The Simple Formula For Speed
Over the coming weeks we are going to dive deep into topics related to performance along with exploring factors impacting its ultimate measure: speed. Before we breakaway and more fully discuss elements such as cycling power, aerodynamics, and weight in forthcoming articles, here’s an overview of how all these things come together. Let us introduce the simple formula for cycling speed.
We are not going to attempt writing out a precise physics equation here. Instead, we are proposing a simple conceptual model to illustrate the directional impact of different forces. The idea is not so much to predict speed given all the inputs (there are tools out there that already do a solid job at this), but to understand the primary factors that can be influenced by a rider.
While environmental factors are part of the physics equation for speed, we will focus on what is in your control as an athlete. We are hence deliberately leaving out the discussion of environmental factors such as gradient and gravitational forces, wind, air density, road surface quality, and wet road surfaces. For now, too, let’s also take out the gear discussion out of the equation, and return to disc wheels and aerodynamic helmets another day.
The focus is on things you can impact with training, to make you faster on the same course, and with the same conditions.
To move forward, the power generated by leg muscles has to overcome the aerodynamic drag (density of the air), weight (gravity), and rolling resistance (friction against the road). We illustrate this in the formula below:
In other words, there’s power, and all the forces that act in the opposite direction to power, holding us back. We can represent this relationship in a simplistic way as:
To improve the speed, one could increase the power output (e.g., through training, better employment of muscles, different position on the bike), or alternatively reduce one of the limiting factors: aerodynamic drag (e.g., improve position on the bike or invest in more aerodynamic components to reduce frontal surface), weight (e.g., improve body composition, invest in lighter bike components), or reduce rolling resistance (this is outside of the scope for training, but can be affected through quality tires at the right tire pressure).
It is important to note, that when riding at 20mph on a flat road, aerodynamic drag accounts for approximately 80% of resistive forces. However, when climbing a 6% gradient, 80% of energy will go towards fighting against the gravity. (source: CyclingTips)
Think of power as a propelling force coming from your legs. It is quantified in watts (w) — same watts that are used to describe light bulbs.
On flat terrain, and over long distance (remove impact of initial acceleration), for two riders with similar aerodynamic drag, absolute power is typically the deciding factor for determining which one of the two riders is going to be faster. That’s why you will hear cyclists often passionately discuss their watts.
On a rolling terrain, weight will play an important role. Going uphill, gravitational forces will slow down the heavier riders, while on descents, the extra weight will give them a little gravitational boost, adding to their speed.
Since most courses are not entirely flat, to account for weight differences, power is usually expressed as a ratio of power and weight (power-to-weight ratio in watts per kg).
The more power you can produce relative to your weight, the more speed you will generate. The standard metric to compare over time is your Functional Threshold Power (FTP). For now, let’s just say it is the maximum power a cyclist can maintain for 60 minutes.
Training is the first step to improving your leg power (of course). How power generated by your legs is translated into the speed at which your wheels rotate depends on mechanical efficiency of your bike. From a mechanical viewpoint, 3–5 percent of the energy delivered by the rider into the pedals is lost during transmission to the wheels (3% assuming a new, well-lubricated chain, and 5% for an old, dry chain). The use of gearing mechanisms reduces this by another 1–7 percent, assuming clean, well-lubricated derailleurs. The higher efficiencies in each range are achieved at higher power levels. This mechanical inefficiency is called drivetrain loss.
That’s why tuning up your bike to work smoothly is critical. You could be putting a lot of power in your legs, but if that power is not efficiently translated into energy propelling your bike forward, this could cost you precious time. Again, this is an important factor that contributes to speed and more importantly, it is an easy fix, so not worth neglecting.
Aerodynamic drag depends on how aerodynamic the rider and the bicycle are. Bigger frontal surfaces act like a kite in the wind. The higher the drag, the harder it is for the bicycle and the rider to slip through the air.
First, it is about the total frontal area of the rider and the bike that must cut through the air. Second, drag is also about how easily the air moves across surfaces of clothing (“sleekness”). The goal is to glide through the wind smoothly, without creating any turbulences.
Your frontal area depends on the shape of the bike, as well as your position on the bike. Your position is driven by how aggressive the bike set-up is (bike fit) as well as your ability to hold that position for an extended period of time. Being in an aerodynamic position reduces the drag, but to be able to stay in that position requires core strength and conditioning.
