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API · /capstan-api

Capstan & Belt Friction API

healthy 4,672 Subscribers

Capstan and belt-friction maths (the Euler-Eytelwein equation) as an API, computed locally and deterministically. The capstan endpoint applies T1/T2 = e^(μ·β) — the ratio of the tight-side to the slack-side tension of a rope or belt wrapped around a drum depends only on the friction coefficient and the wrap angle, not the drum diameter — and solves for whichever of the two tensions, the friction or the wrap angle you leave out, with the wrap angle given in degrees, radians or whole turns. The holding endpoint shows the capstan effect: how a small force holds or moves a large load, holding force = Load·e^(−μβ) and pulling force = Load·e^(+μβ) — a few turns of rope around a bollard lets one person hold a ship. The belt endpoint sizes a belt drive: from the maximum tight-side tension, the friction and the wrap angle it gives the slack-side tension, the effective (net) tension T1 − T2 that drives the load and, with the belt speed, the maximum power transmittable before the belt slips. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical and marine-engineering tools, belt-drive, winch, hoist and band-brake design, climbing and rigging apps, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is belt and rope friction; for belt length, wrap angle and speed ratio use a belt-drive API.

#capstan #belt-friction #euler-eytelwein #mechanical-engineering #rigging #developer-tools
api.oanor.com/capstan-api
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Machine-readable spec so AI agents can integrate this API.

/api/capstan-api/openapi.json
/api/capstan-api/llms.txt

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API health

healthy
Uptime
100.00%
Server probes · 24h
Avg latency
89 ms
Server probes · 24h
Subscribers
4,672
active
Total calls
36
last 7 days
status Full status page → · 24 probes/24h

Pricing

Pick a tier — billed monthly, cancel anytime.

Free

Free

  • 2,000 calls / month
  • 2 requests / second
  • Hard cap (429 above quota, no overage)
  • Euler-Eytelwein T1/T2 = e^(mu*beta) capstan endpoint
  • Single wrap-angle and friction-coefficient inputs
  • Deterministic local compute, no upstream latency
  • Community support
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Starter

€9.00 /month

  • 25,000 calls / month
  • 5 requests / second
  • Hard cap (429 above quota, no overage)
  • Hold-force and required-effort solving in both directions
  • Degrees or radians for wrap angle beta
  • Belt-friction grip-ratio output
  • Email support
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Pro

€24.00 /month

  • 150,000 calls / month
  • 15 requests / second
  • Hard cap (429 above quota, no overage)
  • Multi-turn capstan stacking with cumulative wrap angle
  • Safety-factor and margin annotations on results
  • Batch rigging-load evaluation in one call
  • Priority support
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Mega

€75.00 /month

  • 1,035,000 calls / month
  • 40 requests / second
  • Hard cap (429 above quota, no overage)
  • High-throughput rigging and winch design pipelines
  • Material friction-coefficient presets library
  • Full numeric audit trail for engineering sign-off
  • SLA-backed support
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O-ring seal-design maths as an API, computed locally and deterministically — the squeeze, gland and stretch numbers an engineer or maker designs a seal to. The squeeze endpoint gives the compression that makes the seal: squeeze = (cross-section − gland depth) ÷ cross-section, so a 0.139-inch cord in a 0.113-inch deep groove is squeezed 18.7 %, and it grades the result — roughly 10–16 % suits dynamic (reciprocating) seals and 15–30 % static ones — and, given the groove width, the gland fill percentage, which should stay under about 85 % so the rubber has room to expand from heat or fluid swell. The gland endpoint works the other way: from the cross-section and whether the seal is static or dynamic (or a target squeeze) it returns the groove depth and a width sized for about 70 % fill — typically 1.3 to 1.5 times the cross-section — plus a corner radius. The stretch endpoint checks installation: stretch = (mating diameter − o-ring ID) ÷ ID, which should stay under about 5 % on a rod because stretching thins the cross-section and steals squeeze. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-engineering, hydraulics, pneumatics, vacuum and product-design app developers, seal-selection and gland-design tools, and CAD plugins. Pure local computation — no key, no third-party service, instant. Inches or millimetres. Live, nothing stored. 3 compute endpoints.

