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Traction

Traction, also known as tractive force, is the force used to generate motion between a body and a tangential surface through dry friction or shear.^[1] This frictional interaction enables propulsion, such as a vehicle's tires gripping the road to accelerate or a train's wheels adhering to rails.^[2] In physics and engineering, traction is fundamentally the maximum horizontal force that can be exerted before slipping occurs, calculated as the product of the normal force and the coefficient of traction (μ), where μ varies by surface conditions—for example, 0.26–0.31 on soft soil and 0.43–0.53 on firm soil.^[2] Factors influencing traction include the contact area's material properties, dynamic load distribution, slip ratio (the difference between wheel rotation and actual travel), and environmental conditions like wetness or debris, which can reduce μ significantly, as seen with rubber on wet pavement dropping to around 0.5.^[1]^[3] Net traction is further affected by motion resistance, such as rolling resistance in tires, requiring engine torque to overcome these for effective movement.^[2] Traction plays a pivotal role in various applications, from automotive design—where all-wheel drive systems enhance it for better handling—to agricultural machinery, such as tractors pulling implements on varying terrains, demanding precise matching of power (e.g., 122 kW for a 30-row planter).^[2] In rail engineering, it determines a locomotive's pulling capacity, while in broader mechanics, traction devices like tracks or chains optimize performance in low-grip scenarios.^[1] Beyond mechanics, the term traction denotes a medical procedure involving the controlled pulling of body parts using weights, pulleys, or skeletal pins to realign fractures, relieve spinal pressure, or immobilize injuries, often as a temporary measure before surgery.^[4] This orthopedic application, dating back centuries, underscores traction's versatility across scientific and clinical domains.^[5] The term "traction" is also used in other contexts, such as business and technology where it refers to gaining momentum or user adoption for products or ideas, and in sports and recreation for the grip provided by equipment or surfaces to prevent slipping.)^[6]

Physics and Mechanics

Definition and Basic Principles

Traction, in the context of physics and mechanics, is defined as the maximum frictional force that can be generated between two surfaces in contact, particularly in rolling or sliding contact, enabling the transmission of force to initiate or maintain motion without slippage.^[1] This frictional grip arises from the interaction at the contact interface and is essential for converting applied forces into directed motion.^[7] The historical development of traction concepts traces back to early studies on friction in the 15th century, with Leonardo da Vinci conducting the first systematic investigations around 1493, where he formulated basic laws of sliding friction through empirical experiments on lubricated and dry contacts.^[8] These insights were later formalized in the 17th and 18th centuries through the application of Isaac Newton's laws of motion to contact forces, treating friction as an opposing force in the second law (F = ma) that balances or limits acceleration at interfaces.^[9] By the late 18th century, Charles-Augustin de Coulomb advanced this understanding with experimental work confirming friction's proportionality to normal load, laying the groundwork for modern traction principles in 19th-century mechanics.^[10] Traction is distinguished from broader frictional phenomena by its focus on the resultant force that enables motion without relative slippage, aligning closely with static friction, which resists the onset of sliding, as opposed to dynamic (kinetic) friction, which acts during sustained sliding.^[11] In traction scenarios, such as propulsion, this static component provides the necessary grip to apply torque or force effectively while preventing slip.^[12] The foundational equation for traction force is F_t = \mu N, where F_t is the traction force, \mu is the coefficient of friction, and N is the normal force perpendicular to the contact surface.^[11] This relation derives from Coulomb's friction model, established through 18th-century experiments using inclined planes and pulley systems to measure resistance.^[10] In these tests, Coulomb observed that the maximum opposing force before sliding (static friction, F_s \leq \mu_s N) increases linearly with the compressive normal force N, but remains independent of the contact area's size, leading to the simplified linear model after normalizing by N to define \mu. For traction, F_t represents the peak value \mu_s N, beyond which dynamic friction \mu_k N (typically \mu_k < \mu_s) governs sliding.^[11] This derivation integrates with Newton's second law by incorporating friction as a limiting force in net force calculations for accelerated motion.^[9]

Traction Force and Friction

Traction force arises from the interaction between a surface and an object, such as a tire and road, and can be decomposed into longitudinal and lateral components. The longitudinal component acts parallel to the direction of travel, facilitating acceleration or braking by propelling the object forward or resisting motion backward.^[13] In contrast, the lateral component operates perpendicular to the travel direction, enabling sideways forces during maneuvers like cornering to maintain stability.^[14] When cornering, these components combine, with the total traction limited by the friction ellipse, where the vector sum of longitudinal and lateral forces cannot exceed the maximum available friction.^[15] Friction underpins traction, with static friction dominating to prevent relative motion between surfaces, providing the maximum force before slip occurs.^[12] Kinetic friction, however, acts once slip begins, typically at a lower magnitude than static friction, leading to reduced traction efficiency.^[12] Rolling resistance represents a specialized form of kinetic friction in wheeled applications, arising from deformation in the contact patch and hysteresis losses, which opposes pure rolling motion without slip.^[16] Traction force is quantified using dynamometers, which measure torque and rotational speed to derive force via strain gauges bonded to load cells that detect deformation under applied loads.^[17] Shear stress tests complement this by applying lateral forces to the contact interface and recording the resulting stress distribution, often with mobile rigs simulating real-world conditions.^[18] These techniques express traction in Newtons for absolute force or as the dimensionless coefficient \mu, where \mu = F_t / N and N is the normal force.^[19] The peak traction force is governed by the equation F_{t,\max} = \mu_s N, where \mu_s is the static friction coefficient, representing the maximum ratio of shear to normal force before slip initiates.^[20] This coefficient varies by material pairing, typically ranging from 0.5 to 1.0 for rubber on dry asphalt, and determines the threshold for optimal force transmission.^[21] The relationship between friction and slip is illustrated by the friction curve versus slip ratio, where slip ratio \sigma = (V_w - V_v)/V_v (with V_w as wheel speed and V_v as vehicle speed) starts at zero for pure rolling, rises to a peak \mu at an optimal slip ratio of 10-20% for most tires, and then declines as kinetic friction dominates, indicating the "sweet spot" for maximum traction before instability.^[13]

