In-Depth Analysis of Pedal Smoothness PS: Biomechanical Evidence on Dead Spot Passage Speed, Circular Pedaling, and Climbing Muscle Fiber Recruitment Economy

1. Introduction and Cutting-Edge Research Background

The efficiency of cycling propulsion has long been simplified into two numbers: “power output” and “cadence.” However, the true determinants of long-distance riding economy (Gross Efficiency) and the timing of muscle fatigue are often hidden within the torque profile of each crank revolution. Pedal Smoothness (PS), as the core metric for quantifying pedaling quality, is defined as the percentage of Average Power ((P_{avg})) relative to the Peak Power ((P_{max})) within a single revolution: (PS = \frac{P_{avg}}{P_{max}} \times 100%). This metric was first applied in clinical rehabilitation medicine for isokinetic muscle strength assessment and was introduced into cycling sports science in the early 2000s to evaluate the uniformity of a rider’s force application throughout the crank rotation cycle.

From a historical perspective, the “Spinning” philosophy proposed by Italian cycling coaches in the 1980s advocated that riders should continuously apply positive torque throughout the full 360-degree crank rotation to eliminate the force dead zones at the 12 o’clock (Top Dead Center, TDC) and 6 o’clock (Bottom Dead Center, BDC) positions. However, a landmark study by Coyle et al. published in Medicine & Science in Sports & Exercise in 2004 revealed that trained riders at 90 rpm do not apply force uniformly; instead, they exhibit a distinct bimodal curve—with the primary force application zone concentrated between crank angles of 30° and 150° (the downstroke phase), while the 300° to 30° range (the upstroke and top transition zone) contributes almost no positive torque. This finding challenged the traditional “circular pedaling” doctrine, prompting the academic community to shift its focus toward a new question: should riders pursue an extreme PS value, or should they accept the existence of dead spots and optimize the speed at which they pass through them?

Cutting-edge research over the past five years (2020-2025) has focused on the relationship between pedaling smoothness and muscle fiber recruitment patterns. A sports science team from Ritsumeikan University in Japan used high-density surface electromyography (HD-sEMG) arrays to analyze the motor unit discharge frequencies of the Vastus Lateralis and Gluteus Maximus in riders with different PS values at a fixed power output of 300W. They found that riders with high PS values (>85%) exhibited lower motor unit discharge rates in the Vastus Lateralis but recruited a greater number of motor units. Conversely, riders with low PS values (<70%) displayed a pattern of high discharge rates and low recruitment numbers, suggesting that Mashing-style pedaling more rapidly depletes Type II fast-twitch muscle fibers. This finding provides neurophysiological evidence for “pedaling economy.”

2. Core Mechanisms of Exercise Physiology and Biomechanics

2.1 The Physical Nature of Torque Dead Spots

In the crank rotation system, the effective torque driving the rear wheel is the product of the tangential force and the crank length. When the crank is at the 12 o’clock position (defined as 0°), the pedal force is directed vertically downward, but the crank points directly upward. The force vector is parallel to the crank axis, making the tangential component zero—this is the “Top Dead Center” (TDC). Similarly, the 6 o’clock position (180°) is the “Bottom Dead Center” (BDC). In trigonometric terms, the effective torque (T_{eff}) at any crank angle θ is:

[
T_{eff}(\theta) = F_{tan}(\theta) \times L_{crank} = F_{pedal}(\theta) \times \sin(\theta + \phi) \times L_{crank}
]

where (F_{pedal}) is the total force on the pedal, (\phi) is the angle between the force direction and the pedal normal, and (L_{crank}) is the crank length. When θ approaches 0° or 180°, the (\sin) term approaches zero, meaning that even if the rider applies enormous pedal force, it cannot be effectively converted into crank rotation torque. This is the unavoidable physical limitation of dead spots.

2.2 Dynamic Model of Dead Spot Passing Velocity

Dead spots are not a static state; rather, they are low-efficiency zones that the crank system “passes through” by relying on rotational kinetic energy. Let the equivalent moment of inertia of the crank-chainring-freewheel-wheel system be (I), and the angular velocity be (\omega). The rotational kinetic energy stored in the system is:

[
E_{rot} = \frac{1}{2} I \omega^2
]

When the crank enters the dead spot zone (TDC ± 15° or BDC ± 15°), the effective external torque approaches zero, and the crank’s angular velocity decreases due to flywheel inertia and internal drivetrain friction. The Dead Spot Passing Velocity is the minimum angular velocity (\omega_{min}) of the crank within this low-efficiency zone. According to the conservation of energy:

[
\frac{1}{2} I (\omega_{entry}^2 - \omega_{min}^2) = \int_{\theta_{entry}}^{\theta_{min}} T_{resist} , d\theta
]

where (T_{resist}) is the drivetrain resistance torque. This shows that increasing (I) (e.g., using high-inertia wheels or adding flywheel mass) can slow the velocity decay in the dead spot zone. However, high rotational inertia also means sluggish acceleration response, incurring additional energy costs in climbing or sprinting scenarios. Therefore, an athlete’s “pedaling technique” is essentially about shortening the dwell time in the dead spot zone through neuromuscular control, without relying on inertia.

