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API · /froude-api

Froude Number API

healthy 4,153 Subscribers

Froude-number hydrodynamics as an API, computed locally and deterministically. The number endpoint computes the Froude number Fr = v/√(g·L) — the dimensionless ratio of inertial to gravitational forces — from a velocity and a characteristic length, classifies the flow as subcritical (Fr<1, tranquil), critical (Fr=1) or supercritical (Fr>1, rapid), and returns the critical velocity √(g·L) at which Fr=1; the velocity endpoint inverts it to v = Fr·√(g·L). The channel endpoint gives the open-channel Froude number from a flow velocity and depth, the flow regime, and the critical depth y_c = (q²/g)^(1/3) for the unit discharge q = v·y — the boundary between tranquil and shooting flow used in spillway and weir design. The hull-speed endpoint computes the displacement hull speed of a boat from its waterline length, v = 1.34·√(L_wl in ft) knots, the wave-making speed limit where the bow and stern waves equal the hull length, returned in knots, m/s and km/h with the corresponding Froude number — a 10 m waterline gives about 7.7 knots. Gravity defaults to 9.80665 m/s². Everything is computed locally and deterministically, so it is instant and private. Ideal for naval-architecture, marine, hydraulics, civil-engineering, river-modelling and fluid-mechanics-education app developers, spillway, weir and hull-design tools, and simulation software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 4 endpoints. This is the Froude number and flow regime; for Manning open-channel discharge use a Manning API.

#froude-number #hydrodynamics #open-channel #hull-speed #naval-architecture #developer-tools
api.oanor.com/froude-api
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/api/froude-api/openapi.json
/api/froude-api/llms.txt

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API health

healthy
Uptime
100.00%
Server probes · 24h
Avg latency
79 ms
Server probes · 24h
Subscribers
4,153
active
Total calls
95
last 7 days
status Full status page → · 15 probes/24h

Pricing

Pick a tier — billed monthly, cancel anytime.

Free

Free

  • 4,700 calls / month
  • 2 requests / second
  • Hard cap (429 above quota, no overage)
  • 4,700 calls/month
  • 2 req/sec
  • Froude number + regime + critical depth
  • No credit card
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Starter

€5.50 /month

  • 47,000 calls / month
  • 6 requests / second
  • Hard cap (429 above quota, no overage)
  • 47,000 calls/month
  • 6 req/sec
  • Open-channel regime, hull speed
  • Email support
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Pro

€15.50 /month

  • 218,000 calls / month
  • 15 requests / second
  • Hard cap (429 above quota, no overage)
  • 218,000 calls/month
  • 15 req/sec
  • Spillway, weir & hull-design pipelines
  • Priority support
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Mega

€48.00 /month

  • 1,260,000 calls / month
  • 40 requests / second
  • Hard cap (429 above quota, no overage)
  • 1,260,000 calls/month
  • 40 req/sec
  • Platform scale
  • Dedicated SLA
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Related APIs

Other APIs with overlapping tags.

Weir Flow API — oanor API marketplace

Weir Flow API

Weir flow maths for open-channel discharge measurement as an API, computed locally and deterministically. The rectangular endpoint computes the flow over a rectangular sharp-crested weir, Q = (2/3)·Cd·b·√(2g)·H^1.5, from the crest width and the head of water above the crest — and solves the head back from a known discharge. The vnotch endpoint computes the flow over a triangular V-notch weir, Q = (8/15)·Cd·√(2g)·tan(θ/2)·H^2.5, from the notch angle and head, the most accurate weir for small flows because the discharge varies with the head to the power 2.5. The broadcrested endpoint computes the flow over a broad-crested weir, Q = Cd·(2/3)^1.5·√g·b·H^1.5 ≈ Cd·1.705·b·H^1.5, the rugged field structure used for river gauging. Each device carries its standard discharge coefficient (rectangular 0.62, V-notch 0.58, broad-crested 0.85) which you can override, and each solves either the discharge from a measured head or the head required for a target discharge. Everything is computed locally and deterministically, so it is instant and private. Ideal for hydrology, irrigation and civil-engineering tools, flow gauging in channels and treatment plants, stormwater and water-resource apps, and fluid-mechanics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is weir overflow discharge; for uniform open-channel flow use a Manning API and for differential-pressure pipe metering use an orifice API.