Factors Influencing Traction

Surface properties play a critical role in determining traction effectiveness, primarily through their influence on the friction coefficient \mu. Road surface roughness affects the real contact area between the tire and pavement; higher roughness, such as that from angular aggregates like crushed granite, increases mechanical interlocking and deformation friction, leading to higher \mu values (e.g., 0.6–0.5 on wet open-graded asphalt).^[22] In contrast, polished or smooth surfaces reduce this interlocking, lowering traction, particularly under wet conditions where water films prevent direct contact.^[23] Material composition further modulates traction; rubber on asphalt typically yields \mu \approx 0.74 dry and 0.51 wet, far superior to ice, where \mu drops to 0.1–0.2 due to minimal adhesion and lubrication by thin water films.^[22] Temperature exacerbates these effects: below freezing, rubber stiffens, reducing viscoelastic deformation and contact area, which decreases \mu on icy surfaces (e.g., low friction near 0°C, improving slightly below -5°C but remaining inadequate compared to asphalt).^[24] On dry roads, elevated temperatures soften rubber, increasing the contact area ratio and thus \mu, but excessive heat (e.g., 400–1,000°F during skids) causes melting and a sharp drop in friction.^[25]^[22] Load and pressure distribution directly impact traction by altering the normal force N and contact patch geometry. Increased normal force enhances traction proportionally via F_t = \mu N, up to a saturation point where further loading causes tire deformation without proportional contact area gains, potentially reducing efficiency.^[26] For instance, raising wheel load from 5,000 to 7,000 lb at constant 90 psi inflation expands the contact patch area from 68.2 to 88.4 in² for an 11R24.5 radial tire, distributing pressure more uniformly (e.g., peak pressures around 116 psi) and improving grip.^[26] Conversely, overinflation reduces patch area (e.g., from 68.2 in² at 90 psi to 66.0 in² at 105 psi), concentrating pressure centrally and diminishing overall traction despite higher peak pressures.^[26] Under traction, the contact area can enlarge by up to 26% (e.g., from 0.38 m² passive to 0.48 m² active), lowering mean ground pressure by 28% (65 kPa to 47 kPa) and shifting stress peaks rearward, which optimizes force transmission without increasing total load.^[27] Speed and slip ratio govern dynamic traction, with optimal performance occurring at moderate slip where static friction dominates. The slip ratio s, defined as

s = \frac{\omega r - v}{v}

where v is vehicle speed, \omega is wheel angular velocity, and r is tire radius, quantifies the relative wheel-road slip during acceleration or braking (positive for driving, negative for braking; s = 0 indicates free rolling).^[28] This ratio directly influences the traction force F_t = \mu(s) N, as \mu rises linearly with s at low values due to enhanced shear deformation in the contact patch, peaking at 10–20% slip where maximum static friction is achieved (e.g., \mu_p for ABS-equipped vehicles).^[29] Beyond this peak, excessive slip transitions to kinetic friction dominance, causing \mu to decline sharply (e.g., toward sliding \mu_s), reducing F_t and leading to wheel spin or lockup, which extends stopping distances and compromises control.^[29] At higher speeds, this drop is amplified on low-\mu surfaces, emphasizing the need for slip regulation to maintain peak traction.^[23]

Engineering Applications

Vehicle Traction Systems

Vehicle traction systems in ground vehicles are engineered to optimize the frictional interaction between tires and road surfaces, ensuring effective propulsion, braking, and cornering while maintaining stability. These systems primarily rely on tire-road contact dynamics and power delivery mechanisms to maximize grip, particularly under varying loads and environmental conditions. Key components include tire and wheel designs that enhance contact patch uniformity and drive configurations that distribute engine torque to prevent slippage, allowing vehicles to operate efficiently across diverse terrains from paved roads to off-road environments.^[30] Tire and wheel design plays a central role in traction performance, with tread patterns engineered to channel water and debris away from the contact area, thereby improving grip on wet or uneven surfaces. For instance, longitudinal grooves and sipes in tread blocks facilitate hydroplaning resistance, while blocky patterns provide lateral stability during turns. Rubber compounds incorporating silica reinforcements enhance wet traction by increasing the material's affinity for water-covered roads, reducing stopping distances compared to traditional carbon black fillers. Additionally, tire inflation pressure directly influences the contact area; lower pressures expand the footprint for better load distribution and traction on soft surfaces, though excessive underinflation can lead to uneven wear and reduced handling precision.^[31]^[30] Drive configurations further refine traction by determining how torque is allocated to the wheels. Front-wheel drive (FWD) systems direct power to the front axle, benefiting from weight transfer during acceleration for improved straight-line traction, though they may understeer in corners. Rear-wheel drive (RWD) propels the vehicle via the rear wheels, offering balanced handling and superior weight distribution for high-performance applications. All-wheel drive (AWD) systems enhance overall grip by dynamically distributing torque across all four wheels, often using viscous couplings or electronic controls to shift power to axles with superior traction, thereby minimizing wheel spin on slippery surfaces like snow or gravel.^[32] The historical evolution of vehicle traction systems traces back to the introduction of pneumatic tires in 1888 by John Boyd Dunlop, which replaced solid rubber with air-filled designs to absorb shocks and increase contact compliance, fundamentally improving ride comfort and roadholding. Subsequent advancements in the early 20th century included grooved treads for better grip and synthetic rubber in the 1930s for durability. By the mid-20th century, the integration of four-wheel drive in military and off-road vehicles, such as the Jeep in 1941, marked a shift toward all-terrain capability, evolving into modern all-terrain vehicles (ATVs) with specialized low-pressure tires and selectable drive modes for enhanced slope traversal.^[33]^[34] In off-road scenarios, traction challenges intensify on slopes due to reduced normal force on uphill wheels and potential slippage on loose substrates. Loss of traction often occurs when the incline exceeds the soil's angle of repose—the maximum stable slope angle for granular materials like sand, typically around 30–35 degrees—causing the surface to shift under the tires and halting forward progress. For example, vehicles on sandy inclines beyond this angle experience sinkage and sliding, necessitating techniques like momentum buildup or wider tire tracks to distribute weight and maintain grip. Surface types, such as loose gravel versus compacted dirt, further modulate these limits by altering frictional coefficients.^[35]