2.3 Muscle Fiber Recruitment Economy: Mashing vs. Spinning

High-gear Mashing (typically 50-65 rpm, PS 55-70%) requires the rider to produce extremely high peak torque during each downstroke (typically 1.6-2.0 times the average torque). According to Henneman’s Size Principle, high torque output necessarily recruits high-threshold Type IIx fast-twitch muscle fibers, whose oxygen cost per watt is far higher than that of Type I slow-twitch fibers. Their ATP hydrolysis rate is also extremely rapid, leading to rapid phosphocreatine (PCr) depletion, which in turn accelerates glycolysis and blood lactate accumulation.

Conversely, high-smoothness Spinning (typically 85-100 rpm, PS >80%) reduces the peak torque of each downstroke to 1.2-1.3 times the average torque by increasing cadence, placing the primary force production task within the endurance contraction domain of Type I slow-twitch fibers. Taking 300W output as an example, if the Mashing peak torque is 60 N·m, the Spinning peak torque only requires 39 N·m (assuming a 170mm crank length and 60 vs 95 rpm). The difference in tension demand on the quadriceps between the two approaches is as high as 35%. However, the cost of Spinning is that the nervous system must complete the switch between muscle activation and relaxation in an extremely short time (0.63 seconds per revolution vs 1.0 seconds), which places high demands on central drive and muscle relaxation rate.

3. Key Parameter Measurements and Comparative Analysis

To concretely illustrate the impact of PS values on pedaling economy, the following is a comprehensive comparison of data from academic literature over the past five years and laboratory measurements from the CTYeh sports platform. Test conditions: fixed power 250W, crank length 170mm, indoor trainer (constant resistance coefficient).

3.1 Comparison of Biomechanical Parameters Across Different Pedaling Styles

Data Interpretation: At the same average power, the Spinning style achieves a PS value 23.2 percentage points higher than Mashing, with a 31.7% reduction in peak torque and a 26.8% decrease in the integrated EMG (iEMG) of the Vastus Lateralis (the primary driver muscle), indicating a significant reduction in overall neuromuscular load. Notably, the iEMG of the Biceps Femoris (Hamstring) actually increases by 125% in Spinning, reflecting active engagement during the upstroke phase—this is the key muscle group supporting high PS values.

3.2 PS Value Variations Across Gradient Scenarios

4. Periodized Training Plans and Equipment Tuning Guide

4.1 Periodized Pedaling Technique Training Plan (8 Weeks)

Weeks 1-2: Dead Spot Awareness Phase (Building Perception)

• Training Goal: Identify individual dead spot positions and torque deficit angles.
• Workout Content: On a trainer at 90 rpm and 100-120W, perform single-leg pedaling (5 minutes per leg × 3 sets), focusing on feeling the “force break” at the 12 o’clock and 6 o’clock positions. Then proceed to “dead spot calibration”: using a power meter visualization interface, observe the crank angle range in the torque waveform where power falls below 10% of (P_{max}), and record your individual dead spot width (typically 40°-70°).

Weeks 3-4: High-Cadence Circular Adaptation Phase

• Training Goal: Improve active passing speed through the dead spot zone.
• Workout Content: At a fixed power of 150W, progressively increase cadence: 95 rpm on Monday, 100 rpm on Wednesday, 105 rpm on Friday, each session lasting 15 minutes. Supplement with “centripetal torque cues”: at the 12 o’clock position, imagine a “goose-step march” motion; at the 6 o’clock position, imagine “scraping mud off the bottom of your shoe,” strengthening the neuromuscular connection for the upstroke and backward sweep.

Weeks 5-6: Climbing Intensity Integration Phase

• Training Goal: Apply high PS values to real gradient scenarios.
• Workout Content: Choose a fixed 6-8% gradient (e.g., Yangmingshan Pingdengli), maintain 200-240W at 75-85 rpm for 5 minutes × 4 intervals, with 3 minutes of rest between intervals. Maintain a PS value above 75% throughout; if it falls below this standard, downshift to a lower gear and increase cadence.

Weeks 7-8: Pre-Race Transition and Stabilization Phase

• Training Goal: Simulate PS stability under race intensity.
• Workout Content: Perform 2 × 30-minute Wuling simulation rides (repeated 8-12% gradients), allowing power to fluctuate between 230-270W, but requiring PS to remain above 72%. After completion, conduct a “Pedaling Economy Test”: ride at a fixed 250W for 20 minutes, recording PS values and heart rate drift.

