#mechanical

Riveted-joint strength maths as an API, computed locally and deterministically — the shear, bearing and rivet-count numbers a structural, sheet-metal or aircraft fitter checks a riveted connection by. The shear-capacity endpoint gives the load a rivet group carries across its shanks = the rivet area (π/4·d²) × the shear strength × the number of rivets × the shear planes — a rivet in single shear is cut on one plane, in double shear (the centre plate of a butt joint with cover plates) on two, so it carries twice. The bearing-capacity endpoint gives the load the rivets can press against the sides of their holes before the plate crushes = the projected contact area (diameter × plate thickness) × the bearing strength × the number of rivets; thin plates fail in bearing long before the rivet shears, which is exactly why both must be checked — the joint strength is the lesser of the two. The rivets-required endpoint inverts it: the rivets a design load needs = the load ÷ the allowable load per rivet (area × allowable shear × planes), rounded up to a whole rivet, using the working shear (strength ÷ safety factor) not the raw value. Everything is computed locally and deterministically, so it is instant and private. Ideal for structural and sheet-metal estimating, mechanical-design and fastener tools, and engineering calculators. Pure local computation — no key, no third-party service, instant. Shank-shear and bearing only — also confirm edge tear-out and minimum pitch. 3 compute endpoints. For bolt preload and torque use a bolt-torque API; for thread geometry a thread API; for welded joints a welding API.

api.oanor.com/rivet-api

Winch and cable-drum maths as an API, computed locally and deterministically — the rope-capacity, line-pull and rope-out numbers a winch operator, rigger or recovery driver works a drum with. The capacity endpoint gives the rope a drum holds by exact layer geometry: the sum over every full layer of the turns per layer × π × that layer's mean wrap diameter, where turns per layer = drum width ÷ rope diameter and the number of layers = the flange-to-barrel depth ÷ rope diameter — a 10-inch barrel, 20-inch flange, 12-inch-wide drum on half-inch rope holds about 940 ft over 10 layers. The layer-pull endpoint shows why pull falls as the drum fills: the rated pull is for the bare-drum first layer, and as rope piles on, the growing lever arm cuts the line pull and raises the line speed in the same ratio — pull × (first-layer diameter ÷ this layer's diameter) — so the top layer of a deep drum can pull barely half the bottom-layer rating, which is why you spool off to bare drum for a hard pull or add a snatch block. The length-at-layer endpoint gives the rope wound after a number of full layers, for marking the rope or knowing how much line is out. Everything is computed locally and deterministically, so it is instant and private. Ideal for winch- and hoist-sizing tools, recovery and off-road apps, marine and industrial-rigging utilities, and engineering calculators. Pure local computation — no key, no third-party service, instant. Geometric estimate — allow for nesting and freeboard. 3 compute endpoints. For capstan friction use a capstan API; for block-and-tackle a pulley API.

api.oanor.com/winch-api

Traction-elevator engineering maths as an API, computed locally and deterministically — the counterweight, hoist-motor and rope-traction numbers a lift engineer or building-services designer sizes a passenger elevator with. The counterweight endpoint gives the balancing mass = the empty car plus a fraction of the rated load (the overbalance, typically 40–50 %, 45 % common), so a 1,000 kg car rated for 1,000 kg uses a 1,450 kg counterweight — the car and weight balance near half load and the machine is sized for the worst-case imbalance, not the full load. The motor-power endpoint uses that: because the counterweight cancels most of the car, the motor only lifts the out-of-balance load = rated load × (1 − overbalance), so power = that × g × speed ÷ efficiency (~65–75 % geared) — a 1,000 kg lift at 1.5 m/s needs only about 11–12 kW, half what a counterweight-less hoist would draw. The traction-ratio endpoint checks the friction grip: a traction elevator moves the ropes by friction over the sheave, so the available traction (e^(μθ), the capstan equation) must beat the T1/T2 tension ratio at both worst cases — a full car at the bottom and an empty car at the top — and it returns the governing ratio. Everything is computed locally and deterministically, so it is instant and private. Ideal for lift-design and building-services tools, vertical-transport and MEP utilities, and engineering calculators. Pure local computation — no key, no third-party service, instant. Sizing estimates — follow the lift code and maker data. 3 compute endpoints. For block-and-tackle use a pulley API; for capstan friction a capstan API.

