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Stopping Distance by Sight Calculator and Formulas

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Power Transmission Design and Engineering

Car Stopping Distance by Sight Calculator SSD

A driver’s ability to see ahead is needed for safe and efficient operation of a vehicle on a highway. For example, on a railroad, trains are confined to a fixed path, yet a block signal system and trained operators are needed for safe operation. In contrast, the path and speed of motor vehicles on highways and streets are subject to the control of drivers whose ability, training, and experience are quite varied.

Sight distance is the length of the roadway ahead that is visible to the driver. The available sight distance on a roadway should be sufficiently long to enable a vehicle traveling at or near the design speed to stop before reaching a stationary object in its path.

Stopping sight distance is the sum of two distances: (1) the distance traversed by the vehicle from the instant the driver sights an object necessitating a stop to the instant the brakes are applied, and (2) the distance needed to stop the vehicle from the instant brake application begins. These are referred to as brake reaction distance and braking distance, respectively.

The stopping sight distance is the sum of the distance traversed during the brake reaction time and the distance to brake the vehicle to a stop. The computed distances for various speeds at the assumed conditions on level roadways To calculate SSD

Stopping sight distance on level road

Eq. 1
Imperial Units
SSD = 1.47 V t + ( 1.075 V2 ) / a

where

SSD = stopping distance, ft
V = design or initial speed, mph
t = brake reaction time, typically about 2.5 s
a = deceleration rate, ft/s2 see note 1

Eq. 2
Metric SI Units
SSD = 0.278 V t + ( 0.039 V2 ) / a

where:

SSD = stopping sight distance, m
V = design or initial speed, km/h
t = brake reaction time, 2.5 s
a = deceleration rate, m/s2 see note 1

Effect of Grade on Stopping

When a highway is on a grade, Equations 1 and 2 for braking distance is modified as follows:

Eq. 3
Imperial Units
dB = 1.47 V t + V2 / { 30 [ ( a / 32.2 ) ± G ] }

where:

dB = braking distance on grade, ft
V =design or initial speed, mph
a = deceleration, ft/s2 see note 1
G = grade, rise/run, ft/ft

Eq. 4
Metric SI Units
dB = 0.278 V t + V2 / { 254 [ ( a / 9.81 ) ± G ] }

where:
dB = braking distance on grade, m
V = design or initial speed, km/h
a = deceleration, m/s2 see note 1
G = grade, rise/run, m/m

In these equations, G is the rise in elevation divided by the distance of the run and the percent of grade divided by 100, and the other terms are as previously stated. The stopping distances needed on upgrades are shorter than on level roadways; those on downgrades are longer. The stopping sight distances for various grades shown in the Tables below are the values determined by using Equations 3 and 4 in place of the second term in Equations 1 and 2. These adjusted sight distance values are computed for wet-pavement conditions using the same design speeds and brake reaction times used for level roadways.

Table 1 U.S. Customary Stopping Sight Distance on Level Roadways
Design
Speed
(mph)
Brake
Reaction
Distance
(ft)
Braking
Distance
on Level
(ft)
Stopping
Sight Distance
Calculated
(ft)
Design
(ft)
15
55.1
21.6
76.7
80
20
73.5
38.4
111.9
115
25
91.9
60.0
151.9
155
30
110.3
86.4
196.7
200
35
128.6
117.6
246.2
250
40
147.0
153.6
300.6
305
45
165.4
194.4
359.8
360
50
183.8
240.0
423.8
425
55
202.1
290.3
492.4
495
60
220.5
345.5
566.0
570
65
238.9
405.5
644.4
645
70
257.3
470.3
727.6
730
75
275.6
539.9
815.5
820
80
294.0
614.3
908.3
910
85
313.5
693.5
1007.0
1010

 