api.oanor.com/weir-api

 Open Channel Flow API — oanor API marketplace

Open Channel Flow API

Open-channel flow maths as an API, computed locally and deterministically with the Manning equation. The flow endpoint computes the discharge and velocity of water in an open channel — rectangular, trapezoidal, triangular or circular (a part-full pipe) — from the flow depth, the channel dimensions, the channel slope and the Manning roughness coefficient n: it works out the flow area, the wetted perimeter and the hydraulic radius, then applies Q = (1/n)·A·R^(2/3)·S^(1/2) and V = Q/A, reporting the discharge in cubic metres per second and hour, litres per second, cubic feet per second and US gallons per minute. The normal-depth endpoint reverses it: given a target discharge it solves for the normal depth by bisection and returns the resulting area, velocity and a discharge check. The roughness endpoint is a reference of typical Manning n values, from smooth PVC (0.009) and concrete (0.013) through earth and gravel to rocky natural streams (0.05); pass a material name or an explicit n. Dimensions are metric (metres by default, or cm, mm, ft, in). Everything is computed locally and deterministically, so it is instant and private. Ideal for civil and drainage engineering tools, stormwater and culvert design, irrigation and hydrology apps, and environmental modelling. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is open-channel (Manning) hydraulics; for full-pipe flow rate from diameter and velocity use a pipe-flow API.

api.oanor.com/manning-api

 Ship Stability API — oanor API marketplace

Ship Stability API

Ship initial-stability maths as an API, computed locally and deterministically — the metacentric-height, righting-moment and rolling-period numbers a naval architect, ship officer or marine-surveyor judges a vessel by. The metacentric-height endpoint gives GM = KM − KG, the single most important stability figure: the height of the metacentre (set by the hull form and draught) above the centre of gravity (set by how the ship is loaded), with a classification from a dangerous negative GM, through tender and comfortable, to a stiff GM that rolls violently — naval architects aim for the middle, because too little is unsafe and too much is hard on cargo and crew. The righting-moment endpoint gives the small-angle righting arm GZ ≈ GM · sin(heel) and the righting moment (GZ × displacement) that pushes the ship back upright, valid up to roughly 7–10° before the true GZ curve bends away. The roll-period endpoint gives the natural transverse rolling period T = 2π·k / √(g·GM) from the GM and beam — the same relation sailors run in reverse as the rolling-period test, where a suddenly longer roll warns that GM has dropped. Everything is computed locally and deterministically, so it is instant and private. Ideal for naval-architecture and ship-design tools, marine-surveyor and loading-software utilities, maritime-training apps and stability dashboards. Pure local computation — no key, no third-party service, instant. Initial-stability estimates — use full KN cross-curves for large angles. 3 compute endpoints. For hull speed and design ratios use a sailing API.

api.oanor.com/shipstability-api

 Sailing & Hull Design API — oanor API marketplace

Sailing & Hull Design API

Sailing and naval-architecture maths as an API, computed locally and deterministically — the hull-speed and design-ratio numbers a sailor, boat-shopper or yacht designer sizes a boat with. The hullspeed endpoint gives the theoretical displacement speed limit from the waterline: hull speed = 1.34 × √LWL (feet) in knots, so a 25-foot waterline tops out around 6.7 knots (7.7 mph, 12.4 km/h) — with a tunable coefficient up to about 1.5 for light, easily-driven hulls, since planing boats leave the formula behind entirely. The ratios endpoint computes the two classic performance numbers: the Sail Area/Displacement ratio, SA/D = sail area ÷ (displaced volume in ft³)^⅔ using displaced volume = displacement ÷ 64 lb/ft³ for seawater — around 16–18 is a typical cruiser and 20-plus is sporty — and the Displacement/Length ratio, DLR = (displacement in long tons) ÷ (0.01 × LWL)³, where under 200 is light and over 300 is heavy, each returned with a class label. The ballast endpoint gives the ballast ratio = ballast ÷ displacement × 100, a rough proxy for stiffness and sail-carrying power that most cruisers hit near 35–45 %. Everything is computed locally and deterministically, so it is instant and private. Ideal for sailing, boating, marine, yacht-brokerage and boat-design app developers, boat-comparison and rig-sizing tools, and naval-architecture calculators. Pure local computation — no key, no third-party service, instant. Imperial units. Live, nothing stored. 3 compute endpoints. Design-ratio estimates, not a velocity prediction program.

api.oanor.com/sailing-api

Frequently asked questions

Quick answers about pricing, quotas, and integration.

How do I get an API key for Froude Number API?
Sign up for free at oanor.com, generate an API key from the developer dashboard, and call Froude Number API with the x-oanor-key header. No credit card needed for the free tier.
What's the rate limit for Froude Number 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 Froude Number API cost?
Froude Number API has a free tier with 100 calls / month. Paid plans start at €5.50 / 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 Froude Number API GDPR-compliant?
All requests to Froude Number 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/froude-api/SOME_PATH \
  -H "x-oanor-key: oanor_test_..."
const res = await fetch("https://api.oanor.com/froude-api/SOME_PATH", {
  headers: { "x-oanor-key": "oanor_test_..." }
});
const data = await res.json();
$ch = curl_init("https://api.oanor.com/froude-api/SOME_PATH");
curl_setopt($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/froude-api/SOME_PATH",
    headers={"x-oanor-key": "oanor_test_..."},
)
print(r.json())

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