Highway design is strongly influenced by physical analyses, asapparent in construction of safe circular turns at common highwayspeeds. The following analyses represent common highway designconcerns.
State highway 33 south of Stillwater is scheduled for (extensive)modification between the Cimarron river and US 177 by fall 2012.Dr. Lanee has noticed that one of the curves on this asphalthighway (which is scheduled for replacement) is crowned such thatthe outside lane is banked away from the turn center rather thaninto the turn. Consider a car that negotiates this turn, which willbe assumed to be symmetrically banked at the road center at anglesof 4.00º toward and away from the turn center. For the purposes ofthese calculations, assume that the turn radius for cars in theinside and outside lanes is identical. What is the radius of thiscurve for cars on the inside lane to safely negotiate the turnwithout friction at 65mph (the curveâs posted speed limit)? What isthe maximum safe speed for cars in the outside lane withoutfriction? Determine the minimum frictional coefficient for safetravel in the outside lane at the posted speed limit. Is thiscoefficient reasonable?
Highway design is strongly influenced by physical analyses, asapparent in construction of safe circular turns at common highwayspeeds. The following analyses represent common highway designconcerns.
State highway 33 south of Stillwater is scheduled for (extensive)modification between the Cimarron river and US 177 by fall 2012.Dr. Lanee has noticed that one of the curves on this asphalthighway (which is scheduled for replacement) is crowned such thatthe outside lane is banked away from the turn center rather thaninto the turn. Consider a car that negotiates this turn, which willbe assumed to be symmetrically banked at the road center at anglesof 4.00º toward and away from the turn center. For the purposes ofthese calculations, assume that the turn radius for cars in theinside and outside lanes is identical. What is the radius of thiscurve for cars on the inside lane to safely negotiate the turnwithout friction at 65mph (the curveâs posted speed limit)? What isthe maximum safe speed for cars in the outside lane withoutfriction? Determine the minimum frictional coefficient for safetravel in the outside lane at the posted speed limit. Is thiscoefficient reasonable?
