Week-11 Challenge: Braking
Q1.For a defined driving cycle, calculate the energy required for braking.
Ans:-
The special feature of electric vehicles and hybrid vehicles is their ability to absorb, store and reuse the braking energy. A successfully designed braking system for a vehicle must always meet two distinct demands. While applying the sudden brake, the vehicle must come to rest in the shortest possible distance and at the same time, the vehicle must have control over the vehicle’s direction. The first one requires that the vehicle braking system be able to provide enough braking torque on all wheels. The second demand requires braking force to be distributed on all the wheels equally.
Here, the braking torque required is much larger than the torque that an electric motor can produce. So in order to bring the two demands success in EV and HEVs, both the mechanical braking system and electrical braking system should consider as major roles.
BRAKING :-
Braking is a process which applies energy to decrease the speed of a moving vehicle.When brake is applied in a moving vehicle the kinetic enegy possed by the moving vehicle get opposed by various factor like , air drag , rolling resistance etc , but it takes a lot time and much distance to come to rest which is not a practical scenario. So to stop the moving vehicle with lesser time braking is used which is opposit pheomena to accleration.In braking care the kinetic energy is converted either in the form of heat or we can use to recharge the battery back in case of EV & HEV application. It includes rapid stopping of the electric motor, holding the stopping of the electric motor, holding the motor shaft to a specific position, maintaining the speed to the desired value, or preventing the motor from overspeeding.
A regenerative braking system is the electrical braking of a vehicle using motors as brakes. The total kinetic energy which is to be utilized by the wheels travel a certain distance was being stopped by for some reason by the braking system then the accumulated energy near the power train is directed to travel back to the energy storage through the motor. So here the motor acts like a generator that stores mechanical energy into electrical energy in the battery. This stored energy can be reused by the electric motor for vehicle propulsion. This regenerative system improves motor efficiency by simply converting kinetic energy into electrical energy which is to be generated as heat energy during frictional braking.
Ex:-
If a 1500kg vehicle traveling at 70km/h has 300kJ of kinetic energy, which drops to zero as the vehicle comes to rest. If we can utilize this recovered it would be enough to propel the same vehicle for 1.8km at 70km/h.
This will significantly recover energy which leads to increased vehicle range.
Whenever a force is applied to a vehicle's brakes, there is work done due to the friction between the brakes and the wheel. This reduces the vehicle's kinetic energy, slowing it down and causing the temperature of the brakes to increase.
Decelerating from very high speeds too quickly can cause several problems:
- The brakes could overheat and the material they are made from could shatter. This will lead to the driver losing control.
- Very high temperatures near the tires could cause the tires to explode. This will lead to the driver losing control.
