Overtaking sight distance and critical grades

This page covers the two commands that measure sight distance — one on the plan, one on the profile — and the steep-grade analysis that comes with the second.

What it does

Overtaking sight distance is the distance a driver has to see ahead to start and finish an overtaking manoeuvre safely. Where it is not met, overtaking has to be prohibited — and that prohibition is what becomes the continuous centre line.

The two commands ask the same question in different planes.

Sight distance on the plan (horizontal template)

The obstacle is the curve itself: in a curve the line of sight cuts across the inner ground before it reaches the road ahead. The command models that with two edges, one on each side of the alignment:

1. it walks the alignment step by step;
2. at each station it finds the point exactly one yardstick away in a straight line ahead (the intersection of a circle of that radius with the alignment);
3. it draws the chord between the two points — that is the line of sight;
4. if the chord crosses either edge, sight is obstructed and the station is a prohibition;
5. contiguous stations are merged into one stretch, with optional filling of short gaps.

Sight distance on the profile (vertical template)

The obstacle is the crest of the vertical curve. The command works on the drawn grade line — a polyline in which X is the station and Y is the elevation:

1. it walks the profile step by step;
2. it finds the point one yardstick ahead on the profile itself;
3. it raises both ends by the sight height and draws the line of sight between them;
4. if the profile cuts that line, the crest is in the way and the station is a prohibition;
5. the stretches are merged and, optionally, projected back onto the plan alignment, which is where the line will be drawn.

Both of these read the drawing, not the ground. The profile is drawn with a vertical exaggeration, and neither the sight-distance sweep nor the critical-grade test undoes it: the circle that locates the point one yardstick ahead is cast in drawing coordinates, and the ramp lengths compared against the criteria tables are the drawn 2D lengths, rise included. On a ×10 drawing a 950 m ramp at 5.5 % measures 1084 m and is classified critical against a 1000 m threshold when the real ramp is not. Read the two notes at the end of this page before you rely on a borderline result.

Critical grades

The third analysis is not about sight distance: it walks the ramps (the straight segments of the grade line) and flags the ones long and steep enough to require a warning. Each critical ramp can receive two signs, one at each end, facing the corresponding direction.

Workflow

Sight distance on the plan

1. Run CAPCAD_ANALYTICS_HORIZONTAL_OVERTAKING. The status line shows in blue that speeds are set when the project alignment carries a design speed, and in orange that they are not — in which case Detect from the defined speed (2) is disabled.
2. Choose the Ruler length (1) — the list holds the speed/distance pairs of the shipped table — or tick Detect so the distance comes from the alignment's speed at each point you click.
3. Choose where the edges come from: fixed distance (5, 6) or selected entities (8).
4. Choose the direction (9, 12, 15) and, in Alignment, whether the analysis uses the project alignment (16) or one you select (17).
5. For the whole stretch, set the Step (18) and click Analyse the whole stretch (25). The form hides, the command asks for whatever is missing, and draws the stretches.
6. For a single point, use Draw a standalone template (24) and click points on the alignment; each click draws the chord in green (clear) or red (obstructed). Enter or Esc ends the loop.
7. To learn how far you can see at a point, use Determine the minimum admissible sight distance for a point (23).

Sight distance on the profile, and grades

1. Run CAPCAD_ANALYTICS_VERTICAL_OVERTAKING. The status line reports the state of the speeds and of the profile.
2. On the Util tab, enter the Start length (70) — the alignment station corresponding to the profile's first vertex — the Elevation (69) and the Vertical exaggeration (71) the profile was drawn with.
3. On the Sight distance tab, set the Ruler (33), Sight height (34), Step (46) and the Direction (35, 38, 41).
4. Click Full analysis (48). The command asks for the profile (a polyline with X = station and Y = elevation) and, if Plot the no-overtaking zones found on the alignment (45) is ticked, for the plan alignment too.
5. On the Grades tab, choose the method (57, 58, 59), tick what to plot (53, 54) and whether you want the signs (55), and click Analyse (62).
6. The selected profile is remembered while the form stays open; tick Select input (43 or 56) to pick another.

