November 3, 2026 · v1.5
A preliminary scenario, not a statewide inventory
The annualization panel uses the working assumptions supplied for this project. They are editable scaling inputs, not official counts. A complete Michigan-left maneuver counts once, even though it visits several control points. Ordinary U-turns and diverted through movements must not enter the intended-left total.
| Quantity | Working estimate | Sensitivity range | Role in model |
|---|---|---|---|
| Individual Michigan-left crossovers | 1,000 | 700–1,500 | Context and descriptive average cost per crossover |
| Share of left-turn opportunities | About 0.2% | About 0.1–0.5% | Context only; never scales operating cost |
| All annual left maneuvers in Michigan | 12 billion | 7–20 billion | Contextual denominator for traffic share |
| Annual intended Michigan-left maneuvers | 550 million | 200 million–1.1 billion | Primary annual exposure, N |
| Michigan-left share of actual turns | 4.58% from rounded central inputs | Roughly 1–16% | Derived context; not applied again as a multiplier |
The ranges test uncertain assumptions. They are not statistical confidence intervals. The broad 1–16% range combines separate volume endpoints; it is not a fitted distribution. The main panel allows changing all three annual Michigan-left exposure scenarios, the total-left denominator and the crossover count.
Source audit and derivation
FHWA-HRT-09-060, chapter 3 (2010) describes more than 700 directional crossovers on Michigan’s state highway system. These are individual openings, not complete intersections. It does not establish a current count across state and local road owners. The adjustment to 1,000 is a provisional project assumption.
Surber’s 2005 Michigan geographic-information presentation reports 307,949 network intersections, defined by three or more centerline approaches, including private roads. It is an old, broad count rather than a legal-left-turn inventory. Using 300,000 junctions, three assumed left-turn opportunities per junction, and two assumed routes served per crossover gives 1,000 × 2 ÷ (300,000 × 3) = 0.22%. Shared openings, driveway access, prohibited turns and geometry make this the weakest contextual estimate. It is not a count of the percentage of intersections with Michigan lefts.
MDOT’s 2025 roadway statistics report annual vehicle-miles in thousands: the total 98,722,480 corresponds to 98.72248 billion miles. The table identifies 2025 data submitted in June 2026. It measures travel, not left turns.
AAA Foundation’s 2024 American Driving Survey gives a national average trip distance of 12.7 miles. The project uses an assumed 12.5 miles per vehicle trip and 1.5 left maneuvers per trip: 98.72 billion ÷ 12.5 × 1.5 ≈ 11.85 billion lefts, rounded to 12 billion. Applying a personal-driving average to all Michigan traffic is approximate; 1.5 lefts is not a measured Michigan statistic. Trip lengths of 10–15 miles and 1–2 lefts per trip span approximately 6.58–19.74 billion, rounded to 7–20 billion.
For Michigan lefts, 1,000 openings × an assumed 1,500 intended left maneuvers/day × 365 = 547.5 million/year, rounded to 550 million. The unrounded estimates imply about 4.6% of actual turns. The UI uses the rounded inputs directly: 550 million ÷ 12 billion = 4.58%. At 1,000 openings, this implies 1,507 intended-left maneuvers per crossover per day. It is a descriptive average, not an observed count or equal-flow assumption.
Two operational scopes
All differences are Michigan minus standard. Positive means added cost; negative means a saving. Each comparison uses the same demand cohort, origins, destinations and seed.
| Scope | Per-seed difference used for scaling | Interpretation |
|---|---|---|
| Intended-left drivers only | Michigan left-cohort mean − standard left-cohort mean | Direct effect on intended-left drivers; excludes effects on other movements |
| All affected traffic | (Michigan full-cohort total − standard full-cohort total) ÷ matched intended-left count | All traffic effects per intended-left equivalent under the simulated movement mix |
Network exposure is N × (external entrants ÷ intended-left entrants), computed within each seed. The default 20% left-turn mix implies approximately five external system visits per intended left. This expansion requires a representative mix and nonoverlapping study systems; the same vehicle may visit different systems on one journey, but an overlapping segment or delay must not be charged twice. It is not an estimate of unique people or unique annual vehicles.
Annual arithmetic and uncertainty
For each seed and selected scope:
- Annual fuel difference = N × fuel difference in US gallons.
