SSD/PSD on a Vertical Curve

[jose_maria]

Hey Guys,

I have a few questions regarding stopping sight distance (SSD) and passing sight distance (PSD) on vertical curves.

I am working out a afternoon problem in the school of PE notes which asks you to calculate ACTUAL SSD (its asking for headlight SSD but same thing) on a sag vertical curve. both grades and the lengths are provided.

So using the AASHTO equations L=AS^2/(400+3.5S) I am able to come up with an S of 413 feet which is all fine. This assumes S<L, which is the case (413<600)

It then asks you "What is the maximum design speed (based on SSD)".

So the way I approached this was to determine my actual K value (since we are on a VC):

K=L/A = (600/6.5) = 92.3. Based on AASHTO GB Table 3-36 I would pick 45 mph because it has a required K of 79 while the K for 50mph is 96.

The way the school of PE notes approached it was to compare the 413' actual SSD with the "Stopping Sight Distance" column on table 3-36.So for 45 mph its 360' and 50mph its 425. They also picked 45 mph as the answer.

So my questions are:

1. Since this is on a VC, why not find your K value and use that approach. Aren't the SSD's listed in the "SSD" column adjacent to the K Values for Level Roadways?
   
2.  Do these values have anything in common? For example, If asked what is the minimum length of VC based on SSD for say 30 mph, would that be 500' or L=K/A?
   
   would it be a minimum of 500' if the L from L=K/A was smaller?
   

Thank you!

 

[John QPE]

There are a lot of questions in here, let me try to answer some.

The way you calculate the Design speed as listed in your notes is correct. You can also do it by the K value, you will also get the correct answer. I think if you were to see the 'K' value approach you'd have a problem detailing an exiting vertical curve, and it asking you what the appropriate speed limit would be.

The second question, I have no idea where you are getting 500' from as you didn't post grades, but these are all related. If you had to design a VC for 30 mph you simply use K=37 and multiply by A

 

[jose_maria]

There are a lot of questions in here, let me try to answer some.

The way you calculate the Design speed as listed in your notes is correct. You can also do it by the K value, you will also get the correct answer. I think if you were to see the 'K' value approach you'd have a problem detailing an exiting vertical curve, and it asking you what the appropriate speed limit would be.

The second question, I have no idea where you are getting 500' from as you didn't post grades, but these are all related. If you had to design a VC for 30 mph you simply use K=37 and multiply by A

I realize that I am getting the same maximum speed using the K-value method, I just don't understand how you can theoretically use "SSD on level roadway" to find a maximum speed limit on a vertical curve. It is because when you calculated the Actual SSD (given a length and grades) using the equation  L=AS^2/(400+3.5S) (Solving for S (SSD)), its taking into account the grades and converting it to a level roadway equivalent SSD? So then you can compare the actual SSD to SSD's on level roadways to determine a maximum speed limit? 

Sorry I meant 200' (SSD for 30 mph) and not 500' for the second question I posted. So for example, if asked for a minimum length of a Sag vertical curve (Say -0.50% and +0.75%), would it be 200' (SSD column in previously attached table) or L=KA = 37*(0.50+0.75) = 46.25'? 

Thanks!

 

[ngmakhlo_PE]

I realize that I am getting the same maximum speed using the K-value method, I just don't understand how you can theoretically use "SSD on level roadway" to find a maximum speed limit on a vertical curve. It is because when you calculated the Actual SSD (given a length and grades) using the equation  L=AS^2/(400+3.5S) (Solving for S (SSD)), its taking into account the grades and converting it to a level roadway equivalent SSD? So then you can compare the actual SSD to SSD's on level roadways to determine a maximum speed limit? 

Sorry I meant 200' (SSD for 30 mph) and not 500' for the second question I posted. So for example, if asked for a minimum length of a Sag vertical curve (Say -0.50% and +0.75%), would it be 200' (SSD column in previously attached table) or L=KA = 37*(0.50+0.75) = 46.25'? 

Thanks!

I ran into the same situation this weekend while solving a SSD problem for a vertical curve and my instructor for my EET course said to always use the equation L=AS^2/(400+3.5S) just to be on the safe side. But, just curious, why are you using the K value for 30 mph? Was it given to use that speed? Just doing a quick look at your solution above it appears you got a SSD that falls between 45-50 mph, so there is your answer, you don't need to further calculate anything. Please let me know if I am missing something.

 

[jose_maria]

I ran into the same situation this weekend while solving a SSD problem for a vertical curve and my instructor for my EET course said to always use the equation L=AS^2/(400+3.5S) just to be on the safe side. But, just curious, why are you using the K value for 30 mph? Was it given to use that speed? Just doing a quick look at your solution above it appears you got a SSD that falls between 45-50 mph, so there is your answer, you don't need to further calculate anything. Please let me know if I am missing something.

Sorry for the confusion. The K value for 30 mph was just another example I was using to convey my confusion. As in, if you were asked what would be the minimum length of a vertical curve given a 30 mph design speed, would you say 200' or would you say it was L=KA (given grades of course) even if using the K value method could result in a smaller L compared to the 200'.

So your instructor said if you are given a problem where you are asked what should the posted speed be given 2 grades (sag VC) and a length, you should first calculate the Actual SSD using L=AS^2/(400+3.5S), then compare the actual SSD to the values in Table 3-36 for "level roadways" to determine the posted speed? 

Versus calculating your actual K value, then comparing it to the "design K values" in Table 3-36 to determine what your posted speed should be?

I believe we are on the same page... but can you share the problem you were working on?

Thanks.