- A high deceleration needs a high force (Newton's second law), and these high forces can seriously injure the driver.
Calculation of Braking Energy:
The energy required for braking can be calculated using Newton's second law. Let's assume a drive cycle, FTP 75 with a total gross weight of 1000 kg.
The acceleration/deceleration of the car is given by:
Deceleration = Change in velocity / time
= (Final velocity - Initial velocity) / time
The Braking energy is =1/2(m.v^2) joules
Fig: UDDS Driving Schedule
|
UDDS Driving Cycle |
|||
|
Time (Secs) |
Velocity (mph) |
Braking Energy Required (J) |
Braking Energy (kWh) |
|
0 |
0 |
0 |
0 |
|
1 |
0 |
0 |
0 |
|
2 |
0 |
0 |
0 |
|
3 |
0 |
0 |
0 |
|
4 |
0 |
0 |
0 |
|
5 |
0 |
0 |
0 |
|
6 |
0 |
0 |
0 |
|
7 |
0 |
0 |
0 |
|
8 |
0 |
0 |
0 |
|
9 |
0 |
0 |
0 |
|
10 |
0 |
0 |
0 |
|
11 |
0 |
0 |
0 |
|
12 |
0 |
0 |
0 |
|
13 |
0 |
0 |
0 |
|
14 |
0 |
0 |
0 |
|
15 |
0 |
0 |
0 |
|
16 |
0 |
0 |
0 |
|
17 |
0 |
0 |
0 |
|
18 |
0 |
0 |
0 |
|
19 |
0 |
0 |
0 |
|
20 |
0 |
0 |
0 |
|
21 |
3 |
2011.5 |
0.00055875 |
|
22 |
5.9 |
7780.035 |
0.002161123 |
|
23 |
8.6 |
16530.06 |
0.004591687 |
|
24 |
11.5 |
29557.88 |
0.008210527 |
|
25 |
14.3 |
45703.52 |
0.012695431 |
|
26 |
16.9 |
63833.84 |
0.017731635 |
|
27 |
17.3 |
66891.32 |
0.018580936 |
|
28 |
18.1 |
73220.84 |
0.020339137 |
|
29 |
20.7 |
95767.52 |
0.026602109 |
|
30 |
21.7 |
105243.9 |
0.029234444 |
|
31 |
22.4 |
112143.4 |
0.031150958 |
|
32 |
22.5 |
113146.9 |
0.031429713 |
|
33 |
22.1 |
109159.6 |
0.030322145 |
|
34 |
21.5 |
103312.9 |
0.028698044 |
|
35 |
20.9 |
97627.04 |
0.027118643 |
|
36 |
20.4 |
93011.76 |
0.025836621 |
|
37 |
19.8 |
87620.94 |
0.024339169 |
|
38 |
17 |
64591.5 |
0.017942098 |
|
39 |
14.9 |
49619.24 |
0.013783132 |
|
40 |
14.9 |
49619.24 |
0.013783132 |
|
41 |
15.2 |
51637.44 |
0.014343745 |
|
42 |
15.5 |
53695.88 |
0.014915533 |
|
43 |
16 |
57216 |
0.015893346 |
|
44 |
17.1 |
65353.64 |
0.018153802 |
|
45 |
19.1 |
81535.04 |
0.022648639 |
|
46 |
21.1 |
99504.44 |
0.027640143 |
|
47 |
22.7 |
115167.3 |
0.031990946 |
|
48 |
22.9 |
117205.6 |
0.032557147 |
|
49 |
22.7 |
115167.3 |
0.031990946 |
|
50 |
22.6 |
114154.9 |
0.031709709 |
|
51 |
21.3 |
101399.7 |
0.02816661 |
|
52 |
19 |
80683.5 |
0.022412101 |
|
53 |
17.1 |
65353.64 |
0.018153802 |
|
54 |
15.8 |
55794.54 |
0.015498496 |
|
55 |
15.8 |
55794.54 |
0.015498496 |
|
56 |
17.7 |
70020.32 |
0.019450103 |
|
57 |
19.8 |
87620.94 |
0.024339169 |
|
58 |
21.6 |
104276.2 |
0.028965623 |
|
59 |
23.2 |
120296.6 |
0.03341576 |
|
60 |
24.2 |
130890.5 |
0.036358512 |
|
61 |
24.6 |
135253.3 |
0.03757038 |
|
62 |
24.9 |
138572.2 |
0.038492318 |
|
63 |
25 |
139687.5 |
0.038802114 |
|
64 |
24.6 |
135253.3 |
0.03757038 |
|
65 |
24.5 |
134155.9 |
0.037265551 |
|
66 |
24.7 |
136355.1 |
0.037876451 |
|
67 |
24.8 |
137461.4 |
0.038183764 |
|
68 |
24.7 |
136355.1 |
0.037876451 |
|
69 |
24.6 |
135253.3 |
0.03757038 |
|
70 |
24.6 |
135253.3 |
0.03757038 |
|
71 |
25.1 |
140807.2 |
0.039113152 |
|
72 |
25.6 |
146473 |
0.040686966 |
|
73 |
25.7 |
147619.5 |
0.041005454 |
|
74 |
25.4 |
144193.3 |
0.040053715 |
|
75 |
24.9 |
138572.2 |
0.038492318 |
|
76 |
25 |
139687.5 |
0.038802114 |
|
77 |
25.4 |
144193.3 |
0.040053715 |
|
78 |
26 |
151086 |
0.041968367 |
|
79 |
26 |
151086 |
0.041968367 |
|
80 |
25.7 |
147619.5 |
0.041005454 |
