#statics

Tensioned-line point-load statics as an API, computed locally and deterministically — the line-tension and anchor-force numbers a slackliner, highliner or rigger works out before they weight a line. This is the V a loaded line makes under a person, not a self-weight catenary: the tension endpoint takes the span, the sag and the body load and returns the line tension and the horizontal anchor pull, because vertical balance is 2·T·sin(angle) = the body weight — so the flatter the line (the smaller the sag) the more the tension blows up, which is exactly why drum-tightening a line to kill the bounce can load the anchors to many times body weight. The sag endpoint inverts it: from a known line tension it returns the sag a mid-span load settles to (sin angle = weight ÷ twice the tension), and flags when the tension is too low to hold the load at all. The off-centre-load endpoint handles standing away from the middle, where the two halves carry different tensions: the horizontal pull is equal on both sides (H = weight × a × b ÷ (sag × span)) but the shorter, steeper segment runs at the higher tension and fails first — the reason a highliner near an anchor stresses that leash harder than one in the centre. Everything is computed locally and deterministically, so it is instant and private. Ideal for slackline and highline rigging tools, climbing and outdoor-gear apps, and tension-and-anchor calculators. Pure local computation — no key, no third-party service, instant. Geometric statics — combine with the real webbing and anchor ratings. 3 compute endpoints. For a self-weight hanging cable use a catenary API; for working-load-limit and safety factor a rigging API.

api.oanor.com/slackline-api

Centre-of-mass and barycentre mechanics as an API, computed locally and deterministically. The point-masses endpoint computes the centre of mass of a system of point masses in one, two or three dimensions, applying x_com = Σ(m_i·x_i)/Σm_i to each axis from a list of masses and their x (and optional y and z) coordinates — masses of 1, 2 and 3 at positions 0, 1 and 2 give a centre of mass at 1.333, and four equal masses at the corners of a square sit at its centre. The two-body endpoint computes the barycentre of two masses separated by a distance, r1 = d·m2/(m1+m2) from the first body, which always lies closer to the heavier one — for the Earth-Moon system the barycentre is about 4 670 km from Earth’s centre, still inside the planet. Lists may be passed as comma-separated values (masses=1,2,3&x=0,1,2) or as JSON arrays in a POST body, and units are consistent and unit-agnostic. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics, engineering-statics, astronomy, robotics, game-physics and mechanics-education app developers, balance-point and barycentre tools, and simulation software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 2 endpoints. This is the centre of mass; for the rotational moment of inertia use a moment-of-inertia API.

api.oanor.com/centerofmass-api

Estática y dinámica de plano inclinado y fricción como una API, calculada local y determinísticamente. El endpoint de inclinación analiza un bloque en una rampa: a partir de una masa, el ángulo de inclinación y un coeficiente de fricción, devuelve la fuerza normal N = m·g·cosθ, la componente de la gravedad a lo largo de la pendiente m·g·sinθ, la fricción estática máxima μ·N, si el bloque permanece quieto o se desliza (se desliza cuando tanθ > μ) y, si se desliza, la fuerza neta y la aceleración a = g·(sinθ − μ·cosθ). El endpoint de fricción maneja una superficie plana: la fuerza de fricción f = μ·N (la fuerza normal dada directamente o a partir de una masa), el ángulo de reposo atan(μ), y — dada una fuerza aplicada — si el objeto se mueve y su aceleración. El endpoint de rampa proporciona la fuerza necesaria para mover una carga hacia arriba o hacia abajo por una rampa a velocidad constante, F = m·g·(sinθ ± μ·cosθ), la fuerza sin fricción, la eficiencia y si la rampa es autoblocante. La gravedad por defecto es 9.80665 m/s² y se puede anular. Todo se calcula local y determinísticamente, por lo que es instantáneo y privado. Ideal para herramientas de educación en física y mecánica, manejo de materiales, diseño de transportadores y rampas, y aplicaciones de estática en ingeniería. Cálculo local puro — sin clave, sin servicio de terceros, instantáneo. En vivo, nada almacenado. 3 endpoints. Esto es fuerzas de plano inclinado con fricción; para la ventaja mecánica ideal (sin fricción) de máquinas simples, use una API de palanca.

api.oanor.com/incline-api

杠杆、力矩平衡和简单机械的机械优势计算作为API，本地确定性地计算。杠杆端点应用杠杆定律，力·力臂 = 负载·负载臂，并求解你省略的力、负载、力臂或负载臂中的任意一个，返回机械优势MA = 力臂/负载臂 = 负载/力，以及杠杆是增力还是增速。力矩端点计算单个力矩，M = F·d，或平衡一个绕支点的跷跷板：根据每侧的力和距离，告诉你是否平衡、净力矩和旋转方向，或者求解你省略的一个值以达到平衡。机械端点给出简单机械的理想机械优势——斜面（长度/高度）、螺丝（2πR/螺距）、轮轴（R/r）、楔子（长度/厚度）或滑轮系统（支撑绳数）——并在给定效率和力的情况下，给出实际机械优势和输出力。所有计算都在本地确定性地进行，因此即时且私密。非常适合物理和工程教育工具、力学和静力学应用、机械设计和DIY计算器。纯本地计算——无需密钥，无需第三方服务，即时。实时，不存储任何内容。3个端点。这是杠杆和简单机械的机械优势；对于齿轮和皮带传动比，请使用齿轮或皮带传动API。

api.oanor.com/lever-api

Beam statics as an API, computed locally and deterministically. The simply-supported endpoint analyses a beam on two supports under a point load (anywhere along the span) or a uniformly distributed load: it returns the support reactions, the maximum shear and the maximum bending moment with its location, and — if you pass the Young's modulus E and second moment of area I — the maximum deflection. The cantilever endpoint does the same for a beam fixed at one end, returning the reaction force and fixing moment, the maximum bending moment and the free-end deflection. The section endpoint gives the cross-section properties that those deflections need: the second moment of area (moment of inertia) and the section modulus for a rectangle, a solid circle or a hollow circular pipe. Every result lists the formula used, so you can show your working. Use consistent units — in SI, load in newtons, distributed load in N/m, lengths in metres, E in pascals and I in m⁴ give moments in N·m and deflections in metres. Everything is computed locally and deterministically, so it is instant and private. Linear-elastic, small-deflection theory — a learning and estimating tool, not a substitute for a qualified structural engineer on a real design. Ideal for engineering and architecture tools, education and physics apps, maker and DIY calculators, and CAD helpers. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is structural beam statics; for bolt and fastener torque use a torque API.

api.oanor.com/beam-api