Layer 2 consumes richer sail geometry (width stations / trapezoid stacks) and optional aero overrides from the sail schema. The result is an Edge Map that is not just colored squares, but a defensible engineering artifact: click any cell and trace the delta through coefficients, CE/CLR, depower, and provenance. Partner lofts and naval architects access these capabilities through Expert Mode.
← Overview Layer 3 (Loft) →Every computation in SailEdge™ by SailrScience follows the same cascade. Your ORC certificate enters at Step 1 as the certified baseline. Each subsequent step builds on the previous, and the output is a complete performance picture — with every number traceable back to the ORC data that anchored it.
For a behavior-level walkthrough of this cascade, see The Physics.
Your ORC certificate provides RM@1° — the certified stability anchor. The engine generates a full righting moment curve from 0° to 60° at 1° increments, using a GZ curve family keyed to that single value. Every step downstream builds on this curve.
For each sail configuration, the engine computes lift (CL), drag (CD), and side-force (CY) coefficients along with Center of Effort position (CEx, CEht). Upwind and downwind regimes use separate coefficient models — the aerodynamics above and below beam reach are fundamentally different. Apparent wind derives from the wind triangle.
Between 90° and 120° TWA, the engine blends upwind and downwind coefficients using a smooth λ function — C¹ continuous (smoothstep), no artificial crossover points. CL and CD are blended in coefficient space; derived force components follow. CE shifts are applied smoothly across the same λ window.
The engine runs iterative calibration loops that adjust CE position to match observed behavior. Two independent targets: helm load (rudder angle within expected bounds for the point of sail) and heel angle (compared against ORC heel data when available). CE adjustments are bounded to physically plausible ranges. Every adjustment emits provenance metadata — what moved, how far, and why.
The engine solves for the heel angle where aerodynamic heeling moment equals hydrostatic righting moment from Step 1. Deterministic bisection on [0°, 50°] — no convergence tolerance issues. The equilibrium heel is the physically correct answer for that sail configuration and wind condition, measured as a delta from ORC baseline.
When equilibrium heel exceeds the heel limit, the engine computes a depower factor: the ratio of available righting moment to demanded heeling moment. Five independent transform channels — lift reduction, drag increase, CE height drop, CE aft shift, and effective area reduction. The delta between full-power and depowered performance is what you see in the data.
Drive force, side force, final heel, rudder angle, boat speed, and VMG — all computed for this specific sail configuration at this specific wind condition. Each output carries provenance: RM source (ORC vs. estimate), CE calibration adjustments applied, depower status, and an overall stability confidence flag. Every number is a measured delta from your ORC-certified baseline.
ORC racing sails often differ in performance even when the headline numbers look similar (same area, same rig). Layer 2 captures the distribution of area and chord along the span using stacked stations (a trapezoid stack). That distribution drives centroid/CE placement, effective aspect ratio, induced drag, and ultimately the Edge Map delta.
Ai = ½ (ci + ci+1) · Δz
x̄i = (ci2 + cici+1 + ci+12) / (3(ci + ci+1))
z̄i = zi + Δz · (ci + 2ci+1) / (3(ci + ci+1))
c is chord length at each station and Δz is the vertical separation.
This captures squaretops/blockheads because chord can increase aloft.
C = Σ(Ai · ci) / Σ(Ai)
The centroid is purely geometric. The CE is where the aerodynamic force effectively acts. For simple sails, centroid is a strong proxy. For modern shapes (deep roach, forward-loaded Code/Asym), CE can be forward of the geometric centroid.
Layer 2 therefore treats CE as: geometric planform + bounded, sail-type-aware transforms + regime-aware blending. The transforms are designed to stay physically plausible and to preserve explainability.
When a sail includes an aero block in the sail schema, the model can consume bounded overrides and efficiency modifiers
(e.g., effective aspect ratio and regime-specific multipliers). This allows two sails with the same area to produce different Edge Map outcomes
based on planform quality and loft intent, without requiring a full rewrite of the physics engine.
The mainsail blankets the headsail on deep angles. The engine measures it.
Each headsail sample point is tested for mainsail occlusion. Blocked points receive a wake-attenuation weight:
w(d) = exp(−(d / d0)β)
Feff = Σ(ai · w(di)) / Atotal
A displacement hull can’t outrun its bow wave. The engine enforces a hull-speed fence — a displacement-derived upper bound beyond which predicted deltas lose physical meaning.
Vhull = 1.34 × √LWL
The Edge Map computes a speed delta for every cell in the TWA × TWS matrix. Each cell is a controlled comparison: baseline configuration vs. edge configuration, computed at identical wind conditions within the same regime.
