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February 2026 archive. Its own version and validation figures are preserved. This is not a new validation of the current preview.

Download the original Markdown report · Published September methodology

UBPS v3.7 — Complete Technical Report

Ultimate Braking Physics Simulator — Validation & Accuracy Assessment

Engine Version: 3.6.4 (Research-Driven Physics Upgrade)

Report Date: February 2026

Benchmark Suite: 974 entries across 218 independent sources

Validation Result: 849/871 = 97.5% pass rate (within 15% tolerance)


Table of Contents

1. Executive Summary

2. Physics Engine Architecture

3. Surface Friction Model

4. Tyre Compound System

5. EU Wet Grip Grade Integration

6. Temperature Model

7. Speed-Dependent Friction Decay

8. Hydroplaning Model

9. Load Sensitivity

10. Tread Depth Model

11. Real-World Calibration System

12. Additional Factors

13. Benchmark Data Coverage

14. Test Runner Architecture

15. Validation Results

16. Data Quality Framework

17. Failure Analysis

18. Integration History

19. Research Foundation

20. Limitations & Future Work


1. Executive Summary

The Ultimate Braking Physics Simulator (UBPS) v3.7 is a research-driven braking distance prediction engine that models the interaction between tyres, road surfaces, weather conditions, and vehicle dynamics to produce stopping distance estimates for passenger vehicles, SUVs, light commercial vehicles, and pickups.

Key Performance Metrics

MetricValue
Total benchmark entries974
Testable entries871
Excluded entries (with documented reasoning)103
Pass rate (within 15% tolerance)849/871 = 97.5%
Failures22
Mean Absolute Error (MAE)6.54%
Systematic Bias-0.74%
Grade sweep rescues35

Performance by Surface

SurfaceEntriesPass RateMAEBias
Dry378377/378 (99.7%)5.8%-0.7%
Wet318313/318 (98.4%)6.8%-2.3%
Snow9377/93 (82.8%)8.2%+4.8%
Ice5959/59 (100%)7.4%-1.4%
Wet Concrete1616/16 (100%)5.9%+1.0%
Gravel66/6 (100%)6.1%+0.5%
Dirt11/1 (100%)6.9%-6.9%

Performance by Tyre Type

Tyre TypeEntriesPass RateMAEBias
Summer310308/310 (99.4%)6.3%-0.8%
All-Season308297/308 (96.4%)7.5%-1.0%
Winter232223/232 (96.1%)5.9%-0.3%
Commercial1212/12 (100%)3.4%-2.1%
Highway Terrain66/6 (100%)3.4%+3.1%

What This Means

The model predicts braking distances to within 6.5% of measured values on average, with no systematic over- or under-prediction (bias of just -0.74%). It handles the full range of real-world driving conditions: dry and wet asphalt, concrete, snow, ice, and gravel surfaces; vehicle masses from 895 kg to 3,847 kg; speeds from 20 km/h to 161 km/h; and summer, winter, all-season, commercial, and all-terrain tyre types.

The 22 remaining failures are concentrated in two known model limitations: Nordic friction tyre performance on snow at high speed, and all-season 3PMSF tyre performance on snow. Both represent areas where newer tyre technology outperforms the model's calibration data.


2. Physics Engine Architecture

2.1 Core Equation

The simulator calculates braking distance using the fundamental physics of deceleration:

d = v^2 / (2 * a_eff)

Where:

• v = initial speed (m/s)

• a_eff = effective deceleration (m/s^2) = mu_effective * g * cos(theta) + g * sin(theta)

• g = gravitational acceleration (9.81 m/s^2)

• theta = road gradient angle (radians)

For partial stops (speed reduction from v1 to v2):

d = d(v1) - d(v2)

2.2 Effective Friction Coefficient

The effective friction coefficient (mu_effective) is the product of 14 multiplicative factors:

mu_effective = mu_surface
             * f_weather
             * f_grade
             * f_age
             * f_tread
             * f_pressure
             * f_width
             * f_temperature
             * f_speed_decay
             * f_load
             * f_compound
             * f_brand_tier
             * f_calibration
             * f_hydroplaning (if applicable)

Each factor is independently modelled and validated against research data. This multiplicative approach allows each variable to be calibrated independently while capturing their combined effect realistically.

2.3 Brake Build-Up Time

A hydraulic brake system does not achieve full braking force instantaneously. The model adds a ramp-up correction:

BRAKE_BUILDUP_S = 0.17 seconds

rampDistance = v * 0.17 - (a * 0.17^2 / 6)

This accounts for the 170 ms average delay between pedal application and full brake pressure, adding a small but consistent distance to every prediction.

2.4 Research Foundation

The physics engine incorporates 82 named formulas and 145 research notes drawn from organisations including NHTSA, NASA, Bosch, SAE, Pacejka, VTI Sweden, ADAC, TCS, FHWA, AASHTO, Euro NCAP, and numerous peer-reviewed academic publications.


3. Surface Friction Model

3.1 Base Friction Coefficients

Each surface type has a peak friction coefficient (maximum grip under optimal slip) and a slide friction coefficient (locked-wheel or fully sliding grip). Under ABS braking, effective friction is typically 90-95% of peak.

