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

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

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  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

  2. 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

  3. Deriving the braking distance formula, p.62

  4. u2 u2 a = - a = 2x 2x Deriving the braking distance formula (continued), p.63 Forces acting on this free body is at equilibrium: W*sinr -W*f*cosr = W*a/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) It’s deceleration, so add -. Solve for a:

  5. u2 Db = 2g(f - G) u2 Stopping Sight Distance = ut + 2g(f ± G) 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

  6. u22 u12 Db = 2g(f - G) 2g(f - G) The horizontal distance traveled in reducing the speed from u1 to u2 Derivation of Eq. 3.23 Speed 0 u1 Db for U1 u2 Db for U2 Speed 0

  7. 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.

  8. Minimum Radius of a Circular Curve (p.70) Wac The centrifugal force: Fc = g

  9. Minimum Radius of a Circular Curve (cont) Wac The centrifugal force: Fc = g  Superelevation

  10. 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

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