Designing a rotary means fixing about eight quantities — how fast traffic should travel, how tight each curve should be, how long and wide the weaving section must be, and finally how much traffic the whole thing can carry.
This post works through all of them in order, with every value and formula you need.
The Design Elements
The design elements include design speed, radius at entry, radius at exit, radius of the central island, weaving length and width, and entry and exit widths. In addition, the capacity of the rotary can be determined using an empirical formula.
1. Design Speed
- All vehicles must reduce speed at a rotary. The design speed of a rotary is therefore much lower than that of the roads leading to it.
Urban areas: 30 kmph | Rural areas: 40 kmph
The urban value is lower because urban rotaries sit in constrained space with more pedestrians and more frequent entries.
2. Radii of Curves at Entry and Exit
At Entry
Entry to the rotary is not straight — a curvature is introduced deliberately. This forces the driver to reduce speed.
That is the key idea: the entry curve is a speed control device, not merely a geometric connection. A straight entry would let vehicles arrive on the rotary at full road speed, defeating the whole arrangement.
| Rotary Design Speed (kmph) | Suggested Radius at Entry (m) |
|---|---|
| 40 — generally suitable for rural areas | 20 – 35 |
| 30 — generally suitable for urban areas and other restricted locations | 15 – 25 |
At Exit
- The radii at exit should be larger than those of the central island and the entry, so as to encourage drivers to pick up speed and clear away from the rotary quickly.
- For this reason, the exit radius may be kept about 1.5 to 2 times the radius of the entry curve.
- Exception: if there is large pedestrian traffic across the exit road, radii similar to those at the entrance should be provided, to keep exit speeds reasonably low.
The reasoning is neatly opposite at the two ends. Entry curves are tight to slow vehicles down. Exit curves are generous to speed them up and clear the rotary. Only pedestrian safety overrides the second rule.
3. Radius of the Central Island
- Theoretically, the radius of the central island should equal the radius at entry.
- In practice, it is kept slightly larger than the entry curve radius. This gives sight preference to traffic already on the rotary and slows down approaching traffic.
Radius of central island = 1.33 × radius of entry curve
The phrase “sight preference to traffic already on the rotary” deserves attention. Circulating traffic must have priority — if entering vehicles could push in, the circulating stream would stop, and a stopped rotary is a blocked rotary. Keeping the island a little larger reinforces that priority through geometry.
4. Weaving Length
- The weaving length determines how easily vehicles can manoeuvre through the weaving section, and therefore determines the capacity of the rotary.
- It is decided from the width of the weaving section, the average width of entry, the total traffic, and the proportion of weaving traffic.
General rule: keep the weaving length at least 4 times the width of the weaving section.
Minimum Weaving Lengths
| Design Speed (kmph) | Minimum Weaving Length (m) |
|---|---|
| 40 | 45 |
| 30 | 30 |
A Maximum as Well as a Minimum
To discourage speeding in the weaving sections, the maximum weaving length should be restricted to twice the values above. Larger weaving lengths encourage over-speeding.
This is worth pausing on, because it seems counter-intuitive. Surely more room to weave is better?
No — because a long weaving section starts to feel like an ordinary straight road, and drivers accelerate. Speed is precisely what the rotary exists to control. The weaving length must be long enough to weave safely but short enough to prevent speeding, which is why both a minimum and a maximum are specified.
5. Width of Carriageway at Entry and Exit
- Governed by the amount of traffic entering and leaving the rotary.
- Entry width should be lower than the carriageway width at the approach.
- The minimum carriageway width should be at least 5 m, with the necessary widening to account for curvature.
Why should entry be narrower than the approach road? Because narrowing forces drivers to slow and to sort themselves into a single controlled stream before joining the circulating flow. It is another speed-control measure disguised as a dimension.
Recommended Widths
For entry radius 25–35 m:
| Carriageway Width of Approach Road | Width at Entry and Exit (m) |
|---|---|
| 7 m (2 lanes) | 6.5 |
| 10.5 m (3 lanes) | 7.0 |
| 14 m (4 lanes) | 8.0 |
| 21 m (6 lanes) | 13.0 |
For entry radius 15–25 m:
| Carriageway Width of Approach Road | Width at Entry and Exit (m) |
|---|---|
| 7 m (2 lanes) | 7.0 |
| 10.5 m (3 lanes) | 7.5 |
| 14 m (4 lanes) | 10.0 |
| 21 m (6 lanes) | 15.0 |
Compare the two tables and you will notice the smaller entry radius requires greater width. That is the extra widening principle from geometric design appearing again — a sharper curve means more off-tracking, so more width is needed.