 

[ngmakhlo_PE]

Sorry for the confusion. The K value for 30 mph was just another example I was using to convey my confusion. As in, if you were asked what would be the minimum length of a vertical curve given a 30 mph design speed, would you say 200' or would you say it was L=KA (given grades of course) even if using the K value method could result in a smaller L compared to the 200'.

So your instructor said if you are given a problem where you are asked what should the posted speed be given 2 grades (sag VC) and a length, you should first calculate the Actual SSD using L=AS^2/(400+3.5S), then compare the actual SSD to the values in Table 3-36 for "level roadways" to determine the posted speed? 

Versus calculating your actual K value, then comparing it to the "design K values" in Table 3-36 to determine what your posted speed should be?

I believe we are on the same page... but can you share the problem you were working on?

Thanks.

when I go home tonight I will try and find the example problem I am referring to, but yes that is what my instructor said to do, and I believe there is a note somewhere above or below table 3-36 in AASHTO that says the table is based on SSD, therefore when calculating the design speed or finding design speed I believe it should be based on your SSD.

 

[jose_maria]

when I go home tonight I will try and find the example problem I am referring to, but yes that is what my instructor said to do, and I believe there is a note somewhere above or below table 3-36 in AASHTO that says the table is based on SSD, therefore when calculating the design speed or finding design speed I believe it should be based on your SSD.

Thanks! That would be great. 

 

[ptatohed]

j_m, your question about calculating the SSD on a VC by using level ground SSD values is a good one.  I had the same question when I was studying.  The answer is 'yes', use the flat ground SSDs.  My understanding for the 'why' of it is tlevel ground SSD is a general average provided that the driver could be anywhere on the curve.  If the driver were on the negative grade of a VC, their SSD would be greater, if they were on the positive grade, their SSD would be shorter.  So, by using level SSD, you end up with an average.  If I am wrong, someone please correct me. 

 

[ngmakhlo_PE]

j_m, your question about calculating the SSD on a VC by using level ground SSD values is a good one.  I had the same question when I was studying.  The answer is 'yes', use the flat ground SSDs.  My understanding for the 'why' of it is tlevel ground SSD is a general average provided that the driver could be anywhere on the curve.  If the driver were on the negative grade of a VC, their SSD would be greater, if they were on the positive grade, their SSD would be shorter.  So, by using level SSD, you end up with an average.  If I am wrong, someone please correct me. 

To add on to this, that is why we are given a table with SSD values for crest vertical curves and a table with SSD values for sag vertical curves, as long as you are sure to use the correct table given the type of vertical curve you should be all set.

 

[jose_maria]

To add on to this, that is why we are given a table with SSD values for crest vertical curves and a table with SSD values for sag vertical curves, as long as you are sure to use the correct table given the type of vertical curve you should be all set.

j_m, your question about calculating the SSD on a VC by using level ground SSD values is a good one.  I had the same question when I was studying.  The answer is 'yes', use the flat ground SSDs.  My understanding for the 'why' of it is tlevel ground SSD is a general average provided that the driver could be anywhere on the curve.  If the driver were on the negative grade of a VC, their SSD would be greater, if they were on the positive grade, their SSD would be shorter.  So, by using level SSD, you end up with an average.  If I am wrong, someone please correct me. 

 Thanks guys. On the exam, if asked for SSD on a VC, I will use the L equations from the AASHTO GB solving for S and if asked for a posted speed given L and grades, I will use those same equations to solve for S and compare those S values with the level roadway values (using the appropriate Sag/Crest) tables to determine a speed limit. 

But if asked for the length of a vertical curve, using the K value method I will use the K=LA equation, utilizing the design K values. If asked for a length without the problem specifying using the K value method, I will go back and use the L equations. 

Does that all sound correct? 

 

[ngmakhlo_PE]

 Thanks guys. On the exam, if asked for SSD on a VC, I will use the L equations from the AASHTO GB solving for S and if asked for a posted speed given L and grades, I will use those same equations to solve for S and compare those S values with the level roadway values (using the appropriate Sag/Crest) tables to determine a speed limit. 

But if asked for the length of a vertical curve, using the K value method I will use the K=LA equation, utilizing the design K values. If asked for a length without the problem specifying using the K value method, I will go back and use the L equations. 

Does that all sound correct? 

That is correct, for the most part, someone correct me if I am wrong, but I believe that the only time that you should use the K=LA equation is if the grades are given and a design speed for the vertical curve is given so that you can use the K value that corresponds with that design speed to then calc L, once you have L you can use the L value in your calc to solve for SSD. I don't think they will specify which approach you should be using. Does this make sense?

 

[jose_maria]

That is correct, for the most part, someone correct me if I am wrong, but I believe that the only time that you should use the K=LA equation is if the grades are given and a design speed for the vertical curve is given so that you can use the K value that corresponds with that design speed to then calc L, once you have L you can use the L value in your calc to solve for SSD. I don't think they will specify which approach you should be using. Does this make sense?

That makes sense to me. The school of PE has a problem like that where they give you 2 grades and a design speed and ask you to find the length "using the K value method"..... Its weird that they state the problem like that, almost making it sound like there would be another way to solve for L. Which I don't believe there is.

Ugh.. Maybe I'm just over thinking it all at this point. But no, what you said makes sense. 

 

[ngmakhlo_PE]

That makes sense to me. The school of PE has a problem like that where they give you 2 grades and a design speed and ask you to find the length "using the K value method"..... Its weird that they state the problem like that, almost making it sound like there would be another way to solve for L. Which I don't believe there is.

Ugh.. Maybe I'm just over thinking it all at this point. But no, what you said makes sense. 

Yes, do not over think it, if you are given the grades and design speed and asked for L the quickest way to solve for L and not get involved with finding the SSD and comparing it to L is by using K=LA. And again, if anyone finds this statement to be incorrect please advise.