Industrial and Machinery Traction

In industrial applications, railway traction relies on the frictional interaction at the wheel-rail interface to transmit power from locomotives to the rails, enabling the movement of heavy loads. The adhesion coefficient, which quantifies this friction, typically reaches a maximum of around 0.25 under dry conditions before slipping occurs, limiting the tractive effort to prevent wheelspin during acceleration or braking. This constraint is critical in heavy freight operations, where loads can exceed thousands of tons, and engineers design systems to operate below this threshold for safety and efficiency. To enhance adhesion, especially on contaminated or wet rails where coefficients drop to 0.18–0.22, sanding systems dispense fine sand particles into the contact patch, increasing friction through abrasive roughening and form closure mechanisms.^[36] Post-sanding, adhesion can rise to 0.48–0.63 depending on sand type and conditions, though excessive use accelerates wear on wheels and rails.^[36] The electrification of railways in the 1890s marked a pivotal advancement in traction reliability, surpassing the limitations of steam locomotives that suffered from inconsistent power delivery and frequent maintenance issues. Early electric systems, such as those tested on the Baltimore and Ohio Railroad's experimental tunnel line in 1895, provided smoother acceleration and higher starting tractive effort without the thermal inefficiencies of steam boilers.^[37] By the decade's end, urban rapid-transit lines in cities like London and New York adopted overhead or third-rail electrification, enabling more precise control and reducing downtime compared to steam's variable adhesion affected by weather and fuel quality.^[37] This shift not only improved operational reliability but also allowed for denser scheduling in industrial corridors. Central to electric railway traction are specialized motors that deliver the necessary torque for heavy loads. DC series-wound traction motors, widely used in early electric locomotives, excel at startup by connecting the armature and field windings in series, producing high torque proportional to the square of the armature current when resistance is low. This configuration generates strong magnetic fields under full voltage, enabling rapid acceleration of standing trains without excessive current draw, though starting resistors are employed to limit initial surges and avoid wheel slip.^[38] As speed increases, back electromotive force reduces torque naturally, maintaining balance with train drag. In heavy machinery like construction equipment, traction is optimized through continuous tracks rather than wheels to distribute loads over a larger ground contact area, particularly on soft or uneven terrain. Caterpillar tracks, consisting of linked steel or rubber segments, reduce ground pressure to as low as 4–6 psi compared to 20–30 psi for wheeled systems, preventing sinking and enhancing tractive efficiency on cohesive soils like mud or clay.^[39] For instance, bulldozers equipped with low-ground-pressure (LGP) tracks, such as those on mid-sized earthmovers, achieve superior drawbar pull in soft soil by minimizing shear deformation and maximizing soil-track interaction, allowing effective pushing of overburden in mining or land clearing without excessive slippage.^[39] This design contrasts with wheeled loaders, which compact soil more intensely and lose traction in wet conditions, underscoring tracks' role in industrial power transmission for stability under high loads.