|
81 |
26.1 |
152250.4 |
0.042291821 |
|
82 |
26.7 |
159330.9 |
0.044258623 |
|
83 |
27.5 |
169021.9 |
0.046950558 |
|
84 |
28.6 |
182814.1 |
0.050781724 |
|
85 |
29.3 |
191872.5 |
0.053297963 |
|
86 |
29.8 |
198476.9 |
0.055132527 |
|
87 |
30.1 |
202493.2 |
0.056248166 |
|
88 |
30.4 |
206549.8 |
0.057374979 |
|
89 |
30.7 |
210646.5 |
0.058512968 |
|
90 |
30.7 |
210646.5 |
0.058512968 |
|
91 |
30.5 |
207910.9 |
0.057753067 |
|
92 |
30.4 |
206549.8 |
0.057374979 |
|
93 |
30.3 |
205193.1 |
0.056998133 |
|
94 |
30.4 |
206549.8 |
0.057374979 |
|
95 |
30.8 |
212021 |
0.05889478 |
|
96 |
30.4 |
206549.8 |
0.057374979 |
|
97 |
29.9 |
199811.2 |
0.055503165 |
|
98 |
29.5 |
194500.9 |
0.054028064 |
|
99 |
29.8 |
198476.9 |
0.055132527 |
|
100 |
30.3 |
205193.1 |
0.056998133 |
|
101 |
30.7 |
210646.5 |
0.058512968 |
|
102 |
30.9 |
213400 |
0.059277835 |
|
103 |
31 |
214783.5 |
0.059662131 |
|
104 |
30.9 |
213400 |
0.059277835 |
|
105 |
30.4 |
206549.8 |
0.057374979 |
|
106 |
29.8 |
198476.9 |
0.055132527 |
|
107 |
29.9 |
199811.2 |
0.055503165 |
|
108 |
30.2 |
203840.9 |
0.056622529 |
|
109 |
30.7 |
210646.5 |
0.058512968 |
|
110 |
31.2 |
217563.8 |
0.060434448 |
|
111 |
31.8 |
226012.1 |
0.0627812 |
|
112 |
32.2 |
231733.7 |
0.064370535 |
|
113 |
32.4 |
234621.4 |
0.065172652 |
|
114 |
32.2 |
231733.7 |
0.064370535 |
|
115 |
31.7 |
224592.9 |
0.062386971 |
|
116 |
28.6 |
182814.1 |
0.050781724 |
|
117 |
25.3 |
143060.1 |
0.039738953 |
|
118 |
22 |
108174 |
0.030048357 |
|
119 |
18.7 |
78155.72 |
0.021709938 |
|
120 |
15.4 |
53005.26 |
0.014723695 |
|
121 |
12.1 |
32722.64 |
0.009089628 |
|
122 |
8.8 |
17307.84 |
0.004807737 |
|
123 |
5.5 |
6760.875 |
0.001878022 |
|
124 |
2.2 |
1081.74 |
0.000300484 |
|
125 |
0 |
0 |
0 |
|
126 |
0 |
0 |
0 |
|
127 |
0 |
0 |
0 |
|
128 |
0 |
0 |
0 |
|
129 |
0 |
0 |
0 |
|
130 |
0 |
0 |
0 |
|
131 |
0 |
0 |
0 |
|
132 |
0 |
0 |
0 |
|
133 |
0 |
0 |
0 |
|
134 |
0 |
0 |
0 |
|
135 |
0 |
0 |
0 |
|
136 |
0 |
0 |
0 |
|
137 |
0 |
0 |
0 |
|
138 |
0 |
0 |
0 |
|
139 |
0 |
0 |
0 |
|
140 |
0 |
0 |
0 |
|
141 |
0 |
0 |
0 |
|
142 |
0 |
0 |
0 |
|
143 |
0 |
0 |
0 |
|
144 |
0 |
0 |
0 |
|
145 |
0 |
0 |
0 |
|
146 |
0 |
0 |
0 |
|
147 |
0 |
0 |
0 |
|
148 |
0 |
0 |
0 |
|
149 |
0 |
0 |
0 |
|
150 |
0 |
0 |
0 |
|
151 |
0 |
0 |
0 |
|
152 |
0 |
0 |
0 |
|
153 |
0 |
0 |
0 |
|
154 |
0 |
0 |
0 |
|
155 |
0 |
0 |
0 |
|
156 |
0 |
0 |
0 |
|
157 |
0 |
0 |
0 |
|
158 |
0 |
0 |
0 |
|
159 |
0 |
0 |
0 |
|
160 |
0 |
0 |
0 |
|
161 |
0 |
0 |
0 |
|
162 |
0 |
0 |
0 |
|
163 |
0 |
0 |
0 |
|
164 |
3.3 |
2433.915 |
0.000676088 |
|
165 |
6.6 |
9735.66 |
0.002704352 |
|
166 |
9.9 |
21905.24 |
0.006084792 |
|
167 |
13.2 |
38942.64 |
0.010817409 |
|
168 |
16.5 |
60847.88 |
0.016902201 |
|
169 |
19.8 |
87620.94 |
0.024339169 |
|
170 |
22.2 |
110149.7 |
0.030597174 |
|
171 |
24.3 |
131974.5 |
0.036659617 |
|
172 |
25.8 |
148770.5 |
0.041325183 |
|
173 |
26.4 |
155770.6 |
0.043269635 |
|
174 |
25.7 |
147619.5 |
0.041005454 |
|
175 |
25.1 |
140807.2 |
0.039113152 |
|
176 |
24.7 |
136355.1 |
0.037876451 |
|
177 |
25 |
139687.5 |
0.038802114 |
|
178 |
25.2 |
141931.4 |
0.039425432 |
|
179 |
25.4 |
144193.3 |
0.040053715 |
|
180 |
25.8 |
148770.5 |
0.041325183 |
|
181 |
27.2 |
165354.2 |
0.04593177 |
|
182 |
26.5 |
156952.9 |
0.043598056 |
|
183 |
24 |
128736 |
0.035760029 |
|
184 |
22.7 |
115167.3 |
0.031990946 |
|
185 |
19.4 |
