Model 2.0
Public defaultEmpirical decision: not assessed
Method and Mathematics
Model 2.0 public default91 current and preserved method records
Follow every step from road geometry to comparative output
Read each model in its actual dependency order: where a value comes from, what the formula does, what it produces and whether it contributes to the road headline.
85
Typeset equations
6
Algorithms and rules
118
Constants and thresholds
3
Preserved historical steps
Interpretation boundary. Road Risk produces comparative model output under stated assumptions. It does not calculate observed collision probability, issue an official safety rating, recommend a legal speed or reproduce a Road Safety Authority assessment.
Model ledger
Read every method in its correct model context
A mathematical expression can be implemented correctly while the model using it still lacks empirical validation.
Current model status
Model 2.0.0 is the public default
Model 3.2
Controlled previewEmpirical decision: insufficient evidence
Model 3.3 geometry candidates
Diagnostic onlyEmpirical decision: insufficient evidence
Software verification and deployment status are reported separately from empirical evidence. No model output is an official safety rating or collision prediction.
The register below carries these statuses into every record: Model 2.0 is the deployed comparison model, Model 3.2 is the exact-section controlled preview with insufficient evidence, and Model 3.3 candidates cannot alter the App result.
Guided calculation
Follow each model in dependency order
The R238 chain distinguishes sequential calculations, parallel branches, branch selection, multiplication, numerical bounds, whole-road aggregation and separate diagnostics.
Guided R238 calculation
Follow the value from source evidence to the road headline
The chain distinguishes steps that continue, run in parallel, select a branch, apply a bound or aggregate sections. Every shown R238 value comes from the production model snapshot.
Open this R238 example in the App- Road
- Malin Road, R238
- Road headline
- 0.092%
Worked scope: Local section 34 of 38, followed by the complete-road aggregate.
Step 1 of 8Road, scenario and model inputs
Start with the reviewed road and declared scenario
Starting inputs. This is the source state. Nothing has been combined into a comparative output yet.
Comes from
This chain starts with the external road, scenario and model inputs listed below.
In plain language
In plain language
The calculation must begin from an attributable road, scenario and model version before any branch is evaluated.
R238 result
59 frozen centreline coordinates; local section 34 of 38.
Show operations, inputs and calculation safeguards
How the calculation works
- 1Read the road
Use the frozen OpenStreetMap centreline and tags rather than requesting a live provider.
- 2Choose the local section
Inspect station 3630 m to 3740 m while preserving all other sections for the road aggregate.
- 3Retain provenance
Keep observed tags, scenario choices, fallbacks and model constants distinguishable.
Inputs and where they came from
- Frozen road geometry
- 59 WGS84 coordinates
- Road or source data
- Provides the centreline and road tags.
- Scenario speed
- 80 km/h
- Scenario choice · km/h
- Sets the speed used by physical comparisons.
- Effective friction
- 0.7
- Scenario choice
- Represents the selected vehicle, surface and condition context.
- Traffic exposure input
- 9000 vehicles/day (road class proxy)
- Road or source data · vehicles/day
- Supplies the exposure proxy used to form the traffic factor.
Assumptions
- • Mapped centreline geometry is used as a proxy for the travelled alignment.
Safeguards
- • Invalid geometry or unavailable values are retained as unavailable rather than silently replaced with favourable values.
Limitations
- • The frozen road is a repeatable software example, not an empirical validation case.
Produces
Reviewed calculation state
Section 34: 110 m
A provenance-labelled input bundle ready for the two Model 2 branches.
Continues to
Why this step exists
Without a fixed input state, changes in geometry, scenario or fallbacks could be mistaken for changes caused by the equation itself.
Interpretation boundary. Model 2.0 produces comparative output under declared assumptions. It is not an observed collision probability, official safety rating or legal-speed recommendation.
View the wider method chapter map
- 01 · Road data and provenance
Public road geometry, tags, assumptions, fallbacks and units enter the calculation with their source retained.
- 02 · Coordinate and distance processing
Coordinates are cleaned, measured, projected and located along a road centreline.
- 03 · Road cleaning and section construction
The road is divided into bounded local evidence sections with explicit tail and cap rules.
