Simplified model of on-off driving sequences between 2 speed limits, vmin and vmax, optization
motoring between point 0 (vmin) and point 1 (vmax), coasting between point 1 (vmax) and point 2 (vmin) on a straight level road without wind.
boxes in ligth blue must be filled with your values
ambiant characteristics :
vehicle characteristics :
theoretical performances :
propulsion characteristics :
starting energy (if applicable) :
(50 to 250J)
gravity (m/s2)
9,81
aero friction :
mechanical friction :
theoretical propulsion force Fmean (N)
5,53
engine/motor efficiency (-)
0,25
Estart (J)
200
atmospheric pressure (mb)
1013
frontal area S (m2)
0,42
mechanical friction factor a (-)
0,003
theoretical propulsion power Pmean (W)
46,1
engine/motor torque Cm (Nm)
0,80
intermediate constants (for calculus) :
atmospheric temperature
25
drag factor Cx
0,15
total mass m (kg)
100
race theoretical energy needs Eref (J)
141116
number of teeth of the crown
130
Aon
-0,0289
spec. mass of air (kg/m3)
1,18
equiv. mass of rotational inertia mi (kg)
2
number of teeth of the pinion
11
Aoff
0,3164
race characteristics :
fuel characteristics :
gear ratio
0,086
B
0,0004
imposed mean speed (km/h)
30
race distance distref (km)
25,5
Hcarbl (kJ/l)
32010
wheel radius R (m)
0,25
number of laps
8
transmission efficiency etap (-)
0,95
corresponding duration (s)
3060
lap length (m)
3187,5
propulsion force Fp (N)
35,2
car speed limit with this force vmaxmax (km/h)
105,9
vmin (km/h)
vmax (km/h)
x1-x0 (m, motoring phase)
t1-t0 (s, engine on)
x2-x1 (m, coasting phase)
t2-t1 (s, engine off)
d=x2-x0 (m, total distance)
t=t2-t0 (s, duration of the sequence)
E (J, consumed energy)
e (J/m, specific energy)
ds (km/kWh, specific distance)
vmoy (km/h, average speed)
E (kJ for distance distref)
rpm_min (t/min, minimum engine speed)
rpm_max (t/min, maximum engine speed)
ds' (km/l, specific distance)
number of sequences during a lap
30
30,1
0,80
0,10
4,27
0,51
5,06
0,61
318
62,83
57,3
30,05
1602,2
3687
3699
509
629,4
29,5
30,7
9,58
1,15
51,21
6,13
60,79
7,27
1621
26,67
135,0
30,10
680,0
3626
3773
1200
52,4
29
31,3
18,41
2,20
98,14
11,72
116,54
13,92
2929
25,13
143,2
30,14
640,9
3564
3847
1274
27,4
28,5
31,9
27,27
3,25
145,04
17,31
172,31
20,56
4243
24,62
146,2
30,18
627,9
3503
3921
1300
18,5
28
32,5
36,17
4,30
191,91
22,88
228,08
27,18
5563
24,39
147,6
30,21
622,0
3441
3994
1312
14,0
27,5
33,1
45,11
5,36
238,71
28,44
283,82
33,80
6889
24,27
148,3
30,23
618,9
3380
4068
1319
11,2
27
33,7
54,10
6,41
285,44
33,99
339,54
40,40
8221
24,21
148,7
30,26
617,4
3318
4142
1322
9,4
26,5
34,3
63,13
7,47
332,09
39,53
395,22
47,00
9560
24,19
148,8
30,27
616,8
3257
4216
1323
8,1
26
34,9
72,21
8,53
378,63
45,07
450,84
53,59
10906
24,19
148,8
30,28
616,9
3195
4289
1323
7,1
25,5
35,5
81,34
9,59
425,04
50,60
506,38
60,18
12260
24,21
148,7
30,29
617,4
3134
4363
1322
6,3
25
36,1
90,52
10,65
471,32
56,13
561,84
66,77
13621
24,24
148,5
30,29
618,2
3073
4437
1320
5,7
24,5
36,7
99,75
11,71
517,46
61,65
617,21
73,36
14990
24,29
148,2
30,29
619,3
3011
4511
1318
5,2
24
37,3
109,04
12,77
563,42
67,18
672,46
79,95
16367
24,34
147,9
30,28
620,6
2950
4584
1315
4,7
23,5
37,9
118,39
13,84
609,20
72,70
727,59
86,54
17753
24,40
147,5
30,27
622,2
2888
4658
1312
4,4
23
38,5
127,79
14,90
654,79
78,23
782,58
93,14
19147
24,47
147,1
30,25
623,9
2827
4732
1308
4,1
22,5
39,1
137,26
15,97
700,16
83,76
837,42
99,74
20551
24,54
146,7
30,23
625,8
2765
4806
1304
3,8
22
39,7
146,79
17,04
745,31
89,30
892,10
106,34
21964
24,62
146,2
30,20
627,8
2704
4879
1300
3,6
21,5
40,3
156,39
18,12
790,21
94,84
946,60
112,96
23387
24,71
145,7
30,17
630,0
2642
4953
1296
3,4
21
40,9
166,05
19,19
834,85
100,39
1000,91
119,58
24820
24,80
145,2
30,13
632,3
2581
5027
1291
3,2
20,5
41,5
175,79
20,27
879,23
105,95
1055,02
126,22
26264
24,89
144,6
30,09
634,8
2520
5100
1286
3,0
20
42,1
185,60
21,35
923,31
111,52
1108,91
132,87
27718
25,00
144,0
30,05
637,4
2458
5174
1281
2,9
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