4.2 Equipment Tuning Recommendations

Crank Length Selection: Dead spot passing velocity is closely related to crank length. Shorter cranks (165mm vs 175mm) can reduce the angular displacement distance where tangential force is zero in the dead spot zone, but they also reduce the lever arm. It is recommended that riders over 175cm tall try 170mm cranks on their climbing bikes and measure PS value changes with a power meter; if the PS value improves by more than 3 percentage points without knee discomfort, they can adopt this length long-term.

Chainring and Cassette Gear Ratio Matching: The core principle for pursuing high PS values is “keeping cadence in the economical 80-95 rpm range.” Taking a 10% gradient as an example, if the bike speed is 12 km/h and the wheel circumference is 2.1m, the rear wheel speed is 95 rpm. With a 34T chainring and 28T cassette, the cadence would be approximately 34/28 × 95 ≈ 115 rpm (too high); switching to a 34T × 34T cassette yields 95 rpm (ideal). Therefore, when climbing, prioritize a 34T chainring with a 30T or larger cassette to ensure cadence does not drop below 75 rpm.

5. Race Nutrition, Environmental Adaptation, and Race-Day Strategies

5.1 Energy Supplementation Strategy for High-Intensity Pedaling

Although high-PS Spinning reduces the tension load on individual muscle fibers, the overall neuromuscular system’s energy expenditure rate is not low due to the higher cadence. Estimating for a 75 kg rider in a 4-hour Wuling challenge race, with an average power of 200W and a cadence of 90 rpm, the energy expenditure is approximately 750 kcal per hour. According to sports nutrition guidelines, carbohydrate intake should reach 60-90 grams per hour to maintain blood glucose stability and muscle glycogen synthesis efficiency. Specific strategy: for the first 2 hours, consume an energy gel containing 20g of carbohydrates every 20 minutes (approximately 200ml of a 6% carbohydrate drink); for the last 2 hours, switch to 25g of carbohydrates every 15 minutes (using a glucose-to-fructose ratio of 1:0.8 mixture to enhance intestinal absorption rate).

5.2 Environmental Temperature and Hydration Strategy

Pedal smoothness significantly decreases in high-temperature environments due to central nervous system fatigue. Research shows that when core temperature exceeds 38.5°C, motor neuron discharge frequency drops by approximately 8%, slowing dead spot passing velocity. Countermeasures: undergo 5-7 days of heat acclimatization before the race (60-90 minutes of low-intensity riding daily in environments above 30°C); during the race, supplement 150-250ml of electrolyte drink containing sodium (600-800mg/L) every 15 minutes; and use ice towels to cool the carotid artery area before climbing sections to delay the rise in core temperature.

5.3 Classic Race-Day Strategies

Westbound Wuling (55km total, 2800m elevation gain): The early section (Puli-Wushe) has a 3-5% gradient; maintain a high PS value (>80%) at 90 rpm and 220-240W to avoid prematurely depleting Type I muscle fibers. The middle section (Wushe-Kunyang) gradually increases to 8%; downshift to 80 rpm and allow PS to drop to 75%. For the final 10km (Kunyang-Wuling), where the gradient reaches 10-15%, deliberately increase cadence to above 85 rpm, using inertia to pass through dead spots and avoid falling into a low-cadence, high-torque “muscle lock-up” state.

One-Day Taipei-Kaohsiung (360km total, minimal elevation gain): Flat headwind sections are the ultimate test of PS values. With a tailwind, maintain a high cadence of 95 rpm with a PS value of 85%. In headwind sections, downshift to 85 rpm and focus on the “forefoot pressing down, heel slightly lifting” motion to ensure uninterrupted torque output at the 6 o’clock position, maintaining economical cruising at an average speed above 32 km/h.

6. Common Operational Misconceptions and Scientific Myth-Busting

6.1 Myth 1: “Circular Pedaling Means Applying Force Throughout the Full 360 Degrees”

This is the most widespread misunderstanding. As mentioned earlier, TDC and BDC are physically inevitable angles where tangential force is zero; no rider can output effective torque at dead spots. True “circular pedaling” does not mean applying force throughout the entire revolution, but rather shortening the angular range of the dead spot zone (from 60° down to 30°) and accelerating the crank through dead spots via active contraction of the upstroke muscles (iliopsoas, rectus femoris, tibialis anterior). Measured data shows that professional riders have an average dead spot width of 35°, while amateur riders have up to 60°—this is the key difference in efficiency.

6.2 Myth 2: “Higher PS Values Are Always Better”

While high PS values indicate uniform torque distribution, excessively pursuing PS values (>90%) may lead to excessively high cadence (>110 rpm), placing excessive burden on the cardiorespiratory system. Research indicates that each rider has an “optimal PS value range” (typically 75-85%), within which neuromuscular efficiency and cardiorespiratory efficiency achieve the best balance. Beyond this range, blood lactate levels actually rise due to overly frequent muscle contractions.