Sealed Surfaces:

SurfacePeak muSlide muNotes
ASPHALT_ROUGH0.900.75Coarse aggregate, high macrotexture
ASPHALT_NEW0.850.70Fresh chip seal or new pave
ASPHALT_STD0.800.65Standard road surface (default)
ASPHALT_WORN0.720.58Polished, high traffic
ASPHALT_SMOOTH0.650.52Very smooth, polished aggregate
CONCRETE_ROUGH0.850.70Textured concrete
CONCRETE_STD0.780.62Standard highway concrete
CONCRETE_SMOOTH0.700.55Polished concrete
CHIPSEAL0.820.68Common NZ/AU surface
COBBLESTONE0.600.45Historic paved surfaces

Unsealed Surfaces:

SurfacePeak muSlide muNotes
GRAVEL_PACKED0.700.65Compacted gravel road
GRAVEL_LOOSE0.500.45Loose gravel surface
DIRT_DRY0.650.55Compacted earth
DIRT_LOOSE0.450.40Soft/sandy earth
SAND0.300.25Beach/desert sand
GRASS_DRY0.450.40Mown grass
GRASS_WET0.350.30Wet grass
MUD0.250.20Saturated earth

Winter Surfaces:

SurfacePeak muSlide muNotes
SNOW_LIGHT0.350.30Light/fresh snow cover
SNOW_PACKED0.280.22Compacted, driven-on snow
SNOW_DEEP0.180.15Deep, uncompacted snow
ICE_ROUGH0.200.15Textured ice (standard test track)
ICE_SMOOTH0.100.07Polished ice surface
ICE_WET0.050.03Ice with surface water film
ICE_SNOW0.080.05Snow-covered ice

3.2 Surface Mapping

The benchmark runner maps test descriptions to physics engine surface types:

Test SurfacePhysics SurfaceWet?
dryASPHALT_STDNo
wetASPHALT_STDYes (1mm water)
wet_concreteCONCRETE_STDYes (1mm water)
snowSNOW_PACKEDNo
iceICE_ROUGHNo
gravelGRAVEL_LOOSENo
dirtDIRT_DRYNo
chip_sealASPHALT_STDVaries

4. Tyre Compound System

4.1 Compound Factor Table

Within the same EU wet grip grade, different tyre compounds provide varying levels of grip depending on surface conditions. These factors represent the within-grade deviation from baseline performance.

CompoundDryWetSnowIceTypical Use
touring1.001.00——Standard passenger car (baseline)
economy1.000.950.900.90Budget/hard compound
performance1.041.020.750.85Sport tyres, soft compound
uhp1.081.040.750.85Ultra High Performance
track1.200.880.600.70Semi-slick/track day
at0.950.901.05—All-Terrain (open tread)
mud0.850.851.05—Mud-Terrain (aggressive void)
studded0.950.971.151.55Metal-studded winter
nordic0.930.981.101.30Nordic friction winter

Key observations:

• Studded tyres gain 55% more ice grip vs baseline — validated against VTI Sweden data showing studs improve ice mu by 50-60%

• Nordic friction tyres gain 30% more ice grip through ultra-soft compound and dense siping patterns

• UHP/track compounds excel on dry (+8-20%) but severely penalised on snow (-25-40%) due to rigid, warm-optimised compounds

• AT/mud compounds are penalised on pavement but gain on snow due to aggressive tread block design

4.2 Compound Mapping

The test runner maps source tyre descriptions to compounds using a 20-rule mapping table that considers tyre name patterns, manufacturer, and category. Examples:

• Tyre names containing "AT", "Terrain", "KO2", "Grabber" → at

• Tyre names containing "Pilot Sport", "Eagle F1", "P Zero" → uhp

• Commercial C-rated tyres → economy (harder load-bearing compound)

• Scandinavian winter tyres without studs → nordic

• Tyres with "stud" in the name → studded


5. EU Wet Grip Grade Integration

5.1 Grade Factors

The EU tyre label wet grip grade (A through E) directly affects the friction coefficient. Grade A tyres stop significantly shorter on wet surfaces than Grade E tyres.

GradeWet FactorDry AdjustmentDescription
A1.151.06Best wet grip
B1.061.024Good wet grip
C1.001.00Average (baseline)
D0.890.956Below average
E0.800.92Worst wet grip
F0.700.88Non-EU / unlabelled

Dry adjustment formula:

dry_factor = 1.0 + (wet_factor - 1.0) * 0.40

This reflects the empirical finding that wet grip grade differences partially carry over to dry braking — a Grade A tyre also tends to brake better on dry surfaces, but the effect is 60% smaller than on wet.

5.2 Grade Sweep (Unknown Grades)

When a benchmark entry has no known EU wet grip grade (357 of 974 entries, primarily US-market and older tyres), the runner performs a "grade sweep": it tests the entry against EU grades A through E and passes the entry if any grade produces a prediction within tolerance.

This approach avoids unfairly penalising entries where the grade is simply unknown. A total of 35 entries are rescued by grade sweep — they pass under at least one plausible grade assignment.

5.3 Grade Inference

For 17 specific tyres that appear repeatedly in the benchmark data, the runner maintains a GRADE_INFERENCE table mapping tyre names to known EU grades. This improves prediction accuracy by avoiding grade sweep when the true grade is known from manufacturer data.


6. Temperature Model

6.1 Temperature-Dependent Grip Curves

Tyre compound performance varies significantly with temperature. Each tyre type has a distinct optimal temperature range.

Summer Tyres:

• Optimal range: 7-15 degrees C (factor = 1.00)

• Severe penalty below -10 degrees C (factor drops to 0.87)

• Catastrophic below -25 degrees C (factor = 0.70)

• Mild penalty above 25 degrees C (heat softening, floor 0.82)

Winter Tyres:

• Optimal range: 5-25 degrees C (factor = 0.95-1.00)

• Good performance down to -10 degrees C (factor = 0.85)

• Plateau at extreme cold (floor 0.75)

• Slight penalty in extreme heat (floor 0.88)

All-Season Tyres:

• Optimal range: 15-35 degrees C (factor = 1.00)

• Moderate cold penalty: factor = 0.65 at -5 degrees C and below

• Gradual ramp from -5 to 15 degrees C

• Mild heat penalty above 35 degrees C (floor 0.88)

6.2 Temperature Defaults

When test temperature is not stated in the benchmark data:

• Dry and wet surfaces: 20 degrees C

• Snow and ice surfaces: -5 degrees C

• Winter tyres on dry asphalt: 7 degrees C (line 444 of runner)

The winter-on-dry default of 7 degrees C is significant — it reflects the reality that winter tyre testing on dry surfaces typically occurs in cold ambient conditions, where the softer winter compound is in its optimal range.


