Background: The stoping sight distance is the distance traveled when a person operating perceives the need to the stop and stops the vehicle. The velocity used in calculating stopping sight distance is the referred to as the design speed. The stopping sight distance is the sum of two parts:
1. Reaction Distance, which is the distance while the operator perceives the need to stop, and
2. Breaking Distance, which is the distance traveled while the operator puts the breaks on the vehicle, slowing the vehicle to a stop.
The general formula is:
SSD = v * t_r + v^2/(2*(a + g*G))
where:
v = the design speed of the vehicle
t_r = perceptionreaction time
a = deceleration rate of the vehicle
g = gravity constant (32.174 ft/s^2 or 9.80665 m/s^2)
G = grade of the road. Grade is positive for uphill roads. If a road has a grade of 1%, it means for every 100 ft travelled horizontally, the road has risen 1 ft. In this formula, grade is given as a percentage (i.e. 1%, G = 1)
The AASHTO (American Association of State Highway and Transportation Officials) recommends t_r = 2.5 seconds and a = 11.2 ft/s^2.
The formula for SSD using U.S. units and recommended constants is given as:
SSD = 55/15 * v + (1.075*v^2)/(11.2 + 0.32*G)
Where velocity is given in mph. The HP 32sII program given below has the U.S. Formula.
Source: Goswami, Indramil Ph.D. P.E. "All In One Civil Engineering PE Breadth and Depth Exam Guide" 2nd Edition. McGraw Hill: 2012
PROGRAM
Input:
Y: speed of vehicle or design speed (mi/hr)
X: grade of the road (i.e. for 1% grade enter as 1)
Output:
X: Stopping Sight Distance (in feet)
Formula used:
SSD = 55/15 * V + 1.075*V^2/(11+.32*G)
Assumptions:
* Total reaction time is 2.5 seconds. The deceleration rate of the vehicle is 11 ft/s^2. Both values are recommended by the AASHTO (American Association of State Highway and Transportation Officials).
Program:
S01 LBL S
S02 0.32
S03 *
S04 11.2
S05 +
S06 1/x
S07 1.075
S08 *
S09 x<>y
S10 ENTER
S11 Rdown
S12 x^2
S13 *
S14 Rup
S15 55
S16 *
S17 15
S18 ÷
S19 +
S20 RTN
Examples:
Input:
Y: 65 (V)
X: 2 (G)
Result (Fix 4): 621.9376 ft
Input:
Y: 35 (V)
X: 4 (G)
Result: 261.0828
This blog is property of Edward Shore. 2014
A blog is that is all about mathematics and calculators, two of my passions in life.
Monday, April 14, 2014
Program  HP 32SII: Stopping Sight Distance
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ReplyDeleteThe velocity used in calculating stopping sight distance is the referred to as the design speed. The stopping sight distance is the sum of two parts. Unites States city distances
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