Lec 5, Ch3, pp'6272, Vehicle Characteristics Continued Objectives

1
Lec 5, Ch3, pp.62-72, Vehicle Characteristics
(Continued) (Objectives)

• Understand how the braking distance formula is
  derived
• Know how to use the braking distance formula
• Understand how the minimum radius of a circular
  curve formula is derived
• Know how to use the minimum radius formula

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What we discuss in the lecture

• Derivation of the braking distance formula
• A few examples of using the braking distance
  formula
• Derivation of the formula for determining the
  minimum radius of a circular curve
• A few examples of using the minimum radius
  formula

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Deriving the braking distance formula, p.62
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Deriving the braking distance formula
(continued), p.63
Forces acting on this free body is at equilibrium
Wsinr -Wfcosr Wa/g
a is unknown. We want to use the known values
(initial speed u, and distance x) to determine a.
We assume first the vehicle accelerated from
speed 0 to u.
x ½at2 u at
Now t u/a. Plug in this in the RHS of x
x ½a t2 ½a(u2/a2)
Now, we get
x (½)(u2/a)
Its deceleration, so add -.
Solve for a
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Deriving the braking distance formula (continued)
The braking distance is a horizontal distance (do
you know why we use a horizontal distance?) while
x is the distance along the slope therefore,
Db x cosr
Once you know this, you can easily follow the
derivation in the text. Go to page 64.
Eq. 3.18
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The horizontal distance traveled in reducing the
speed from u1 to u2
Derivation of Eq. 3.23
Speed 0
u1
Db for U1
u2
Speed 0
Db for U2
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Example 3-7, Another way to solve this problem
Estimates of velocities There is no need to use
Eqs, 3.25, 3.26, 3.27. Use Eqs. 3.19 and the case
where speed reduces from u1 to u2.
Use the blackboard!!
Go to pages 69.
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Minimum Radius of a Circular Curve (p.70)
Wac
The centrifugal force Fc
g
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Minimum Radius of a Circular Curve (cont)
Wac
The centrifugal force Fc
g
?
Superelevation
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Warning!
Coefficient of skidding friction and Coefficient
of side friction ARE different!
Braking distance ? Use coefficient of skidding
friction (longitudinal friction). Usually
Minimum radius ? Use coefficient of side
friction, Table 3.3