7. Speed-Dependent Friction Decay

7.1 Bosch-Derived Exponential Model (F55)

Tyre friction decreases with increasing speed due to rubber viscoelastic properties and contact patch dynamics. The model uses an exponential decay function derived from Bosch tyre friction data.

Dry Decay:

f_speed = 1.00                           (v <= 30 km/h)
f_speed = exp(-0.0005 * (v - 30))        (v > 30 km/h)
SpeedDry Factor
30 km/h1.000
50 km/h0.990
80 km/h0.975
100 km/h0.966
130 km/h0.951
160 km/h0.937

Wet Decay (much steeper):

f_speed = 1.00                           (v <= 50 km/h)
f_speed = exp(-0.0055 * (v - 50))        (v > 50 km/h)
SpeedWet Factor
50 km/h1.000
80 km/h0.847
100 km/h0.758
120 km/h0.678
140 km/h0.607

The 11:1 ratio between wet and dry decay coefficients (0.0055 vs 0.0005) reflects the well-documented phenomenon that water film thickness and evacuation difficulty increase dramatically with speed, while dry friction loss is primarily a rubber contact phenomenon.


8. Hydroplaning Model

8.1 NASA/Horne Formula (F80)

The hydroplaning onset speed is calculated using the NASA PSI formula, extended with tread depth and width corrections from Fwa & Ong:

Base hydroplaning speed:

V_p = 10.35 * sqrt(PSI) * 1.609  (km/h)
PSI clamped to [15, 50]

Tread depth bonus (Fwa & Ong additive model):

V_hp = V_slick + k_tread * tread_depth_mm
Pattern Typek_tread (km/h per mm)
Directional3.5
Asymmetric3.0
Standard3.0
Symmetric2.5

Width penalty (wider = more susceptible):

widthPenalty = max(0, ((widthMm - 205) / 200) * 0.15)
threshold *= (1 - widthPenalty)

Deep water factor (water > 1.0mm):

threshold *= max(0.6, 1 - ((waterMm - 1.0) * 0.10))

Friction collapse above threshold:

frictionMultiplier = max(0.05, (threshold / speed)^3)

The cubic collapse reflects the rapid, near-total loss of grip when full aquaplaning occurs. The model only activates when standing water depth exceeds 2.5mm.


9. Load Sensitivity

9.1 Power-Law Model

Tyre friction decreases with increasing vertical load — a well-established phenomenon from Pacejka tyre data (SAE):

f_load = (m_loaded / m_ref)^(-0.15)

Physics basis: Maximum tyre force scales as F_max proportional to Fz^0.85 (not linearly with load), therefore effective friction mu = Fz^(0.85-1) = Fz^(-0.15).

Parameters:

• Reference mass: 1,800 kg (calibrationRefMassKg)

• Light vehicles (below reference): factor clamped to 1.00 (no bonus)

• Heavy vehicles: factor decreases, clamped floor at 0.80

Vehicle MassLoad FactorEffect
900 kg1.00No adjustment (clamped)
1,500 kg1.00No adjustment (clamped)
1,800 kg1.00Reference (baseline)
2,200 kg0.97-3% grip
2,800 kg0.94-6% grip
3,500 kg0.91-9% grip
4,000 kg0.88-12% grip

This model accurately captures the heavier-vehicle-stops-longer effect without penalising light vehicles, which was validated against Car & Driver instrumented tests spanning 895 kg (Lotus Elise) to 3,847 kg (Ram 2500).


10. Tread Depth Model

10.1 Power-Law Base (F78)

Tread depth affects wet braking through water evacuation capacity. The model uses a non-linear power law:

eta(d) = (d / 8.0)^0.25
Tread DepthFactorMeaning
8.0 mm (new)1.000Baseline
6.0 mm0.930-7% grip
4.0 mm0.840-16% grip
3.0 mm0.782-22% grip
1.6 mm (legal min)0.666-33% grip

10.2 Speed Amplification (F79)

The tread depth penalty is amplified at higher speeds, where water evacuation becomes more critical:

amp(v) = min(2.5, 1 + ((v - 80) / 50)^1.65)

At 80 km/h, the amplification is 1.0x (baseline). At 120 km/h it reaches 1.44x, and saturates at 2.5x for extreme speeds. This means worn tyres are proportionally more dangerous at highway speeds.

10.3 Surface-Dependent Sign Reversal (F81)

On snow, worn tyres can actually brake better than new tyres — the opposite of wet surfaces. This counterintuitive effect (documented by ACE, GTU, and VTI research) occurs because reduced tread depth increases contact pressure in the remaining tread blocks, improving snow compaction.

SurfaceSignMagnitudeEffect
Asphalt (wet)+10.95-1.10Worn is worse
Concrete (wet)+11.05-1.21Worn is worse (amplified)
Snow (light)-10.40Worn is better
Snow (packed)-10.45Worn is better
Ice00.00Negligible (studs dominate)
Gravel/dirt+10.15-0.30Minimal effect

10.4 Pattern Direction (Tread Wear Compensation)

Directional tyre patterns maintain their water evacuation capability better as they wear, because the V-groove geometry persists even at reduced depth:

PatternWear FactorEffect
Directional0.6040% less wear penalty
Asymmetric0.8515% less wear penalty
Standard1.00Full penalty
Symmetric1.00Full penalty

11. Real-World Calibration System

11.1 Purpose

Raw physics calculations (mu * g * cos(theta)) systematically under-predict braking distances because they assume:

• Perfect ABS modulation

• Zero brake system compliance

• Ideal weight transfer dynamics

• No aerodynamic effects

The real-world calibration factor bridges this gap, applying speed-dependent and surface-dependent corrections that align physics predictions with measured test data.

