Highway profiles following a second order equation 4

[CivilG]

Could someone please advise me why designed highway profiles always follow a second degree equation (ax^2+bx+c). I have always been curious about this.

Thanks,
Civil G

 

[fel3]

See the top of the second page:

http://www.cpp.edu/~hturner/ce220/vertical_curves.pdf

Parabolas have a constant rate of change of slope, which makes for a smooth transition along the curve.

==========
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

 

[Tommy385]

My knowledge of highway engineering ist totally rusty, but isn't it a Euler spiral (Klotoide) a curve with constant rate of change of slope and not a parabola?

 

[caenright]

@Tommy385 -
Clothoid and Euler spirals are typically used for horizontal curve transitions, not so much for vertical. Vertical tends to be simply a parabola as this is a smooth enough transition for vertical curves.

 

[Tommy385]

@ca_enright
haven't notice it's about vertical curves....
regards

 

[beej67]

"Profile" implies vertical. "Plan" implies horizontal.

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[chicopee]

I may be off on this subject but I believe that parabolic curves for profiling highways was based on the stopping distances required when drivers are braking their vehicles. A reference of interest is Route Surveys and Design by Hickerson

 

[BUGGAR]

The constant rate of change of slope eliminates problems with cars that suffer from bump steer? Ever notice the old cars with drag link steering arranged bump steer to pull the car away from on-coming traffic? Works in Europe, too, only upside down.