⚡ electrical engineering

Vibration-Induced Power Loss in Cycling: Experimental Quantification on a Simulated Cobblestone Surface

This study experimentally quantifies substantial vibration-induced power losses in cycling on simulated cobblestones, revealing that these losses increase quadratically with speed and tyre pressure while being mitigated by an off-the-saddle posture, thereby highlighting their critical impact on overall cycling efficiency.

Original authors: E. Vázquez Fernández, G. Dell'Orto, J. K. Moore

Published 2026-08-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: E. Vázquez Fernández, G. Dell'Orto, J. K. Moore

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are riding a bicycle down a smooth, flat road. You feel the wind pushing against you, and you feel the tires rolling against the pavement. For a long time, scientists and engineers have treated these two forces—wind resistance and tire friction—as the only things stealing your energy. It's like a video game where you only have to dodge two types of obstacles. But what if there's a third, invisible thief? What if the road itself is shaking the bike, and your body is absorbing that shaking like a sponge soaking up water? This hidden energy loss is called "vibration-induced power loss." It happens when a bumpy road sends ripples through the bike frame, into the tires, and finally into your bones and muscles. Your body, acting like a complex system of springs and dampers, has to work hard to stay stable, burning energy just to keep from bouncing around. While we know bumps are uncomfortable, we haven't really measured exactly how much of your pedal power is wasted just fighting that shaking. This is the mystery a team of researchers set out to solve: how much energy do cyclists actually lose just because the road is shaking them?

To crack this case, the researchers from Delft University of Technology and KTH Royal Institute of Technology turned a sports hall into a laboratory. They didn't use a real, chaotic cobblestone street; instead, they built a "simulated" version using five wooden planks spaced out on the floor. Think of it like a giant, rhythmic drumbeat for the bike's tires. They had a cyclist coast down this track (meaning they stopped pedaling and let the bike roll) at different speeds, ranging from 10 to 30 km/h. They tested the bike with different tire pressures (from 350 to 550 kPa) and asked the rider to change their style: sitting normally, sitting but relaxing their muscles, sitting but tensing up like a statue, and even standing up on the pedals.

The team used special sensors to measure exactly how much the bike slowed down. By subtracting the energy lost to wind and the energy lost to the tires just rolling, they could isolate the "vibration loss"—the energy that disappeared just because the bike was shaking.

Here is what they found, and it's a big deal for anyone who cares about speed or comfort:

The Speed Trap
The biggest factor was speed. The faster you go, the more energy you lose to vibration, and it doesn't just go up a little bit—it goes up like a rocket. The researchers found that vibration loss increases with the square of the speed. Imagine if walking up a hill takes 10 steps, but running up it takes 40 steps because you have to jump over every single pebble. At 30 km/h, the vibration loss was massive, reaching up to 351 Watts. To put that in perspective, a professional cyclist might only be putting out a few hundred Watts more than that to go faster; this vibration was stealing a huge chunk of their power. In fact, on these bumpy surfaces, vibration loss accounted for up to 61.38% of the total energy the bike lost. That means more than half the effort was just fighting the shaking!

The Tire Pressure Paradox
You might think that pumping your tires up makes them harder and bouncier, which would be better on bumps. But the study suggests the opposite on rough ground. As they increased the tire pressure from 350 kPa to 550 kPa, the vibration loss actually got worse, especially at high speeds. At 30 km/h, raising the pressure caused the vibration loss to jump by about 95%. It seems that while hard tires roll easier on smooth roads, on a bumpy surface, they transmit more of the shock to the rider, wasting more energy. The "soft" tires acted like better shock absorbers, soaking up the bumps rather than bouncing the rider around.

The Standing vs. Sitting Secret
One of the most surprising findings was about posture. When the rider stood up on the pedals (the "off-the-saddle" position), they lost significantly less energy to vibration than when they were sitting down. Standing up allowed the rider's legs and arms to act like extra suspension, absorbing the bumps. At 25 km/h, the standing rider lost about 140 Watts to vibration, while the sitting rider lost over 200 Watts. That's a huge difference. However, the researchers noted that standing up is hard to hold for a long race, and it changes how the rider controls the bike, so it's not a perfect magic solution for every situation.

The "Relax" Factor
The team also tested if the rider's muscle tension mattered. They asked the rider to be "relaxed," "normal," or "stiff." The results were a bit messy and didn't show a clear winner like speed or posture did. Sometimes being relaxed helped at low speeds, but at higher speeds, the difference between being stiff or relaxed wasn't consistent. It suggests that while your body's stiffness matters, it's not as simple as "just relax" to save energy.

The Bottom Line
The researchers concluded that we can't just look at wind and tire friction anymore. On rough roads, vibration is a massive energy thief that needs its own spot in the math. They created a simple formula to predict this loss, showing that it depends on how fast you go, how hard your tires are pumped, and whether you are sitting or standing. While this study was done in a controlled indoor setting with one rider and a specific bike, it proves that on bumpy surfaces, the energy you lose just from shaking is substantial—sometimes stealing more than half your power. So, the next time you hit a cobblestone street, remember: you aren't just fighting the wind; you're fighting the shake, and standing up might be your best defense.