api.oanor.com/elevator-api

HVAC air-side heat maths as an API, computed locally and deterministically with the classic standard-air factors — the sensible, latent and airflow numbers a mechanical engineer or HVAC technician sizes ducts and equipment with. The sensible endpoint gives the sensible heat an airflow carries to change temperature: Qs = 1.08 × CFM × ΔT (dry-bulb difference), where the 1.08 bundles standard-air density and specific heat — 2,000 CFM across a 20 °F difference is 43,200 BTU/hr, 3.6 tons — with the result in BTU/hr, tons and kW. The latent endpoint gives the latent (moisture) heat: Ql = 0.68 × CFM × ΔW, where ΔW is the humidity-ratio difference in grains of water per pound of dry air, the dehumidification part of a cooling load that runs high in humid climates and from people and cooking, and why air conditioners are sized on total, not just temperature. The airflow endpoint inverts the sensible relation: CFM = sensible load ÷ (1.08 × ΔT), the supply air needed at a chosen supply-to-room temperature difference (comfort cooling runs ~18–22 °F below room), the number that sets fan and duct size — sanity-checked against ~400 CFM per ton. Everything is computed locally and deterministically, so it is instant and private. Ideal for HVAC-design and load-calc tools, mechanical-estimating and commissioning utilities, and building-engineering apps. Pure local computation — no key, no third-party service, instant. Standard-air factors — adjust for altitude. 3 compute endpoints. For room rule-of-thumb sizing use an HVAC API; for moist-air properties a psychrometric API; for duct sizing a ductwork API.

api.oanor.com/hvacload-api

Worm-gear engineering maths as an API, computed locally and deterministically — the ratio, lead-angle and efficiency numbers a machine designer or millwright sizes a worm drive with. The ratio endpoint gives the reduction = wheel teeth ÷ worm starts, so a single-start worm on a 40-tooth wheel is a big 40:1 reduction in one compact stage — the high ratio in a small package is the whole appeal of a worm drive. The geometry endpoint gives the lead (= starts × axial pitch, with axial pitch = π × module) and the lead angle = atan(lead ÷ (π × worm pitch diameter)), and tests for self-locking: a small lead angle (roughly under 5–6° for typical steel-on-bronze) means the wheel cannot back-drive the worm — invaluable for hoists and holding loads, at the cost of efficiency. The efficiency endpoint gives the mesh efficiency when the worm drives = tan(lead angle) ÷ tan(lead angle + friction angle), which is low for the small lead angles that give big ratios — often 50–70 %, which is why worm gears run warm and need good lubrication — while high-lead multi-start worms reach 90 %+; when the lead angle drops to the friction angle the drive becomes self-locking. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-design and gearbox tools, machine-building and CAD utilities, and engineering calculators. Pure local computation — no key, no third-party service, instant. Confirm self-locking dynamically — vibration can unlock a marginal pair. 3 compute endpoints. For spur gears use a spur-gear API; for a general ratio a gear-ratio API.

