Question Regarding Lost Time

[jose_maria]

Hey guys,

I am looking through my notes (School of PE) and I am unsure about what exactly makes up cycle lost time (L) in the cycle length time equation (HCM EQ 18-17). I believe from HCM, L is the total all red (clearance) lost time and the total startup lost time for all phases that would be used for that equation.

The reason I am confused, is because if given a saturated(s) and actual flow rate(v) for an approach, you can find the effective green time (g) by using g=(v/s)*(C/Xc) where C it the total cycle time and Xc is the critical volume to capacity ratio. So how is the YELLOW TIME accounted for here? Almost seems like its getting lumped into the effective green time since total C is being used. Unless the actual saturation V is accounting for the yellow time behind the scenes since v is how many cars get through on a green for an hour? Or the yellow is included in the LOST TIME, L used in HCM EQ 18-17

Later in the notes I have an equation for effective green time= phase length - lost time = (Green time+ Yellow time+ all red)- (startup + clearance lost times). I thought Phase length only includes effective green time and yellow time and that all red (clearance) would be subtracted with the other lost times?

The above effective green time equation is being used to find effective green time (g) in the following capacity (c) equation: c=N*S(g/C), where N = No of lanes, S= saturation flow rate & C = total cycle length).

Hope the above wasn't to confusing. I think I basically need a break down of Cycle time (what what makes up lost time, where does the yellow and red times go, what is included in the Phase Time etc.)

Thanks!

 

[jose_maria]

Hey Guys,

Can someone explain what makes up the Lost time in the following capacity (c) equation:

c=Ns(g/C)

N- no of lanes
s- saturation flow rate
g- effective green time (Phase Length - Lost Time) = (Green time+ yellow time+ All Red time) - ( Startup and Clearance Times)

Why is the ALL RED Time (clearance interval?) added to the Phase Length Side? Shouldn't it be subtracted as a lost time?

Here is the example problem: At a 90 second cycle four-legged signalized intersection, one lane SB approach has a 30 second green time, a 3 second yellow time, and a 1 second all red time. The intersection has saturation headway of 2 sec/veh., startup lost time of 2 seconds per phase, and clearance lost time of 3 seconds per phase. Under these conditions, what would be the approximate capacity of this SB approach?

For the effective green time they use this: (30+3+1)-(2+3) .... which seems incorrect to me... shouldn't it be (30+3)-(2+3+1)?

Also, I thought clearance lost time and all red time where the same??

Thanks!

 

[ptatohed]

You had two threads back to back with the same exact thread title so I merged them. 

 

[jose_maria]

Thanks! It Kept giving me an error when I hit submit thread so I didn't realize the were actually posting.

 

[wannacape]

I don't know what is right solution, but I assume book's way is correct because it matches with how I think~

AR is the all-red time set and displayed on all approaches. AR is theoretically meant for the vehicles to clear the intersection but it may not be what the vehicles actually take. 

All capital letters in equations G, Y, R, AR, C are how they are 'set' ie what is 'displayed'.  All the small letters g, r, tL are what you actually 'get' or 'effective' as a result how drivers actually react to the set times. 

 Some feel free to correct me..

 

[ptatohed]

j_m,

You asked a lot of questions so it is not completely feasible to answer them all, sorry.  But, if it helps, what really made some of the concepts sink in for me was HCM 2010 Exhibit 18-14 on page 18-40.  Being able to visualize the components of Cycle Length, C, really helped me.  I'm sure you've seen this exhibit but I thought I'd mention it just in case.    

 

[John QPE]

I'm sorry you are struggling with this concept, and the HCM isn't exactly the best book to learn from. However, effective green time 'g' small 'g' NOT big 'G' is g = G + Y + AR - (tl)

See the attached.

View attachment tl.pdf

 

[zzzvvvzzz]

Hey guys,

I am looking through my notes (School of PE) and I am unsure about what exactly makes up cycle lost time (L) in the cycle length time equation (HCM EQ 18-17). I believe from HCM, L is the total all red (clearance) lost time and the total startup lost time for all phases that would be used for that equation.

The reason I am confused, is because if given a saturated(s) and actual flow rate(v) for an approach, you can find the effective green time (g) by using g=(v/s)*(C/Xc) where C it the total cycle time and Xc is the critical volume to capacity ratio. So how is the YELLOW TIME accounted for here? Almost seems like its getting lumped into the effective green time since total C is being used. Unless the actual saturation V is accounting for the yellow time behind the scenes since v is how many cars get through on a green for an hour? Or the yellow is included in the LOST TIME, L used in HCM EQ 18-17

Later in the notes I have an equation for effective green time= phase length - lost time = (Green time+ Yellow time+ all red)- (startup + clearance lost times). I thought Phase length only includes effective green time and yellow time and that all red (clearance) would be subtracted with the other lost times?

The above effective green time equation is being used to find effective green time (g) in the following capacity (c) equation: c=N*S(g/C), where N = No of lanes, S= saturation flow rate & C = total cycle length).

Hope the above wasn't to confusing. I think I basically need a break down of Cycle time (what what makes up lost time, where does the yellow and red times go, what is included in the Phase Time etc.)

Thanks!

In my notes these are some equations used for steps for calculating Signal Timing...  L= total  lost time in all phases ;  l = total lost time in each phase; C = optimum cycle length; g = effective green time to each phase based on its critical v/s; G = Green interval; Y = yellow; R = Red; (v/s)i = critical v/s in each phase ; E(v/s)i = sum of the critical (v/s)i in all phases. Xc = is the critical volume to capacity ratio

g = (C-L) x (v/s)i / E(v/s)i  ;this is for each phase

Phase time = g + l , for each phase

G = phase time - Y - R , for each phase

C = L (Xc) / Xc - E(v/s)i

 

[jose_maria]

Thanks for all of the replies. I think I have a better understanding of it now.