- 04 · Heading, turn, curvature and radius
Heading changes and station-aligned geometry describe how the mapped centreline bends.
- 05 · Speed, friction and stopping comparisons
Simplified physical relationships compare speed, curvature, friction, reaction and braking demand.
- 06 · Scenario, vehicle and road context
Selected conditions, vehicle properties, road tags and traffic proxies modify the relevant model branches.
- 07 · Model 2.0 calculation
The public-default model combines baseline and curvature branches before traffic and road aggregation.
- 08 · Model 3.2 calculation
The controlled preview uses exact 100 m sections and local signed-curvature evidence.
- 09 · Route, Hotspot and Isochrone methods
Spatial tools reuse model outputs with separate sampling, clipping, coverage and cap rules.
- 10 · Statistics and Graphs
Distribution summaries describe position, spread and tails within a sampled comparison set.
- 11 · Observed collision comparison
RSA records remain an external historical context used by evaluation procedures.
- 12 · Presentation
Percent conversion, fixed scales, clipping and colour interpolation affect display only.
- 13 · Model 3.3 diagnostics
Candidate geometry estimators are compared without changing the App result.
Worked mathematics
Calculate the same frozen R238 road through both current models
Every displayed substitution and result is composed from the current production trace at build time. The page does not maintain a copied set of model outputs.
Open the production trace browser
Use this advanced view to compare the canonical trace records, substitutions and results after following the guided dependency chain above.
Frozen real-road walkthrough
Malin Road, R238
OpenStreetMap way 302735492, version 21
Geometry and Inputs
Speed Conversion
Converts the scenario speed from kilometres per hour to metres per second.
Real OpenStreetMap centreline geometry, frozen for repeatable software demonstration. It is not a surveyed lane alignment, collision record, safety rating or empirical validation case. The two model versions may construct different local sections and their outputs are not observed collision probabilities.
Controlled examples
Small examples for branches one road cannot show clearly
These are explanatory fixtures, not named-road results or empirical validation cases. Open an example to see its given values, calculated result and purpose.
Haversine distanceOpen exampleClose example
Given: (53.000°, −7.000°) to (53.000°, −6.999°)
Calculated result: Production Haversine helper: 66.92 m.
What this demonstrates: Shows why latitude affects the east-west distance represented by one degree.
Signed heading wrapOpen exampleClose example
Given: 179° followed by −179°
Calculated result: Production heading-wrap helper: +2°, not −358°.
What this demonstrates: Preserves turn direction across the ±180° boundary.
Constant-radius arcOpen exampleClose example
Given: A controlled circular arc with radius 200 m
Calculated result: Known curvature 1/R = 0.005 m⁻¹.
What this demonstrates: Separates geometry-method recovery from real-road uncertainty.
Short final sectionOpen exampleClose example
Given: A 430 m road divided into 100 m sections
Calculated result: 5 sections: 100 m, 100 m, 100 m, 100 m, 30 m; total 430 m.
What this demonstrates: Shows why the final section is shorter without being discarded.
Length-weighted meanOpen exampleClose example
Given: Outputs 0.2 and 0.8 over lengths 100 m and 25 m
Calculated result: (0.2×100 + 0.8×25) / 125 = 0.32.
What this demonstrates: Prevents a short section from carrying the same road-wide weight as a long section.
Midrank percentileOpen exampleClose example
Given: Values 1, 2, 2, 4 with selected value 2
Calculated result: Production percentile helper: (1 + 0.5×2) / 4 = 0.50.
What this demonstrates: Handles tied model outputs without arbitrary ordering.
Histogram and KDEOpen exampleClose example
Given: Values 1, 2, 2, 4; two requested histogram bins
Calculated result: Production helpers return bin counts 3 and 1 and KDE bandwidth 0.379.
What this demonstrates: Shows that graph shape depends on a declared display method, not new road evidence.
Missing evidence and clippingOpen exampleClose example
Given: Unavailable curvature and an output above the 2% display maximum
Calculated result: Curvature remains unavailable; only the colour position is clipped while the exact output remains visible.
What this demonstrates: Shows that missingness and visual clipping do not alter model values.