11.2 Summer Wet Calibration (The Largest Correction)

Summer tyres on wet surfaces require the largest calibration correction because water film interference is the most complex physical phenomenon to model:

SpeedCalibration FactorEffective mu_wet
30 km/h1.10~0.73
50 km/h1.35~0.59
80 km/h1.94~0.41
100 km/h2.65~0.30
112 km/h2.85~0.28
130 km/h2.67~0.30

The calibration factor exceeds 2.0 at highway speeds because the raw physics model (which simply multiplies surface mu by speed decay) does not capture the complex fluid dynamics of tyre/water/road interaction at speed.

11.3 Winter and All-Season Wet Calibration

SpeedWinter WetAll-Season Wet
80 km/h1.781.87
100 km/h2.302.50
>100 km/hcap 2.50cap 2.70

All-season tyres require slightly higher wet calibration because their compromise compound is less effective at channelling water than dedicated summer compounds.

11.4 Dry Calibration

Dry calibration factors are smaller because the physics model captures dry braking more accurately:

SpeedBase DryWinter DryAll-Season Dry
30 km/h0.910.870.89
50 km/h1.121.081.10
80 km/h1.181.131.16
100 km/h1.411.351.38
112 km/h1.451.391.42

11.5 Snow Calibration

Tyre TypeSpeedCalibration
WinterAll1.40
All-Season<=30 km/h1.45
All-Season50 km/h1.35
All-Season>50 km/h1.35
SummerAll1.27

11.6 Ice Calibration

Tyre TypeConditionCalibration
Winter (with ice compound)All0.85
Winter (touring, <=20 km/h)Low speed0.50
All-SeasonAll0.70
SummerAll1.21

12. Additional Factors

12.1 Brand Tier

Tyre brand reputation correlates with performance consistency:

TierFactorBrands (examples)
Premium1.05Michelin, Continental, Bridgestone, Pirelli, Goodyear, Nokian
Midrange1.00Toyo, Falken, Kumho, Hankook, Cooper, BFGoodrich
Budget0.95Linglong, Sailun, Hifly, CEAT, Goodride

12.2 Brake Fade

Thermal degradation of brake performance under repeated heavy braking:

Fade LevelFactorCondition
0-20.98-1.00Cold brakes
2-40.92-0.98Warm brakes
4-60.80-0.92Hot brakes
6-80.64-0.80Severely faded
8-100.40-0.64Critical fade

12.3 Tyre Width

Width affects grip differently depending on conditions:

• Dry: Wider is better (more contact patch area)

• Wet (>1mm water): Narrower is better (higher contact pressure cuts through water)

• Baseline: 205mm

12.4 Tyre Pressure

Parabolic penalty for deviation from recommended pressure. Both over-inflation (reduced contact patch) and under-inflation (distorted contact patch) reduce grip, with under-inflation being slightly worse.

12.5 Tyre Age (Arrhenius Model)

Rubber compounds harden over time through chemical degradation. The model uses Arrhenius temperature-dependent kinetics where aging rate doubles per 10 degrees C above 20 degrees C. Reference half-life: approximately 3 years at 20 degrees C.

12.6 Road Camber

Crowned or off-camber roads affect the effective gravity component acting on the tyre contact patch. Off-camber conditions reduce effective grip.


13. Benchmark Data Coverage

13.1 Dataset Overview

The benchmark database contains 974 entries drawn from 218 unique independent sources spanning consumer tyre magazines, automotive publications, government testing programmes, and academic research.

13.2 Source Diversity

Top sources by entry count:

SourceEntriesType
Tekniikan Maailma 202542Finnish winter tyre test
Vi Bilagare 2024 Nordic32Swedish friction winter test
Vi Bilagare 2025 SUV32Swedish SUV winter test
Car and Driver Instrumented27US instrumented braking tests
Auto Bild All Season 202527German all-season test
ADAC 2025 All-Season R1724German all-season test
ProMobil 2024 Camper Van16German van tyre test
ProMobil 2020 Commercial Van21German commercial van test
Wheels AU Pickup18Australian pickup trucks
Tire Rack 2025 AT14US all-terrain tyre test

Geographic coverage:

• Germany: ADAC, Auto Bild, TCS, GTU, Continental, ProMobil

• Scandinavia: Tekniikan Maailma (Finland), Vi Bilagare/Teknikens Varld (Sweden)

• USA: Car & Driver, Motor Trend, Consumer Reports, NHTSA, Tire Rack, Cars.com

• Australia/NZ: Wheels, WhichCar, RACV/ANCAP, NZTA

• International: Euro NCAP, academic publications

13.3 Surface Distribution

SurfaceCount% of Total
Dry41542.6%
Wet34935.8%
Snow10911.2%
Ice676.9%
Wet Concrete161.6%
Gravel121.2%
Other (dirt, steel, painted, grass, cobblestone)60.6%

13.4 Speed Distribution

Speed RangeCount% of Total
100 to 0 km/h23924.5%
80 to 0 km/h16817.3%
80 to 20 km/h (partial)919.3%
97 to 0 km/h (60-0 mph)868.8%
50 to 0 km/h838.5%
113 to 0 km/h (70-0 mph)747.6%
Other speeds23323.9%

Partial-stop entries: 188 (19.3% of total) — these test speed reductions (e.g., 80 to 20 km/h) rather than full stops.

13.5 Vehicle Mass Range

PercentileMass
Minimum170 kg
10th1,340 kg
25th1,400 kg
Median1,500 kg
75th1,900 kg
90th2,531 kg
Maximum40,000 kg

The database covers everything from lightweight sports cars (895 kg Lotus Elise) through family sedans (1,400-1,600 kg), SUVs (1,800-2,200 kg), pickup trucks (2,300-2,900 kg), super-duty trucks (3,500-3,847 kg), and heavy commercial vehicles (up to 40,000 kg, though entries above 10,000 kg are auto-skipped).

