Sag vertical curves
Highway Capacity Manual signalized intersection procedure for oversaturated conditions
Cycle Lengths
Volume density traffic control

Sag Vertical Curves (8 April 2005)
A public works director had the following question: A developer has proposed a road to provide access to a new development that is less than AASHTO standard. A 300 foot sag vertical curve would connect a 9 percent and 7 percent downgrades. According to the calculations that he has done, the minimum curve length should be 360 feet.

(1) Does the 60 feet difference make a difference?
(2) Is the only issue night vision for stopping sight distance?
(3) Are there other important issues here?

Response #1 The primary issues with sags are night time sight distance (headlights that don't provide sight distance). This can be addressed with street lighting. Driver comfort and expectation is another consideration. If this is the only abrubt vertical curve in an otherwise flat sement it would be different than a network of rolling and curving alignments. The overall context is a consideration. 60 feet really makes little difference, especially in a low speed environment. The variations in vehicles headlight height and ambiant lighting is outside the accuracy of the model. In extreme sag conditions, truck clearance (hanging up) can be an issue. I doubt that applies here. Hope this helps. Let me know how this turns out.

Response #2 It is essentially a night sight distance issue. At some point, it could be a comfort issue, but I think that is mainly for crests. If the street where lighted, the issue would not exist. I assume it will not be an arterial. I would not be concerned.

Response #3 Good to hear from you. My take on it is that the 60 feet will likely not make a difference. If he had chosen a lower design speed the 300-foot curve would have probably met the standard. Headlight illumination of the back side of the curve is the design issue, but as far as I know there are not convincing collision data showing that violation of that standard leads to many crashes. Besides headlights, the other issue I can think of there is comfort and vehicle bounciness at the bottom of the sag. That sag could be a test for many vehicle suspensions. It might be a good bit of marketing for the developer to lengthen the curve to make it easier on his potential customers.  

Highway Capacity Manual signalized intersection procedure for oversaturated conditions (19 April 2005)
A consultant team is working on a traffic study for a new river crossing. They have been asked to analyze the different project alternatives assuming that no additional through lanes would be added to the principal roadways. Analyzing forecasted traffic for the 20 year analysis year, several of the intersections are significantly oversaturated, with a couple of the critical v/c ratios exceeding 1.3. The HCM incremental delay, d2, accounts for oversaturation queues, but they haven't been able to find a v/c limit for the delay equation. Their concern is the validity of the analysis results for intersections with critical v/c ratios greater than 1.0, and in using the results to compare the traffic operations of different alternatives. Do you have any suggestions of where to find documentation on limitations of the HCM analysis of oversaturated intersections?

Response #1:  Because of the problems described below, the HCM 2000 went to a multi-period analysis that carries over the unmet demand from period to period. The "initial unmet demand" must be entered for each period and the "final unmet demand" computed for the period must be carried over to the next period (remind you of doing your taxes?). It is important that the analysis begin before the unmet demand starts to accumulate. It must be continued long enough to satisfy all unmet demand. The HCS now requires you to do this manually, but I believe that the next release, which may already be available, will handle multiple periods automatically.

Response #2:  HCS+ does this automatically and is due out in a couple of weeks.

Response #3: They need to look at Appendix F in Chapter 16, which discusses how to conduct an analysis of oversaturated conditions (using the D3 term of the delay equation). I would also let them know that the D2 term is only valid up to v/c's that are less than or equal to the inverse of the peak hour factor. So if the PHF is 0.9, the max v/c for a 15 minute analysis would be 1.11. Anything over that would require an analysis of multiple time periods. Appendix F documents how to do it.  

Response #4:  In the 1997 and 2000 HCM for signals, any formal limit on the v/c has been removed. That is to say, if the demand volume is believed to be accurate and no diversion is anticipated, any v/c value is valid and the d2 term will account for the oversaturated delay that results. In reality, we know that at some point traffic WILL divert, but that is an assumption in the hand of the analyst. The 1985 and 1994 HCM had a loosely-defined limit of 1.2 on v/c, but that no longer exists. There was also some sort of theoretical limit regarding PHF (I think it was v/c couldn't exceed 1/PHF, maybe just for the d1 term), but I don't recall that it applies anymore. For an accurate analysis, the impact of d3 must also be considered, which brings to the table the effect of the existence of a residual queue at the beginning of the analysis period. If the analysis period is significantly oversaturated, in most likely has a residual queue at it's start, and the analysis is not valid if this queue is not quantified and included. This also leads to the likelihood of a residual queue at the end of the analysis period, which then requires the analysis of the subsequent period and all following periods until the residual queue is eliminated. Things can get messy when all this is included, but that's the nature of over-saturated analysis.

Cycle Lengths (26 April 2005)
Do you have any experience in an agency running short cycle lengths (about 45 seconds) in their downtown area? Is this too short?

