Old Daytona / Marsh Rd Curve, 1903 β 1820 Marsh Rd β DeLand, Volusia County, FL
β 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 OpenStreetMapβ¦
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.
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
Source
AASHTO Green Book, Exhibit 2-3
Tractor wheelbase Lβ
20.0 ft
Kingpin to trailer rear axle Lβ
41.0 ft
Body width W
8.5 ft (federal max)
Front overhang
4.0 ft
Rear overhang
3.0 ft
Min inner turning radius
45.0 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΄) / Lβ
Hinged trailer:
dΞΈ_tr/dt = (v/Lβ) Β· sin(ΞΈ_t β 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 β β(RΒ² β LβΒ² β LβΒ²)
For WB-62: LβΒ² + LβΒ² = 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
Model
Pure pursuit on steer axle
Lookahead L_d
max(15, 0.7Β·v + 8) ft
Steering law
Ξ΄ = atan2(2Β·LβΒ·sin Ξ±, L_d)
Steer angle clamp
Β±28Β° (AASHTO WB-62 spec)
Reference path
Lane 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)
50
29.53
33.64
1.14
75
15.47
20.23
1.31
100
11.01
14.02
1.27
150
7.10
8.76
1.23
200
5.27
6.32
1.20
300
3.49
4.14
1.19
Result: the simulator runs 18β30% 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 0β3 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 15β30% relative to the WHI lower bound β see validation table above.
OSM polyline smoothing. OSM stores residential roads as sparse polylines (typically 3β6 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 β€ Lane Width
8.5 + MOT β€ 10
MOT β€ 1.5 ft
R β β(RΒ² β 2,081) β€ 1.5
R β₯ 694.4 ft
Loading measured radiusβ¦
How to use this simulator
A live transient swept-path analysis for the Marsh Rd curve in DeLand, FL. Drives a selected vehicle along the real road geometry pulled from OpenStreetMap and shows whether its body envelope fits inside the lane through the curve.
Headline stat cards (top of page)
Peak Off-Tracking β max lateral lag of the trailer rear wheels behind the front wheels through the curve.
Total Swept Width β widest cross-section the truck's body sweeps. Vehicle width + off-tracking.
Opposing Lane Encroachment β how far past the road centerline any part of the trailer reaches.
Measured Min Curve Radius β tightest radius found on the road, fitted from OSM.
Left control panel β Vehicle
Primary β which vehicle YOU are driving. The headline stats track this one.
Direction β which way you drive on Marsh Rd. The curve is geometrically asymmetric; behavior differs between directions.
Speed β your speed in mph (5β35). Affects the path-following lookahead.
Left control panel β Traffic
Mode β Solo (just you), Single oncoming (one other vehicle the other way), or Random mixed (filled in both directions).
Pool β which vehicle types are eligible for random traffic. Uncheck to exclude that type.
Density β how many traffic vehicles per direction in Random mode (1β8).
Left control panel β View
Lane Width β assumed width of each lane (8β12 ft). Affects encroachment math.
SAT β toggle real Esri satellite imagery under the simulation. Gold = on.
Mouse wheel on the map zooms toward the cursor.
Click & drag on the map pans.
Bottom-bar action buttons
βΆ Play / βΈ Pause β start or stop the animation.
β³ Loop β when active (gold), the simulation auto-replays end-to-end forever.
βΊ Reset β jump back to frame 1, leave settings as-is.
Envelope β toggle the green/red swept-path band that shows where the vehicle's body has been.
Reroll β generate a new random traffic config (different types, slight speed jitter). Same seed otherwise replays the same scene.
What the colors on the canvas mean
Grey strip / satellite β the road pavement, either as a flat polygon or the real aerial photo when SAT is on.
Yellow dashed line β the road's centerline. Trailer crossing this = lane violation.
Blue rectangle β your tractor.
Green rectangle β your trailer (turns red when it crosses the centerline).
Cyan trail β front (steer) axle path.
Pink trail β trailer rear axle path. The gap between cyan and pink IS the off-tracking.
Faint green / red band β full swept envelope through the curve. Red = trailer crosses centerline.
Other-color rectangles β random traffic vehicles (each type has its own color from the pool).
Yellow outline on a vehicle β flagged as currently colliding with another vehicle.
Frame HUD (top-left of canvas)
Frame N/M β current frame and total frame count.
Steer angle β current steering wheel input (degrees).
Off-track now β instantaneous lateral lag between front and rear axles. At the very first frame this may read large momentarily (run-in transient) β the headline stat is the true peak.
Past centerline β how far any trailer corner currently reaches across the yellow line.
Min curve radius (measured) β fitted curve radius for this road.
Collisions box
Counts distinct collision events in the current run (transitions from not-overlapping to overlapping).
Headline = how many involve YOUR vehicle.
Subline = total across all vehicles + per-type roster of who was in this scene.
No driver-avoidance behavior is modeled β these are geometric path conflicts, not predicted crashes.
Engineering interpretation
The static Engineering Math section below is the rock-solid proof: Western Highway Institute steady-state off-tracking formula MOT = R β β(RΒ² β LβΒ² β LβΒ²). For a WB-62 (Lβ = 20, Lβ = 41), keeping the swept width inside a 10 ft lane requires curve radius β₯ 694 ft. The simulator is illustration β the formula is proof.