84116.46 |
0.023365702 |
|
186 |
17.7 |
70020.32 |
0.019450103 |
|
187 |
17.2 |
66120.24 |
0.018366748 |
|
188 |
18.1 |
73220.84 |
0.020339137 |
|
189 |
18.6 |
77322.06 |
0.021478367 |
|
190 |
20 |
89400 |
0.024833353 |
|
191 |
22.2 |
110149.7 |
0.030597174 |
|
192 |
24.5 |
134155.9 |
0.037265551 |
|
193 |
27.3 |
166572.3 |
0.046270125 |
|
194 |
30.5 |
207910.9 |
0.057753067 |
|
195 |
33.5 |
250822.9 |
0.069673077 |
|
196 |
36.2 |
292883.3 |
0.081356548 |
|
197 |
37.3 |
310953.3 |
0.08637599 |
|
198 |
39.3 |
345193.5 |
0.095887164 |
|
199 |
40.5 |
366595.9 |
0.101832269 |
|
200 |
42.1 |
396133.6 |
0.110037209 |
|
201 |
43.5 |
422917.9 |
0.117477281 |
|
202 |
45.1 |
454601.2 |
0.126278222 |
|
203 |
46 |
472926 |
0.131368438 |
|
204 |
46.8 |
489518.6 |
0.135977509 |
|
205 |
47.5 |
504271.9 |
0.140075633 |
|
206 |
47.5 |
504271.9 |
0.140075633 |
|
207 |
47.3 |
500034.3 |
0.138898532 |
|
208 |
47.2 |
497922.2 |
0.138311844 |
|
209 |
47 |
493711.5 |
0.137142193 |
|
210 |
47 |
493711.5 |
0.137142193 |
|
211 |
47 |
493711.5 |
0.137142193 |
|
212 |
47 |
493711.5 |
0.137142193 |
|
213 |
47 |
493711.5 |
0.137142193 |
|
214 |
47.2 |
497922.2 |
0.138311844 |
|
215 |
47.4 |
502150.9 |
0.139486462 |
|
216 |
47.9 |
512800.6 |
0.142444735 |
|
217 |
48.5 |
525727.9 |
0.146035638 |
|
218 |
49.1 |
538816 |
0.149671241 |
|
219 |
49.5 |
547630.9 |
0.152119809 |
|
220 |
50 |
558750 |
0.155208458 |
|
221 |
50.6 |
572240.5 |
0.15895581 |
|
222 |
51 |
581323.5 |
0.161478879 |
|
223 |
51.5 |
592777.9 |
0.164660653 |
|
224 |
52.2 |
609001.7 |
0.169167285 |
|
225 |
53.2 |
632558.6 |
0.175710874 |
|
226 |
54.1 |
654142 |
0.181706266 |
|
227 |
54.6 |
666289.3 |
0.185080498 |
|
228 |
54.9 |
673631.2 |
0.187119937 |
|
229 |
55 |
676087.5 |
0.187802234 |
|
230 |
54.9 |
673631.2 |
0.187119937 |
|
231 |
54.6 |
666289.3 |
0.185080498 |
|
232 |
54.6 |
666289.3 |
0.185080498 |
|
233 |
54.8 |
671179.4 |
0.186438882 |
|
234 |
55.1 |
678548.2 |
0.188485772 |
|
235 |
55.5 |
688435.9 |
0.19123234 |
|
236 |
55.7 |
693406.5 |
0.192613075 |
|
237 |
56.1 |
703401.4 |
0.195389444 |
|
238 |
56.3 |
708425.7 |
0.196785078 |
|
239 |
56.6 |
715995.7 |
0.198887842 |
|
240 |
56.7 |
718527.9 |
0.199591247 |
|
241 |
56.7 |
718527.9 |
0.199591247 |
|
242 |
56.5 |
713467.9 |
0.198185679 |
|
243 |
56.5 |
713467.9 |
0.198185679 |
|
244 |
56.5 |
713467.9 |
0.198185679 |
|
245 |
56.5 |
713467.9 |
0.198185679 |
|
246 |
56.5 |
713467.9 |
0.198185679 |
|
247 |
56.5 |
713467.9 |
0.198185679 |
|
248 |
56.4 |
710944.6 |
0.197484758 |
|
249 |
56.1 |
703401.4 |
0.195389444 |
|
250 |
55.8 |
695898.5 |
0.193305305 |
|
251 |
55.1 |
678548.2 |
0.188485772 |
|
252 |
54.6 |
666289.3 |
0.185080498 |
|
253 |
54.2 |
656562.5 |
0.182378629 |
|
254 |
54 |
651726 |
0.181035145 |
|
255 |
53.7 |
644504.7 |
0.179029231 |
|
256 |
53.6 |
642106.6 |
0.178363076 |
|
257 |
53.9 |
649314.4 |
0.180365265 |
|
258 |
54 |
651726 |
0.181035145 |
|
259 |
54.1 |
654142 |
0.181706266 |
|
260 |
54.1 |
654142 |
0.181706266 |
|
261 |
53.8 |
646907.3 |
0.179696627 |
|
262 |
53.4 |
637323.7 |
0.177034492 |
|
263 |
53 |
627811.5 |
0.174392223 |
|
264 |
52.6 |
618370.9 |
0.171769821 |
|
265 |
52.1 |
606670.6 |
0.168519756 |
|
266 |
52.4 |
613677.4 |
0.17046607 |
|
267 |
52 |
604344 |
0.167873468 |
|
268 |
51.9 |
602021.8 |
0.167228421 |
|
269 |
51.7 |
597390.9 |
0.165942054 |
|
270 |
