## The Solution

In a wind tunnel the drag measurements are taken by placing a force gauge between your bike and the floor, measuring the full drag on bike and rider. On the road you can’t isolate the point between the bike and the road because it’s a constantly changing point on your tires. So people have tried to do the next best thing and measure power going to the road, then back calculate drag. Along the way they have to make assumptions for rolling resistance, chain and other bearing friction, and rider/bike weight. Just to pick one of those, chain friction, the value can vary nearly 5% depending on which gear you’re in (or really how crossed up your chain is) and how worn your chain is. Riders going into a wind tunnel are happy to see a 5% improvement, so building a system with at least a 5% error doesn’t make much sense to us.

Is there another way? Yes! To get high accuracy it’s necessary to measure, not estimate. We looked at the problem and realized that the bike isn’t what people are going into a wind tunnel to improve. The bike, the wheels, and all the components were already designed before the athlete ever enters the wind tunnel. The only way to improve the bike is to buy a new one. Athletes go into the wind tunnel to improve the aerodynamics of their bodies. And there is a way to measure that.

It works like this; If you look at the picture on the left, this is a cyclist in a wind tunnel. His bike is fixed to the floor, an artificial wind is blown over him, and force measurements are taken at the point between bike and floor. That’s your drag force. The cyclist on the right is on the road. He creates wind by moving through the air. Unlike in the wind tunnel there’s no stationary point between the road and bike to take a measurement, but there is a stationary point between the cyclist and his bike. Drag force can be measured right there!

By measuring the force between the bike and rider it’s still possible to get all the important information you would expect from a wind tunnel. What happens when you change handlebar positions or heights? When you slide your saddle forward? Which outfit is faster? What is the most aero you can get before starting to lose power? Plus questions that a wind tunnel isn’t able to answer. Is a teardrop helmet more efficient or do you move your head too much to benefit? Do you start out the race with ideal aerodynamics but slowly get worse as you begin to fatigue? Is the optimum position for a flat race the same as the optimum position for a hilly race? What was your average drag over the course of an event?

Our technology is built around this concept and our goal is to answer these questions by bringing constant, real-time aerodynamic data to cyclists at all levels of the sport.

## The Fundamentals

In order to determine the drag force produced by a cyclist in motion we have to understand the forces and environmental conditions experienced within the specific time frame. Let’ start by considering the situation in which the cyclist finds himself on the road. He applies power to the system in order to obtain a specific velocity. But there are also resistive forces he has to overcome. This can be illustrated using this overall equation for the system in motion:

Where, P is the power input into the system, v is the relative cruising velocity and F_total is the summary of resistive forces.

The first variable we can measure is that of power. Let’s look at three most common ways in which power can be measured. The first is at the spider of the crank where strain gauges are positioned. This torque is then multiplied by the angular velocity of the crank, i.e. cadence. The second method is by measuring again the strain gauges placed at the hub of the rear wheel which in turn is multiplied by the angular velocity of the hub. The third method is by measuring the force applied to the pedals specifically which in turn is multiplied by the crank arm length and cadence. [1] The general equation to measure this is by:

Where, P is the power, T is the torque and ω is the angular velocity of the crank. By calibration in a controlled environment the measured voltage of the strain gauges can be equated to a torque.

The cruise velocity can be measured through the placement of a sensor at the front fork and a magnet on the wheel to track the revolutions which is then multiplied by the circumference which gives you distance travelled and divided by time provides the velocity. You could also measure this with GPS enabled gear. It comes down to how accurately you want the measurements to be.

Now let’s look at the summary of all resistive forces on the system (bicycle + cyclists) as described by:

C_mech is a coefficient that accounts for the mechanical efficiency of the system,

While the full calculations are complicated it is basically a correction for the losses in bearings and several factors in the drivetrain including gear selection, gear and chain alignment, chain tension and overall system wear. While this is often assumed a constant this can vary up to 5%.

The force required to overcome the slope resistance is a standard measurable method by calculating:

Where, k is the slope gradient, m is the system mass and g is the gravitational force.

The third variable is the force required to accelerate:

Where, m is the system mass and a is the acceleration.

The fourth parameter is the rolling resistance between the wheels and the surface of the road is by calculating:

Where, C_r is the coefficient of rolling resistance, m is the system mass and g is the gravitational force. Factors such as temperature, tire pressure, tire construction and tire tread affect the rolling resistance.

The last final parameter is that of the aerodynamic drag. This has been shown to be around 70% of all the forces the cyclist has to overcome at cruising speed:

Where, ρ is the local air density, C_D is the drag coefficient, A is the projected frontal area and v is the velocity which takes into account the cruising speed as well as the wind speed component relative to the direction of motion.

Until now the only method to measure drag has been in the wind tunnel. Inside the wind tunnel, sensors measure the force on the system due to the air being blown over the system and with the addition of digitising the projection of the frontal area of the system the drag coefficient can be determined.

The first assumption that creeps into the system is that the frontal area remains constant and the second error is that the coefficient of drag remains constant.

The most recent attempts have incorporated power output to determine a changing coefficient of drag. Unfortunately these systems still depend on constant drive-train friction (as mentioned previously for C_mech), constant rolling resistance and constant system mass. In reality drive-train efficiency can vary up to 5%, rolling resistance changes depending on road surface and road quality, and body mass can vary two to three kilograms within a week. Over a course of a long ride the rider can lose an additional 2 kg of weight. This produces additional errors in rolling resistance, acceleration and slope calculations. When used in the real world a system like this will never see an error lower than 10%.

In contrast by isolating the athlete, BodyRocket simply removes all errors associated with drive-train friction and rolling resistance. The system also takes real time readings of the athletes mass meaning there is no estimation in the system. A BodyRocket drag calculation is a fully calibratable and verifiable measurement of an athlete’s drag.

To conclude the choice of measuring aerodynamics has been limited to two methods and their limitations are described below:

Wind tunnels limitations:

Climatic conditions are very hard to replicate and time consuming

Availability and cost limits the access to the average cyclist

The wind tunnel measurement is a snapshot in time, in doesn’t tell you what is happening right now

Mobile estimation techniques:

Assumed Coefficient of Drag

Assumed frontal area

Neglects changes in drivetrain efficiency, rolling resistance and body mass

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