Race Your Track: Professional Bike Simulation and Analysis

Cycling physics: why some watts translate into more speed than others

Whether you ride road, gravel, time trial, or commute: three forces largely determine how much power you need to hold a given speed. If you understand when aerodynamics dominates, when tires matter most, and why gradients get expensive fast, you can make smarter choices about equipment and pacing.

The total resisting force is the sum of:

$$ F_{\text{tot}} = F_{\text{aero}} + F_{\text{roll}} + F_{\text{grav}} $$

Required power (ignoring drivetrain losses) is force times speed:

$$ P = F_{\text{tot}} \cdot v $$

In reality, a small part is lost in drivetrain/mechanics. You can model that with an efficiency factor $\eta$ (typically about 0.96–0.99):

$$ P_{\text{rider}} \approx \frac{P}{\eta} $$

Aerodynamic drag

Aerodynamic drag dominates at higher speeds. The force grows with the square of speed:

$$ F_{\text{aero}} = \frac{1}{2} \, \rho \, C_dA \, v^2 $$

Here, $\rho$ is air density and $C_dA$ is the key aero parameter (body position, clothing, helmet, cockpit, bags). From force we get aero power:

$$ P_{\text{aero}} = F_{\text{aero}} \cdot v = \frac{1}{2} \, \rho \, C_dA \, v^3 $$

That $v^3$ relationship is why small improvements to position or setup can save a lot of time at high speeds on flat terrain (and especially into a headwind).

Gravity (gradient)

On climbs you work against gravity. For a road gradient $g$ (e.g., 5% $\Rightarrow g=0.05$), the resisting component can be approximated as:

$$ F_{\text{grav}} = m \cdot g_0 \cdot g $$

where $m$ is total system mass (rider + bike + gear) and $g_0 \approx 9.81\,\text{m/s}^2$ is gravitational acceleration. The corresponding power is:

$$ P_{\text{grav}} = F_{\text{grav}} \cdot v = m \cdot g_0 \cdot g \cdot v $$

This term scales linearly with $v$. That’s why mass, gradient, and pacing are tightly linked on climbs.

Rolling resistance

Rolling resistance comes from tire deformation and surface losses. It’s commonly modeled as:

$$ F_{\text{roll}} = C_{rr} \cdot m \cdot g_0 $$

$C_{rr}$ is the rolling resistance coefficient (tire model, width, pressure, casing, asphalt vs. gravel). Rolling power becomes:

$$ P_{\text{roll}} = F_{\text{roll}} \cdot v = C_{rr} \cdot m \cdot g_0 \cdot v $$

This part is also linear in $v$. That’s why good tires and sensible pressure can buy speed very efficiently.

A compact power model: where your watts actually go

Putting the three contributions together gives a useful approximation for power at a given speed (and vice versa):

$$ P \approx \frac{1}{2} \, \rho \, C_dA \, v^3 + C_{rr} \cdot m \cdot g_0 \cdot v + m \cdot g_0 \cdot g \cdot v $$

This explains most real-world questions: aerodynamics reduces the $v^3$ term (big at high speed), tires reduce a linear loss (relevant almost everywhere), and mass/gradient mainly affects the climbing term (dominant uphill).

FAQ: practical consequences for setup & pacing

How should I prioritize upgrades on flat, fast routes?
At higher speeds, aerodynamics usually dominates because $P_{\text{aero}} \propto v^3$. A better position, smoother clothing, and a cleaner cockpit reduce $C_dA$ and save the most time there.

What’s the biggest aero lever without expensive parts?
Your position. Lower $C_dA$ directly reduces drag. The key is a position you can hold comfortably for a long time.

Do better tires really make a measurable difference?
Yes. Via $C_{rr}$, rolling resistance is a steady linear loss ($P_{\text{roll}} \propto v$). Better tires and appropriate setups can save watts at almost any speed.

Should I just run maximum tire pressure?
Not necessarily. On rough surfaces, too much pressure can be slower because more energy is lost to vibration. Aim for pressure that matches tire width, system weight, and surface.

Why does a small increase in gradient feel so brutal?
Because $P_{\text{grav}} = m \cdot g_0 \cdot g \cdot v$ scales directly with gradient $g$. Small changes in slope quickly increase the power required.

How should I pace climbs?
More steady, less spiky. On climbs, extra watts are especially “expensive”, and surges fatigue you quickly. A controlled, constant effort is usually more efficient. If you want to optimize course-dependently (more power where an extra watt saves disproportionate time, less where it barely helps), see: TrackIQ – Optimizing your pacing strategy.

Is weight reduction always the best lever?
It pays off most on routes with lots of climbing because it directly reduces the gravity term. On flatter routes, aero ($C_dA$) and rolling resistance ($C_{rr}$) are often the bigger levers.

How does wind change the equation?
For drag, what matters is speed relative to the air. A headwind increases the effective speed in the aero term and makes aerodynamics even more important; a tailwind reduces it.