- Annual vehicle-hours = N × full-trip difference in seconds ÷ 3,600.
- Annual operating subtotal = annual gallons × assumed USD/gallon + annual vehicle-hours × assumed USD/vehicle-hour.
The default $3.50/US gallon and $20/vehicle-hour are illustrative scenario inputs, not current price quotes or official economic guidance. Time is valued per vehicle-hour, so no extra passenger-occupancy factor is applied. Enter a consistently defined valuation and dollar year when replacing these assumptions. Fuel expenditure and time value are different components: the subtotal is an economic scenario, not all cash spending.
Full-trip time includes detour driving, queue time, turning and acceleration losses. Fuel already includes detour distance, idling and each modeled restart, including separate U-turn and return-signal starts. Displayed queue savings, restart fuel and detour fuel are components, not extra charges. Do not add them to totals again. One additional 10-second difference at 550 million maneuvers corresponds to 1,527,778 vehicle-hours/year.
Annual operations always use the actual matched crash-free simulations retained by the engine, even when the animation displays incident closures or the 1,000× demonstration. They do not subtract a recorded delay or divide an amplified result by 1,000. This keeps arbitrary rare-event sampling and demonstrations out of the operating extrapolation.
The panel averages annual results across paired seeds. Its 95% Student-t interval uses the per-seed total cost and n−1 degrees of freedom, retaining covariance between time and fuel. One seed has no interval. The interval measures simulation sampling variation only. The 200M/550M/1.1B rows are separate exposure assumptions, not confidence bounds. Censored, unmatched or zero-left cohorts block annualization; small left samples and excess approximate queue storage are flagged.
Crash costs are a separate conditional scenario
Version 1.5 activates a provisional FHWA cost preset with economic and comprehensive options. Costs are national per-crash values in 2024 dollars. Independent severity distributions for Standard and Michigan start from the same Michigan statewide 2024 all-road proportions. Four groups have source-based mixtures; the combined head-on/object/overturn group remains unknown. The user can edit either layout separately or retain custom per-group costs.
The default rate source uses the applied replay base rates and type shares as an explicitly illustrative sensitivity scenario. Their full-system geographic boundaries remain unverified. Changing the replay multiplier or incident on/off switch does not affect annual monetization. The table reports priced-group subtotals, expected unpriced crashes and coverage; no incomplete value is a bound on the full difference.
Alternatively, enter custom rates per million unique external entrants and confirm compatible boundaries, crash definitions, periods and exposure. A complete Michigan-left maneuver enters once despite repeated control visits. Expected annual type counts multiply these rates by the implied all-entrant exposure, never by left-turn counts alone.
For each layout, type cost = sum over K/A/B/C/O of severity probability × FHWA crash-unit cost. Annual cost difference = Michigan expected count × Michigan type cost − Standard expected count × Standard type cost. Economic and comprehensive are alternatives; comprehensive already includes economic cost. Injury costs are not multiplied again by occupants or vehicles.
A combined operational-plus-crash scenario requires network scope, complete valuations, confirmed custom-rate compatibility and matching dollar years. It is not available for the provisional replay-rate preset, even if all severity rows are completed. Operations remain based on true crash-free runs, preventing double counting of incident delay/fuel. Full provenance, unit costs, severity shares and expected counts are retained in exports. Detailed sources, mappings and calculation audit.
What this calculation leaves open
One demand/timing scenario cannot represent every Michigan site and hour. A stronger annual study would weight observed crossover volumes and hourly turning mixes by geometry, lane arrangements, signal control, coordination, congestion, vehicle fleet and season. Capital construction, land, maintenance, emissions, vehicle wear, route changes, induced demand, pedestrians and physical spillback remain outside this subtotal. The standard shared lane and dedicated left-pocket alternatives can produce materially different comparisons. Neither layout is optimized in this experiment.
The full downloadable model includes annual-tests.cjs, run-annual-study.cjs and analysis/annual-study.json. Run node annual-tests.cjs to verify accounting and node run-annual-study.cjs to reproduce the 20-seed shared-lane, left-pocket and coordinated-red-turn scenarios.
Complete traffic methods · Crash evidence · Return to annual costs