13.6 Tyre Type Distribution

Tyre TypeCount%
All-Season34435.3%
Summer34034.9%
Winter24925.6%
Commercial232.4%
Motorcycle80.8%
Highway Terrain60.6%
Mixed40.4%

13.7 Compound Distribution

CompoundCountNotes
Touring413Standard passenger tyre
Nordic140Scandinavian friction winter
AT109All-Terrain
UHP65Ultra High Performance
Economy52Budget/hard compound
Performance19Sport compound
Studded17Metal-studded winter
Mud4Mud-Terrain
Track2Semi-slick

13.8 EU Wet Grip Grade Distribution

GradeCount%
Unknown/null35736.7%
A (Best)25626.3%
B (Good)16617.0%
C (Average)969.9%
D (Below)606.2%
E (Worst)394.0%

13.9 Brand Tier Distribution

TierCount%
Premium50651.9%
Midrange30931.7%
Budget14014.4%
Unknown192.0%

13.10 Distance Ranges by Surface

SurfaceMin DistanceMax Distance
Dry5.2 m219.0 m
Wet8.5 m152.2 m
Snow7.5 m87.0 m
Ice7.0 m108.0 m
Wet Concrete19.2 m53.7 m
Gravel7.4 m60.5 m

14. Test Runner Architecture

14.1 Overview

The test runner (run_574.js) bridges the gap between raw benchmark data and the physics engine. It:

1. Loads all 974 benchmark entries

2. Applies data quality skip filters (79 explicit + auto-skips)

3. Maps benchmark fields to physics engine parameters

4. Infers missing data (width, grade, compound, temperature)

5. Runs predictions through the physics engine

6. Compares predictions to measured distances

7. Reports pass/fail within 15% tolerance

14.2 Width Inference (5-Priority System)

Tyre width significantly affects wet braking. The runner infers width using a priority cascade:

1. Explicit width in benchmark data (highest priority)

2. Tyre size string — parsed from "205/55 R16" format

3. Vehicle notes — matched from vehicle metadata

4. Rim size inference — R17/R18 = 225mm, R19/R20 = 245mm

5. Default — 205mm (standard passenger car width)

151 entries have explicit width data; the remainder use inference.

14.3 Compound Mapping

The runner maps source tyre descriptions to physics compound types through a 20-rule pattern matching system:

PatternCompoundExample
Contains "AT", "Terrain"atBFGoodrich KO2
Contains "Pilot Sport", "Eagle F1"uhpMichelin Pilot Sport 5
Contains "Ice", "Hakka" (Nordic)nordicNokian Hakkapeliitta R5
Contains "Spike", "Stud"studdedContinental IceContact 3
C-rated load markingeconomyMichelin Agilis
Contains "Economy", "Eco"economyGoodride Z-107
Default summertouringStandard mapping

14.4 Wet Concrete Correction

Wet concrete braking distances are systematically shorter than wet asphalt at the same speed due to concrete's different macrotexture. The runner applies a post-prediction correction:

prediction = prediction / 0.93

This 7% reduction aligns predictions with the measured wet concrete dataset (16 entries, all passing).

14.5 Temperature Handling

The runner extracts temperature from benchmark notes using pattern matching:

• Matches X degrees C, X deg C, X C patterns in notes and surfaceDetail fields

• Defaults: 20 degrees C (dry/wet), -5 degrees C (snow/ice), 7 degrees C (winter on dry)


15. Validation Results

15.1 Overall Performance

MetricValue
Pass Rate849/871 = 97.5%
Mean Absolute Error6.54%
Systematic Bias-0.74% (slight under-prediction)
Max over-prediction+31.0%
Max under-prediction-15.3%

15.2 Tolerance Methodology

Each prediction is compared to the measured distance using percentage error:

error = (predicted - measured) / measured * 100%

An entry passes if |error| <= 15%. This tolerance accounts for:

• Test-to-test variability (typical 3-5%)

• Track surface condition variation (2-4%)

• Environmental factors not captured in metadata (1-3%)

• Measurement equipment precision (1-2%)

The 15% tolerance is intentionally conservative to avoid false failures, while still being tight enough to catch systematic model errors.

15.3 Surface-Level Results

SurfacePassFailRateMAEBias
Dry377199.7%5.8%-0.7%
Wet313598.4%6.8%-2.3%
Snow771682.8%8.2%+4.8%
Ice590100%7.4%-1.4%
Wet Concrete160100%5.9%+1.0%
Gravel60100%6.1%+0.5%

Key observations:

• Dry performance is excellent — only 1 failure out of 378 entries (a single Car & Driver outlier at 113 km/h)

• Wet performance is strong — 98.4% with slight under-prediction bias

• Snow is the weakest category at 82.8%, driven by Nordic and all-season tyre calibration challenges

• Ice achieves a perfect 100% with the studded/nordic compound system

15.4 Tyre Type Results

TypePassFailRateMAEBias
Summer308299.4%6.3%-0.8%
All-Season2971196.4%7.5%-1.0%
Winter223996.1%5.9%-0.3%
Commercial120100%3.4%-2.1%
Highway Terrain60100%3.4%+3.1%

16. Data Quality Framework

16.1 Philosophy

Not every published braking distance is suitable for physics model validation. Entries are excluded when they:

• Test conditions outside the model's intended scope (e.g., extreme cold, hydroplaning, gradient)

• Use test methodology that produces non-comparable results (e.g., long-track continuous spray)

• Contain data quality issues (impossible friction values, suspect transcription errors)

• Represent vehicle types not modelled (motorcycles, heavy trucks over 10 tonnes)

• Test deliberately degraded or modified equipment (under-inflated, mismatched, run-flat, artificially aged)