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Gear Ratio API

Gear-train ratio, speed and torque maths as an API, computed locally and deterministically. The ratio endpoint computes the gear ratio of a single pair from the driver and driven tooth counts (or pitch diameters), ratio = N_driven/N_driver, classifies it as a reduction (more torque, less speed) or an overdrive, and — given an input speed and torque — returns the output speed (input/ratio) and the output torque (input·ratio·efficiency). The train endpoint computes a compound gear train: the overall ratio is the product of the individual stage ratios, and it returns each stage ratio, the output speed and torque, noting that idler gears change only the direction of rotation, not the ratio. The solve endpoint finds the missing one of the input speed, the output speed and the ratio from the other two — for example, the ratio needed to drop a 1500 rpm motor to a 500 rpm output. Everything is computed locally and deterministically, so it is instant and private. Ideal for drivetrain, robotics and machine-design tools, gearbox and transmission selection, bicycle and vehicle gearing, and mechanical-engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is gear-train ratio and torque; for spur-gear tooth geometry use a spur-gear API.

api.oanor.com/gearratio-api

Belt Conveyor API

Belt-conveyor design maths as an API, computed locally and deterministically. The capacity endpoint computes the throughput of a belt conveyor — the volumetric capacity Q = A·v·3600 (m³/h) from the belt cross-section and speed, and the mass capacity Q·ρ/1000 (t/h) from the bulk density — and, when only the belt width is given, estimates the cross-section as A ≈ load_factor·width². The power endpoint computes the drive power as the sum of the horizontal friction power, μ·g·(material + 2·belt + idler mass per metre)·length·speed, and the vertical lift power, ṁ·g·height, then divides by the drive efficiency to give the motor power. The tension endpoint computes the belt tensions from the effective tension Te = P/v: the tight-side tension T1 = Te·e^(μθ)/(e^(μθ)−1) and the slack-side tension T2 = T1 − Te, using the Euler-Eytelwein grip of the belt on the drive pulley. Everything is computed locally and deterministically, so it is instant and private. Ideal for bulk-materials-handling, mining and plant-design tools, conveyor selection and motor sizing, and mechanical-engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is a simplified belt-conveyor model; for rope/belt capstan friction use a capstan API and for belt-drive geometry use a belt-drive API.

api.oanor.com/conveyor-api

Pulley System API

Pulley and block-and-tackle mechanics as an API, computed locally and deterministically. The advantage endpoint computes the mechanical advantage of a pulley system — the ideal MA equals the number of rope parts supporting the load, which is also the velocity ratio — and returns the effort needed to hold or raise a load, effort = load/(n·efficiency), the length of rope that must be pulled (n times the lift height) and the work in and out. The friction endpoint models a real block and tackle where every sheave loses a little tension: the mechanical advantage becomes MA = e·(1−eⁿ)/(1−e) for a per-sheave efficiency e (≈0.96 for a plain bearing, ≈0.98 for a ball bearing), so it returns the true MA, the overall efficiency and the extra effort friction costs you. The solve endpoint takes any two of the load, the effort and the number of rope parts and returns the third — for example, how many parts you need so a given person can raise a given load, or the heaviest load a winch can lift. Everything is computed locally and deterministically, so it is instant and private. Ideal for rigging, lifting and hoist-design tools, sailing, climbing and theatre-rigging apps, crane and winch sizing, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is pulley and block-and-tackle mechanics; for lever and moment balance use a lever API and for rope-around-a-drum capstan friction use a capstan API.

api.oanor.com/pulley-api

Frequently asked questions

Quick answers about pricing, quotas, and integration.

How do I get an API key for Capstan & Belt Friction API?
Sign up for free at oanor.com, generate an API key from the developer dashboard, and call Capstan & Belt Friction API with the x-oanor-key header. No credit card needed for the free tier.
What's the rate limit for Capstan & Belt Friction API?
Free tier allows 1 request per second. Paid plans scale up to 50 requests per second on the Mega tier. Hard limits return HTTP 429 above the quota — no surprise overage charges.
How much does Capstan & Belt Friction API cost?
Capstan & Belt Friction API has a free tier with 100 calls / month. Paid plans start at €9.00 / month with higher quotas and faster rate limits.
Can I cancel my subscription anytime?
Yes. Plans are billed monthly and you can cancel anytime from your billing dashboard. No long-term contracts and no cancellation fee.
Is Capstan & Belt Friction API GDPR-compliant?
All requests to Capstan & Belt Friction API go through our EU-based gateway. Your upstream API key never leaves our server and no personal data is shared with the upstream provider beyond the request you send.

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Code snippets

Sign up to get an API key, then call any path under your slug.

curl https://api.oanor.com/capstan-api/SOME_PATH \
  -H "x-oanor-key: oanor_test_..."
const res = await fetch("https://api.oanor.com/capstan-api/SOME_PATH", {
  headers: { "x-oanor-key": "oanor_test_..." }
});
const data = await res.json();
$ch = curl_init("https://api.oanor.com/capstan-api/SOME_PATH");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_HTTPHEADER, ["x-oanor-key: oanor_test_..."]);
$response = curl_exec($ch);
import requests
r = requests.get(
    "https://api.oanor.com/capstan-api/SOME_PATH",
    headers={"x-oanor-key": "oanor_test_..."},
)
print(r.json())

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