Crest Curves - Heights of Eye & Objects as related to G1 & G2

[PeonPE]

So I am here working through problems on a very fun Friday night (can you say commitment?!). I have a question regarding several example problems I am working through regarding Crest Curves. Normally you are given the Stoping Sight Distance or Passing Sight Distance, the approach and leave grades then asked what the minimum length of the curve should be.

Now I am using the current standard book, the AASHTO Green Book 2011 and the 12th Edition CERM. I am looking specifically at section 3.4.6 in the Green Book (pages 3-149 thru 3-157) as well as all of Chapter 78 - Vertical Curves in the CERM.

The Equation is L = 2S - ((200(SQRT h1 + SQRT h2)^2)/A)

L = length of curve, ft

A = Algebraic difference in grades

S = Sight Distance (Stopping, Passing, Decision, etc.), ft

h1 = height of eye above roadway, ft

h2 = height of object above roadway surface, ft

The issue I have is, frequenty in the example problems, (PPi Exam Cafe, Online, etc.) I am always getting the wrong answer because my assumptions for h1 and h2. Unless defined in the problem the Green Book says for:

SSD: h1 = 3.5' h2 = 2.0'

PSD: h1 = 3.5' h2 = 3.5'

DSD: Same as SSD

This is where I have my issue. In these example problems where h1 and h2 are not given explictly the problem writer somehow correlates h1 and h2 with the Grades G1 and G2.

For example PPi somehow concludes that if G1 = 3% and G2 = 0% then somehow they have extrapolated that h1 = 3.5' and h2 = 4.25' when doing a SSD problem.

This guy here seems to say the same thing but for PSD:

http://www.webpages.uidaho.edu/niatt_labmanual/chapters/geometricdesign/theoryandconcepts/CrestVerticalCurves.htm

And again for SSD:

http://www.webpages.uidaho.edu/niatt_labmanual/chapters/geometricdesign/exampleproblems/crestverticalcurves.htm

Is there a mathematical correlation between Approach and Exit Grades G1 and G2 or are the authors of these examples just using older standards from the Blue Book, Older Green Books, ITE Manual, conservative State Standards?

I guess for the PE Exam I just want to have the right "assumptions" for my h1 and h2 elevations. Normally I just go with what the Green Book says, but since I have seen the above examples and many others where they seem to pull the h1 and h2 values out of the sky I thought I would ask here.

Thanks.

 

[civilized_naah]

It's simply a matter of those solutions written using older 'default values'. Use those in the current GDHS and you'll be OK

 

[ptatohed]

That is interesting. I have never read about h2 = 0.5' or h2 = 4.25' (as assumptions). I have the 2004 5th Ed and 2011 6th Ed GDHS and both show that h1 = 3.5' (car) or h1 = 7.6' (or 8') (truck) and h2 = 2.0' (stopping sight) or h2 = 3.5' (passing sight). <-- I think you are safe to assume these values (unless the problem statement provides otherwise, of course). Remember, using the assumed values for h1/h2, reduces eqns (3-41) and (3-42) to (3-43) and (3-44), respectively (stopping sight), and eqns (3-41) and (3-42) to (3-45) and (3-46), respectively (passing sight).

 

[PeonPE]

I appreciate the responses.

Amongst other materials, I am using a massive printout of the PPi Exam Cafe Problems circa 2005. There are a substantial number of errors, omissions, unexplained assumptions in many problems. Since I don't have access to the errata without paying the fee I am using it as a good learning experience. I am not the kind of personality that simply accepts the answer because it was printed, I spend a long time looking at material. For me its a good study aide since my nature is forcing me to really read into these concepts. It's extra beneficial for me since I am a MechE studying to take the CivilTranspo exam. This was just one of those problems where the printed material, manual and Google searches weren't getting me anyplace. I am grateful for this forum's existence.