51.5 |
592777.9 |
0.164660653 |
|
271 |
51.6 |
595082.2 |
0.165300732 |
|
272 |
51.8 |
599704.1 |
0.166584617 |
|
273 |
52.1 |
606670.6 |
0.168519756 |
|
274 |
52.5 |
616021.9 |
0.171117324 |
|
275 |
53 |
627811.5 |
0.174392223 |
|
276 |
53.5 |
639712.9 |
0.177698163 |
|
277 |
54 |
651726 |
0.181035145 |
|
278 |
54.9 |
673631.2 |
0.187119937 |
|
279 |
55.4 |
685957.3 |
0.190543836 |
|
280 |
55.6 |
690919 |
0.191922087 |
|
281 |
56 |
700896 |
0.194693489 |
|
282 |
56 |
700896 |
0.194693489 |
|
283 |
55.8 |
695898.5 |
0.193305305 |
|
284 |
55.2 |
681013.4 |
0.189170551 |
|
285 |
54.5 |
663850.9 |
0.184403168 |
|
286 |
53.6 |
642106.6 |
0.178363076 |
|
287 |
52.5 |
616021.9 |
0.171117324 |
|
288 |
51.5 |
592777.9 |
0.164660653 |
|
289 |
51.5 |
592777.9 |
0.164660653 |
|
290 |
51.5 |
592777.9 |
0.164660653 |
|
291 |
51.1 |
583605.4 |
0.162112751 |
|
292 |
50.1 |
560987.2 |
0.155829912 |
|
293 |
50 |
558750 |
0.155208458 |
|
294 |
50.1 |
560987.2 |
0.155829912 |
|
295 |
50 |
558750 |
0.155208458 |
|
296 |
49.6 |
549845.8 |
0.152735056 |
|
297 |
49.5 |
547630.9 |
0.152119809 |
|
298 |
49.5 |
547630.9 |
0.152119809 |
|
299 |
49.5 |
547630.9 |
0.152119809 |
|
300 |
49.1 |
538816 |
0.149671241 |
|
301 |
48.6 |
527898.1 |
0.146638467 |
|
302 |
48.1 |
517091.8 |
0.143636736 |
|
303 |
47.2 |
497922.2 |
0.138311844 |
|
304 |
46.1 |
474984.4 |
0.131940226 |
|
305 |
45 |
452587.5 |
0.125718851 |
|
306 |
43.8 |
428771.3 |
0.119103245 |
|
307 |
42.6 |
405598.9 |
0.11266644 |
|
308 |
41.5 |
384922.9 |
0.106923106 |
|
309 |
40.3 |
362984.1 |
0.100829001 |
|
310 |
38.5 |
331282.9 |
0.092023094 |
|
311 |
37 |
305971.5 |
0.084992151 |
|
312 |
35.2 |
276925.4 |
0.076923795 |
|
313 |
33.8 |
255335.3 |
0.07092654 |
|
314 |
32.5 |
236071.9 |
0.065575573 |
|
315 |
31.5 |
221767.9 |
0.061602237 |
|
316 |
30.6 |
209276.5 |
0.058132397 |
|
317 |
30.5 |
207910.9 |
0.057753067 |
|
318 |
30 |
201150 |
0.055875045 |
|
319 |
29 |
187963.5 |
0.052212125 |
|
320 |
27.5 |
169021.9 |
0.046950558 |
|
321 |
24.8 |
137461.4 |
0.038183764 |
|
322 |
21.5 |
103312.9 |
0.028698044 |
|
323 |
20.1 |
90296.24 |
0.025082308 |
|
324 |
19.1 |
81535.04 |
0.022648639 |
|
325 |
18.5 |
76492.88 |
0.021248038 |
|
326 |
17 |
64591.5 |
0.017942098 |
|
327 |
15.5 |
53695.88 |
0.014915533 |
|
328 |
12.5 |
34921.88 |
0.009700529 |
|
329 |
10.8 |
26069.04 |
0.007241406 |
|
330 |
8 |
14304 |
0.003973337 |
|
331 |
4.7 |
4937.115 |
0.001371422 |
|
332 |
1.4 |
438.06 |
0.000121683 |
|
333 |
0 |
0 |
0 |
|
334 |
0 |
0 |
0 |
|
335 |
0 |
0 |
0 |
|
336 |
0 |
0 |
0 |
|
337 |
0 |
0 |
0 |
|
338 |
0 |
0 |
0 |
|
339 |
0 |
0 |
0 |
|
340 |
0 |
0 |
0 |
|
341 |
0 |
0 |
0 |
|
342 |
0 |
0 |
0 |
|
343 |
0 |
0 |
0 |
|
344 |
0 |
0 |
0 |
|
345 |
0 |
0 |
0 |
|
346 |
0 |
0 |
0 |
|
347 |
1 |
223.5 |
6.20834E-05 |
|
348 |
4.3 |
4132.515 |
0.001147922 |
|
349 |
7.6 |
12909.36 |
0.003585936 |
|
350 |
10.9 |
26554.04 |
0.007376127 |
|
351 |
14.2 |
45066.54 |
0.012518493 |
|
352 |
17.3 |
66891.32 |
0.018580936 |
|
353 |
20 |
89400 |
0.024833353 |
|
354 |
22.5 |
113146.9 |
0.031429713 |
|
355 |
23.7 |
125537.7 |
0.034871615 |
|
356 |
25.2 |
141931.4 |
0.039425432 |
|
357 |
26.6 |
158139.7 |
0.043927718 |
|
358 |
28.1 |
176477.8 |
0.04902166 |
|
359 |
30 |
201150 |
0.055875045 |
|
360 |
30.8 |
212021 |
0.05889478 |
|
361 |
31.6 |
223178.2 |
0.061993983 |
|
362 |
32.1 |
230296.6 |