Complete register
Search every equation, algorithm and supporting method
The register reconciles the complete historical audit with current formula definitions, Model 3.2 geometry, spatial tools, presentation rules and diagnostic methods.
Open only the records you need, or prepare the entire method for printing. Exact equations use KaTeX; procedures remain ordered algorithms rather than being disguised as equations.
More filters
Showing 10 of 91 matching steps · 91 total
Constants, thresholds and defaults
Inspect every material value that controls a calculation, fallback or display rule
Unsourced project choices are identified directly. A value appearing in a formula does not make it an external standard.
Showing 10 of 118 matching constants · 118 total
C001Earth radius6,371,008.8 msupporting method · public default · Low risk
Purpose
Haversine/projection
Source or rationale
Standard mean Earth radius
Basis
road risk heuristic
Applicable model
2.0.0 or shared supporting method
Limitation: Interpret with the stated purpose, model version and source rationale.
C002Gravity9.81 m/s^2supporting method · public default · Low risk
Purpose
Physics equations
Source or rationale
Established approximation
Basis
engineering simplification
Applicable model
2.0.0 or shared supporting method
Limitation: Interpret with the stated purpose, model version and source rationale.
C003Responsible-driver factor0.015supporting method · public default · High risk
Purpose
Curvature annual branch
Source or rationale
No source found
Basis
road risk heuristic
Applicable model
2.0.0 or shared supporting method
Limitation: Road Risk design choice; no validating source recorded.
C004Baseline coefficient1.5e-6 per mmodel output · public default · High risk
Purpose
Baseline raw
Source or rationale
No source found
Basis
road risk heuristic
Applicable model
2.0.0 or shared supporting method
Limitation: Road Risk design choice; no validating source recorded.
C005Curvature minimum step2 mavailability · public default · Medium risk
Purpose
Point filtering
Source or rationale
Road Risk stability choice
Basis
road risk heuristic
Applicable model
2.0.0 or shared supporting method
Limitation: Interpret with the stated purpose, model version and source rationale.
C006Curvature epsilon1e-6 kmavailability · public default · Low risk
Purpose
Divide guard
Source or rationale
Numerical guard
Basis
numerical guard
Applicable model
2.0.0 or shared supporting method
Limitation: Interpret with the stated purpose, model version and source rationale.
C007Mean-curvature lower anchor0.8 rad/kmmodel output · public default · High risk
Purpose
Score normalisation
Source or rationale
No source found
Basis
road risk heuristic
Applicable model
2.0.0 or shared supporting method
Limitation: Road Risk design choice; no validating source recorded.
C008Mean-curvature upper anchor4 rad/kmmodel output · public default · High risk
Purpose
Score normalisation
Source or rationale
No source found
Basis
road risk heuristic
Applicable model
2.0.0 or shared supporting method
Limitation: Road Risk design choice; no validating source recorded.
C009Sharp-curvature lower anchor2 rad/kmmodel output · public default · High risk
Purpose
Score normalisation
Source or rationale
No source found
Basis
road risk heuristic
Applicable model
2.0.0 or shared supporting method
Limitation: Road Risk design choice; no validating source recorded.
C010Sharp-curvature upper anchor12 rad/kmmodel output · public default · High risk
Purpose
Score normalisation
Source or rationale
No source found
Basis
road risk heuristic
Applicable model
2.0.0 or shared supporting method
Limitation: Road Risk design choice; no validating source recorded.
Preserved methods
Historical models remain readable without being presented as current
Model 1, Model 3.0 and Model 3.1 artifacts remain provenance records. Their formulae and limitations are discoverable through the Historical lifecycle filter in the register.
Historical methods explain older imports without being promoted or silently recalculated. Known limitations, including the preserved Model 2 radius construction and superseded RGB presentation rule, remain attached to their records. Current citations or statuses are not inherited merely because a title is similar.
Reading rule
Correct mathematics and validated road-safety prediction are different claims
Speed, radius, friction and stopping relationships are simplified comparisons, not surveyed design checks or driving advice. The Annual Comparative Index is model-specific, not an expected collision count. RSA history can support future evaluation, but current context displays do not prove a named-road result.