The form: Horizontal Template

The numbers on this page are unique and continuous: 1 to 31 on the Horizontal Template form and 32 to 71 on Vertical Profile Analytics.

The screenshots are of a Portuguese session, and so are the labels inside the generated figures further down; the layout, the control numbering and the geometry are identical in an English session. The English captions of each control are the ones quoted in the tables.

The form as it opens with no project alignment: the options that depend on the alignment are disabled and the status line warns that no speeds are set.

Parameters

Reference (edges)

The edges are the lines that "cut" the line of sight. They stand for the lateral obstacle.

Direction

The two coloured squares beside the buttons are the legend of the colours used in the drawing: cyan up-station, violet down-station.

Alignment (source)

Full analysis

The stretches go to layers whose names carry the run's parameters — ALIGNMENT_CRES_VISIBILITY_<ruler>_B<edge> and the down-station pair — so that two runs with different yardsticks do not mix.

Individual analysis

The form: Vertical Profile Analytics

The Sight distance tab. The status area carries two lines: the alignment's speeds and the profile currently selected.

Tab 1: Sight distance

In the full analysis, gaps shorter than the yardstick itself are filled automatically: a clear stretch shorter than the sight distance is no use for overtaking, so it does not become a permitted interval.

Tab 2: Grades

The Grades tab. The two notes at the bottom remind you that the analysed profile does not have to contain the vertical curves (the VPI polyline is enough) and that the arrows are drawn in the descending direction.

Tab 3: Util

The Util tab: the two zooms, the profile annotations, and the initial values that tie the profile to the alignment's chainage.

Fields 69 and 70 stand in for the properties that would be stored on the profile itself; the profile-definition form is not available in this version, as the grey label says.

How the options combine

The figures below came from real runs of the sight-distance and critical-grade engines on a sample alignment and grade line. Their labels are from a Portuguese run.

The line of sight on the plan

The mechanism of the standalone template, at a reduced scale so the edges are visible: alignment solid, edges dashed at ±3.5 m, yardstick 60 m. On the tangent and on the open curve the chord passes between the edges — sight clear. On the tight curve the chord cuts the inner edge — sight obstructed. On a real road the numbers are larger (yardstick 210 m, edge 3.5 m), and the ratio between them makes the edges invisible in the drawing, but the arithmetic is the same.

Full analysis on an alignment with one curve of R 350 m and another of R 2500 m, yardstick 210 m, edge 3.5 m, step 10 m. The tight curve produces 540 m of prohibition in each direction; the open curve, none. The two stretches do not coincide: the up-station one runs km 140 to 680 and the down-station one km 350 to 890 — each direction is prohibited before reaching the curve, in its own "before".

What the yardstick changes

The same alignment, up-station, at four sight distances. At 180 m and 210 m only the tight curve prohibits. At 280 m the open curve starts prohibiting too and the total jumps from 540 m to 1780 m. At 355 m, 2000 m of the alignment's 2737 m are prohibited.

The yardstick is not a sensitivity knob: it is the design speed. Raising the road's class prohibits far more than proportionally.

The speed → sight-distance lookup is banded: a speed between two rows uses the lower row, a speed above the top row keeps the top distance, and a speed below the bottom row returns nothing, in which case the command falls back to the fixed yardstick. The table itself is the one of the shipped country profile and is reproduced on the Portuguese edition of this page.

How far you can see at a point

The answer of button 23 at four points on the same alignment. Inside the R 350 m curve with the edge at 3.5 m, the greatest distance the line of sight still clears is 98 m — far below the 210 m required at 70 km/h. In the R 2500 m curve it is 264 m, enough up to 90 km/h. On the final tangent the search reaches the top of the table and the command reports that the distance exceeds or equals 355 m.

The line of sight on the profile

Spot analysis on a grade line with a 250 m crest between ramps of +3 % and −4 %, and a sag further on. Sight height 1.20 m, yardstick 210 m. The template is drawn as a Z: the two verticals of the height and the line of sight between them. On the ramp and on the descent the sight line passes above the grade; over the crest, the grade cuts it. The vertical scale of the figure is stretched for legibility.