0.063971339 |
|
363 |
32.8 |
240450.2 |
0.066791787 |
|
364 |
33.6 |
252322.6 |
0.070089656 |
|
365 |
34.5 |
266020.9 |
0.073894747 |
|
366 |
34.6 |
267565.3 |
0.074323743 |
|
367 |
34.9 |
272225.2 |
0.075618181 |
|
368 |
34.8 |
270667.4 |
0.07518546 |
|
369 |
34.5 |
266020.9 |
0.073894747 |
|
370 |
34.7 |
269114.1 |
0.074753981 |
|
371 |
35.5 |
281665.9 |
0.078240583 |
|
372 |
36 |
289656 |
0.080460064 |
|
373 |
36 |
289656 |
0.080460064 |
|
374 |
36 |
289656 |
0.080460064 |
|
375 |
36 |
289656 |
0.080460064 |
|
376 |
36 |
289656 |
0.080460064 |
|
377 |
36 |
289656 |
0.080460064 |
|
378 |
36.1 |
291267.4 |
0.080907686 |
|
379 |
36.4 |
296128.6 |
0.082257999 |
|
380 |
36.5 |
297757.9 |
0.082710587 |
|
381 |
36.4 |
296128.6 |
0.082257999 |
|
382 |
36 |
289656 |
0.080460064 |
|
383 |
35.1 |
275354.2 |
0.076487349 |
|
384 |
34.1 |
259888 |
0.072191179 |
|
385 |
33.5 |
250822.9 |
0.069673077 |
|
386 |
31.4 |
220362.1 |
0.061211732 |
|
387 |
29 |
187963.5 |
0.052212125 |
|
388 |
25.7 |
147619.5 |
0.041005454 |
|
389 |
23 |
118231.5 |
0.03284211 |
|
390 |
20.3 |
92102.12 |
0.025583941 |
|
391 |
17.5 |
68446.88 |
0.019013036 |
|
392 |
14.5 |
46990.88 |
0.013053031 |
|
393 |
12 |
32184 |
0.008940007 |
|
394 |
8.7 |
16916.72 |
0.004699091 |
|
395 |
5.4 |
6517.26 |
0.001810351 |
|
396 |
2.1 |
985.635 |
0.000273788 |
|
397 |
0 |
0 |
0 |
|
398 |
0 |
0 |
0 |
|
399 |
0 |
0 |
0 |
|
400 |
0 |
0 |
0 |
|
401 |
0 |
0 |
0 |
|
402 |
0 |
0 |
0 |
|
403 |
2.6 |
1510.86 |
0.000419684 |
|
404 |
5.9 |
7780.035 |
0.002161123 |
|
405 |
9.2 |
18917.04 |
0.005254738 |
|
406 |
12.5 |
34921.88 |
0.009700529 |
|
407 |
15.8 |
55794.54 |
0.015498496 |
|
408 |
19.1 |
81535.04 |
0.022648639 |
|
409 |
22.4 |
112143.4 |
0.031150958 |
|
410 |
25 |
139687.5 |
0.038802114 |
|
411 |
25.6 |
146473 |
0.040686966 |
|
412 |
27.5 |
169021.9 |
0.046950558 |
|
413 |
29 |
187963.5 |
0.052212125 |
|
414 |
30 |
201150 |
0.055875045 |
|
415 |
30.1 |
202493.2 |
0.056248166 |
|
416 |
30 |
201150 |
0.055875045 |
|
417 |
29.7 |
197147.1 |
0.054763131 |
|
418 |
29.3 |
191872.5 |
0.053297963 |
|
419 |
28.8 |
185379.8 |
0.051494441 |
|
420 |
28 |
175224 |
0.048673372 |
|
421 |
25 |
139687.5 |
0.038802114 |
|
422 |
21.7 |
105243.9 |
0.029234444 |
|
423 |
18.4 |
75668.16 |
0.02101895 |
|
424 |
15.1 |
50960.24 |
0.014155632 |
|
425 |
11.8 |
31120.14 |
0.00864449 |
|
426 |
8.5 |
16147.88 |
0.004485524 |
|
427 |
5.2 |
6043.44 |
0.001678735 |
|
428 |
1.9 |
806.835 |
0.000224121 |
|
429 |
0 |
0 |
0 |
|
430 |
0 |
0 |
0 |
|
431 |
0 |
0 |
0 |
|
432 |
0 |
0 |
0 |
|
433 |
0 |
0 |
0 |
|
434 |
0 |
0 |
0 |
|
435 |
0 |
0 |
0 |
|
436 |
0 |
0 |
0 |
|
437 |
0 |
0 |
0 |
|
438 |
0 |
0 |
0 |
|
439 |
0 |
0 |
0 |
|
440 |
0 |
0 |
0 |
|
441 |
0 |
0 |
0 |
|
442 |
0 |
0 |
0 |
|
443 |
0 |
0 |
0 |
|
444 |
0 |
0 |
0 |
|
445 |
0 |
0 |
0 |
|
446 |
0 |
0 |
0 |
|
447 |
0 |
0 |
0 |
|
448 |
3.3 |
2433.915 |
0.000676088 |
|
449 |
6.6 |
9735.66 |
0.002704352 |
|
450 |
9.9 |
21905.24 |
0.006084792 |
|
451 |
13.2 |
38942.64 |
0.010817409 |
|
452 |
16.5 |
60847.88 |
0.016902201 |
|
453 |
19.8 |
87620.94 |
0.024339169 |
|
454 |
23.1 |
119261.8 |
0.033128314 |
|
455 |
26.4 |
155770.6 |
0.043269635 |
|
456 |
27.8 |
172729.7 |
0.047980522 |
|
457 |
29.1 |
189262 |
0.05257283 |
|
458 |
31.5 |
221767.9 |
0.061602237 |
|
459 |
33 |
243391.5 |
0.067608804 |
|
460 |
33.6 |
252322.6 |
0.070089656 |