api.oanor.com/wormgear-api

Hydraulic-cylinder engineering maths as an API, computed locally and deterministically — the force, speed and oil-volume numbers a fluid-power designer, machine builder or hydraulics technician sizes a cylinder with. The force endpoint gives the push and pull from the bore, rod diameter and working pressure: extending, the oil acts on the full bore area, so the cylinder is strongest pushing out; retracting, it acts only on the annulus left by the rod, giving less force — a 100 mm bore with a 56 mm rod at 160 bar pushes about 125.7 kN out but pulls only 86.3 kN back, which is why a press or an excavator does its hard work on the extend stroke. The speed endpoint gives the piston speed from the pump flow (speed = flow ÷ area), so extending is the slower stroke and retracting the faster, the trade-off every circuit designer balances against force. The volume endpoint gives the swept oil volume per stroke for extend and retract, the rod displacement and the bore-to-annulus area ratio — the differential (regeneration) ratio used to speed the extend stroke in a regen circuit — so the pump, tank and lines can be sized for the larger volume. Everything is computed locally and deterministically, so it is instant and private. Ideal for fluid-power and machine-design tools, hydraulics-sizing calculators, mobile- and industrial-equipment utilities, and engineering apps. Pure local computation — no key, no third-party service, instant. Ideal-area estimates — allow for friction, back-pressure and efficiency. 3 compute endpoints. For Pascal force-multiplication use a hydraulics API; for valve sizing a valve-flow (Cv/Kv) API.

api.oanor.com/hydrauliccylinder-api

Interference (press and shrink) fit engineering maths as an API, computed locally and deterministically from the Lamé thick-wall equations — the contact-pressure, holding-capacity and assembly-temperature numbers a mechanical designer or machinist sizes a shaft-and-hub joint with. The pressure endpoint gives the contact pressure that builds at the interface from the diametral interference, the shaft and hub diameters and the elastic modulus, plus the tensile hoop stress at the hub bore — the highest stress in the joint, which a thin hub can split if it exceeds the yield: a 50 mm solid steel shaft in a 100 mm hub with 0.05 mm interference makes about 75 MPa of contact pressure and 125 MPa of bore hoop stress, and doubling the interference doubles the pressure. The holding endpoint turns that pressure into the axial push-out force and the transmissible torque through the friction at the interface (force = pressure × contact area × friction, torque = force × shaft radius), the figures that decide whether the joint slips under load. The assembly-temperature endpoint gives the heating (hub) or cooling (shaft) temperature change for a shrink fit — ΔT = (interference + clearance) ÷ (α × diameter) — so the part slides on freely and grips as it returns to temperature. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-design and machine-building tools, manufacturing and CAD utilities, and engineering calculators. Pure local computation — no key, no third-party service, instant. Same-material Lamé estimates — verify against the material yield with a safety factor. 3 compute endpoints. For thin-wall pressure-vessel stress use a pressure-vessel API.

api.oanor.com/pressfit-api

Pipe-insulation heat-loss maths as an API, computed locally and deterministically — the radial heat loss, thickness and energy-cost numbers a mechanical engineer or energy auditor sizes lagging with. The heat-loss endpoint gives the loss per linear foot through cylindrical insulation, Q/L = 2π·(k/12)·ΔT ÷ ln(r2/r1), where k is the insulation conductivity (BTU·in/hr·ft²·°F, ~0.25 for fibreglass), r1 the pipe radius and r2 the outer radius — a 2-inch line at 300 °F with one inch of fibreglass loses about 43 BTU/hr per foot, and because the relationship is logarithmic, doubling the thickness does not halve the loss. The thickness endpoint inverts it for a target loss: ln(r2/r1) = 2π·(k/12)·ΔT ÷ target, then thickness = r2 − r1, showing the economic-thickness point beyond which more material rarely pays. The annual-cost endpoint turns loss per foot into the yearly heat lost and fuel cost over a run of pipe, the number that justifies the lagging. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-design and energy-audit apps, insulation-contractor and process-piping tools, building-services calculators, and engineering aids. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 compute endpoints. Ignores the outer air film (real loss slightly lower). For flat walls and roofs use a U-value API.