Traction Control Technologies

Traction control technologies refer to electronic systems that actively monitor and regulate wheel slip to optimize vehicle grip and stability during acceleration, braking, and cornering. These systems integrate sensors, actuators, and control algorithms to detect deviations from optimal traction conditions and intervene automatically, preventing skids and enhancing safety. By managing the slip ratio—the relative difference between wheel speed and vehicle speed—traction control ensures maximum friction utilization without loss of control.^[40] Anti-lock braking systems (ABS) form a core component of traction control by preventing wheel lockup under heavy braking, which could otherwise lead to uncontrolled skids. ABS operates by rapidly pulsing brake pressure via solenoid valves, allowing wheels to rotate slightly while maintaining high braking force and steering responsiveness.^[41] First commercialized in the 1970s, ABS integrates seamlessly with traction control systems to provide bidirectional slip management, reducing stopping distances on varied surfaces by up to 30% in some tests while preserving directional stability.^[42] This integration, common since the 1980s, enables unified electronic oversight of both braking and acceleration phases. Electronic stability control (ESC) extends ABS functionality to address lateral instability, such as oversteer or understeer during turns. ESC employs yaw rate sensors to measure vehicle rotation around its vertical axis, steering angle sensors for input monitoring, and lateral accelerometers for side-force detection; deviations from expected dynamics trigger selective braking on individual wheels to generate a corrective yaw moment.^[43] Differential braking, applied via the hydraulic modulator shared with ABS, restores traction without driver input, reducing fatal single-vehicle crashes by approximately 50% according to regulatory evaluations.^[44] Mandated for new light vehicles in the U.S. since 2012, ESC systems process data at rates exceeding 100 Hz for near-instantaneous response.^[45] At the heart of these technologies lies a feedback control algorithm executed by the electronic control unit (ECU). Wheel speed sensors, typically Hall-effect or inductive types mounted at each wheel hub, provide rotational velocity data to the ECU, which estimates vehicle speed via averaging non-slipping wheels and computes slip thresholds. Upon detecting excessive slip—often defined as exceeding 10-20%—the ECU modulates throttle via engine management or activates brakes through the ABS module, prioritizing stability over raw acceleration.^[46] Bosch pioneered widespread adoption of such algorithms in the 1990s, with the introduction of traction control (ASR) as a complementary system to ABS in 1987 for enhanced drive-line stability in passenger cars.^[47]^[48] By 1994, Bosch's integrated ABS/ASR units achieved production volumes supporting global vehicle fleets, emphasizing real-time slip regulation.^[49] Post-2020 advancements leverage artificial intelligence to enable predictive traction management in autonomous vehicles, shifting from reactive to anticipatory control. Machine learning models, such as neural networks trained on sensor fusion data (including LiDAR and cameras), forecast slip risks by analyzing road conditions, vehicle load, and dynamics ahead, allowing preemptive torque redistribution or path adjustments.^[50] For example, AI-driven model-free controllers have demonstrated global exponential stability in anti-slip scenarios, outperforming traditional methods in variable-friction environments through adaptive learning. These systems, integrated into level 4 autonomy platforms, reduce slip-induced deviations by up to 40% in simulations of adverse weather, paving the way for safer unmanned operation.^[51]

Medical Applications

Principles of Medical Traction

Medical traction operates on the biomechanical principle of applying a controlled tensile force to realign musculoskeletal tissues, such as bones, joints, and surrounding soft structures, thereby reducing displacement, alleviating pressure on nerves, and promoting tissue decompression. This force counteracts pathological misalignments by stretching contracted muscles and ligaments, facilitating anatomical restoration without surgical intervention. In bone-muscle interactions, Newton's third law manifests as the applied traction force eliciting an equal and opposite reaction from the body's counter-traction, often anchored by the patient's body weight or fixed supports, which maintains equilibrium and prevents excessive motion.^[52]^[53] The magnitude of traction force is carefully calibrated to achieve therapeutic effects while minimizing risks like tissue ischemia or nerve compression, typically ranging from 5-10% of the patient's body weight for initial skin traction applications, though higher percentages (up to 30-50%) may be used in skeletal methods under monitoring. Forces are applied either continuously for sustained alignment in fracture cases or intermittently to allow tissue recovery and avoid damage from prolonged loading. For instance, in lower limb traction, weights of 4.5-14 kg are common, adjusted based on patient tolerance and clinical response.^[52]^[54]^[55] Historically, the concept of medical traction traces back to the Hippocratic method around 400 BCE, where a ladder or board was employed to apply longitudinal spinal traction for correcting deformities like kyphosis through manual extension and counter-extension. This ancient technique laid the groundwork for traction's use in managing spinal and limb injuries. Modern standardization emerged in the post-1800s era of orthopedics, with innovations like Hugh Owen Thomas's splint in the late 19th century enabling more precise force application during World War I, evolving into today's regulated systems.^[53]^[52]^[56] In limb positioning, the traction force often balances the gravitational component acting on the elevated body part, expressed by the equation F_{\text{traction}} = mg \sin \theta, where m is the mass of the limb segment, g is gravitational acceleration, and \theta is the angle of elevation from the horizontal. This formulation ensures the applied force counters the sine-resolved weight component along the traction axis, optimizing alignment without overload; for example, in Russell traction setups, adjustments to \theta modulate the effective pull to suit the injury site.^[57]^[58]

Skeletal Traction Methods

Skeletal traction involves the direct attachment of traction devices to the bone using pins, wires, or screws, providing stable immobilization and alignment for severe fractures or dislocations where skin traction is insufficient. This invasive method applies controlled forces directly to the skeletal structure, often through insertion sites in long bones or the cranium, to maintain reduction until definitive surgical intervention or healing occurs.^[59]^[60] Common procedures include the insertion of Steinmann pins, which are smooth or threaded metal rods drilled into the bone perpendicular to the long axis to avoid slippage or bending under load. For femoral fractures, a Steinmann or Denham pin is typically placed in the distal femur, approximately 2-4 cm proximal to the condyles, under local anesthesia and fluoroscopic guidance to ensure precise alignment and avoid neurovascular structures; this allows for longitudinal traction up to 15% of body weight to achieve axial reduction. In cervical spine injuries, halo traction employs four to six skull pins inserted into the outer table of the cranium, connected to a rigid halo ring that is suspended via a pulley system, gradually applying 5-10 pounds of upward force to realign the spine and decompress neural elements.^[59]^[60]^[61] These methods are particularly applied in post-trauma scenarios requiring precise alignment, such as vertically unstable pelvic fractures, where, for vertical shear and combined injuries, ipsilateral skeletal traction via a distal femoral pin is required in approximately 27% of cases, in addition to external fixation, to help restore length and rotation pending operative fixation. In pelvic injuries, traction counters vertical shear forces, reducing displacement and associated soft tissue damage, though it is most effective when combined with pelvic binders for initial stabilization.^[62]^[63] Complications of skeletal traction primarily include pin-site infections, with reported incidences ranging from 5-20% depending on care protocols and patient factors, though superficial infections predominate and rarely progress to osteomyelitis if addressed promptly. Risk factors include prolonged pin dwell time beyond 6 weeks and poor hygiene; to mitigate this, standardized pin-site care involves daily cleansing with chlorhexidine solution (2 mg/ml) or normal saline using sterile gauze, followed by loose application of dry dressings without routine antibiotics unless drainage occurs, and monitoring for erythema, discharge, or loosening. Neurovascular injury during pin insertion is minimized by anatomical landmarks and imaging, occurring in less than 1% of properly executed procedures.^[64]^[65]^[66] The evolution of skeletal traction traces back to the early 1900s with the introduction of the Steinmann pin in 1907, which replaced less reliable skeletal wires and enabled effective external fixation for lower extremity fractures. By the mid-20th century, advancements like the halo device in 1959 expanded applications to the spine, while contemporary techniques incorporate minimally invasive external fixators with hydroxyapatite-coated pins to reduce infection rates and promote osseointegration, allowing shorter traction durations and hybrid use with internal hardware.^[67]^[61]^[66]

