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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/api/bankedcurve-api/openapi.json

/api/bankedcurve-api/llms.txt

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Banked Curve API — live data on the oanor API marketplace

API health

healthy

Uptime: 100.00%; Server probes · 24h
Avg latency: 72 ms; Server probes · 24h
Subscribers: 4,050; active
Total calls: 80; last 7 days

Full status page → · 16 probes/24h

Pricing

Pick a tier — billed monthly, cancel anytime.

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

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

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

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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PremiumApi

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

Earthwork Volume API

Earthwork volume maths as an API, computed locally and deterministically — the cut/fill-quantity and soil-state numbers a civil engineer, estimator or grading contractor runs for a road, trench or site. The average-end-area endpoint gives the volume between two cross-sections = the mean of the two end areas × the distance between them, ÷ 27 for cubic yards — the everyday earthwork-quantity method you sum section by section down an alignment (a 100 ft²/150 ft² pair 100 ft apart is about 463 cy). The prismoidal endpoint gives the more accurate Simpson volume = length ÷ 6 × (A₁ + 4·A_mid + A₂) using the true middle-section area, preferred for payment quantities where the average-end-area over-estimate would matter. The soil-state endpoint converts between the three states earth passes through: loose = bank × (1 + swell %) (excavating loosens it, ~25 %, so you haul more cubic yards than you cut) and compacted = bank × (1 − shrinkage %) (placing and compacting shrinks it, ~10 %) — which is why a balanced cut-and-fill needs more bank cut than the compacted fill, with the load factor for truck sizing. Everything is computed locally and deterministically, so it is instant and private. Ideal for grading and site-work estimating, surveying and civil-design tools, and earthmoving calculators. Pure local computation — no key, no third-party service, instant. US units (ft², ft, cy). 3 compute endpoints. For tank/storage volumes use a tank API; for concrete mix a concrete API.

api.oanor.com/earthwork-api

Highway Vertical Curve API

Vertical (parabolic) road-curve geometry as an API, computed locally and deterministically — the K-value, profile-elevation and design-length numbers a highway engineer or surveyor lays a crest or sag curve out with. The geometry endpoint takes the incoming and outgoing grades and the length and returns the algebraic grade difference A = g2 − g1 (negative is a crest, positive a sag), the K value = length ÷ |A| (the headline number on every design chart), the high or low point offset −g1·L/A from the PVC, and — given the PVI station and elevation — the PVC and PVT coordinates and the turning-point station and elevation. The elevation endpoint evaluates the parabola at any station: elevation = PVC elevation + (g1/100)·x + (A/(200·L))·x², with the instantaneous grade g1 + (A/L)·x that sweeps smoothly from g1 to g2 — the smooth change of grade that makes the ride and sight line comfortable. The min-length endpoint gives the AASHTO minimum length for stopping sight distance: crest L = A·S² ÷ 2158 and sag (headlight) L = A·S² ÷ (400 + 3.5·S), with the controlling K, because a crest hides the road over the hump and a sag limits the headlight reach at night. Everything is computed locally and deterministically, so it is instant and private. Ideal for highway- and rail-design tools, surveying and civil-engineering utilities, and CAD/GIS profile work. Pure local computation — no key, no third-party service, instant. US units (ft, %, mph). 3 compute endpoints. For horizontal curves use a horizontal-curve API; for slope conversion a slope API.

api.oanor.com/verticalcurve-api

Highway Horizontal Curve API

Horizontal road-curve geometry as an API, computed locally and deterministically — the curve-element, stationing and design-radius numbers a highway engineer, surveyor or civil-design tool lays out a road or railway curve with. The geometry endpoint takes the radius and the intersection (deflection) angle and returns the full simple circular curve: the tangent T = R·tan(Δ/2), the curve length L = R·Δ in radians, the long chord LC = 2R·sin(Δ/2), the middle ordinate M = R(1−cos(Δ/2)) and the external distance E = R(sec(Δ/2)−1), plus the degree of curve (arc definition) = 5729.578 ÷ R, the US shorthand for sharpness. The stations endpoint lays the curve out from the PI: the PC (point of curvature) = PI − tangent and the PT (point of tangency) = PC + curve length — and it reminds you the PT is reached along the arc, not by adding the tangent again. The min-radius endpoint gives the minimum radius for a design speed (AASHTO) R = V² ÷ (15·(e + f)), where e is the superelevation and f the side-friction factor, the banking-plus-grip that holds a vehicle in the turn. Everything is computed locally and deterministically, so it is instant and private. Ideal for highway- and rail-design tools, surveying and civil-engineering utilities, and CAD/GIS road layout. Pure local computation — no key, no third-party service, instant. US units (ft, mph). 3 compute endpoints. For slope and grade use a slope API; for open-channel drainage a Manning API.

api.oanor.com/horizontalcurve-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.

Banked Curve 3

Meta 1

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

GET /v1/bank-angle

Ideal banking angle for a design speed

Playground

Parameters

Custom headers

Language: Client:

GET /v1/flat-curve

Unbanked curve speed & radius limits

Playground

Parameters

Custom headers

Language: Client:

GET /v1/speed

Safe speeds on a banked curve

Playground

Parameters

Custom headers

Language: Client:

GET /v1/meta

Spec

Playground

Custom headers

Language: Client:

Code snippets

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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Banked Curve API

API health

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Related APIs

Circular Motion API

Earthwork Volume API

Highway Vertical Curve API

Highway Horizontal Curve API

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