6. Width of the Non-Weaving and Weaving Sections
- The width of the non-weaving section should equal the widest single entry into the rotary, and should generally be less than the width of the weaving section.
- The width of the weaving section should be one traffic lane (3.5 m) wider than the mean entry width.
Wweaving = (e1 + e2)/2 + 3.5
| Symbol | Meaning |
|---|---|
| e1 | Entry width (m) |
| e2 | Exit width (m) |
| 3.5 | One traffic lane width (m) |
The extra 3.5 m exists because the weaving section has to accommodate two streams passing through one another — vehicles merging in and vehicles diverging out at the same time. The non-weaving section carries only one stream, so it needs less width.
7. Entry and Exit Angles
- Entry angles should be larger than exit angles.
- It is desirable that entry angles be 60° if possible.
- Exit angles should be small, even tangential.
- An idealised design has entry angles of 60° and exit angles of 30°.
Once again the same philosophy: entry geometry slows vehicles, exit geometry releases them. A large entry angle forces a sharper turn on the way in; a small, near-tangential exit angle lets vehicles leave smoothly.
8. Capacity of the Rotary
- The capacity of the rotary is determined by the capacity of each weaving section, and the overall capacity is reported as the minimum value.
- The capacity of an individual weaving section depends on: (i) width of the weaving section, (ii) average width of entry, (iii) weaving length, and (iv) proportion of weaving traffic.
The Capacity Formula
Qw = 280 w (1 + e/w)(1 − p/3) ÷ (1 + w/l)
Notation and Valid Ranges
| Symbol | Meaning | Valid Range |
|---|---|---|
| Qw | Practical capacity of the weaving section, in PCU per hour | — |
| w | Width of the weaving section (m) | 6 to 18 m |
| e | Average entry width (m) — the average of entry and exit width | e/w between 0.4 and 1.0 |
| l | Length of the weaving section between the ends of the channelizing islands (m) | w/l between 0.12 and 0.4 |
| p | Proportion of weaving traffic | 0.4 to 1.0 |
Proportion of Weaving Traffic
p = (b + c) / (a + b + c + d)
This is the ratio of the sum of the crossing streams to the total traffic on the weaving section.
Reading the Formula
Each term does something you can reason about:
- 280 w — capacity rises with the width of the weaving section.
- (1 + e/w) — a wider entry relative to the weaving width increases capacity.
- (1 − p/3) — capacity falls as the proportion of weaving traffic rises. More weaving means more disturbance.
- ÷ (1 + w/l) — since w/l appears in the denominator, a longer weaving section (larger l, smaller w/l) increases capacity. More room to weave means more throughput.
Applying the Formula
- p is calculated at every weaving section, and the highest value is adopted.
- If e, w and the other quantities differ between weaving sections, the capacity of every section must be calculated and the minimum value adopted.
This follows directly from the principle established earlier — a rotary is only as good as its worst weaving section.
Capacity Adjustments
| Condition | Adjustment |
|---|---|
| Entry angle between 0° and 15° | Deduct 5 percent |
| Entry angle between 15° and 30° | Deduct 2.5 percent |
| Exit angle between 60° and 75° | Deduct 2.5 percent |
Notice that every adjustment is a deduction, and that they penalise exactly the geometry the design rules warn against — small entry angles (which fail to slow vehicles) and large exit angles (which fail to release them smoothly).
Formula Summary
| Quantity | Value or Expression |
|---|---|
| Design speed | 30 kmph urban, 40 kmph rural |
| Entry radius | 20–35 m at 40 kmph; 15–25 m at 30 kmph |
| Exit radius | 1.5 to 2 × entry radius |
| Central island radius | 1.33 × entry radius |
| Weaving length, general rule | At least 4 × weaving width |
| Minimum weaving length | 45 m at 40 kmph; 30 m at 30 kmph |
| Maximum weaving length | Twice the minimum values |
| Weaving width | (e1 + e2)/2 + 3.5 |
| Minimum carriageway width | 5 m |
| Entry and exit angles | 60° entry, 30° exit (idealised) |
| Capacity | Qw = 280w(1 + e/w)(1 − p/3)/(1 + w/l) |
| Proportion of weaving traffic | p = (b + c)/(a + b + c + d) |
Quick Revision Notes
- Rotary design speed is much lower than the approach roads: 30 kmph urban, 40 kmph rural.