Table 2 Metric Stopping Sight Distance on Level Roadways
Design
Speed
(km/h)
Brake
Reaction
Distance
(m)
Braking
Distance
on Level
(m)
Stopping
Sight Distance
Calculated
(m)
Design
(m)
20
13.9
4.6
18.5
20
30
20.9
10.3
31.2
35
40
27.8
18.4
46.2
50
50
34.8
28.7
63.5
65
60
41.7
41.3
83.0
85
70
48.7
56.2
104.9
105
80
55.6
73.4
129.0
130
90
62.6
92.9
155.5
160
100
69.5
114.7
184.2
185
110
76.5
138.8
215.3
220
120
83.4
165.2
248.6
250
130
90.4
193.8
284.2
285
140
97.3
224.8
322.1
325

Note: Brake reaction distance predicated on a time of 2.5 s; deceleration rate of 11.2 ft/s2 [3.4 m/s2] used to determine calculated sight distance.

Table 3 U.S. Customary Stopping Sight Distance on Grades
Design
Speed
(mph)
Stopping Sight Distance (ft)
Downgrades
Upgrades
3%
6%
9%
3%
6%
9%
15
80
82
85
75
74
73
20
116
120
126
109
107
104
25
158
165
173
147
143
140
30
205
215
227
200
184
179
35
257
271
287
237
229
222
40
315
333
354
289
278
269
45
378
400
427
344
331
320
50
446
474
507
405
388
375
55
520
553
593
469
450
433
60
598
638
686
538
515
495
65
682
728
785
612
584
561
70
771
825
891
690
658
631
75
866
927
1003
772
736
704
80
965
1035
1121
859
817
782
85
1070
1149
1246
949
902
862

 

Table 4 Metric Stopping Sight Distance on Grades
Design
Speed
(mph)
Stopping Sight Distance (m)
Downgrades
Upgrades
3%
6%
9%
3%
6%
9%
20
 20 20 20 19 18 18
30
32 35 35 31 30 29
40
 50 50 53 45 44 43
50
66 70 74 61 59 58
60
87 92 97 80 77 75
70
110 116 124 100 97 93
80
136 144 154 123 118 114
90
164 174 187 148 141 136
100
194 207 223 174 167 160
110
 227 243 262 203 194 186
120
263 281 304 234 223 214
130
302 323 350 267 254 243
140
341 367 398 302 287 274

Notes:

  1. Studies documented have shown that most drivers decelerate at a rate greater than 14.8 ft/s2 [4.5 m/s2] when confronted with the need to stop for an unexpected object in the roadway. Approximately 90 percent of all drivers decelerate at rates greater than 11.2 ft/s2 [3.4 m/s2]. Such decelerations are within the driver’s capability to stay within his or her lane and maintain steering control during the braking maneuver on wet surfaces. Therefore, 11.2 ft/s2 [3.4 m/s2] (a comfortable deceleration for most drivers) is recommended as the deceleration threshold for determining stopping sight distance. Implicit in the choice of this deceleration threshold is the assessment that most vehicle braking systems and the tire-pavement friction levels of most roadways are capable of providing a deceleration rate of at least 11.2 ft/s2 [3.4 m/s2]. The friction available on most wet pavement surfaces and the capabilities of most vehicle braking systems can provide braking friction that exceeds this deceleration rate.
  2. Brake Reaction Time. This is the time interval between when an obstacle in the road can first be physically seen and when the driver first applies the brakes. The assumed value is 2.5 s. This time is considered adequate for 90% of drivers in simple to moderatelycomplex highway environments.
  3. Speed. The SSD tables provide a minimum value which is based on the design speed.
  4. Grade Adjustment. AASHTO 's A Policy on Geometric Design of Highways and Streets provides values to adjust the SSD for each grade which, theoretically, affects braking distances. Due to the conservative SSD model and the nature of the State's terrain, the use of the grade adjustment is not required.

Related:

Source

AASHTO A policy on Geopmetric Design of Highways and Streets, 2018 7th Edition

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