Horizontal Sight Distance Obstruction Calculator

Enter curve radius and design speed to get the AASHTO minimum lateral clearance to any roadside obstruction — or check whether an existing obstruction provides adequate stopping sight distance.

Middle Ordinate Formula AASHTO SSD Tables Metric & Imperial AASHTO Compliance Check Free — No Account

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Returns minimum lateral clearance or available SSD with AASHTO compliance check.

How the Middle Ordinate Formula Works

Plan-view schematic of a horizontal road curve showing the sight line chord, the middle ordinate m, and the required clearance zone.

The chord (sight line S) cuts across the inside of the curve. The middle ordinate m is the perpendicular distance from the chord midpoint to the road centreline. Any obstruction closer than m to the centreline blocks the driver's view.

What Is Horizontal Sight Distance and Why Does It Matter?

Horizontal sight distance is the length of road a driver can see ahead when travelling around a horizontal curve. Unlike straight roads — where sight is limited mainly by headlights or vertical geometry — curves place physical obstructions (cut slopes, retaining walls, vegetation, median barriers, buildings) directly in the driver's line of sight.

When a driver cannot see far enough ahead to stop safely before reaching a hazard, the road fails to provide adequate Stopping Sight Distance (SSD). AASHTO (American Association of State Highway and Transportation Officials) specifies the minimum SSD for each design speed in the Green Book — A Policy on Geometric Design of Highways and Streets. Failing to clear obstructions to the required distance is a leading factor in run-off-road and head-on collisions on horizontal curves.

The critical design question is: how far back from the road centreline must the roadside be kept clear? That distance is the middle ordinate m, computed from the curve radius and the required SSD.

The Middle Ordinate Formula Explained

The geometry of a horizontal curve yields a straightforward relationship between the curve radius R, the required sight distance S, and the minimum clearance m:

m = R × (1 − cos(S / 2R))

where S/(2R) is in radians

Here, m is the perpendicular distance from the lane centreline to the nearest face of the obstruction, measured at the mid-angle point of the arc. The formula assumes the sight line is the chord of the arc spanning the full sight distance S. This is a standard AASHTO approximation — accurate to within 1–2 % for typical highway curves where S is much smaller than the circumference.

The inverse formula — given an obstruction at offset m, find the available sight distance — is:

S = 2R × arccos(1 − m/R)

Both equations use only basic trigonometry and are exact for circular horizontal curves. For compound curves, apply the formula to each arc separately and use the minimum available SSD.

AASHTO Stopping Sight Distance by Design Speed

AASHTO Green Book 2018, Table 3-1. These values assume a 2.5-second perception-reaction time and wet-pavement friction factors.

Metric

Design Speed (km/h)	SSD (m)
30	35
40	50
50	65
60	85
70	105
80	130
90	160
100	185
110	220
120	250
130	285

Imperial

Design Speed (mph)	SSD (ft)
30	200
40	305
50	425
55	495
60	570
65	645
70	730
75	820
80	910

How to Check Obstruction Compliance on an Existing Curve

When auditing an existing road, measure the lateral distance from the lane centreline to the obstruction face (use a total station, tape, or GIS layer). Then use the Check Available SSD mode to enter that measured offset and the curve radius. The tool calculates the available SSD and flags non-compliance against the posted speed limit's AASHTO SSD requirement.

Common obstructions encountered during road safety audits include cut slopes on the inside of curves, retaining walls, jersey barriers, crash attenuators, large trees, noise walls, sign support structures, and drainage culvert headwalls. Each must be assessed at the mid-angle point of the relevant sight arc.

Minimum Clearance Reference — Metric (80 km/h, SSD = 130 m)

Curve Radius (m)	Min. Clearance (m)	Typical Application
100	21.1	Very tight urban curve
150	14.1	Tight urban arterial
200	10.6	Urban arterial
300	7.1	Rural two-lane highway
500	4.2	Rural primary road
1000	2.1	Expressway / motorway

Values computed using m = R(1 − cos(130/(2R))). Larger radii require less clearance because the sight line chord barely deviates from the arc.