Full analysis on the same grade line, step 20 m. The crest prohibits from km 320 to km 520 for the driver going up and from km 520 to km 740 for the one going down — the two stretches meet exactly at the high point, each on the side of the driver who has not yet crossed it. The sag prohibits nothing: a sag vertical curve does not hide the road.

Critical grades

The two built-in tables differ in one row only: in the default table a 5 % gradient needs 1000 m to be critical; in the stricter one, 600 m is enough. Everything else — 600/6, 300/7, 230/8, 150/9 — is the same.

Six ramps of a sample grade line, straight from the engine:

The column that decides is the drawing one, not the real one — see the note below. Ramp 6 is the case: 950 real metres at 5.5 % would not reach the default table's 1000 m step, but measured in the drawing, with vertical exaggeration 10, it is 1084 m and becomes critical.

Segments shorter than 10 m in the drawing are ignored, and segments with curvature (the vertical curves, when the profile carries them) enter the report with their radius only, without a gradient or a verdict.

The figures that show the two criteria tables and the classified ramps are labelled with the two bodies' names and with the sign codes, so they are not reproduced here.

Remembered between sessions

Nothing. Both forms are built from scratch on every run: yardstick 210, height 1.2, step 10 (plan) and 20 (profile), edge 3.5, exaggeration 10, the default grade table, direction Increasing on the plan and Both on the profile.

What survives is only within a run: the profile form keeps the selected profile while it stays open, and the horizontal template keeps the edge selection during the full analysis.

What stays in the drawing is the real memory: the analysis layers carry the yardstick and the edge in their own names, and that is how an old analysis is told apart from a new one.

Notes

• The profile analysis runs in drawing coordinates. The circle that locates the point one yardstick ahead is cast over the already-exaggerated profile, so the distance measured is the one on the paper, not the one on the ground. With vertical exaggeration 10, a 4 % ramp becomes 40 % in the drawing and the effective yardstick shrinks by a few per cent. The greater the exaggeration and the steeper the ramp, the greater the difference; on a grade line of gentle ramps it is negligible.
• Ramp lengths are measured in the drawing. The critical-grade criterion compares the 2D length of the drawn segment — which includes the exaggerated rise — against the table's steps, not the horizontal projection. On a 5.5 % ramp with exaggeration 10, the measured length is about 14 % greater than the real one. When checking a borderline result, use the length column of the report and not the distance between the stations.
• Detect does not apply to the full analysis, in either command. The speed-driven yardstick only works on the point-by-point paths (standalone template and spot analysis). Tick it and run the full analysis and the command says on the command line that the part is pending, and uses the fixed yardstick. For an alignment with stretches at different speeds, run the full analysis once per stretch, with each stretch's yardstick.
• The full analysis on a selected alignment runs one direction only. With Select (17) ticked, the analysis uses the state of the Increasing option (9) alone: ticking Both does not expand to the two directions on that path. With the project alignment (16), Both works normally.
• The minimum admissible distance ignores the edge choice. Button 23 always generates the edges by offsetting ±value (6), even with Select entities (8) ticked — for speed, since it repeats the calculation up to 355 times per point.
• The critical-grade signs are those of the Brazilian catalogue on every profile. The check box caption spells one of them out, and on another country profile the command still asks for those two blocks.
• Neither analysis writes anything onto the alignment. The result is drawing: entities on the prohibition layers. It is CAPCAD_MARKING_AXIS (Consolidated) that reads those layers, merges the two directions and stores the consolidated stretches on the alignment. The horizontal template's status line says as much when it finishes: writing to the alignment is pending.
• A few labels are untranslated. The two grade-method radios, the label above the vertical-exaggeration box and the profile window's title keep their original text in an English session.
• For the classification of the same curves into sharp and signable, and the curve-warning signs, see Curve Utilities. For sign-support heights, see Vertical signage management.