Geometry > Entry Geometry > Entry Angle Phi (Ф)

## Entry Angle Phi (Ф)

The Phi angle for an entry is the angle between the mean path of the entering traffic and the mean path of the circulating traffic.

The HCM model does not use the entry angle Phi.

Phi has a range in the geometric model from 10 to 60 degrees. Values between 20 and 40 degrees are recommended. Entry angle Phi has a minor capacity effect. However, there is limited scope for changing Phi, as low values below 20 degrees should be avoided as this makes visibility to the left more difficult especially with larger diameter roundabouts.

Capacity Effects of Phi Angle (Ф)

Measuring Phi is complicated by having two methods each applying to different types of roundabout. Phi is a proxy for the angle between entering and circulating traffic.

### Mean Path

The mean path of the entering traffic is considered as it crosses the yield. (This is the centerline of an approach, single- to multi-lane).

The circulating traffic is the mean circulating path of the traffic that is first crossed by the mean entering traffic.

### Measuring Phi - Two Methods

There are two methods for measuring Phi:

Method 1: On modern style roundabouts entries are close to the following exit. Consequently the mean path of exiting traffic diverges from the mean path of circulating traffic before the mean path of entering traffic. Entering traffic therefore crosses circulating traffic traveling along two mean paths. In such cases the entry angle is defined as half the angle between the mean entering path and the mean exit path. This is shown on the following diagram.

It is used with a nearby exit, as the entering traffic first conflicts with the exiting traffic that has diverged from the circulating traffic. In this case, the angle between the two streams is 2Phi, so Phi is the angle/2 as illustrated in the graphic below.

Source excerpted from the UK TRRL Laboratory Report 942, Transport and Road Research Laboratory

The line a-b is tangential to the median line on the southbound entry at the point it meet the yield line.

The line c-d is tangential to the median line of the following exit at the point where it meets the outer circle. The angle between a-b and c-d is 2 Phi.

Method 2 is used if the mean path of the entering traffic first conflicts with the mean path of the circulating traffic (before exiting traffic has diverged). The angle between the two streams is Phi (not the 2Phi of method 1) as illustrated in the graphic below.

The second method applies where an entry and exit are too removed from each other to use the above method. This is shown below.

The line A-B is tangential the entry mean where it crosses the yield line, the same as the former method. However, the line CD is tangential to the median of the circulating road at the point where it is intersected by the line A-B. Phi is the angle between A-B and B-C.

Phi is not a parameter in the accident models, but small values should be avoided to make visibility left at the entry difficult and very large angles direct traffic towards the central island causing entry path overlap.

### Discussion

The Phi Angle for an entry is a proxy for the conflict angle between the entering traffic on each entry lane and the circulating traffic. Usually, if Phi for an entry is within the acceptable range, then the Phi for each lane is also within the range (the proxy represents each lane well).

However, for multilane entries with 3 and 4 lanes, the Phi for each lane can be very different from the Phi for the whole entry (the proxy Phi), with the outside lanes (3rd or 4th lanes) having a very small unacceptable Phi even when Phi for the other lanes, and for the entry as a whole, is within the accepted range.

In addition, a design may have the lane Phi on all lanes within the acceptable range, but have an unacceptably poor view-angle to the left. In such cases, realignment and adjustment of the approach can significantly mitigate, if not remove, these problems.