Response #1: Downtown Oakland is now on a short cycle length. Don't remember if it is quite that short but it is close. In many CBD areas the key really gets to be peds so you could design the cycle length around what is needed to serve them. If it gets too long you tend to have a lot of jay walkers. I also think that San Francisco has some short cycles. 

Response #2: I think Portland is in the mid-fifties. The issue is minimum walk and pedestrian clearance time at the widest combination of streets. The question with 45 seconds is whether 15 seconds of green is adequate.

Response #3: The entire downtown CBD area in Oakland (120 signals) was retimed at one point using a 45 second cycle and quarter-cycle offsets due to the short block distances and one-way couplets. The 45 second cycle was adequate for pedestrians at the smaller intersections which made up about 90% of the project. This resulted in coordinated speeds of about 17 mph on the shortest blocks to about 22 mph on the longer blocks. It worked well for over 8 years. In about the past two to three years, the City has made some modifications including increasing the cycle lengths at some of the larger intersections to accommodate pedestrians a little better and installing a "ped scramble" (i.e., exclusive pedestrian phase).

Response #4: This depends on the cross section of the street, traffic, and one-way vs. two-way. 45 seconds is not too short in some downtown settings. Portland runs 46 secs off-peak.

Response #5: We recently retimed the downtown area in the City of Newport News with 2 phase intersections. When we retimed this system 4 years ago, we had two plans a 45 sec and 55 seconds. This time around our minimum was actually 55 and we increased the cycle to 65 seconds to get better progression. During non peak times, instead of a short coordinated cycles, we opted for a free mode While I am a firm believer in short cycle lengths. With 2 phase intersections, it is very hard to get two way progressions and if you are in a grid system it is even harder to get progression on the minor streets. However, I believe a 45 seconds would work on a one way street system

Response #6: Timing is not my greatest expertise, but I know here in the Triangle, DOT does not use a lot of cycle lengths that short anywhere. I have copied several peers to obtain their opinion.

Response #7: We just retimed the Fort Worth CBD (129 intersections) and much of the area runs on a 44-second cycle during the off-peak. This area includes relatively narrow streets for which 21-seconds is the minimum ped time. I've used 50-second cycles quite often in the downtowns of smaller Texas cities including Abilene and Odessa. (Both of those cities can run on a minimum ped cycle all the time since there's not much traffic.

Response #8: The shortest cycle we used when I was at the City of Greensboro was a 55 second for late night operation. Alot would depend on block spacing and street width. The challenge with a cycle length that short would be accommodating pedestrians. Assuming two phase operation and 5 second clearance intervals (4 amber + 1 all red) would leave you with 35 seconds of green time per cycle. Split equally would give you about 18 seconds per approach. Assuming a 7 second walk interval, you could provide an 11 second flashing don't walk if you had streets that were less than or equal to 44' in width. Most downtown areas have on-street parking and street widths greater than 44'.

Response #9: As long as pedestrian crossing times are adequate for both phases (I assume that we must be talking about a 2-phase intersection if the cycle is 45 seconds) and as long as both of the green intervals are long enough to meet driver expectation (I would not be comfortable with using a minimum green of less than 10 seconds for a through movement even on a slow-speed downtown street), I see no problem with running a cycle as short as 45 seconds under low-volume conditions.

Response #10: San Francisco uses 60 second cycle lengths in its downtown area and on most commercial streets. We have found that these cycle lengths minimize delay for pedestrians and otherwise work well for traffic flow. We don't use shorter cycle lengths out of concern that we will not provide enough crossing time for pedestrians. We typically try to provide enough time for a pedestrian to cross from beginning of green to end of yellow at a rate of 2.5 feet per second. That is typically not feasible or efficient with cycle lengths shorter than 60 seconds. Please, let me know if I can provide any other information.

Response #11: The core of downtown Portland is unique with its true one-way grid and short block spacing. In the core we run 46 seconds at night, 56 seconds during most of the day, and 60 seconds at night. The 46 is based on the largest intersection's ped min time (C = the min W + FDW + Y + AR for the two phases). I won't mind running 40 seconds if I could. We always run a varient of 1/4 cycle offsets, so the lower the cycle length, the faster the progression speed. Right now the night progression speed is about 20 mph. So the determining factor in cycle length is generally meeting the minimum pedestrian times (assuming downtown Moscow uses ped recall in all directions). Another factor in considering a low C may be the need to provide some sort of vehicle progression on certain streets. That may require more than this ped min C.

Response #12: (1) The majority of the downtown area consists of a series of one-way couplets, and all signals operate with two signal phases. However, there are several two-way streets in the area. As you can tell, one direction along the two-way streets was totally uncoordinated using the quarter-cycle offsets, but this was the sacrifice the City was willing to make. (2) Since the cycle length was quite short, we basically allocated half to each signal phase (or split 23s and 22s) with 4 seconds of walk time for each phase. The quarter cycle offset coded was 11 seconds.