Question

A building is next to a horizontal curve with a 132 ft. radius on a 2 lane rural highway. The inside lane is 10 feet wide, and the building is 6 feet from the shoulder, which is 4 feet wide.

a) What sight distance is available to the driver at the critical point?

b) Assuming design values for driver perception and reaction time and longitudinal deceleration, What is the maximum speed that would provide appropriate stopping sight distance?

PLEASE EXPLAIN YOUR ANSWER TO UNDERSTAND THE CONCEPT.

Answer 1

a)The first thing that we need to do is calculate the distance from the edge of the Building to the center of the nearest lane.

This turns out to be 6+10=16ft

Next, we need to calculate the degree of the curve using the equation R = 5730/D. R=132ft

R=5730/132=43.41

The degree of the curve turns out to be 43.41°. The last step involves solving for the sight distance using the equation below.

M = (5730/D)*(1 - cos(SD/200))

Where:
M = Distance from the center of the inside lane to the obstruction, 16 ft
D = Degree of the curve, 43.41°.

Where R = 5730/D

S = Sight distance (ft)
R = Radius of the curve, 132 ft

16=132*(1-cos(S*43.41/200)

16/132=1-cos(S*43.41/200)

0.122=1-cos(S*0.22)

cos(0.22S)=1-0.122

cos(0.22S)=0.878

0.22S=Cos^-1 (0.878)

0.22S=28.6

S=28.6/0.22

S=130ft

b)

Adequate stopping sight distance must be provided on 100% of the street and highway system so a driver with the standard eye height can see an object of standard height with sufficient time to stop safely. This assumes a certain level of alertness on the part of the driver and no influence on a driver’s perception and reaction due to added complexity of traffic, control and local environmental condition

Stopping sight distance is applied where only one obstacle must be seen in the roadway and dealt with. Decision sight distance is different for urban versus rural conditions, and also for maneuvers ranging from stopping to speed, path or direction change within the traffic stream.

SSD = 1.47 Vt + ​^{1.075 V2}⁄_a

where SSD = required stopping sight distance, ft. or m ,

V = speed, mph or kn/n,

t = perception-reaction time, sec., typically 2.5 sec. for design,

g = grade, decimal,

a = deceleration rate, ft/sec2 or m/sec2 .

The NCHRP Report 400 recommended new design criteria to AASHTO using a deceleration rate of 11.2 ft/sec2 or 3.4 m/sec2

a=11.2ft/sec2

The running speed is the average operating speed on the roadway and is typically less than design speed, about 83% to 100% of design speed for 20 mph to 70 mph (32 kph to 113 kph),

assume V=50mph=

SSD=1.47*50*2.5+1.075((50)^2) /11.2

SSD=183.75+240

SSD=423.8ft