Common Obstructions on Horizontal Curves

Cut Slopes

Earthwork on the inside of the curve is the most frequent obstruction. AASHTO specifies the required set-back, but slopes may have encroached due to erosion or vegetation growth.

Retaining Walls

Concrete or masonry walls supporting embankments on the inside of curves are common on mountain roads and interchange ramps. Measure clearance to the wall face.

Median Barriers

Jersey barriers and wire-rope median systems on divided highways may limit sight distance on curves with short radii or high design speeds.

Vegetation

Trees, hedges, and tall roadside vegetation need periodic trimming or removal to maintain the required m clearance. This is an ongoing maintenance obligation.

Buildings & Signs

Structures adjacent to the road right-of-way on the inside of curves. The roadway designer must ensure the future development envelope respects the sight triangle.

Drainage Structures

Culvert headwalls and bridge abutments at the inside of curves can create localised reductions in available sight distance that are easily missed in a design check.

Frequently Asked Questions

What is the middle ordinate in road design?

The middle ordinate m is the perpendicular distance from the midpoint of a chord (the driver's straight-line sight) to the nearest point on the road centreline arc. It equals the minimum lateral clearance that must be kept free of obstructions on the inside of a horizontal curve to ensure the driver can see the full required stopping sight distance.

How do I calculate sight distance clearance for a retaining wall on a curve?

Measure the perpendicular distance from the lane centreline to the wall face (this is your obstruction offset m). Enter the curve radius R and the measured offset into the 'Check Available SSD' mode. The tool returns the available SSD and compares it to the AASHTO requirement for your design speed.

What is the AASHTO stopping sight distance for 60 mph?

Per AASHTO Green Book 2018, the stopping sight distance at 60 mph is 570 ft (174 m). This assumes a 2.5-second perception-reaction time and a deceleration rate of 11.2 ft/s² (3.4 m/s²) on a wet, level pavement.

What is the difference between stopping sight distance and passing sight distance?

Stopping sight distance (SSD) is the minimum distance needed to stop safely before a stationary object. Passing sight distance (PSD) is the much longer distance needed to safely complete an overtaking manoeuvre on a two-lane road. For horizontal curve clearance calculations, SSD is the standard AASHTO check. PSD checks require a larger m value and are typically only feasible on curves with very large radii.

How does curve radius affect required sight distance clearance?

A smaller radius requires a much larger clearance for the same SSD. This is because a tighter curve brings the inside edge closer to the driver's sight line. Doubling the radius roughly halves the required clearance. On very tight curves (R < SSD), the required clearance can exceed the full lane width, making adequate sight distance geometrically impossible without raising the design speed.

What counts as an obstruction for horizontal sight distance?

Any physical object on the inside of the curve that rises above the driver's line of sight (approximately 1.08 m AASHTO) counts as an obstruction — cut slopes, retaining walls, noise barriers, jersey barriers, crash cushions, large trees, hedges, buildings, sign posts, and drainage structure headwalls. Objects below 0.6 m (the AASHTO target object height) do not affect SSD calculations.

Related Calculators

Stopping Sight Distance Calculator

Compute SSD from speed, reaction time, grade, and friction

Horizontal Curve Calculator

Degree of curve, tangent length, arc length, and chord

Superelevation Calculator

Cross-slope design for safe curve traversal

Spiral Transition Curve Calculator

Clothoid parameters for smooth curve entry and exit

Vertical Curve Calculator

K-value, length, and crest/sag sight distance

Road Grade Calculator

Grade %, angle, ADA compliance, and truck resistance

External Resources

AASHTO Green Book — A Policy on Geometric Design of Highways and Streets (authoritative SSD tables) FHWA — Sight Distance and Road Safety Countermeasures Wikipedia — Sight distance (SSD, PSD, and decision sight distance)