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API · /bankedcurve-api

Banked Curve API

healthy 4,050 Subscribers

Banked-curve and circular-motion dynamics as an API, computed locally and deterministically. The speed endpoint takes the radius of a curve and its banking (bank) angle and returns the frictionless ideal (design) speed at which the banking alone supplies the centripetal force, v = √(r·g·tanθ); give a coefficient of friction as well and it also returns the maximum safe speed before the vehicle slides outward up the bank, v = √(r·g·(tanθ+μ)/(1−μ·tanθ)), and the minimum speed before it slides inward down the bank — every speed in metres per second, km/h, mph and knots, plus the centripetal acceleration. The bank-angle endpoint inverts this: from a design speed and radius it returns the ideal banking angle θ = atan(v²/(r·g)) and the equivalent superelevation as a ratio and a percentage, the cant a road or railway needs so no side friction is used at that speed. The flat-curve endpoint handles an unbanked curve from the coefficient of friction: the maximum cornering speed v = √(μ·r·g) for a given radius and the minimum radius v²/(μ·g) for a given speed. Gravity defaults to standard 9.80665 m/s² and can be overridden. Everything is computed locally and deterministically, so it is instant and private. Ideal for road and racetrack design tools, vehicle-dynamics and driving-simulator apps, civil and transportation engineering, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is curve banking and cornering dynamics; for projectile and SUVAT kinematics use a physics API.

#banked-curve #circular-motion #vehicle-dynamics #civil-engineering #physics #developer-tools
api.oanor.com/bankedcurve-api
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Machine-readable spec so AI agents can integrate this API.

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

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API health

healthy
Uptime
100.00%
Server probes · 24h
Avg latency
99 ms
Server probes · 24h
Subscribers
4,050
active
Total calls
32
last 7 days
status Full status page → · 20 probes/24h

Pricing

Pick a tier — billed monthly, cancel anytime.

Free

Free

  • 3,000 calls / month
  • 2 requests / second
  • Hard cap (429 above quota, no overage)
  • Ideal banked-curve speed from radius + banking angle
  • No-friction circular-motion solver
  • JSON response, deterministic results
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Starter

€5.00 /month

  • 40,000 calls / month
  • 5 requests / second
  • Hard cap (429 above quota, no overage)
  • Speed, radius and angle solving in any direction
  • Friction-coefficient inclusive curve dynamics
  • Centripetal force & acceleration outputs
  • Email support
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Pro

€15.00 /month

  • 250,000 calls / month
  • 15 requests / second
  • Hard cap (429 above quota, no overage)
  • Full vehicle-dynamics curve suite
  • Min/max safe speed envelopes with friction
  • Batch curve evaluation
  • Priority support
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Mega

€49.00 /month

  • 1,500,000 calls / month
  • 40 requests / second
  • Hard cap (429 above quota, no overage)
  • High-volume road & track design throughput
  • All circular-motion & banked-curve endpoints
  • Bulk batch solving
  • Top-priority SLA support
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Related APIs

Other APIs with overlapping tags.

Circular Motion API

Uniform circular-motion physics as an API, computed locally and deterministically. The centripetal-force endpoint computes the centripetal acceleration a = v²/r = ω²·r — always pointing toward the centre — and the centripetal force F = m·a that holds a body on its circular path, from the mass, the radius and either the linear or the angular velocity, and reports the equivalent g-force. The angular endpoint converts between every way of describing rotation — angular velocity (rad/s), revolutions per minute, frequency, period and, given a radius, the linear (tangential) velocity — using ω = 2π·f = 2π/T = v/r. The centrifuge endpoint computes the relative centrifugal force (RCF, in g) of a centrifuge rotor from its speed in rpm and radius, RCF = ω²·r / g, or inverts it to give the rpm needed to reach a target RCF. Masses are in kg, radii in m (mm for the centrifuge), velocities in m/s, angular velocities in rad/s and forces in N. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics-education, mechanical, automotive, lab-centrifuge and amusement-ride app developers, rotational-motion and g-force tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is uniform circular motion; for gravitational orbits use a gravitation API, for a vehicle on a banked curve a banked-curve API and for pendulum oscillation a pendulum API.

