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 (f

t)

a= 4 ft/s2 d= -10 ft/s2

L= 1300 ftS

lim= 25 mph

Di= 260 ft

Twait

= 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

tan

ce (

ft)

a= 4 ft/s2 d= -10 ft/s2

L= 1300 ftS

lim= 25 mph

Di= 260 ft

Twait

= 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 (f

t)

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 (

mph

)

a1, d

1, D

i1, S

lim1

Snet1

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 (

mph

)

a= 6 ft/s2 d= -6.5 ft/s2

L= 4000 ftD

i= 260 ft

Twait

= 10 sec

Slim

= 30 mphS

net= 7.76 mph

Slim

= 25 mphS

net= 7.74 mph

Slim

= 35 mphS

net= 7.76 mph

Slim

= 40 mphS

net= 7.76 mph

Slim

= 20 mphS

net= 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 (

mph

)

Slim

= 40 mphS

net= 11.63 mph S

lim= 30 mph

Snet

= 11.52 mph

Slim

= 25 mph S

net= 11.17 mph

a= 6 ft/s2 d= -6.5 ft/s2

L= 4400D

i= 440 ft

Twait

= 10 sec

10 20 30 40 50 608

10

12

14

16

18

20

Speed limit (mph)

Net

Spe

ed (

mph

)

a= 6 ft/s2 d= -6.5 ft/s2

L= 4400 ftD

i= 880 ft

Twait

= 10 sec

Slim

= 45 mphS

net= 18.81 mph

Slim

= 25 mphS

net= 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 (

mph

)

a= 6 ft/s2 d= -6.5 ft/s2

L= 4000 ftD

i= 260 ft

Twait

= 10 sec

Slim

= 30 mphS

net= 7.76 mph

Slim

= 25 mphS

net= 7.74 mph

Slim

= 35 mphS

net= 7.76 mph

Slim

= 40 mphS

net= 7.76 mph

Slim

= 20 mphS

net= 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 (

mph

)

a= 6 ft/s2 d= -6.5 ft/s2 L= 4000 ft T

wait= 10 sec

Slim

= 25 mph

Downtown PortlandDi= 260 ft

Snet= 7.74 mph

Downtown Los Angeles N-S

Di= 660 ft

Snet= 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 (

mph

)

L= 4000 ft T

wait= 10 sec

Slim

= 25 mph

a= 12 ft/s2 d= -13 ft/s

2

a= 6 ft/s2 d= -6.5 ft/s

2

a= 9 ft/s2 d= -9.75 ft/s

2

a= 3 ft/s2 d= -3.25 ft/s

2

0 500 1000 1500 2000 2500 3000 3500 40000

5

10

15

20

25

30

35

Intersections Distance (feet)

Net

Spe

ed (

mph

) L= 4000 ft T

wait= 10 sec

a= 9 ft/s2 d= -9.75 ft/s

2

Slim= 25 mpha= 6 ft/s

2 d= -6.5 ft/s

2

Slim= 25 mph

a= 6 ft/s2 d= -6.5 ft/s

2

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 (

mph

)

d= -15 ft/s2

L= 4000 ftD

i= 260 ft

Slim

= 25 mph T

wait= 10 sec

a= 3.6 ft/s2

Traffic Engineering HandbookS

net= 7.59 mph

a= 4.5 ft/s2

AASHTO Green BookS

net= 7.94 mph

a= 12.49 ft/s2

FHWA (sport cars)S

net= 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 (

mph

)

d= -6.5 ft/s2

L= 4000 ftS

lim= 25 mph

Di= 260 ft

Twait

= 10 sec

a= 3.6 ft/s2

Traffic Engineering HandbookS

net= 7.10 mph

a= 4.5 ft/s2

AASHTO Green BookS

net= 7.40 mph

a= 3.6 ft/s2

FHWA (sport cars)S

net= 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 (

mph

)

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 BookS

net= 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 (

ft/s)

a= 6 ft/s2 d=-6.5 ft/s2 L= 4000 ft D

i= 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