difference between winning and second place for a race decided by a few minutes at the most.

## In Summary…

Of the forces resisting a rider, three of those forces can be reduced by reducing body weight. With that being said, rolling resistance generally accounts for less than 10% of the resistance in road cycling, so the main benefits come from improvements in aerodynamics and the reduction in work from overcoming gravity. Whether you ride on flats or climb the hills, reducing weight can show improvements in speed.

A word of warning: be careful as you lose weight. Do it slowly and during non-peak training times. Remember, too much weight loss can reduce the other side of the equation. The human force production starts to go down eventually. Finding the right balance between losing weight to improve aerodynamics and climbing and not losing so much that your performance drops off is a delicate balance and task of the performance cyclist.