|
461 |
34.8 |
270667.4 |
0.07518546 |
|
462 |
35.1 |
275354.2 |
0.076487349 |
|
463 |
35.6 |
283255 |
0.078681996 |
|
464 |
36.1 |
291267.4 |
0.080907686 |
|
465 |
36 |
289656 |
0.080460064 |
|
466 |
36.1 |
291267.4 |
0.080907686 |
|
467 |
36.2 |
292883.3 |
0.081356548 |
|
468 |
36 |
289656 |
0.080460064 |
|
469 |
35.7 |
284848.5 |
0.079124651 |
|
470 |
36 |
289656 |
0.080460064 |
|
471 |
36 |
289656 |
0.080460064 |
|
472 |
35.6 |
283255 |
0.078681996 |
|
473 |
35.5 |
281665.9 |
0.078240583 |
|
474 |
35.4 |
280081.3 |
0.077800412 |
|
475 |
35.2 |
276925.4 |
0.076923795 |
|
476 |
35.2 |
276925.4 |
0.076923795 |
|
477 |
35.2 |
276925.4 |
0.076923795 |
|
478 |
35.2 |
276925.4 |
0.076923795 |
|
479 |
35.2 |
276925.4 |
0.076923795 |
|
480 |
35.2 |
276925.4 |
0.076923795 |
|
481 |
35 |
273787.5 |
0.076052144 |
|
482 |
35.1 |
275354.2 |
0.076487349 |
|
483 |
35.2 |
276925.4 |
0.076923795 |
|
484 |
35.5 |
281665.9 |
0.078240583 |
|
485 |
35.2 |
276925.4 |
0.076923795 |
|
486 |
35 |
273787.5 |
0.076052144 |
|
487 |
35 |
273787.5 |
0.076052144 |
|
488 |
35 |
273787.5 |
0.076052144 |
|
489 |
34.8 |
270667.4 |
0.07518546 |
|
490 |
34.6 |
267565.3 |
0.074323743 |
|
491 |
34.5 |
266020.9 |
0.073894747 |
|
492 |
33.5 |
250822.9 |
0.069673077 |
|
493 |
32 |
228864 |
0.063573384 |
|
494 |
30.1 |
202493.2 |
0.056248166 |
|
495 |
28 |
175224 |
0.048673372 |
|
496 |
25.5 |
145330.9 |
0.04036972 |
|
497 |
22.5 |
113146.9 |
0.031429713 |
|
498 |
19.8 |
87620.94 |
0.024339169 |
|
499 |
16.5 |
60847.88 |
0.016902201 |
|
500 |
13.2 |
38942.64 |
0.010817409 |
|
501 |
10.3 |
23711.12 |
0.006586426 |
|
502 |
7.2 |
11586.24 |
0.003218403 |
|
503 |
4 |
3576 |
0.000993334 |
|
504 |
1 |
223.5 |
6.20834E-05 |
|
505 |
0 |
0 |
0 |
|
506 |
0 |
0 |
0 |
|
507 |
0 |
0 |
0 |
|
508 |
0 |
0 |
0 |
|
509 |
0 |
0 |
0 |
|
510 |
0 |
0 |
0 |
|
511 |
1.2 |
321.84 |
8.94001E-05 |
|
512 |
3.5 |
2737.875 |
0.000760521 |
|
513 |
5.5 |
6760.875 |
0.001878022 |
|
514 |
6.5 |
9442.875 |
0.002623023 |
|
515 |
8.5 |
16147.88 |
0.004485524 |
|
516 |
9.6 |
20597.76 |
0.005721605 |
|
517 |
10.5 |
24640.88 |
0.006844693 |
|
518 |
11.9 |
31649.84 |
0.008791628 |
|
519 |
14 |
43806 |
0.012168343 |
|
520 |
16 |
57216 |
0.015893346 |
|
521 |
17.7 |
70020.32 |
0.019450103 |
|
522 |
19 |
80683.5 |
0.022412101 |
|
523 |
20.1 |
90296.24 |
0.025082308 |
|
524 |
21 |
98563.5 |
0.027378772 |
|
525 |
22 |
108174 |
0.030048357 |
|
526 |
23 |
118231.5 |
0.03284211 |
|
527 |
23.8 |
126599.3 |
0.035166511 |
|
528 |
24.5 |
134155.9 |
0.037265551 |
|
529 |
24.9 |
138572.2 |
0.038492318 |
|
530 |
25 |
139687.5 |
0.038802114 |
|
531 |
25 |
139687.5 |
0.038802114 |
|
532 |
25 |
139687.5 |
0.038802114 |
|
533 |
25 |
139687.5 |
0.038802114 |
|
534 |
25 |
139687.5 |
0.038802114 |
|
535 |
25 |
139687.5 |
0.038802114 |
|
536 |
25.6 |
146473 |
0.040686966 |
|
537 |
25.8 |
148770.5 |
0.041325183 |
|
538 |
26 |
151086 |
0.041968367 |
|
539 |
25.6 |
146473 |
0.040686966 |
|
540 |
25.2 |
141931.4 |
0.039425432 |
|
541 |
25 |
139687.5 |
0.038802114 |
|
542 |
25 |
139687.5 |
0.038802114 |
|
543 |
25 |
139687.5 |
0.038802114 |
|
544 |
24.4 |
133063 |
0.036961963 |
|
545 |
23.1 |
119261.8 |
0.033128314 |
|
546 |
19.8 |
87620.94 |
0.024339169 |
|
547 |
16.5 |
60847.88 |
0.016902201 |
|
548 |
13.2 |
38942.64 |
0.010817409 |
|
549 |
9.9 |
21905.24 |
0.006084792 |
|
550 |