api.oanor.com/pipeinsulation-api

Matemática de transmissão de potência por corrente de rolos como uma API, computada local e deterministicamente. O endpoint de relação calcula a relação de velocidade de uma transmissão por corrente (dentes movidos ÷ dentes motrizes), a rpm de saída e o multiplicador de torque, a velocidade linear da corrente v = N·p·rpm/60 e o diâmetro primitivo de cada roda dentada, PD = p/sen(π/N), a partir do número de dentes da roda motriz e movida, da velocidade de entrada e do passo da corrente. O endpoint de comprimento calcula o comprimento da corrente em passos e o arredonda para um número par de elos — os elos devem vir em pares — usando L = 2C/p + (N1+N2)/2 + ((N2−N1)/2π)²·p/C a partir do número de dentes, da distância entre centros e do passo. O endpoint de distância entre centros inverte essa relação para fornecer a distância exata entre centros para um número par de elos escolhido, C = (p/8)·[(2L−N1−N2) + √((2L−N1−N2)² − 8·((N2−N1)/2π)²)]. Os números de dentes são inteiros, o passo e a distância entre centros em metros (o passo padrão 0,0127 m é ANSI 40, ½ polegada) e as velocidades em rpm. Tudo é computado local e deterministicamente, portanto é instantâneo e privado. Ideal para desenvolvedores de aplicativos mecânicos, de projeto de máquinas, transportadores, motocicletas e equipamentos industriais, ferramentas de dimensionamento de rodas dentadas e seleção de correntes, e educação em engenharia. Cálculo puramente local — sem chave, sem serviço de terceiros, instantâneo. Ao vivo, nada armazenado. 3 endpoints. Isto é para transmissões por corrente de rolos industriais; para engrenagens de bicicleta, use uma API de engrenagens de bicicleta e para relações de correia ou engrenagem, use uma API de relação de engrenagens.

api.oanor.com/chain-api

Thin-walled pressure-vessel engineering maths as an API, computed locally and deterministically. The thin-wall endpoint computes the wall stresses in a cylindrical or spherical vessel under internal pressure: for a cylinder the hoop (circumferential) stress σ_h = p·r/t and the longitudinal stress σ_l = p·r/(2t), which is half the hoop — so cylinders tend to split along their length — together with the von Mises equivalent stress, and for a sphere the single biaxial stress σ = p·r/(2t); it also reports the radius-to-thickness ratio and whether the thin-wall assumption (r/t ≳ 10) holds. The thickness endpoint computes the wall thickness required to keep the hoop stress within an allowable value, t = p·r/(σ_allow·E), with a weld-joint efficiency factor. The burst endpoint computes the theoretical burst pressure of a pipe from Barlow's formula, p = 2·S·t/OD, using the ultimate tensile strength. Pressures and stresses are in pascals (megapascals also returned) and dimensions in metres. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical, chemical-plant, piping, boiler and tank-design app developers, ASME-style sizing and safety tools, and engineering education; for code work consult the applicable standards. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is thin-walled vessel stress; for general stress transformation use a Mohr-circle API and for fatigue a fatigue API.

api.oanor.com/pressurevessel-api

Mechanical-fatigue engineering maths as an API, computed locally and deterministically. The stress-cycle endpoint decomposes a cyclic load given by its maximum and minimum stress into the alternating stress σa = (σmax − σmin)/2, the mean stress σm = (σmax + σmin)/2, the stress range and the stress ratio R = σmin/σmax, and names the loading (fully reversed at R = −1, repeated at R = 0). The criteria endpoint computes the infinite-life safety factor against fatigue using the three classic mean-stress theories — Goodman (1/n = σa/Se + σm/Sut, standard and safe), Soderberg (uses the yield strength, conservative) and Gerber (a parabola, least conservative) — from the alternating and mean stress, the endurance limit Se, the ultimate strength Sut and an optional yield strength. The endurance-limit endpoint estimates the corrected endurance limit Se = ka·kb·kc·kd·ke·Se' from the ultimate strength, with Se' = 0.5·Sut for steel and the Marin modifying factors for surface finish, size, load type, temperature and reliability. Stresses and strengths use any one consistent unit (MPa is typical). Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical, structural, automotive and aerospace-design app developers, durability and safety-factor tools, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is fatigue and endurance; for static stress transformation use a Mohr-circle API and for column buckling a buckling API.