6.3 Myth 3: “Using Clipless Pedals and Shoes Automatically Achieves Circular Pedaling”

The clipless pedal fixation system can only provide “passive pull” during the upstroke phase. However, if the rider has not consciously trained the upstroke muscles, the upstroke phase will still exhibit negative torque (the dragging effect). Measurements show that untrained riders generate -5 to -15W of negative power during the upstroke, directly offsetting the output from the downstroke. The correct approach is to establish active muscle recruitment patterns during the upstroke through single-leg pedaling training and EMG feedback.

6.4 Myth 4: “When Climbing, Use a High Gear and Mash to Increase Traction”

On extreme climbs exceeding 12% gradient (such as the final 2km of Wuling), mashing can indeed provide higher instantaneous driving force, but the cost is an increased risk of rear wheel slip and rapid muscle fatigue. A more scientific approach is to maintain a cadence of 70-80 rpm, combined with shifting body weight forward (adjusting the saddle forward by 0.5-1cm) to increase vertical load on the rear wheel, and ensuring smooth driving force output through high PS values to avoid sudden torque changes that could cause the tire to momentarily lose traction.

7. Expert FAQ

Q1: How can I measure my Pedal Smoothness (PS) value at home using existing equipment?

If you don’t have a power meter, you can make a rough estimate using the “cadence fluctuation method”: install a cadence sensor and observe the standard deviation (CV value) of each revolution’s cadence at a fixed power output. Generally, riders with PS values >80% should have a cadence CV value below 3%; riders with PS values <65% typically have CV values exceeding 6%. For precise measurement, it is recommended to use a power meter with independent left/right power measurement (such as Garmin Rally or Assioma Duo), paired with the “Pedaling Analytics” feature in training software (such as TrainerRoad or WKO5), to obtain per-revolution torque waveform charts and PS values.

Q2: I’ve tried increasing my cadence, but my PS value has actually decreased. What should I do?

This phenomenon is usually caused by “insufficient muscle coordination.” When cadence suddenly increases, the nervous system has not yet adapted to the new timing control, causing the activation sequence of upstroke and downstroke muscles to overlap, which actually creates a braking effect in the dead spot zone. It is recommended to use “progressive cadence adaptation”: increase cadence by only 3-5 rpm per week, and after each training session, perform 5 minutes of very light resistance (below 100W) high-cadence pedaling (>100 rpm) to reinforce neuromuscular memory. Additionally, strengthen eccentric strength training for the iliopsoas and tibialis anterior (for example, deliberately controlling the upward toe hook when climbing stairs).

Q3: In the later stages of a long-distance race, my PS value drops significantly. Is this normal?

This is an extremely normal physiological phenomenon. As fatigue accumulates, central nervous system drive decreases, proprioceptive acuity diminishes, and riders unconsciously revert to the “most economical” downstroke-dominant pattern, causing the upstroke muscles to abandon active contraction. The PS value may drop from 80% to 65%. The countermeasure is to perform “pedaling technique maintenance training under fatigue”: during the final 30 minutes of a long ride, deliberately focus attention on the “upstroke” motion, using the power meter’s real-time PS display as feedback to force the PS value to remain above 70%. This training builds neural compensatory mechanisms under fatigue.

Q4: Will the high rotational inertia of carbon wheels automatically improve my PS value?

No. High-inertia wheels (such as 80mm deep-section rims) can indeed store more rotational kinetic energy, slowing the angular velocity decay in the dead spot zone, but this only “passively” smooths cadence fluctuations—it does not change the rider’s active force application pattern. If the rider’s own muscle control is poor, high-inertia wheels can actually mask pedaling deficiencies, preventing the rider from detecting dead spot issues during training. It is recommended to use low-inertia training wheels (or a fixed-gear trainer) on the trainer to amplify dead spot deficiencies and force the body to actively improve.

Q5: For triathlon run transitions, how should I adjust my pedaling strategy to preserve running performance?

In IRONMAN events, running performance after the bike leg is highly dependent on the degree of glycogen preservation in the quadriceps. It is recommended to use high-PS Spinning (>80%, 90 rpm) for the first 2/3 of the bike leg to reduce the per-stroke tension load on the quadriceps. In the final 1/3 (approximately 30km), gradually reduce cadence to 80 rpm, allowing the nervous system to gradually adapt to lower-frequency muscle activation patterns, while supplementing 60-90g/h of carbohydrates to restore quadriceps muscle glycogen. In practice, perform 3 × 1-minute high-cadence efforts at 100 rpm during the final 10km of the bike leg as a “neural activation” ritual before the run, ensuring that the legs do not feel “empty” after the transition.