vertical curve

[CivilTyro]

I am trying find out lentgh of a sag vetical curve.
Design speed, V = 50 mph
sight Distance, S = 425 ft (AASHTO Green Book)
Algebraic difference of Grades, A = 2.2%

There are two formulas one for S<L and other for S>L
Which one should I use? Also, is K value needed here? if yes, how do I find out?

Any help is greatly apprciated.

 

[Maury]

Go to Exhibit 3-75 in the AASHTO Green Book. (2004 Edition)

For a 50 mph design speed, the rate of vertical curvature (K) should have a minimum design value of 96.

L = K x A, L = 96 x 2.2 = 211.2. I would round up to 220' for the length of curve.

 

[CivilTyro]

Thanks Maury. So that means sight distance is not a factor in designing vertical curves then? Is K value a function of sight distance?

 

[francesca]

You have two formulae; one for S<L (sight distance less than the length of the curve) and one for S>L. According to Maury, L=220', and according to your data, S=425'. You would then need the S>L equation.

Is this homework?

 

[CivilTyro]

Thanks for the prompt reply Francesca. I am new to this highway geometry stuff so please do not mind, if I sound naive. Why would I use S>L equation, I know S based on my design speed 50 mph as 425 ft and founf out L based on K and A?

I have used S>L equation like you suggested for Sag vertical curve and got 1005 ft for S value. So you mean this should be the sight distance not 425 ft?
I am reviewing paving plans for a City in Arizona, I wish it was my homework

 

[francesca]

The S>L equation calculates length of curve, not sight distance (which is a constant for curve type/speed). The equation gives the same answer as the L=KA (being that L is a linear function of A), but removes the need to look up a K value. Plugging in your values gives L=210.5', the difference being rounding in the K value.

 

[CivilTyro]

gotcha!!!
Thanks again.

 

[CivilTyro]

Francesca,
The L value you got (210.5) is based on the S<L equation not S>L. Based on S>L (equation 3-52 on page 277), I got -7 ft for L which clearly not close to L obtained from K*A!!!
What do you think?