api.oanor.com/fatigue-api

Rotational and shaft-power maths as an API, computed locally and deterministically. The power endpoint relates mechanical power, torque and rotational speed — give any two of the power, the torque in newton-metres and the speed in rpm and it returns the third using P = T·ω with ω = 2πN/60, reporting the angular velocity and the power in watts, kilowatts, mechanical horsepower and metric horsepower (PS). The angular endpoint converts a rotational speed freely between rpm, radians per second, degrees per second and hertz (revolutions per second), and — given a radius — the tangential speed and centripetal acceleration at the rim. The units endpoint converts power across watts, kilowatts, mechanical horsepower (745.7 W), metric horsepower or PS (735.5 W), foot-pounds per second and BTU per hour. Everything is computed locally and deterministically, so it is instant and private. Ideal for automotive, motor, drivetrain, robotics and machinery app developers, engine and gearbox tools, and mechanical-engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is mechanical shaft power; for bolt tightening torque use a torque API and for electrical power factor a power-factor API.

api.oanor.com/shaftpower-api

Matemáticas de transmisión por correa y poleas como una API, calculadas local y determinísticamente. El endpoint de correa calcula la longitud de una correa trapezoidal abierta o correa plana a partir de los dos diámetros de polea y la distancia entre centros con L = 2C + (π/2)(D1+D2) + (D1−D2)²/(4C), y devuelve la longitud de la correa más el ángulo de contacto en cada polea; si se proporciona una rpm del conductor, también da la velocidad superficial de la correa. El endpoint de relación calcula la relación de velocidad de un par de poleas (diámetro conducido ÷ diámetro conductor, ya que N1·D1 = N2·D2): proporcione una rpm del conductor o del conducido y devuelve la otra, la relación de par y la velocidad de la correa. El endpoint de centros invierte la ecuación de longitud para encontrar la distancia entre centros para una longitud de correa objetivo, resolviendo la ecuación numéricamente. Los diámetros y distancias aceptan milímetros, centímetros, metros, pulgadas o pies, y las longitudes se informan en varias unidades. Todo se calcula local y determinísticamente, por lo que es instantáneo y privado. Ideal para herramientas de diseño de máquinas y trenes de transmisión, aplicaciones de mantenimiento y MRO, proyectos de fabricación y CNC, y calculadoras de ingeniería mecánica. Cálculo local puro — sin clave, sin servicio de terceros, instantáneo. En vivo, nada almacenado. 3 endpoints. Esta es transmisión de potencia por correa y polea; para relaciones de engranajes de bicicleta y desarrollo use una API de engranajes de bicicleta y para torque de apriete de pernos use una API de torque.

api.oanor.com/beltdrive-api

Bolt and fastener torque maths as an API, using the standard short-form relation T = K · D · F — torque equals the nut factor times the bolt diameter times the clamp load (preload). The torque endpoint computes the tightening torque, in newton-metres, foot-pounds, inch-pounds and kilogram-force metres, from the bolt diameter, the target clamp load and a nut factor — given directly or chosen from a condition preset (dry, lubricated, zinc-plated, galvanized, waxed and more). The preload endpoint solves the inverse: the clamp load a given torque produces on a bolt of a given diameter and friction. The convert endpoint converts a torque value between newton-metres, foot-pounds, inch-pounds and kilogram-force metres. Everything is computed locally and deterministically, so it is instant and private. The K·D·F short form is an estimate that depends heavily on friction — it is engineering guidance only, so always follow the manufacturer's torque specification. Ideal for mechanical, automotive and aerospace tools, maker and assembly apps, maintenance and field-service software, and engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is fastener torque; for wire gauge and resistance use a wire-gauge API and for Ohm's law use an electronics API.

api.oanor.com/torque-api