Skin and Soft Tissue Traction

Skin and soft tissue traction involves the application of pulling forces to the body through non-invasive means, such as adhesive tapes, straps, or padded slings that distribute pressure over the skin and underlying soft tissues, typically using weights not exceeding 4.5 kg to avoid tissue damage.^[52] This method contrasts with more invasive skeletal traction by relying on friction and soft tissue resistance rather than direct bone attachment, making it suitable for milder or temporary interventions in musculoskeletal conditions.^[52] Common techniques include Buck's traction, which uses non-adhesive tape or adhesive straps applied to the lower leg for hip and knee alignment, often in femoral neck or shaft fractures and hip dislocations.^[52] Another approach is the pelvic sling, a padded belt or harness positioned around the iliac crests and lower rib cage to apply upward traction for spinal decompression, commonly integrated into systems like the Thomas splint for lower limb support.^[52] These methods aim to reduce muscle spasms, alleviate pain, and maintain alignment without penetrating the skin.^[52] Indications for skin and soft tissue traction focus on temporary relief in low-severity cases, such as preoperative stabilization for femoral fractures or management of non-specific low back pain with or without sciatica, which affects an estimated 5-10% of low back pain patients.^[68]^[69] For sciatica-related symptoms, pelvic sling traction provides distractive force to the lumbar spine, potentially easing radicular pain from disc herniation or nerve compression.^[68] It is particularly useful in acute or subacute phases to immobilize and reduce soft tissue strain prior to further treatment.^[68] Treatment duration is typically short-term, ranging from 24-48 hours for preoperative use in fractures to 10-20 minute sessions over 1-6 weeks for back pain management, with follow-up assessments at 1-12 weeks to evaluate progress.^[52]^[68] Monitoring involves regular skin inspections every 4-6 hours to detect early signs of breakdown, ischemia, or pressure sores, alongside adjustments to traction weights based on patient tolerance and clinical response to prevent complications like nerve injury or compartment syndrome.^[52] Originating in the 19th century— with Gurdon Buck introducing adhesive skin traction in the 1860s as an alternative to heavier weights and bandages—this approach evolved as a safer option for soft tissue applications, offering lower infection risk than skeletal methods by eliminating pin site entry points.^[70]^[71] Modern evidence indicates limited overall efficacy for long-term outcomes in low back pain but supports its role in short-term pain control and alignment.^[68]

Other Uses

Traction in Sports and Recreation

In sports and recreation, traction refers to the frictional or mechanical grip that enables athletes to maintain control and stability on challenging surfaces, enhancing performance and safety in activities like climbing and winter sports. This is achieved through specialized equipment that optimizes contact with rock, ice, or snow, often by increasing the coefficient of friction or providing mechanical penetration. Such aids are essential for preventing slips and allowing precise movements in dynamic environments. Climbing gear plays a pivotal role in enhancing traction on rock surfaces, where friction between the climber's hands, feet, and the rock is crucial for ascent. Friction-based climbing shoes feature soft, high-friction rubber soles designed to maximize grip on small holds and slabs; these formulations, such as Vibram XS Grip or Stealth rubber, achieve static coefficients of friction up to 1.0 or higher on clean rock, far exceeding standard shoe rubbers, by incorporating specialized polymers that promote adhesion without excessive wear.^[72]^[73] Complementary to shoes, climbing chalk—typically magnesium carbonate—absorbs hand moisture to improve grip; a 2012 study found it increases the coefficient of friction between skin and rock by approximately 20% on limestone and sandstone, though an earlier 2001 study suggested a decrease and debate continues.^[74]^[75] This combination enables techniques like smearing on low-friction slabs, where the shoe rubber conforms to microscopic surface irregularities for enhanced contact.^[76] In winter sports such as mountaineering and ice climbing, traction is provided by crampons and ice axes, which rely on mechanical penetration rather than pure friction to secure footing on frozen surfaces. Crampons are metal frames with 10 to 14 sharpened steel points that attach to boots, allowing spikes to embed into ice or snow under body weight; the physics involves the points exceeding the ice's compressive strength (around 1-10 MPa near 0°C), creating a mechanical interlock that resists shear forces during movement.^[77] Ice axes feature a spiked head and adze for chopping or anchoring, with the spike at the base penetrating ice similarly to provide self-arrest capability in falls by leveraging the axe's leverage and the ice's resistance to penetration.^[78] These tools are critical on steep, icy terrain, where surface friction alone is insufficient due to ice's low coefficient (0.02-0.1), and improper use can lead to catastrophic slips.^[79] For off-season training, traction boards—also known as balance or wobble boards—simulate ski edge control and stability by providing an unstable platform that mimics snow resistance, helping athletes build proprioception and leg strength without snow. These devices, often featuring a rounded base for multi-directional tilting, allow skiers to practice carving motions and weight shifts, improving traction management on variable slopes during the season.^[80] Historically, the introduction of gymnastic chalk to rock climbing in the 1950s by John Gill, the pioneer of modern bouldering, revolutionized hand grip by enabling drier, more reliable friction on rock holds, shifting bouldering from a preparatory exercise to a distinct discipline.^[81] The later development of sticky rubber in the early 1980s, such as Boreal's 1982 Firé compound, further transformed foot traction, allowing climbers to stick to vertical faces previously deemed impossible.^[82]