Technical Summary: Vibration-Induced Power Loss in Cycling

Problem Statement
Cycling performance is traditionally modeled through an energy balance accounting for aerodynamic drag, gravitational forces, inertial forces, drivetrain friction, and rolling resistance. While aerodynamic drag and gravitational forces are well-understood, rolling resistance is often modeled solely as a function of tire deformation and hysteresis ( $F_r = F_N C_{rr}$ ). This conventional formulation fails to capture energy dissipated as road-induced vibrations propagate through the bicycle frame and into the rider's body. On rough surfaces, such as cobblestones, these vibrations cause significant energy loss through the deformation of body tissues and internal damping mechanisms. Despite the recognition of vibration as a source of discomfort, its specific contribution to propulsive efficiency and total power loss has not been independently quantified or separated from classical rolling resistance in controlled settings.

Methodology
To isolate and quantify vibration-induced power loss, the authors conducted controlled coast-down experiments on a simulated cobblestone surface within an indoor sports hall. The study utilized a "Bicycle Roughness Index" (BRI) to model road excitation, translating the spectral characteristics of a real cobblestone surface into an artificial profile consisting of five evenly spaced wooden planks (20 mm height, 90 mm width).

Experimental Setup: A road-racing bicycle (Giant TCR Advanced, carbon frame) equipped with 28mm tires was used. Three tri-axial IMUs were mounted on the rear wheel hub, handlebar stem, and seatpost, with a fourth on the rider's sternum to measure transmissibility.
Test Conditions: The study analyzed 334 valid trials across speeds of 10–30 km/h and tire pressures of 350–550 kPa. Two rider postures were tested (seated and off-the-saddle), and seated trials included three behavioral variations: normal, relaxed (loosened muscles), and stiff (maximal muscle contraction).
Data Processing: Total power loss ( $P_{loss}$ ) was calculated from the change in kinetic energy over the test section. To isolate vibration loss ( $P_{vl}$ ), reference coast-down trials on a smooth surface were used to estimate aerodynamic drag area ( $C_dA$ ) and the rolling resistance coefficient ( $C_{rr}$ ). Vibration loss was computed as the residual: $P_{vl} = P_{total} - P_{aero} - P_{rr}$ .
Modeling: Linear and quadratic regression models were fitted to the data to determine the relationship between vibration loss and speed/pressure. A predictive empirical model was proposed incorporating speed, tire pressure, and posture.

Key Results

Magnitude of Loss: Vibration-induced power loss was substantial, ranging from approximately 5 W to 351 W. In the most extreme conditions (30 km/h, 550 kPa, seated), vibration loss accounted for up to 61.38% of the total measured power loss.
Speed Dependence: Speed was the dominant factor. Vibration loss increased quadratically with speed. For a seated rider at 550 kPa, loss increased from 43.9 W at 10 km/h to 351.4 W at 30 km/h (a ~700% increase). Quadratic regression fits ( $R^2$ up to 0.978) consistently outperformed linear fits, suggesting vibration loss should be decoupled from the linear speed dependence of classical rolling resistance.
Tire Pressure: Higher tire pressures generally increased vibration loss, particularly at higher speeds. At 30 km/h, increasing pressure from 350 to 550 kPa resulted in a ~114% increase in vibration loss. This indicates that on rough surfaces, the reduction in classical rolling resistance ( $C_{rr}$ ) achieved by higher pressure can be offset or exceeded by increased vibration dissipation.
Rider Posture: The off-the-saddle posture consistently yielded lower vibration losses than the seated posture across all tested conditions. At 10 km/h and 350 kPa, off-the-saddle loss was ~~6 W compared to 45 W for seated (an 87% reduction). At higher speeds, the reduction remained significant (~~23% at 25 km/h).
Rider Behavior: The effect of rider behavior (relaxed vs. stiff) was less consistent. While relaxed behavior showed the lowest losses at low speeds, the pattern became unclear at higher speeds, with no monotonic trend observed across the full parameter space.

Significance and Claims
The paper claims that vibration-induced power loss is a critical, yet often overlooked, component of cycling energy expenditure on rough surfaces. The authors argue that the traditional rolling resistance model is insufficient for rough terrain because it cannot account for the quadratic speed dependence of vibrational dissipation. By separating vibration loss from classical rolling resistance, the study provides a more accurate framework for modeling cycling performance.

The proposed empirical model ( $P_{vl} = K \cdot a \cdot P \cdot v^2$ ) offers a first-order approximation for predicting these losses based on speed, tire pressure, and posture. The authors conclude that minimizing vibration loss is essential for performance optimization, particularly in races over rough terrain where margins are measured in seconds. However, they modestly note limitations, including the use of a single rider and bicycle, the simplified nature of the artificial road profile, and the passive nature of the coast-down tests (lacking active pedaling dynamics). Future work is suggested to include broader rider/bicycle configurations and physiological measurements like EMG.

Technical Summary: Vibration-Induced Power Loss in Cycling

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