🚗📐 Driving into Data: How Math Models Reveal Road Risks Using Vehicle Dynamics & Geometry

📊 What’s the Equation Behind Road Safety?

Safety ≠ Just luck. It's a complex mathematical function of:

🔁 Vehicle dynamics (speed, acceleration, braking)
📏 Geometric features (curve radius, lane width, grade)
🌦️ Non-geometric elements (weather, signals, lighting)

We turn these factors into real-time safety predictors using 🚘 Connected Vehicle (CV) data + 🔢 Mathematical modeling.

🧠 The Research Formula

Let’s define:

Surrogate Safety Measures (SSMs) = Indicators 🚨 that predict crash risk before it happens!

Using math-based indicators like:

TTC (Time to Collision)
PET (Post-Encroachment Time)
DRAC (Deceleration Rate to Avoid Crash)

📈 We analyze the derivatives of danger across different roads and traffic scenarios.

🛣️ Data Inputs (The Variables)

Equation Inputs (X):

🚙 Vehicle data: position(t), velocity(t), acceleration(t)
🛤️ Geometry: curve radius, slope, cross-section
🌦️ Conditions: weather, congestion, signal status

These values form a time series matrix — fed into math models to estimate SSMs as functions of space and time.

🤖 Modeling It Mathematically

We apply:

📐 Multivariate regression for impact quantification
💡 Machine learning to detect nonlinear patterns
📊 Probability distributions to estimate crash likelihood
🧠 Deep learning to predict safety violations across space-time

Think of it like a dynamic function of safety:

Safety(t) = f(vehicle dynamics, geometry(x,y), conditions, driver behavior)

📌 Key Findings (Math in Motion)

✅ Certain road designs (like sharp curves + low banking) consistently increase SSM violations
✅ High acceleration changes → more critical TTC events
✅ Poor weather + complex geometry → exponential rise in PET occurrences
✅ Mathematical models accurately classify 85% of near-miss cases

🧠📐 Why Math Matters in Mobility

Mathematics isn't just for classrooms — it's saving lives on the road!

📉 SSMs predict risk faster than crash reports
📡 Real-time connected vehicle data feeds dynamic safety functions
🧠 Math helps planners simulate “what if” crash scenarios before infrastructure is built

🚀 Impact & Future Scope

🔮 Create AI safety advisors in CVs that compute SSMs live
📍 Pinpoint risky roads using math heatmaps
📊 Recommend safer road designs with predictive geometry simulations
🧪 Combine math + sensors + behavior = the next-gen road safety equation ✅

🧮 Conclusion: Math is the Co-Pilot

By turning vehicle behavior and road geometry into mathematical models, we give cities the tools to predict and prevent crashes — before they occur.
🧠🛣️ Math isn’t just part of the solution. It is the solution.