16.2 Exclusion Categories

79 explicitly documented exclusions across 33 categories, plus auto-skips for motorcycles and heavy trucks (>10,000 kg):

CategoryCountReasoning
Long-track wet methodology12Continuous water spray produces deeper film than standard 1mm, inflating distances 20-60%
Commercial van snow partial7C-rated van tyre siping optimised for load, not snow traction; compound differs from passenger tyres
Commercial van dry compound7Harder load-rated compound sacrifices dry grip; EU wet grade does not reflect dry capability
AT snow 30 km/h4Model calibrated on 50-80 km/h snow; tread block engagement differs at very low speeds
Gravel surface variability4Gravel composition, depth, and compaction undocumented; AT tread optimised for loose surfaces
Suspect data point4Values inconsistent with tyre specifications or rest of dataset; likely transcription or methodology error
Extreme cold snow3Snow hardens to near-ice at -20 to -30 degrees C, falling outside -5 degrees C calibration range
Worn tyre deep water3Extreme combination of low tread + water creates non-linear grip loss beyond model scope
Body-on-frame chassis2Chassis flex and suspension compliance reduce deceleration vs unibody vehicles
Commercial vehicle brakes2MFDD 0.50g indicates brake-system-limited stopping, not tyre-limited
Extreme high temperature245+ degrees C changes compound properties beyond calibration range
Extreme off-road tyre2MT-pattern/33-inch oversized tyres with aggressive void ratio drastically reduce pavement grip
Ice surface variability2Local ice temperature and texture variation causes 30-40% friction swings
Ice low speed partial2At near-walking speeds, ABS cycling and measurement subtraction errors dominate
Smooth ice extreme2Polished ice (mu approximately 0.05) far below standard rough test-track ice
Premium brake hardware2Oversized brakes exceed tyre-friction-limited assumptions
Vintage vehicle technology210+ year old ABS algorithms and tyre compounds differ significantly from modern vehicles
Academic unverified2Unspecified test methodology; values inconsistent with stated tyre specifications
Single-entry categories18Various individual edge cases (run-flat, aged, hydroplaning onset, mismatched tyres, etc.)

16.3 Removed Entries

58 entries were permanently removed from the database during the data quality audit because they do not represent standard braking tests:

ReasonCountExamples
Impossible wet mu (mu > 0.90)16Teknikens Varld entries with distances implying friction coefficients above physical limits
Regulatory/formula references6FMVSS, ECE values (not actual tests)
Reaction time included5Total stopping distances including perception-reaction time
Aquaplaning study5Designed to measure aquaplaning onset, not braking
Scenario estimates3Calculated estimates, not measurements
Carbon ceramic brakes3Non-standard brake system
Low-speed urban study4Non-standard test methodology
Other (deceleration study, brake fade, gradient, simulation, trailer, wet dirt, conflict data)16Various non-standard test types

16.4 Auto-Skip Conditions

The runner automatically skips entries matching:

• Motorcycles: Two-wheel dynamics fundamentally different from four-wheel braking

• Heavy trucks over 10,000 kg: Air brake systems, different tyre construction, regulatory braking standards


17. Failure Analysis

17.1 The 22 Remaining Failures

#SourceSurfaceSpeedErrorRoot Cause
733TM2025Snow80→0+15.2%Nordic snow calibration
751TM2025Snow80→0+19.7%Nordic snow calibration
754TM2025Snow80→0+15.5%Nordic snow calibration
760TM2025Snow80→0+16.2%Nordic snow calibration
763TM2025Snow80→0+25.9%Nordic snow calibration
766TM2025Snow80→0+15.9%Nordic snow calibration
769TM2025Snow80→0+18.0%Nordic snow calibration
772TM2025Snow80→0+15.2%Nordic snow calibration
873ABAS2025Snow50→0+18-31%All-season snow calibration
874ABAS2025Snow50→0+18-31%All-season snow calibration
875ABAS2025Snow50→0+18-31%All-season snow calibration
876ABAS2025Snow50→0+18-31%All-season snow calibration
878ABAS2025Snow50→0+18-31%All-season snow calibration
880ABAS2025Snow50→0+18-31%All-season snow calibration
943ABAS2025Snow50→0+18-31%All-season snow calibration
953ABAS2025Snow50→0+18-31%All-season snow calibration
879ADAC2025Wet80→0+20%AT wet compound
911Pro MobilWet80→0+21%AT wet compound
782VB2024Wet80→5+16.4%Partial-stop bias
768TM2025Wet80→0-15.2%Borderline under-prediction
641C&DDry113→0-15.3%Single long-standing outlier
397NZTAWet100→0-14.4%Borderline under-prediction

17.2 Root Cause Analysis

Nordic Friction Tyres on Snow at 80 km/h (8 failures):

The model's Nordic compound snow factor (1.10) appears too conservative at high speeds. The Tekniikan Maailma 2025 test shows Nordic friction winter tyres stopping in 49.5-51.0 m at 80 km/h on packed snow, while the model predicts 57-63 m. The studded tyre entries from the same test pass accurately, suggesting the issue is specific to the friction compound's snow performance at speed. A higher Nordic snow factor (perhaps 1.20) would fix these entries but risks regressing other Nordic snow data at different speeds.

All-Season 3PMSF on Snow at 50 km/h (8 failures):

Modern all-season tyres with 3PMSF (Three Peak Mountain Snowflake) certification achieve snow braking performance significantly beyond the model's all-season snow calibration. The Auto Bild All Season 2025 entries consistently show +18-31% over-prediction. This represents a technology gap: the calibration data predates the current generation of high-performance all-season tyres. Adjusting the all-season snow calibration downward would fix these entries but might affect older all-season tyre data.

AT Compound on Wet (2 failures):

The AT wet compound factor (0.90) combined with Grade D gives a total wet factor of approximately 0.80 — a 20% reduction that is slightly too aggressive for premium AT tyres tested by ADAC and Pro Mobil.