- Entry curvature exists to force drivers to reduce speed.
- Exit radius = 1.5 to 2 times entry radius, unless heavy pedestrian traffic requires entry-like radii.
- Central island radius = 1.33 × entry radius, giving sight preference to circulating traffic.
- Weaving length ≥ 4 × weaving width; minimum 45 m at 40 kmph and 30 m at 30 kmph.
- Maximum weaving length = twice the minimum, since longer sections encourage over-speeding.
- Entry width should be lower than the approach carriageway width; minimum carriageway width 5 m.
- Weaving width = mean entry width + 3.5 m.
- Non-weaving width = widest single entry, and less than the weaving width.
- Entry angle 60°, exit angle 30° in an idealised design.
- Capacity is the minimum among all weaving sections.
- Deduct 5 % for entry angles 0–15°, and 2.5 % for entry angles 15–30° or exit angles 60–75°.
Mistakes Students Commonly Make
- Making the exit radius smaller than the entry radius. It should be larger, to help vehicles clear away.
- Using 1.33 for the exit radius. That factor belongs to the central island; the exit is 1.5 to 2 times.
- Forgetting that weaving length has a maximum as well as a minimum.
- Making entry width equal to or greater than the approach width. It must be lower.
- Omitting the + 3.5 in the weaving width formula.
- Taking the average or sum of weaving section capacities. The minimum governs.
- Ignoring the valid ranges of w, e/w, w/l and p — the formula is empirical and only valid within them.
- Adding the angle corrections instead of deducting them.
- Swapping the entry and exit angles. Entry is the larger angle.
Conclusion
Every design element of a rotary serves one of two purposes: slow vehicles down as they arrive, or give them room to weave once inside. Tight entry radii, narrowed entry widths and large entry angles all do the first. Weaving length, weaving width and generous exit radii do the second. The capacity formula then ties these dimensions to a number of PCU per hour — and because a rotary fails at its weakest point, that number is always the minimum across all weaving sections, never the average.
Frequently Asked Questions
What are the design elements of a rotary?
Design speed, radius at entry, radius at exit, radius of the central island, weaving length and width, entry and exit widths, and the capacity of the rotary.
What design speeds are used for rotaries?
30 kmph for urban areas and 40 kmph for rural areas — much lower than the roads leading to the rotary.
Why is a curve introduced at the entry?
To force the driver to reduce speed before joining the circulating stream.
How is the exit radius related to the entry radius?
The exit radius is kept about 1.5 to 2 times the entry radius, so drivers can pick up speed and clear the rotary quickly. Where pedestrian traffic across the exit is heavy, entry-like radii are used instead to keep exit speeds low.
What is the radius of the central island?
Theoretically equal to the entry radius, but in practice about 1.33 times it, so as to give sight preference to traffic already on the rotary and slow approaching traffic.
What is the general rule for weaving length?
It should be at least four times the width of the weaving section, with minimum values of 45 m at 40 kmph and 30 m at 30 kmph.
Why is there a maximum weaving length?
Because a longer weaving section encourages over-speeding, which defeats the purpose of the rotary. The maximum is restricted to twice the minimum value.
How is the width of the weaving section calculated?
As the mean of the entry and exit widths plus one traffic lane: (e1 + e2)/2 + 3.5 metres.
What is the capacity formula for a rotary?
Qw = 280w(1 + e/w)(1 − p/3)/(1 + w/l), giving the practical capacity of the weaving section in PCU per hour.
Which weaving section governs the rotary capacity?
Capacity is calculated for every weaving section and the minimum value is adopted, since the rotary fails at its weakest section.
What adjustments are made to the calculated capacity?
Deduct 5 percent where the entry angle is between 0° and 15°, and 2.5 percent where the entry angle is between 15° and 30° or the exit angle is between 60° and 75°.