QUICK SOLUTION : Transportation Engg.

SOME IMPORTANT QUESTIONS

(DCE Semester)

⚫ Prove the Super Elevation equation for a highway : 

V²/127R = (e + f)

➤ Let assume a car moving on a curve with V km/h velocity and wt. of the car is W. Super elevation in curve e in 1.

Then, super elevation, CP = (WV²/gR)

[where, R = radius of Curve]

From, above pic,

∑H = 0 

or, fR' + WSin𝛉 = PCos𝛉 ............(1)

∑V = 0

or, R' = WCos𝛉 + PSin𝛉 ..............(2)

---

Putting the value of R' in equation (1), 

f(WCos𝛉 + PSin𝛉) + WSin𝛉 = PCos𝛉 

or, fWCos𝛉 + fPSin𝛉 + WSin𝛉 = PCos𝛉

or, f + fP/W + tan𝛉 = P/W – tan𝛉

or, f(1 + Ptan𝛉/W) = P/W – tan𝛉

or, fPtan𝛉/W + P/W = – tan𝛉 – f

or, P/W(ftan𝛉 – 1) = – tan𝛉 – f

or, P/W = (f + tan𝛉 )/(1 – ftan𝛉)

or, P/W = (f + e)/(1–fe) ...........(3)

---

So, from equation (3)

P/W = f + e

or, f + e = (WV²/gR)/W

[ where, P = WV²/gR ]

or, f + e =  V²/gR

or, f + e = (0.2780)²/(9.81×R)

[ where, V km/h = (v×1000)/(60×60) m/sec = 0.2780 m/sec ]

or, f+e = V²/127R (proved)

Subscribe our Blog for more Study Material