A 2500-lb passenger vehicle originally traveling on a straight and level road gets onto a section of the road with a horizontal curve of radius = 850 ft. If the vehicle was originally traveling at 55 mi/h, determine (a) the additional horsepower on the curve the vehicle must produce to maintain the original speed, (b) the total resistance force on the vehicle as it traverses the horizontal curve, and the total horsepower. Assume that the vehicle is traveling at sea level and has a front crosssectional area of 30 ft2.
What will be an ideal response?
First, determine all of the resistive forces, air and rolling, acting on the vehicle while it is traveling straight and then determine its horsepower requirement.
The air resistance is (using Equation 3.13):
Ra = 0.5 × [(2.15pCDAu2) / g]
Ra = 0.5 × [(2.15(0.0766)(0.4)(30)(55)2 / 32.2]
Ra = 92.83 lb
The rolling resistance is (using Equation 3.14):
Rr = (Crs + 2.15Crvu2) × W
Rr = (0.012 + 2.15(0.65 × 10–6)(55)2) × 2500
Rr = 40.57 lb
Since these are the only forces acting on the vehicle, one can now determine the horsepower requirement on the straight segment. Use Equation 3.17.
P = 1.47Ru / 550
P = [(1.47(92.74 + 40.57)(55)) / 550]
P = 19.60 hp
The curve resistance is (using Equation 3.16):
Rc = 0.5 × [(2.15u2W) / gR]
Rc = 0.5 × [(2.15(55)2(2500) / (32.2)(850)]
Rc = 297.03 lb
Determine the additional horsepower for the vehicle to maintain its original speed on the curve section of roadway.
P = 1.47Ru / 550
P = [(1.47(297.03)(55)) / 550]
P = 43.66 hp
Thus, the additional horsepower needed for the vehicle to maintain its original speed on the curve section of the roadway is 43.7 hp.
The total resistive force acting on the vehicle while in the curve is:
Rtotal = Ra + Rr + Rc
Rtotal = 92.8 + 40.6 + 297.0
Rtotal = 430.4 lb
Therefore, the total resistive force acting on the vehicle in the curve is 430 pounds.
Determine the total required horsepower for the vehicle to maintain its original speed.
hprequired = hpcurve + hpstraight
hprequired = 43.66 + 19.60
hprequired = 63.26 hp
Therefore, the vehicle will need to produce 63.26 horsepower to traverse the curve at its original velocity.
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