Traction in Business and Technology

In business and technology contexts, "traction" refers metaphorically to the momentum a startup or product gains through user adoption, revenue growth, or market validation, distinct from its physical meaning as frictional force.^[83] This usage emphasizes sustainable progress, where early indicators of demand signal viability for scaling. For instance, startups often measure traction via key metrics such as monthly active users (MAUs), which quantify consistent engagement and retention.^[84] In the startup ecosystem, gaining traction is critical for securing investment and demonstrating product-market fit, with benchmarks established by accelerators like Y Combinator since its founding in 2005. Y Combinator advises consumer startups to target rapid user growth, such as achieving 100 paying users at $100 per month or showing exponential increases in MAUs, as these signal potential for hyper-growth and attract venture capital.^[85] Representative examples include early-stage companies aiming for 10-20% week-over-week growth in active users to validate demand before broader expansion.^[86] The term gained prominence during the 2010s tech boom, particularly through Eric Ries' 2011 book The Lean Startup, which promoted validated learning—testing assumptions via minimum viable products (MVPs) to build traction incrementally based on real customer feedback.^[83] For technology products, traction testing involves empirical methods like A/B testing to assess feature uptake and optimize adoption. A/B testing compares variations of software elements, such as user interfaces or onboarding flows, to identify which drives higher engagement metrics, enabling data-driven iterations that boost retention and usage.^[87] A key indicator of sustained growth is the viral coefficient, calculated as the average number of invitations sent per user multiplied by the conversion rate; a value greater than 1 indicates exponential, self-sustaining expansion through organic referrals, as each user acquires more than one new user.^[88] This figurative application of traction focuses purely on conceptual momentum in adoption and scalability, without any literal mechanical implications.^[83]

