Net speed calculator
Mar 23, 2016
Net speed calculator
Program
• Input:– Acceleration (a) & Deceleration rates (d) in ft/s2– Distance traveled (L) in feet– Distance between intersections (Di) in feet– Speed Limit (Slim) in mph– Average waiting time at an intersection (Twait) in
seconds
– Time step (h) in seconds (can be change in the program, but it isn’t ask to the user)
• Output:– Net Speed (Snet)– Time-Distance-Speed Matrix
– Time-Space Diagram
Run the program• Set the Current
Directory in the right folder (the one that contains MainProgram4 and the other functions)
• Open MainProgram4
• Run MainProgram4
0 20 40 60 80 100 120 1400
200
400
600
800
1000
1200
1400
Time (sec)
Dis
tanc
e (ft
)
a= 4 ft/s2 d= -10 ft/s2
L= 1300 ftSlim= 25 mphDi= 260 ftTwait= 15 sec
Matlab Command Window
Time-Space Diagram
Illustration of Inputs and Outputs
Time-Space Diagram Detail
10.5 11 11.5 12 12.5 13 13.5 14 14.5225
230
235
240
245
250
255
260
265
Time (sec)
Dis
tanc
e (ft
)
a= 4 ft/s2 d= -10 ft/s2
L= 1300 ftSlim= 25 mphDi= 260 ftTwait= 15 sec
h=0.05 sec
Instantaneous Speed and Distance traveled are recorded at each time step during non constant speed phases (acceleration end deceleration phases), otherwise (when the speed limit is reached, or when the vehicle is stopped), they are recorded only at the beginning and end of the phase)
Assumptions
• Constant Acceleration/Deceleration• Intersections are equidistant • Same waiting time at every intersection
(uncoordinated intersections)• No queuing space
Acceleration rate Deceleration rate
AASHTO Green book
4 to 4.5 ft/s2 (From 0 to 25-40mph)
11.2 ft/s2 (comfortable)>=14.8 ft/s2 (emergency)
Traffic Engineering Handbook
3.6 ft/s2 9.8 ft/s2
FHWA 7.84 ft/s2 (sedans) (0-60mph)12.49 ft/s2 (sport cars) (0-60mph)
Spurr 6.4 ft/s2 (0.16-0.37g; avg: 0.2g)
Haas, Inman, Dixson, Warren
4.5 ft/s2 (0.14g) (all speed) 5.79 ft/s2 (0.18g) (initial speed 35-40 mph)
Acceleration/Deceleration rates
A lot of different values. But Deceleration rate always > Acceleration rate (cf. hypotheses)
Distance between intersection:
• Portland downtown: 1intersection every 260ft• Phoenix downtown: 1intersection every 385ft• Tucson: 440ft• Los Angeles downtown N-S: 1intersection
every 660ft (410ft E-W)• Manhattan E-W: 1intersection every 880ft
(255ft N-S)• Lyon downtown (2è): 1intersection every 185ft
*Distances calculated with Google Earth
Acc. rate 6 ft.sec-2Dec. rate -6.5 ft.sec-2Speed limit 25 mphDistance traveled 4000 ftDistance between intersections 260 ftAverage waiting time 10 sec
Snet= 11.3621 ft/s = 7.75 mph
Reference situation:
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
3000
3500
4000
4500
Time (sec)
Dis
tanc
e (ft
)
Time-Space Diagram
Snet1= 6.61 mph Snet2= 7.15 mph Snet3= 9.48 mph Snet4= 9.78
Time-Space Diagram for different situations
a1, d1, Di1, Slim2 Snet= 6.63 mph ~ Snet1= 6.61 mph
0 50 100 150 200 2500
5
10
15
20
25
30
35
Time (sec)
Spe
ed (m
ph)
a1, d1, Di1, Slim1Snet1
An increase in the Speed Limit (from 25mph to 45mph) doesn’t change the Net Speed much with Di1 (260), a1 and d1 (6 and -6.5 ft/s2), because the maximum speed that can be reached is around 26.8 mph.