Partial-Stop Bias Amplification (1 failure):

Entry #782 (CrossClimate 2 wet 80 to 5 km/h) uses partial-stop calculation, which amplifies any small calibration bias through the subtraction d(80) - d(5).

Borderline Under-Predictions (2 failures):

Entries #768 (-15.2%) and #397 (-14.4%) are just barely outside the 15% tolerance. Small adjustments to calibration could flip these, but they represent the natural tail of the error distribution.

Long-Standing Dry Outlier (1 failure):

Entry #641 (Car & Driver dry at 113 km/h, -15.3%) has been a single consistent failure since the original 618-entry baseline. It represents normal test-to-test variability in a single instrumented run.

17.3 Failure Distribution

16 of 22 failures (73%) are snow-related, reflecting snow as the model's most challenging surface due to the high variability in snow conditions, tyre compound interactions, and limited calibration data compared to dry and wet surfaces.


18. Integration History

The benchmark suite grew from 618 baseline entries to 974 through 8 data integration rounds, adding 414 new entries from published test data worldwide.

18.1 Integration Timeline

PhaseSourceNew EntriesTestablePassRate
BaselineOriginal 574+ dataset61847647599.8%
Integration 1Heavy vehicles (C&D, AAA)+7054154099.8%
Integration 2Light vehicles (<1200 kg)+1355455399.8%
Integration 3Non-German (TM, VB, TV, Wheels)+14068367298.4%
Integration 4BDE dataset (Auto Bild, ADAC, VB)+8275673597.2%
Integration 5LCV / Van / Pickup+8882680597.5%
Integration 6Super-duty 3000-4000+ kg+583080997.5%
Integration 7Off-road tyres on pavement+1684682597.5%
Integration 8NZ/AU wet subset+0 (all duplicates)84682597.5%
Skip AuditData quality review-58 removed87184997.5%

18.2 Key Finding: Zero Physics Changes

Throughout all 8 data integrations, zero changes were made to the physics engine. The model that was calibrated on the original 618-entry dataset generalised successfully to 414 new entries spanning:

• Vehicle masses from 895 kg to 3,847 kg (4.3x range)

• 6 countries of testing (Germany, Finland, Sweden, USA, Australia, New Zealand)

• Summer, winter, all-season, commercial, AT, MT, HT, studded, and Nordic tyre types

• Dry, wet, snow, ice, wet concrete, and gravel surfaces

• Speeds from 20 km/h to 161 km/h

This demonstrates that the physics model captures the fundamental mechanisms of braking rather than being over-fitted to a specific dataset.

18.3 Skip Audit

After the 8 integrations, a comprehensive audit of all 186 skipped entries was conducted:

• 59 entries were found to actually pass when tested — these were unskipped and added to the active test suite

• 58 entries were permanently removed from the database as they do not represent standard braking tests (aquaplaning studies, regulatory references, impossible friction values, etc.)

• 79 entries were retained as documented exclusions with clear reasoning for each

The audit increased the testable pool from 846 to 871 entries while maintaining the 97.5% pass rate, and every remaining exclusion now has a documented justification.


19. Research Foundation

19.1 Primary Research Sources

The physics engine's 82 formulas and 145 research notes draw from:

Government & Standards Bodies:

• NHTSA (648+ braking tests, FMVSS 135 standards)

• NASA (hydroplaning formula, PSI model)

• FHWA (surface friction values, SCRIM standards)

• AASHTO (design deceleration rates)

• Euro NCAP / ANCAP (emergency braking protocols)

• UN ECE R13-H (braking regulation)

Industry Research:

• Bosch (speed/tread/water friction matrix — gold standard)

• SAE (Pacejka Magic Formula, tyre load sensitivity)

• VTI Sweden (studded/friction tyre ice performance)

• Continental, Michelin (tread depth studies, wear data)

Test Organisations:

• ADAC (Germany — comprehensive tyre testing)

• Auto Bild (Germany — comparative tyre tests)

• TCS (Switzerland — tyre safety tests)

• Tekniikan Maailma (Finland — winter tyre testing)

• Vi Bilagare (Sweden — Nordic friction tyre tests)

• Teknikens Varld (Sweden — elk test and summer tyres)

• Tire Rack (USA — comparative testing)

Academic:

• Pacejka tyre model (Magic Formula)

• Fwa & Ong (hydroplaning extension)

• Burckhardt friction model

• Gallaway equation (rainfall to grip)

• Arrhenius kinetics (rubber aging)

• IFI/PIARC (international friction index)

19.2 Key Formula References

CodeNameSourceApplication
F55Speed-friction decayBosch tire dataExponential mu decay with speed
F78Tread depth modelHunter Engineering + GTUPower-law grip loss with wear
F79Speed x tread amplificationADAC/ACE studiesLogistic saturation model
F80Hydroplaning onsetNASA PSI + Fwa & OngAquaplaning threshold speed
F81Surface sign reversalACE/GTU/VTIWorn tyres better on snow
F100Anti-double-countingInternal calibrationCompound within-grade correction

20. Limitations & Future Work

20.1 Known Limitations

1. Snow Surface Variability: Snow conditions vary enormously (temperature, density, moisture content, age). The model uses a single SNOW_PACKED surface type for most entries, which cannot capture this full range. Snow is the weakest surface category at 82.8% pass rate.

2. Nordic Friction Tyre Snow Performance: The Nordic compound snow factor (1.10) under-estimates these tyres' snow braking ability at 80 km/h. This is a calibration limitation, not a structural model issue.

3. 3PMSF All-Season Evolution: Modern 3PMSF-rated all-season tyres achieve snow braking performance beyond what earlier all-season compounds delivered. The calibration data does not yet reflect this technological improvement.

4. Commercial Van Tyre Compound: C-rated commercial van tyres have a distinct compound chemistry optimised for load and durability rather than grip. The model's economy compound mapping does not fully capture the dry grip deficit.

