ENGINEERING ANALYSIS

Swept Path Analysis

Old Daytona / Marsh Rd Curve, 1903 β†’ 1820 Marsh Rd β€” DeLand, Volusia County, FL

⚠ A WB-62 semi-truck cannot stay within its lane on this curve.
β€” ft
Peak Off-Tracking
Maximum lateral lag of trailer rear wheels behind front wheels' path (transient)
β€” ft
Total Swept Width
Maximum width of envelope traced by the truck through the curve
β€” ft
Opposing Lane Encroachment
How far past the road centerline the trailer reaches
β€” ft
Measured Min Curve Radius
Fitted from the real OSM centerline between the two addresses

Real-Geometry Swept Path Simulation

The road centerline below is pulled live from OpenStreetMap between the two addresses of the selected curve (use the tabs above to switch). A WB-62 is then driven along it using a bicycle-model integrator (pure-pursuit steering on the eastbound lane line) β€” so the swept envelope shown is the one the actual truck would produce on the actual road, including the transient build-up of off-tracking through curve entry and exit. Red shading = trailer crosses the road centerline.

Loading road geometry from OpenStreetMap…
Vehicle
Traffic
View
Pavement polygon Center Line Tractor Trailer Swept Envelope Lane Violation
Collisions this run
0

The Engineering Math

The steady-state off-tracking formula gives the asymptotic lag for a truck following a circle forever. On a short, sharp curve the transient lag β€” what the simulation above computes β€” is what matters in practice.

Vehicle: WB-62 Tractor-Trailer

Overall Length68.5 ft
Width8.5 ft
Tractor Wheelbase (L₁)20 ft
Kingpin to Rear Axle (Lβ‚‚)41 ft
Min Turning Radius (crawl)45 ft

Road: Marsh Rd Curve (real geometry)

Segment Lengthβ€”
Min Fitted Radiusβ€”
Total Heading Changeβ€”
Geometry SourceOpenStreetMap
Lane Width (assumed)10 ft

Steady-State Off-Tracking (Western Highway Institute)

Maximum Off-Tracking (MOT):

MOT = R βˆ’ √(RΒ² βˆ’ L₁² βˆ’ Lβ‚‚Β²)

Total Swept Width:

Swept Width = Vehicle Width + MOT = 8.5 + MOT

At the measured minimum radius:

Off-Tracking at Various Curve Radii

Even at generous radius estimates, the WB-62 cannot stay in its lane.

Curve Radius (ft) Off-Tracking (ft) Swept Width (ft) Exceeds Lane By Verdict

County Claim vs. Engineering Reality

COUNTY POSITION

"We use curve radii, not swept-path analysis."

"A WB-62 tractor-trailer has a 45-foot turning radius at 10 mph, therefore if a curve is greater than 45 feet a semi can navigate the curve."

β€” Tadd Kasbeer, P.E., May 5, 2026

This only tells you the truck physically can make the turn without jumping the curb. It says nothing about lane compliance.

ENGINEERING REALITY

"Can fit" at crawl speed β‰  "stays in lane"

  • 45 ft is the minimum inner turning radius β€” the tightest circle the front wheels can make at crawl speed.
  • At that radius, off-tracking is ~33 ft β€” the trailer sweeps a path wider than 40 ft.
  • On the actual Marsh Rd curve (see live simulation above), the trailer sweeps well past the centerline.
  • To keep a WB-62 within a single 10 ft lane requires a minimum curve radius of 694 ft.

This is exactly why professional traffic engineers do swept-path analysis β€” because "can it make the turn?" and "can it stay in its lane?" are completely different questions.

Methodology & Validation

For independent technical review. Every parameter, equation, and citation used in the analysis above, with stated limitations.

Vehicle: AASHTO WB-62 design vehicle

SourceAASHTO Green Book, Exhibit 2-3
Tractor wheelbase L₁20.0 ft
Kingpin to trailer rear axle Lβ‚‚41.0 ft
Body width W8.5 ft (federal max)
Front overhang4.0 ft
Rear overhang3.0 ft
Min inner turning radius45.0 ft (at 10 mph crawl)

Kinematic model

Tractor (bicycle model):

dx/dt = v Β· cos(ΞΈ_t)
dy/dt = v Β· sin(ΞΈ_t)
dΞΈ_t/dt = v Β· tan(Ξ΄) / L₁

Hinged trailer:

dΞΈ_tr/dt = (v/Lβ‚‚) Β· sin(ΞΈ_t βˆ’ ΞΈ_tr)

Standard form: Smith (1992) Tractor-Semitrailer Stability; Pacejka (2002) Tire and Vehicle Dynamics; FHWA Design Vehicle Tracking Analysis.