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Car - Traction Force - The Engineering ToolBox
The tractive force between a car wheel and the surface can be expressed as F = μ t W = μ t ma g (1) where F = traction effort or force acting on the wheel from ...<|separator|>
[19]
[PDF] FRICTION COEFFICIENTS BETWEEN TIRES AND ... - DTIC
Many factors affecting the friction coefficient between tires and pavement surfaces have been found through laboratory and field investigations. These factors ...
[20]
[PDF] PHYSICAL FACTORS IN TYRE TRACTION
By far the most important variables are the nature of the road surface texture and the tread pattern.
[21]
Comparison between rubber–ice and sand–ice friction and the effect ...
Close to the melting point the friction of rubber on ice was low and increased with decreasing ice temperature. Below −5 °C, reasonably high friction levels ( ...
[22]
Impact of the tire/road local contact area on tire friction, with a novel ...
Furthermore, this ratio is significantly affected by the roughness of the road surface, the tire's viscoelastic properties and its operating conditions.
[23]
[PDF] Truck Tire Pavement Contact Pressure Distribution Characteristics ...
Low inflation pressures tended to cause the wheel load to be distributed more heavily to the contact patch's central area for the radial tire and more heavily ...
[24]
Traction modifies the contact area and the vertical and horizontal ...
Under traction, the tyre-soil contact area enlarged, and with no change in wheel load, the mean ground pressure was reduced. The distribution of vertical ...
[25]
Slip Ratio - an overview | ScienceDirect Topics
Slip ratio is defined as one minus the ratio of the distance traveled per revolution of the traction element under operating conditions.
[26]
The Effect of Tire Age and Anti-Lock Braking System on the ... - MDPI
The slip ratio generally reaches the maximum value of the friction coefficient at about 10–20% of the slip ratio for ABS vehicles [3,4]. Sustainability 15 06945 ...
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10-05-03-0021: Analysis and Prediction of Tire Traction Properties ...
Apr 20, 2021 · It is found that if the loaded radius of the tire is kept constant, the inflation pressure has little effect on the contact area between the ...
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Silica in Tires has Enabled Greater Safety and Sustainability on the ...
Mar 11, 2025 · "Silica in rubber compounds was a revolution in tire technology, enabling us to almost halve braking distances on wet road surfaces. This is ...
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All-Wheel Drive Systems Explained - Car and Driver
Jul 29, 2016 · When wheelslip occurs in the real world, torque distribution is ultimately determined by the available traction at each tire. That makes torque ...Open Differential · Torque Split: The Gripping... · Limited-Slip Center...
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John Boyd Dunlop - National Inventors Hall of Fame®
Scotsman John Dunlop developed the first practical pneumatic tire in 1888. His tire provided the foundation for the Dunlop Tire Company.
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Twice the Traction, a Hundred Times More Problems: A Brief History ...
Nov 13, 2018 · 4x4 development started in the 19th/20th century, with first proper cars in the 1960s. Early attempts faced challenges, and the first real 4x4 ...Missing: evolution pneumatic tires<|control11|><|separator|>
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[PDF] UPDATES OF INTERNATIONAL SOCIETY FOR TERRAIN-VEHICLE ...
7 Schematic of vehicle for angle of pitch. Angle of repose, α. Angle between the horizontal and the maximum slope that a soil assumes through natural ...
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Mechanisms of Adhesion Increase in Wet Sanded Wheel–Rail ...
Adhesion is increased by sanding, where sand grains are blasted towards the wheel–rail contact. Despite the successful use of sanding in practice and extensive ...
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Electric Railways, 1880-1990 | IET Digital Library
In the early 1890s, the steam-worked rapid-transit railway had reached a practically unsurpassable limit, and electrification was the only means of upgrading ...
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Electric Traction Control | PRC Rail Consulting Ltd
Most DC motor circuits are arranged to control two or four motors. The control range is enhanced by changing the connections to the motors as the train ...Missing: startup | Show results with:startup
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(PDF) Tracks or Wheels – Perspectives and Aspects in Agriculture
Tracked vehicles demonstrate superior traction compared to wheeled vehicles under comparable conditions. Soil moisture content significantly influences the ...
[37]
[PDF] Sliding Mode Measurement Feedback Control for Antilock Braking ...
Vehicle traction control can greatly improve the performance of vehicle motion and stability by providing anti-skid braking and anti- spin acceleration.<|separator|>
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[PDF] NHTSA Light Vehicle Antilock Brake Systems Research Program ...
Drivers in the ABS group showed significantly increased stability and control relative to conventional brakes. 17. Key Words. Antilock Brake Systems, ABS, Crash ...
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Antilock Braking System And Traction Control - IEEE Xplore
... integration of the ABS function within a hydraulic booster could result in cost savings. This was the reason why integrated ABS systems came on the market ...
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Clemson Vehicular Electronics Laboratory: Active Yaw Control
ESC systems brake individual wheels of the vehicle in order to control yaw moment to improve handling performance and cornering capability. Though stability is ...
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[PDF] esc - NHTSA
Apr 9, 2010 · ESC systems use automatic computercontrolled braking of individual wheels to assist the driver in maintaining control in critical driving ...
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Federal Motor Vehicle Safety Standards; Electronic Stability Control ...
Jun 23, 2015 · An ESC system enhances the RSC functions because it has the added information from the steering wheel angle and yaw rate sensors, as well as ...
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On the Stability of Nonlinear Wheel-Slip Zero Dynamics in Traction ...
We propose a robust nonlinear control design based on input–output linearization to solve the traction control problem. The oscillatory behavior of the ...
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[PDF] Annual Report 1992 - Bosch
For the production of a new generation of anti- lock braking systems (ABS) and traction con- trols (ASR), we started operations in a new manufacturing facility ...
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[PDF] Annual Report 1994
Worldwide, we introduced our new generation of antilock braking systems. (ABS), together with its complemen tary traction control system (ASR). We started ...Missing: history | Show results with:history
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[PDF] Artificial Intelligence Integration Enhances Vehicle Safety and ... - arXiv
Dec 11, 2024 · At the same time, by using machine learning algo- rithms and real-time data analytics, AI enhances performance, personalizes the driving ...
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Longitudinal Control for Autonomous Racing with Combustion ...
Apr 24, 2025 · The proposed control concept enables a close tracking of the high-level control command. An anti-lock braking system, traction control, and ...
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Keeping the Traction on in Orthopaedics - PMC
Aug 25, 2020 · Tractions' main goals are to control pain from muscle spasm, reduce fractures maintaining anatomical reduction, and to prevent and correct deformity.Introduction And Background · Review · Figure 7. Halter's Traction
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Cervical Traction - StatPearls - NCBI Bookshelf
Mechanical traction includes pinning, with the placement of a Halo device around the head; where anterior pins are placed 1 cm above each of the eyebrows, and ...
[50]
Lumbar Traction - Physiopedia
Research by Judovich showed that a traction force of 26% of the patient's body weight is necessary to overcome friction. Using a split tabletop with friction- ...
[51]
Effect of 10%, 30%, and 60% body weight traction on the straight leg ...
30% and 60% body weight traction significantly improved straight leg raise measurements compared to 10% and pre-traction levels, indicating improved mobility.
[52]
The history of modern spinal traction with particular ... - PubMed