What’s interesting is that air drag increases with the square of speed, which means that to increase your speed by 25 percent, you need to nearly double your power (speed created results in counteracting wind that works against the rider). In economics, this concept is called marginal returns. Every bit of additional power created results in smaller speed gains.
Hence aerodynamics becomes increasingly important at high speeds, and “drafting” (riding on the wheel and slipping into the air stream of the rider ahead of you) is so critical and can save a lot of energy. Magnitude of drafting benefits depends on many factors, and in a group ride drag can be reduced by up to 25–40%, depending on the position. (source: CyclingTips)
Two opportunities for riders are to improve position on the bike to reduce the frontal surface, and to strengthen core to be able to hold this position for longer.
From sleekness perspective (often called “drag coefficient”), there are some gains from wearing shoe covers, aerodynamic helmets, and non-floppy clothing, amongst others. These are no-brainers, but again, will provide a marginal benefit compared to your position on the bike.
Weight, including rider, bicycle, components, and anything that is being carried on the bike, is subject to gravitational forces. Spare fat adds weight but doesn’t help produce power the way muscles do, so there are certainly benefits of being lean and improving body composition.
Muscle mass is trickier as the reduction in speed due to muscle loss (lower power output) could exceed the increase in speed due to weight loss. As mentioned earlier, weight really only is a factor on a hillier course, and not as much of an issue on flats. We will discuss this more fully later on in the series, but for now, the discussion is about weight in general as an enemy of speed.
It’s worth mentioning that as far as weight is concerned, you could find some minor savings in selection of components, but we are not focused on gear improvements in this article. These benefits will be marginal compared to the benefits that come from physical training.
This is not to say you should not be smart about how much water you carry between the aid stations. You’ll also need to train your body to be more efficient at absorbing energy, needing to carry less calories with you on the bike. This all adds up, but it is minor compared to the overall weight of the body.
There’s really little an athlete can do to improve rolling resistance as it mainly depends on the quality of the road and your tires. Good hygiene — invest in quality tires. Not a focus here, since we rarely have a choice of the road where we are racing.
All of these elements are interconnected. If you can improve one without impacting the other, you will get faster. It is hard to change one element without also changing other elements in some way, so the key is to weigh the pros and cons before making any changes.
WEIGHT VS. POWER: for cycling on flat course, weight reduction saves only a negligible amount of power. On a hillier course, a 10% reduction in weight could result in 10% power saving (source: Wikipedia). The power-to-weight ratio can improve with improved body composition (gain of muscles, fat loss, or both), however, this is mainly important on hillier courses.
WEIGHT VS. AERODYNAMIC DRAG: losing weight reduces the front surface that must cut through the air, and hence reduces drag. On the contrary, it is usually beneficial to add weight in the form of aerodynamic improvements, as the extra weight on a flat course costs negligible amount of power, while providing aerodynamic boost.
AERODYNAMIC DRAG VS. POWER: A more aerodynamic position can result in lower power output, however the net speed gains from reduced drag outweigh the loss of speed due to power reduction. Finding this balance is often accomplished during bike fit and wind tunnel testing.
Later on in this series, we will feature articles on more specific topics related to power, aerodynamics and weight. In the meantime, here are a few steps you can do starting today that will make you faster.
Power: Start tracking your power output and work on improving it (our following articles will explain how)
Aerodynamic Drag: Experiment to find your best body position on the bike. This is the position that lets you generate most power, while being aerodynamic and comfortable throughout the ride.
Weight: Invest in eating healthy to get rid of that extra fat that isn’t helping your power. At the same time, don’t worry about developing some extra leg muscles. You need them to get faster.
Power: Regularly maintain your bike to ensure it is mechanically efficient and you are not losing precious watts due to an old, dry chain.
Aerodynamic Drag: Even if you don’t test in the wind tunnel, make sure your bike is sleek, and your clothes fit snugly against your body.
Rolling Resistance: Invest in a good set of tires and keep them at the right pressure.
About the author
phantastic is a superhuman performance lab, on a mission to help athletes reimagine the possible and realize their potential. We are a team of athletes, coaches, and scientists. But more importantly hackers, tinkerers and experimenters, obsessed with chasing faster.
About the illustrator
Matt Chinworth is an American illustrator based in Tulsa, OK. His editorial work has been featured in The New Yorker, The New York Times, The Atlantic, The Washington Post, The Boston Globe, Harvard Business Review and many other awesome publications.
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