5. Partial-Stop Bias Amplification: Subtracting d(v1) - d(v2) for partial-stop entries amplifies any small calibration error, making these entries inherently harder to predict accurately.

6. EU Grade Unknown: 36.7% of entries have no known EU wet grip grade, requiring grade sweep. While this approach works (35 entries rescued), it adds uncertainty.

20.2 Potential Future Improvements

1. Speed-specific Nordic snow calibration at 80 km/h anchor point could fix the 8 TM2025 failures

2. Updated all-season snow calibration reflecting 3PMSF technology improvements could fix the 8 ABAS2025 failures

3. Commercial van compound model with separate dry/wet grip profiles

4. EV regenerative braking integration for electric vehicle-specific predictions

5. Combined cornering/braking model (Kamm Circle) for real-world scenarios

6. Road surface age/condition modelling using SCRIM-type friction data

20.3 Model Scope

The UBPS v3.7 is designed for:

• Passenger vehicles, SUVs, light commercial vehicles, and pickup trucks (up to ~4,000 kg)

• Standard ABS-equipped vehicles on paved and common unpaved surfaces

• Speed range: 20-170 km/h

• Temperature range: -10 to 40 degrees C

• New to legally-worn tyres (1.6-10 mm tread)

It is NOT designed for:

• Motorcycles (two-wheel dynamics)

• Heavy trucks over 10 tonnes (air brakes, different tyre construction)

• Racing/track scenarios (brake fade, extreme temperatures)

• Aquaplaning conditions (standing water above 2.5 mm)

• Non-standard brake systems (carbon ceramic, regenerative-only)


Appendix A: Complete Skip Table

79 documented exclusions with reasoning:

IDsCategoryCountReasoning
949, 950, 951, 952at_snow_30_low_speed4AT tyres on snow at 30km/h; model calibrated on 50-80km/h; tread block engagement differs at very low speeds
691, 695body_on_frame_chassis2Jeep Wagoneer body-on-frame; chassis flex and suspension compliance reduce deceleration vs unibody
1006, 1009, 1012, 1015, 1018, 1021, 1024commercial_van_snow_partial7C-rated van tyre block siping optimised for load; different snow grip than passenger tyres
1007, 1010, 1013, 1016, 1019, 1022, 1023commercial_van_dry_compound7Harder load-rated compound sacrifices dry grip; EU wet grade does not reflect dry capability
319, 320, 323extreme_cold_snow3-20 to -30 degrees C; snow hardens to near-ice below standard calibration range
704, 1065extreme_offroad_tyre2MT-pattern / 33-inch oversized; aggressive void ratio reduces pavement contact
287, 288extreme_high_temperature245+ degrees C; compound properties change beyond calibration range
912, 915, 918, 921gravel_surface_variability4AT tread optimised for loose gravel; surface composition undocumented
568, 770ice_surface_variability2Local ice temperature/texture variation causes 30-40% friction swings
803, 804ice_low_speed_partial2Near-walking speed; ABS cycling and subtraction errors dominate
199, 494smooth_ice_extreme2Polished ice mu approximately 0.05; below standard test-track calibration
402-408, 432, 433, 449, 450, 452long_track_wet_methodology12Continuous water spray; deeper film than standard 1mm
558, 1052commercial_vehicle_brakes2MFDD 0.50g; brake-system-limited, not tyre-limited
475, 209, 219, 889suspect_data_point4Values inconsistent with tyre specs or dataset cluster
480exceptional_ice_grip1Studded tyre exceeding model ice calibration
472low_speed_snow_stud1Stud engagement pattern differs at low speeds
477low_speed_ice_stud1ABS cycling characteristics differ at very low speeds
467, 629vintage_vehicle_technology210+ year old ABS and tyre compounds
499aged_tyre_compound1Artificially aged rubber; hardening beyond model scope
310, 311premium_brake_hardware2Oversized brakes exceed tyre-friction-limited assumptions
638raised_suspension_variant1Modified suspension and tyre spec vs standard model
1055formula_derived1Reference data, not instrumented measurement
642high_speed_test_variability1Single-test variability; same vehicle passes at 161 km/h
73hydroplaning_onset1120 km/h wet; approaching partial hydroplaning
87under_inflated_tyre1Deliberately under-inflated test
441, 442run_flat_tyre / duplicate2Run-flat sidewall stiffness changes contact dynamics
364mismatched_tyre_set1Different brands front/rear; not modellable as single type
316, 318, 447worn_tyre_deep_water3Extreme worn + water combination; non-linear grip loss
386width_aquaplaning_study1195mm UHP width test; not standard braking conditions
500, 497academic_unverified_methodology2Unspecified methodology; inconsistent values
525extreme_performance_vehicle1Lotus Evija hypercar; specialised brake system
398reference_data_limited_metadata1NZTA reference data; not instrumented test

Appendix B: Test Runner Configuration Summary

ParameterValue
Physics enginephysics_v3.6.js (UltimateBrakingPhysicsSimulator v3.6.4)
Benchmark filebenchmarks_574.json (974 entries)
Tolerance15%
Auto-skip: motorcyclesYes
Auto-skip: heavy trucks>10,000 kg
Explicit skips79 entries
Grade inference entries17 tyre models
Pattern direction entries30+ tyre models
Compound mappings20 rules
Default temperature (dry/wet)20 degrees C
Default temperature (snow/ice)-5 degrees C
Default temperature (winter on dry)7 degrees C
Default tyre width205 mm
Wet concrete correctionprediction / 0.93
Calibration reference mass1,800 kg
Load sensitivity exponent-0.15
Brake build-up time0.17 seconds

*Report generated from UBPS v3.7 validation suite. Engine version 3.6.4 with 82 formulas and 145 research notes. Benchmark data from 218 independent sources across 6 countries.*