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# Highway Verical Curve alingment following a quadratic equation

## Highway Verical Curve alingment following a quadratic equation

(OP)
Could someone please tell me why highway vertical curve alignments follow a quadratic equation? (ax^2+bx+c=y). Is it because this curve is the most smoothest between to tangent lines? I build a lot of highways but am not sure why this is the common convention by my DOT and engineers.

Thanks,

### RE: Highway Verical Curve alingment following a quadratic equation

I'm not a transpo guy, but I would presume it goes back to G forces. The effective gravity you feel is due to your acceleration in the vertical direction. Think about it in terms of rates of change.

Vertical velocity is rate of change (integral) of elevation. Vertical acceleration is rate of change (integral) of vertical velocity. If you want a constant G force, you want a constant vertical acceleration, which would mean a 1st order (linear) relationship with velocity, and a 2nd order (quadratic) relationship with elevation.

(did I do that right?)

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East - http://www.campbellcivil.com

### RE: Highway Verical Curve alingment following a quadratic equation

It is a parabolic curve.

### RE: Highway Verical Curve alingment following a quadratic equation

I was told by a very old man that it was to eliminate any changes to the vertical g forces on the cars. vertical g forces flexed the cars suspensions and early cars (Model T's, et al) had solid axles with steering drag links that were shorter than the axle control arms resulting in bump steer. I believe most early cars were designed to pull to the right on bump and bounce.

### RE: Highway Verical Curve alingment following a quadratic equation

(did I do that right?)

Acceleration is the first derivative of the velocity function.

### RE: Highway Verical Curve alingment following a quadratic equation

The second derivative of the parabolic position function gives 2a. Thus constant grade change per incremental distance.

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