The study starts at the end of the 18th century with the works of JA Venel (1789) who tried to apply the Hippocratic idea to modern surgery.
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Calculating Traction Force
Apr 15, 2017 · The relationship of friction between a person and a mat table/treatment table has been found to equal 0.5 or 50% of body weight undergoing lumbar traction.
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To immobilize a fractured femur (the thigh bone), doctors of | Quizlet
F total = F sin ⁡ ( θ ) sin ⁡ ( 20 ) \begin{align*} &F_{\text{ total} ... (b) What is the horizontal component of the traction force acting on the leg?Missing: limb | Show results with:limb
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Skeletal traction - AO Surgery Reference
Skeletal traction can be applied either through a distal femoral or proximal tibial pin. The application of the latter is shown here.
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Educational Module for Orthopaedic Residents: Skeletal Traction
Apr 14, 2023 · The distal femoral traction (DFT) pin allows for longitudinal traction up to 15% bodyweight and allows for axial fracture reduction and soft- ...
[57]
Halo Brace - StatPearls - NCBI Bookshelf
Mar 2, 2024 · This method involves specific procedural steps, which differentiates it from other cervical spine immobilization methods.
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Management of pelvic injuries in hemodynamically unstable ... - PMC
... skeletal traction is also needed in 27% of injuries. ... NSCB Medical College, Vidyarthi D.A. Study of incidence and prevalence of pelvic fractures in Central ...
[59]
Anaesthesia for the management of traumatic pelvic fractures
May 21, 2018 · The correct application of the pelvic binder should be confirmed, and skeletal traction should be considered where vertical instability is ...
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Pin-site Infection: A Systematic Review of Prevention Strategies - PMC
After a mean of 100 days, there was 18% per-pin infection rate with weekly dressing and 13% in daily dressings, a difference which is not statistically ...Missing: traction | Show results with:traction
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[PDF] Incidence of Infection Associated with Placement of Skeletal Traction ...
Incidence of Infection Associated with Placement of Skeletal Traction Pins Using Unsterile Drills ... femur and pelvic fractures at a single Level 1 Trauma ...
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Low Complication Rates Associated With the Application of Lower ...
Conclusions: Temporary lower extremity traction pins have low infection rates and can be safely placed at the bedside. Careful pin placement and review of ...Missing: skeletal | Show results with:skeletal
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Eponymous Instruments in Orthopaedic Surgery. - Europe PMC
Skeletal traction also controlled shortening better than plaster casts. Without a doubt, Steinmann revolutionized the management of acute fractures. An external ...Steinmann Pin · Cobb's Periosteal Elevator · Kocher Clamp<|control11|><|separator|>
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Traction for low‐back pain with or without sciatica - PMC - NIH
RCTs involving traction to treat acute (less than four weeks' duration), subacute (four to 12 weeks' duration) or chronic (more than 12 weeks' duration) non‐ ...
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Diagnosis and treatment of sciatica - PMC - NIH
In general an estimated 5%-10% of patients with low back pain have sciatica, whereas the reported lifetime prevalence of low back pain ranges from 49% to 70%.
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Innovations in Treatment of Femoral Fractures Throughout History
Jul 30, 2024 · In the 1860's Gurdon Buck suggested an alternative method of traction by utilizing friction between tape and skin to provide traction attached ...
[67]
Traction for Complete transverse, simple - AO Surgery Reference
Traction for 6 weeks is an expensive use of hospital resources and should only be considered when other option are unavailable. Whilst length is often ...Missing: pelvic | Show results with:pelvic
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Testing of Climbing Shoe Rubbers | Veryst Engineering
On wooden panels, the Vibram XS Edge rubber has a larger static coefficient of friction. For climbers, this translates to the shoe being less likely to slip ...
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Sticky feet: a tribological study of climbing shoe rubber
Sep 13, 2024 · The SMi6 rubber yields the highest static friction coefficient under both loading scenarios, with SC4 having the second highest under 30 N but ...
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Use of 'chalk' in rock climbing: sine qua non or myth? - PubMed
Magnesium carbonate, or 'chalk', is used by rock climbers to dry their hands to increase the coefficient of friction, thereby improving the grip of the holds.
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Learn This: Friction Science - Climbing
Nov 25, 2014 · Climbing shoe manufacturers design their rubber to work best in a specific temperature range—approximately 68° to 77°F. (Of course, all rubber ...
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[PDF] A Penetrating Look at Ice Friction - PHYSICS - APS.org
Feb 8, 2021 · A sphere moving across the surface will penetrate the surface when the ice hardness is below the sphere's contact pressure. In this case, the ...Missing: crampon | Show results with:crampon
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How to Use an Ice Axe for Mountaineering | REI Expert Advice
Spike: This is the sharp bottom point of the axe that penetrates snow and ice. ... Crampons are a crucial traction device for walking on firm snow and ice.Missing: physics | Show results with:physics<|separator|>
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Unravelling the physics and mechanisms behind slips and falls on ...
Michael Faraday stated in his friction theory that, “pressure melts the icy surface and ice turns from solid to liquid under pressure near to the freezing point ...
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Best Balance Boards for Snowboarding (Off-Season 101)
Aug 8, 2025 · Find the best balance boards for snowboard training. Improve your stability, core strength, and balance in the off-season. You need it.
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Legacy Series: John Gill - American Alpine Club
Jul 26, 2022 · John Gill is widely considered the father of modern bouldering and the individual responsible for introducing gymnastic chalk as well as dynamic movement to ...
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How Climbing Gear Has Evolved Over the Past 50 Years
Sep 9, 2022 · The major breakthrough in shoe rubber was made by Boreal in 1982 with the Firé, the first of the “sticky-rubber” shoes. The new rubber was ...
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Methodology - The Lean Startup
The unit of progress for Lean Startups is validated learning-a rigorous method for demonstrating progress when one is embedded in the soil of extreme ...Missing: traction | Show results with:traction<|separator|>
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YCombinator Application: The Guide to Getting In (2025) - Zyner.io
Sep 17, 2025 · Active Users: Daily, weekly, or monthly active users (DAUs, WAUs, MAUs) are the gold standard. Show a graph, and make sure it's going up and to ...
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Startup = growth : YC Startup Library | Y Combinator
A startup is a company designed to grow fast, with the only essential thing being growth. It's a commitment to starting a fast-growing company.Startup = Growth · Ideas · Compass
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Benchmarks for Valuation and Traction at Y Combinator - Tremendous
Nov 27, 2024 · Top YC companies have $150k-$500k ARR, $20-25M post-money valuation. Mid-tier have $3-5k/month, $20M post-money. Lower tier have zero revenue, ...
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What is A/B Testing? A Practical Guide With Examples | VWO
A/B testing (also called split testing) is comparing two versions of a web page to figure out the better performing variation. Learn more with examples.15 Best A/B Testing Tools... · What is Mobile App A/B... · eCommerce · SaaSMissing: uptake | Show results with:uptake
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Viral Coefficient | SaaS Formula + Calculator - Wall Street Prep
The viral coefficient (K-Factor) is an estimate of the number of new users that the average customer can refer to using a company's product or services.Missing: technology | Show results with:technology