api.oanor.com/centripetal-api

Soil Bearing Capacity API

Geotechnical foundation maths as an API, computed locally and deterministically. The factors endpoint computes the Terzaghi/Vesic bearing-capacity factors Nc, Nq and Nγ from a soil friction angle — Nq = e^(π·tanφ)·tan²(45+φ/2), Nc = (Nq−1)·cotφ and Nγ = 2(Nq+1)·tanφ. The bearing-capacity endpoint computes the ultimate, net and allowable bearing capacity of a strip, square or circular footing from the cohesion, friction angle, soil unit weight, footing width and founding depth, qu = sc·c·Nc + γ·D·Nq + sγ·γ·B·Nγ, breaking it into its cohesion, surcharge and self-weight components and dividing by a factor of safety (default 3) for the allowable value. The settlement endpoint computes the immediate elastic settlement of a footing, s = q·B·(1−ν²)·I / E, from the applied pressure, the footing width, the soil elastic modulus and Poisson's ratio. Cohesion and pressures are in kilopascals, unit weight in kN/m³ and lengths in metres. Everything is computed locally and deterministically, so it is instant and private. Ideal for civil-engineering, geotechnical, foundation-design and construction app developers, footing-sizing and feasibility tools, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is foundation bearing capacity; for lateral earth pressure on walls use an earth-pressure API and for open-channel flow a Manning API.

api.oanor.com/soil-api

Rebar Calculator API

Reinforcement-steel (rebar) maths as an API, computed locally and deterministically. The area endpoint computes the cross-sectional area of a reinforcing bar, a = π/4·d², its mass per metre (a·7850/1e6, steel ρ = 7850 kg/m³), the total area and mass for a number of bars, and — given a required steel area — the number of bars needed and the area provided. The spacing endpoint lays out bars across a section: from the width, the cover, the bar diameter and either a centre-to-centre spacing or a bar count it returns the other, n = floor((width − 2·cover − d)/spacing) + 1, the total steel area and the area per metre of width. The ratio endpoint computes the reinforcement ratio ρ = As/(b·d) of a section from the steel area (or the bars) and the section width and effective depth, as a fraction and a percentage, the single number that governs whether a beam is under- or over-reinforced. Everything is computed locally and deterministically, so it is instant and private. Ideal for structural and site-engineering tools, reinforced-concrete detailing, bar-bending schedules and steel take-off, and civil-engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is rebar geometry and quantities; for concrete mix proportions use a concrete API.

api.oanor.com/rebar-api

Concrete Mix API

Concrete mix-design maths as an API, computed locally and deterministically. The mix endpoint breaks down a volume of concrete into its materials from a nominal mix ratio (cement:sand:aggregate, for example 1:2:4): it applies the 1.54 dry-volume allowance, then returns the cement in cubic metres, kilograms and 50 kg bags, the sand and aggregate volumes and masses, and the water from the water-cement ratio — the complete batch for the pour. The quantity endpoint computes the concrete volume of a slab, footing, or round or square column from its dimensions, adds a wastage allowance and gives the dry material volume. The watercement endpoint solves the water-cement ratio, the water or the cement from the other two — the single most important number for concrete strength and durability. Densities used are cement 1440, sand 1600 and aggregate 1450 kg/m³, with a 50 kg cement bag. Everything is computed locally and deterministically, so it is instant and private. Ideal for construction, estimating and site-engineering tools, material take-off and ordering, DIY and builder apps, and civil-engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is nominal volume-batch concrete estimating; for retaining-wall earth pressure use an earth-pressure API.

api.oanor.com/concrete-api

Frequently asked questions

Quick answers about pricing, quotas, and integration.

How do I get an API key for Banked Curve API?
Sign up for free at oanor.com, generate an API key from the developer dashboard, and call Banked Curve API with the x-oanor-key header. No credit card needed for the free tier.
What's the rate limit for Banked Curve 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 Banked Curve API cost?
Banked Curve API has a free tier with 100 calls / month. Paid plans start at €5.00 / 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 Banked Curve API GDPR-compliant?
All requests to Banked Curve 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.

Pick an endpoint from the list on the left to see its details and try it.

Code snippets

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

curl https://api.oanor.com/bankedcurve-api/SOME_PATH \
  -H "x-oanor-key: oanor_test_..."
const res = await fetch("https://api.oanor.com/bankedcurve-api/SOME_PATH", {
  headers: { "x-oanor-key": "oanor_test_..." }
});
const data = await res.json();
$ch = curl_init("https://api.oanor.com/bankedcurve-api/SOME_PATH");
curl_setopt($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/bankedcurve-api/SOME_PATH",
    headers={"x-oanor-key": "oanor_test_..."},
)
print(r.json())

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