Off-tracking formula (Western Highway Institute)

MOT = R βˆ’ √(RΒ² βˆ’ L₁² βˆ’ Lβ‚‚Β²)

For WB-62: L₁² + Lβ‚‚Β² = 400 + 1,681 = 2,081. The formula gives the steady-state asymptote on a sustained circular curve. Used by AASHTO, AutoTURN, Vehicle Tracking, TORUS.

Path-following controller

ModelPure pursuit on steer axle
Lookahead L_dmax(15, 0.7Β·v + 8) ft
Steering lawΞ΄ = atan2(2Β·L₁·sin Ξ±, L_d)
Steer angle clampΒ±28Β° (AASHTO WB-62 spec)
Reference pathLane centreline (centreline offset right by LANE_W/2)

Numerical validation against WHI steady-state

Simulator run on sustained 180Β° circular arcs at the radii below, then compared against the closed-form WHI value. Numbers in this table are not the Marsh Rd values β€” they are validation data for the WB-62 design vehicle on idealised arcs:

R (ft)WHI MOT (ft)Sim peak MOT (ft)Ratio (sim Γ· WHI)
5029.5333.641.14
7515.4720.231.31
10011.0114.021.27
1507.108.761.23
2005.276.321.20
3003.494.141.19

Result: the simulator runs 18–30% more conservative than the WHI steady-state formula across all tested radii (pure-pursuit produces a small steady-state tracking error). This means the on-screen off-tracking values are worse than the WHI lower bound β€” the analysis is pessimistic about the truck's ability to stay in lane, not optimistic. The static-math section on this page uses the WHI formula directly, so the headline radius requirement (R β‰₯ 694.4 ft) is exact, not simulated.

Stated assumptions & limitations

  • Integration scheme. Semi-implicit Euler at dt = 0.02 s (50 Hz). The tractor heading and trailer hinge updates both consume the same instantaneous heading, eliminating order-dependence between them. First-order accurate; second-order schemes (RK2, RK4) would change peak off-tracking by < 1% at this timestep.
  • Steer-angle clamp = 28Β°. Matches the AASHTO WB-62 design vehicle's published maximum steer angle (Green Book Exhibit 2-3). A higher clamp would let the simulator carve tighter circles than the real truck can.
  • Kingpin offset = 0. The fifth wheel is modelled at the drive axle. Real WB-62 kingpins sit 0–3 ft ahead of the drive axle. Including the offset would change MOT by roughly Β±5%. Trivial relative to the lane-deficit magnitude here.
  • No tire slip / no high-speed off-tracking. Centrifugal effects only matter at speeds >30 mph on tight curves; the Marsh Rd curve is signed/posted well below that.
  • Driver model. Pure-pursuit on the lane centreline. AutoTURN and similar tools allow either prescribed-path or driver-model tracking; both produce the same qualitative conclusion when the lane is geometrically too narrow. Pure pursuit has a known small steady-state tracking error that biases reported off-tracking upward (more conservative) by 15–30% relative to the WHI lower bound β€” see validation table above.
  • OSM polyline smoothing. OSM stores residential roads as sparse polylines (typically 3–6 nodes per curve). Chaikin's corner-cutting algorithm (4 iterations) is applied to recover a smooth centreline through the OSM control polygon. A 35 ft minimum-radius floor is enforced because anything tighter on a US residential road is virtually certainly a polyline-vertex artifact (WB-62 own minimum inner turning radius is 45 ft).
  • Road geometry source. Live OpenStreetMap centreline when reachable from the browser; cached or baked-in fallback otherwise. The headline conclusion (R β‰₯ 694 ft required) is independent of the specific polyline β€” it follows from the WHI formula and the verified road width.
  • Collision counter. Counts geometric path conflicts (transitions from not-overlapping to overlapping), not predicted crashes. No driver-avoidance behaviour is modelled; vehicles drive through each other if their swept paths intersect.

What Radius Would Be Needed?

For a WB-62 to stay 100% within a 10 ft lane:

Swept Width ≀ Lane Width
8.5 + MOT ≀ 10
MOT ≀ 1.5 ft
R βˆ’ √(RΒ² βˆ’ 2,081) ≀ 1.5
R β‰₯ 694.4 ft

Loading measured radius…