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Banking of Highway Curves

This document discusses the banking of highway curves to prevent cars from sliding up or down the road when turning. It defines the ideal angle of banking as the angle at which there is no tendency to slide due to centrifugal force being balanced by the normal reaction force. It provides the equation to calculate the ideal banking angle based on the car's velocity and curve radius. It also discusses friction force on banked curves and how friction can prevent skidding when velocity is greater than the rated speed for a curve. Examples are given to calculate the necessary banking angle and maximum non-skidding speed for different curve radii and coefficients of friction.

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ben joshua mercado
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403 views12 pages

Banking of Highway Curves

This document discusses the banking of highway curves to prevent cars from sliding up or down the road when turning. It defines the ideal angle of banking as the angle at which there is no tendency to slide due to centrifugal force being balanced by the normal reaction force. It provides the equation to calculate the ideal banking angle based on the car's velocity and curve radius. It also discusses friction force on banked curves and how friction can prevent skidding when velocity is greater than the rated speed for a curve. Examples are given to calculate the necessary banking angle and maximum non-skidding speed for different curve radii and coefficients of friction.

Uploaded by

ben joshua mercado
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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BANKING OF HIGHWAY CURVES

• Consider a car of weight W (lb, N, kN) that


makes a horizontal turn on curve of radius r
(ft, m) while traveling at v (ft per s, m per s)
BANKING OF HIGHWAY CURVES
• Ideal angle of banking – angle θ (with the
horizontal) in which curve is banked so there is
no tendency for a car to slide up or down the
road
• Assuming centrifugal force is applied through
center of gravity to create dynamic
equilibrium, and resultant normal pressure
against wheels is represented by N
BANKING OF HIGHWAY CURVES
• Centrifugal Force – inertial force directed away
from axis of rotation that appears to act on all
objects when viewed in a rotating reference
frame
* Dimensions of car are negligibly small
compared to path, so the car s considered as a
particle
• The equation defines ideal angle of banking in
terms of velocity of car and radius of turn,
independent of weight of car
• v – rated speed of curve
• g = 9.81 m/s2 or 32.2 ft/s2
• r – radius of curve
FRICTION FORCE ON BANKING CURVE

• Friction force – exerted by road on tires when


car is rounding a banked curve with velocity
greater than rated speed of curve; acts down
at plane of banking
• When car is traveling at greatest speed and
about to skid up, F = fN
• F and N are components of total reaction R
• f – tangent of angle of friction; coefficient of
friction
• If car is on point of slipping down the plane of
banking (because of insufficient speed)
EXAMPLE 1
Traffic travels at 65 mph around a banked
highway curved with a radius of 300 ft. What
banking angle is necessary such that friction will
not be required to resist centrifugal force?
Note: 1 mi = 5280 ft
EXAMPLE 2
The rated speed of a highway curve of 60 m
radius is 50 kph. If coefficient of friction
between tires and road is 0.6, what is the
maximum speed at which car can round the
curve without skidding?
EXAMPLE 3
An automobile travels on a perfectly
horizontal, unbanked circular track of radius R.
The coefficient of friction between tires and
track is 0.3. If car’s velocity is 15 m per sec, what
is the smallest radius it may travel without
skidding?

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