Regimes are independent. A sail that gains 0.3 kt reaching doesn’t inherit credit from a different regime. Apples to apples, cell by cell.
Every delta carries its upstream signals: centroid CE, occlusion correction, hull-speed fence, depower status. Tap any cell and trace the number back through the pipeline.
The engine is stateless — the View sends boat, sails, and polars with every request. The physics engine retains nothing between computations. Same inputs produce the same outputs, every time. Partner environments maintain tuning profiles and model parameters in the application layer — the physics computation itself remains stateless.
Every computed point carries provenance: RM source (ORC certificate vs. estimate), CE calibration adjustments applied, depower status, and a confidence flag. When the Edge Map shows +0.3 kt, you can see whether that number is anchored to a full ORC stability curve or an estimated one — and whether the engine had to adjust CE to make the helm behave.
The delta is still real. The provenance tells you how much to trust it.
The model has been validated against 20+ ORC-certified boats, including a Cape 31 that won its class at Key West Race Week. Validation checks include: boat speed vs ORC target polars, force-balance behavior under depower, CE position vs helm angle, and heel convergence at stability limits.
Where the model diverges from an ORC target, provenance tags show exactly where the divergence originates — estimated RM, CE calibration offset, or aero coefficient bounds. The gap is visible, not hidden.
Every computed point produces outputs, constants, and diagnostic signals. On the public site we describe what they mean without exposing internal API key names.
| Output | Units | Description |
|---|---|---|
| Equilibrium heel | deg | Equilibrium heel before clamping — the raw physics answer |
| Final heel | deg | Final heel after depower clamp |
| Depower factor | 0–1 | Ratio of available RM to demanded heeling moment |
| Certified RM@1° | kg·m | ORC-certified righting moment (baseline anchor) |
| Righting moment at equilibrium heel | N·m | Righting moment at equilibrium heel |
| Righting moment at heel limit | N·m | Righting moment at heel limit (depower reference) |
| Heeling arm | m | Effective moment arm: CE height + CLR depth |
| Heeling moment (raw) | N·m | Heeling moment before depower |
| Heeling moment (post-depower) | N·m | Heeling moment after depower application |
| Output | Units | Description |
|---|---|---|
| Rudder angle (clamped) | deg | Rudder angle after clamping |
| Rudder angle (unclamped) | deg | Raw rudder angle before safety clamp |
| Helm load index | kN | Yaw-moment-to-arm ratio — helm load index |
| Yaw moment | kN·m | Net yaw moment from CE–CLR offset |
| CE–CLR longitudinal separation | m | Fore–aft distance between CE and CLR |
| Rudder force needed | N | Force required to balance yaw moment |
| Dynamic pressure (water) | Pa | Hydrodynamic pressure at boat speed |
| Output | Units | Description |
|---|---|---|
| Driving force | kN | Net forward driving force |
| Side force | kN | Net lateral (heeling) force |
| Boat speed | kt | Predicted boat speed (with depower coupling) |
| VMG | kt | Velocity made good toward wind or mark |
| % of ORC baseline polar | % | Performance as percentage of ORC baseline polar |
| Combined CE fore–aft | m | Combined CE fore–aft position (from mast datum) |
| Combined CE height | m | Combined CE height above deck |
| Combined CE lateral offset | m | Combined CE lateral offset under heel |
| Constant | Value | Notes |
|---|---|---|
| ρair | 1.225 kg/m³ | Standard sea-level air density |
| ρwater | 1025 kg/m³ | Seawater density |
| g | 9.81 m/s² | Gravitational acceleration |
| kts → m/s | 0.5144 | Knots to meters per second |
Layer 2 uses a small set of bounded tuning parameters to keep CE/CLR behavior physically plausible across the boat library. We do not publish parameter names or values publicly. Partner-private coefficient sets and overrides live in Layer 3 under NDA.
| Category | What it governs | Why it matters |
|---|---|---|
| CE geometry | CE height, fore–aft position, heel-induced shifts | Sets heeling arm and helm balance; drives heel and yaw moment |
| CLR geometry + dynamics | CLR position, depth, speed effects | Sets CE–CLR separation and lift response; affects helm load |
| Rudder + helm limits | Rudder lift slope and angle limits | Converts yaw moment into a feasible rudder angle and flags constraints |
| Depower thresholds | Heel limits and depower floors | Controls when the model transitions from full power to depowered behavior |
| Coupling + convergence | Iteration count and damping | Ensures stable, deterministic performance solutions across conditions |
Every computed point carries a diagnostic bitfield. When the engine encounters edge cases or physically unusual conditions, it flags them rather than hiding them. Public pages describe the signal meaning (not the internal bit numbers).