Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

596 Chapter 18 Mathematics in Engineering

0.005

0.01

0.095

0.01

second-order polynomial and the slope of this type of model is not constant (it

changes withr). For the given example, for any 0.01 m change inr, the dependent vari-

ableuchanges by different amounts depending on where in the pipe you evaluate the

change.

Stopping Sight Distance A model known asstopping sight distanceis used by civil engineers

to design roadways. This simple model estimates the distance a driver needs in order to stop

his car while traveling at a certain speed after detecting a hazard. The model proposed by

the American Association of State Highway and Transportation Officials (AASHTO) is

given by

(18.7)

where

Sstopping sight distance (ft)

Vinitial speed (ft /s)

gacceleration due to gravity, 32.2 ft /s

2

f coefficient of friction between tires and roadway

Ggrade of road

Tdriver reaction time (s)

a

%

100

b

S

V

2

2 g 1 f G 2

TV

u u

slope

change in velocity value

change in position value



1 0.495 2  1 0.5 2

1 0.01 02

0 0.095

0.10.09

u u

Initial speed  V Final speed  0

S

In the above equation, the typical value for the coefficient of friction between tires and

roadwayfis 0.33, the driver reaction time varies between 0.6 to 1.2 seconds; however, when

designing roadways, a conservative value of 2.5 second commonly is used. In the denomi-

nator of Equation (18.7), plus () indicates upgrade, whereas minus () is for downgrade.

A graph showing the stopping sight distance for a flat roadway as a function of initial speed

is shown in Figure 18.7 (G0,f0.33, andT2.5 seconds were used to generate this

graph). This is another example where a second-order polynomial describes an engineering

situation.

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