Freeways is an extremely cool game, in which the player designs interchanges for one-lane roadways. This page is an index for some more-or-less-realistic renditions of solved Freeways puzzles, organized by puzzle ID number and by minimum speed.
Slow (red), intermediate (green), and fast (blue) roadways support speeds of 36 ft/s (approximately 25 mi/h or 40 km/h), 72 ft/s, and 108 ft/s, respectively. Yellow and cyan roadways accommodate acceleration and deceleration.
Side friction factor is 9 ft/s ÷ speed, superelevation is 1/12, and gravitational acceleration is 32 ft/s2.
Deceleration is 12 ft/s2 and acceleration is 6 ft/s2.
The Greenshields traffic model is used: speed = free-flow speed × (1 − jam density ÷ density). Jam density is 1 vehicle per 18 feet (same as vehicle length). The effects of merging and diverging are ignored.
Each roadway, along with its traffic, occupies 12 ft of horizontal space and 24 ft of vertical space. Maximum grade is 1/48. Curves cannot be combined with acceleration or deceleration, but they can be combined with grades, as long as the grade does not begin or end on the curve.
Obviously, these simulations should not be used in real-life design. (Gap acceptance? Offtracking? Shoulders? Never heard of 'em.)
Depicting acceleration and deceleration in SVG animation would be rather complicated (each individual car would have to be a separate element), so each yellow or cyan roadway instead uses its space mean speed to inform its CSS animation.
Nominal scale is one pixel per foot, but the image won't become blurry if you zoom in or out: this is SVG, not GIF. (Elevated roadways are narrower than they should be, in order to avoid blocking the view of what's beneath them.) Precision is to the nearest one-tenth of a foot (i. e., ±0.05 ft).
Maximum flow is achieved when density is half of jam density (i. e., 1 vehicle per 36 feet). The bottleneck of an interchange is maximum flow at minimum speed (108 ft/s ÷ 36 ft/veh = 3 veh/s, 72 ft/s ÷ 36 ft/veh = 2 veh/s, or 36 ft/s ÷ 36 ft/veh = 1 veh/s), which may occur at the start of an acceleration roadway, at the end of a deceleration roadway, or at the intersection of multiple roadways: not segments, but points, must be evaluated.
Centripetal acceleration a = v2/r ≤ g(f + e) → r ≥ v2/g/(f + e) = v2 ÷ 32 ft/s2 ÷ (9 ft/s ÷ v + 1/12) = v3/(288 ft2/s3 + 8/3 ft/s2 × v). The minimum (centerline) radius of a slow roadway is 121.5 ft, that of an intermediate roadway is 777.6 ft, and that of a fast roadway is 2187 ft. (All curves are circular, not spiral.)
If a symmetrical reverse curve joining two parallel line segments has radius r and produces an offset of y, each of that curve's two circular arcs has a length (not along the arc, but perpendicular to the line segments) of r√(1 − (1 − y/(2r))2). For example, if a car traveling at 108 ft/s wants to switch between two adjacent 12-ft lanes, each of the two arcs in the maneuver takes 2187 ft × √(1 − (1 − 12 ft ÷ (2 × 2187 ft))2) ≈ 161.9 ft of longitudinal space.
The space required for acceleration or deceleration is (v12 − v02)/(2a). For example, if a car wants to decelerate from 108 ft/s to 72 ft/s, the maneuver requires ((72 ft/s)2 − (108 ft/s)2)/(2 × −12 ft/s2) = 270 ft.