Cannonball Monte Carlo Simulation

10,000-iteration Monte Carlo model: OSRM route geometry × TomTom traffic × vehicle physics
Vehicle Comparison
Vehicle Sustained Speed (mph) Median Time P10 P90 Spread (min) Avg Stops
Key Insight: Traffic luck (P10–P90 spread of ~3h 20m) dwarfs vehicle differences (~1h 44m). A lucky Explorer beats an unlucky Sedan Diesel 8.6% of the time.

Why similar speeds, different times? All three 111 mph vehicles face identical traffic in each sim run — the gap comes from fuel stops. The 535d's smaller aero profile (CdA ~0.68 m²) gives it ~15+ mpg at cruise, needing only 2 stops. The Q7 V12 TDI shares the diesel efficiency advantage but its SUV body (CdA ~1.03 m², 50% more drag) burns fuel faster, forcing 3 stops. The Sedan Gas matches the 535d's sleek shape but gasoline's lower energy density means 4 stops. Each stop costs ~6 minutes — so the spread between 2 and 4 stops is the full 12-minute vehicle gap you see above. The Q7 partially claws back time with its higher top speed (170 vs 155 mph), recovering ~4 minutes on open segments where the 535d is speed-limited.
Record-Breaking Probability
Monte Carlo Results (10,000 iterations): Under Stowell's exact traffic conditions (Sun 9 PM → Mon evening, Aug 25–26 2024), the Sedan Diesel has a 6.7% chance of beating the COVID-era record (25:39). The Audi Q7 V12 TDI sits at 6.3%, Sedan Gas at 6.6%, and the Explorer at just 0.04%. Increasing simulation count from 10k to 100k would tighten the confidence intervals on these percentages (~±0.3% → ±0.07%) but would NOT change the underlying distribution spread — that's driven by real traffic variance in the TomTom data, not sampling noise.
Time Distribution — 10,000 Iterations per Vehicle
Each distribution shows the full range of outcomes from traffic luck. The overlap between vehicles shows that a lucky run in a slower car often beats an unlucky run in a faster one.
Speed Profile — Sedan Diesel (535d) vs Route
P95 band shows that drivers regularly hit 150+ mph on open highway (NM, AZ). Traffic hotspots at NYC, OKC, and LA drop speeds to 20-60 mph.
Optimal Departure Time — Sedan Diesel (535d)
Bottom Line

Among vehicles capable of sustaining 111 mph, 99.98% of the variation in crossing time comes down to traffic — pure luck. The difference between a P10 run and a P90 run is over 3 hours. The difference between the best and worst vehicle at that speed is 3 minutes.

The only thing left within a driver's control is how often they stop for fuel. That's a function of three things: fuel capacity (tank size + aux), fuel efficiency (aerodynamic drag is the dominant factor at these speeds), and fuel energy density (diesel packs ~13% more energy per gallon than gasoline). The 535d wins on all three — small frontal area, diesel efficiency, and enough range to cross the country in just two fills. Everything else is weather.

Related Analysis
535d Thesis → Explorer Interceptor → Q7 V12 TDI vs PIU → Fuel Math → Aero Analysis → Stowell Traffic Segments →