10 20 30 40 50
6
6.5
7
7.5
8
8.5
Speed Limit (mph)
Net
Spe
ed (m
ph)
a= 6 ft/s2 d= -6.5 ft/s2
L= 4000 ftDi= 260 ft
Twait= 10 sec
Slim= 30 mphSnet= 7.76 mph
Slim= 25 mphSnet= 7.74 mph
Slim= 35 mphSnet= 7.76 mph
Slim= 40 mphSnet= 7.76 mph
Slim= 20 mphSnet= 7.54 mph
~26.8 mph
Time-Space Diagram for different situations
Net Speed and Posted Speed Limit
10 20 30 40 507
7.5
8
8.5
9
9.5
10
10.5
11
11.5
12
Speed Limit (mph)
Net
Spe
ed (m
ph)
Slim= 40 mphSnet= 11.63 mph Slim= 30 mph
Snet= 11.52 mph
Slim= 25 mph Snet= 11.17 mph
a= 6 ft/s2 d= -6.5 ft/s2
L= 4400Di= 440 ftTwait= 10 sec
10 20 30 40 50 608
10
12
14
16
18
20
Speed limit (mph)
Net
Spe
ed (m
ph)
a= 6 ft/s2 d= -6.5 ft/s2
L= 4400 ftDi= 880 ftTwait= 10 sec
Slim= 45 mphSnet= 18.81 mph
Slim= 25 mphSnet= 15.84 mph
34.1 mph49.5 mph
Net Speed and Posted Speed Limit
10 20 30 40 50
6
6.5
7
7.5
8
8.5
Speed Limit (mph)
Net
Spe
ed (m
ph)
a= 6 ft/s2 d= -6.5 ft/s2
L= 4000 ftDi= 260 ft
Twait= 10 sec
Slim= 30 mphSnet= 7.76 mph
Slim= 25 mphSnet= 7.74 mph
Slim= 35 mphSnet= 7.76 mph
Slim= 40 mphSnet= 7.76 mph
Slim= 20 mphSnet= 7.54 mph
26.8mph
Net Speed and Di
0 500 1000 1500 2000 2500 3000 3500 40000
5
10
15
20
25
Intersections Spacing (feet)
Net
Spe
ed (m
ph)
a= 6 ft/s2 d= -6.5 ft/s2 L= 4000 ft Twait= 10 sec Slim= 25 mph
Downtown PortlandDi= 260 ft
Snet= 7.74 mph
Downtown Los Angeles N-S
Di= 660 ftSnet= 13.10 mph
Lyon 2 Di= 185 ft
Snet= 6.10 mph
TucsonDi= 440 ft
Snet= 10.66 mph
Manhattan E-WDi= 895 ft
Snet= 15.28 mph
0 500 1000 1500 2000 2500 3000 3500 40000
5
10
15
20
25
Intersections Distance (feet)
Net
Spe
ed (m
ph)
L= 4000 ft Twait= 10 sec Slim= 25 mph
a= 12 ft/s2 d= -13 ft/s2
a= 6 ft/s2 d= -6.5 ft/s2
a= 9 ft/s2 d= -9.75 ft/s2
a= 3 ft/s2 d= -3.25 ft/s2
0 500 1000 1500 2000 2500 3000 3500 40000
5
10
15
20
25
30
35
Intersections Distance (feet)
Net
Spe
ed (m
ph)
L= 4000 ft Twait= 10 sec
a= 9 ft/s2 d= -9.75 ft/s2
Slim= 25 mpha= 6 ft/s2 d= -6.5 ft/s2
Slim= 25 mph
a= 6 ft/s2 d= -6.5 ft/s2
Slim= 35 mph
2 4 6 8 10 12 14 166
6.5
7
7.5
8
8.5
9
9.5
Acceleration Rate (ft/s2)
Net
Spe
ed (m
ph)
d= -15 ft/s2
L= 4000 ftDi= 260 ft
Slim= 25 mph Twait= 10 sec
a= 3.6 ft/s2
Traffic Engineering HandbookSnet= 7.59 mph
a= 4.5 ft/s2
AASHTO Green BookSnet= 7.94 mph
a= 12.49 ft/s2
FHWA (sport cars)Snet= 9.03 mph
Net Speed and acceleration/deceleration rates
0 5 10 155
5.5
6
6.5
7
7.5
8
8.5
Acceleration Rate (ft/s2)
Net
Spe
ed (m
ph)
d= -6.5 ft/s2
L= 4000 ftSlim= 25 mphDi= 260 ftTwait= 10 sec
a= 3.6 ft/s2
Traffic Engineering HandbookSnet= 7.10 mph
a= 4.5 ft/s2
AASHTO Green BookSnet= 7.40 mph
a= 3.6 ft/s2
FHWA (sport cars)Snet= 8.32 mph
-15 -14 -13 -12 -11 -10 -9 -8 -7 -67.6
7.7
7.8
7.9
8
8.1
8.2
8.3
8.4
Deceleration Rate (ft/s2)
Net
Spe
ed (m
ph)
a= 6 ft/s2
L= 4000 ftDi= 260 ft
Slim= 25 mph Twait= 10 sec
d= -9.8 ft/s2 Traffic Engineering Handbook
Snet= 8.08 mph
d= -6.5 ft/s2
Snet= 7.74 mph
d= -11.2 ft/s2 AASHTO Green Book
Snet= 8.17 mph
d= -14.8 ft/s2
AASHTO Green BookSnet= 8.33 mph
Net speed and waiting time
0 10 20 30 40 50 60 70 801
2
3
4
5
6
7
8
9
10
Waiting time (sec)
Net
Spe
ed (f
t/s)
a= 6 ft/s2 d=-6.5 ft/s2 L= 4000 ft Di= 260 ft Slim= 25 mph
Limitations
• In practice: variable waiting time, coordinate intersections
• Non constant acceleration/deceleration:
Acceleration vs speed for different gears schema
Speed
Acceleration1st gear
2nd gear
3rd gear4th gear
5th gear