6.6 |
9735.66 |
0.002704352 |
|
551 |
3.3 |
2433.915 |
0.000676088 |
|
552 |
0 |
0 |
0 |
|
553 |
0 |
0 |
0 |
|
554 |
0 |
0 |
0 |
|
555 |
0 |
0 |
0 |
|
556 |
0 |
0 |
0 |
|
557 |
0 |
0 |
0 |
|
558 |
0 |
0 |
0 |
|
559 |
0 |
0 |
0 |
|
560 |
0 |
0 |
0 |
|
561 |
0 |
0 |
0 |
|
562 |
0 |
0 |
0 |
|
563 |
0 |
0 |
0 |
|
564 |
0 |
0 |
0 |
|
565 |
0 |
0 |
0 |
|
566 |
0 |
0 |
0 |
|
567 |
0 |
0 |
0 |
|
568 |
0 |
0 |
0 |
|
569 |
3.3 |
2433.915 |
0.000676088 |
|
570 |
6.6 |
9735.66 |
0.002704352 |
|
571 |
9.9 |
21905.24 |
0.006084792 |
|
572 |
13 |
37771.5 |
0.010492092 |
|
573 |
14.6 |
47641.26 |
0.013233694 |
|
574 |
16 |
57216 |
0.015893346 |
|
575 |
17 |
64591.5 |
0.017942098 |
|
576 |
17 |
64591.5 |
0.017942098 |
|
577 |
17 |
64591.5 |
0.017942098 |
|
578 |
17.5 |
68446.88 |
0.019013036 |
|
579 |
17.7 |
70020.32 |
0.019450103 |
|
580 |
17.7 |
70020.32 |
0.019450103 |
|
581 |
17.5 |
68446.88 |
0.019013036 |
|
582 |
17 |
64591.5 |
0.017942098 |
|
583 |
16.9 |
63833.84 |
0.017731635 |
|
584 |
16.6 |
61587.66 |
0.017107697 |
|
585 |
17 |
64591.5 |
0.017942098 |
|
586 |
17.1 |
65353.64 |
0.018153802 |
|
587 |
17 |
64591.5 |
0.017942098 |
|
588 |
16.6 |
61587.66 |
0.017107697 |
|
589 |
16.5 |
60847.88 |
0.016902201 |
|
590 |
16.5 |
60847.88 |
0.016902201 |
|
591 |
16.6 |
61587.66 |
0.017107697 |
|
592 |
17 |
64591.5 |
0.017942098 |
|
593 |
17.6 |
69231.36 |
0.019230949 |
|
594 |
18.5 |
76492.88 |
0.021248038 |
|
595 |
19.2 |
82391.04 |
0.022886418 |
|
596 |
20.2 |
91196.94 |
0.025332504 |
|
597 |
21 |
98563.5 |
0.027378772 |
|
598 |
21.1 |
99504.44 |
0.027640143 |
|
599 |
21.2 |
100449.8 |
0.027902756 |
|
600 |
21.6 |
104276.2 |
0.028965623 |
|
601 |
22 |
108174 |
0.030048357 |
|
602 |
22.4 |
112143.4 |
0.031150958 |
|
603 |
22.5 |
113146.9 |
0.031429713 |
|
604 |
22.5 |
113146.9 |
0.031429713 |
|
605 |
22.5 |
113146.9 |
0.031429713 |
|
606 |
22.7 |
115167.3 |
0.031990946 |
|
607 |
23.7 |
125537.7 |
0.034871615 |
|
608 |
25.1 |
140807.2 |
0.039113152 |
|
609 |
26 |
151086 |
0.041968367 |
|
610 |
26.5 |
156952.9 |
0.043598056 |
|
611 |
27 |
162931.5 |
0.045258786 |
|
612 |
26.1 |
152250.4 |
0.042291821 |
|
613 |
22.8 |
116184.2 |
0.032273426 |
|
614 |
19.5 |
84985.88 |
0.023607206 |
|
615 |
16.2 |
58655.34 |
0.016293163 |
|
616 |
12.9 |
37192.64 |
0.010331296 |
|
617 |
9.6 |
20597.76 |
0.005721605 |
|
618 |
6.3 |
8870.715 |
0.002464089 |
|
619 |
3 |
2011.5 |
0.00055875 |
|
620 |
0 |
0 |
0 |
|
621 |
0 |
0 |
0 |
|
622 |
0 |
0 |
0 |
|
623 |
0 |
0 |
0 |
|
624 |
0 |
0 |
0 |
|
625 |
0 |
0 |
0 |
|
626 |
0 |
0 |
0 |
|
627 |
0 |
0 |
0 |
|
628 |
0 |
0 |
0 |
|
629 |
0 |
0 |
0 |
|
630 |
0 |
0 |
0 |
|
631 |
0 |
0 |
0 |
|
632 |
0 |
0 |
0 |
|
633 |
0 |
0 |
0 |
|
634 |
0 |
0 |
0 |
|
635 |
0 |
0 |
0 |
|
636 |
0 |
0 |
0 |
|
637 |
0 |
0 |
0 |
|
638 |
0 |
0 |
0 |
|
639 |
0 |
0 |
0 |
|
640 |
0 |
0 |
0 |
|
641 |
0 |
0 |
0 |
|
642 |
0 |
0 |
0 |
|
643 |
0 |
0 |
0 |
|
644 |
0 |
0 |
0 |
|
645 |
0 |
0 |
0 |
|
646 |
2 |
894 |
0.000248334 |
|
647 |
4.5 |
4525.875 |
0.001257189 |
|
648 |
7.8 |
13597.74 |
0.003777153 |
|
649 |
10.2 |
23252.94 |
0.006459155 |
|
650 |
12.5 |
34921.88 |
0.009700529 |
|
651 |
14 |
43806 |
0.012168343 |
|
652 |
15.3 |
52319.12 |
0.014533099 |
|
653 |
17.5 |
68446.88 |
0.019013036 |
|
654 |
19.6 |
85859.76 |
0.023849952 |
|
655 |
21 |
98563.5 |
0.027378772 |
|
656 |
22.2 |
110149.7 |
0.030597174 |
|
657 |
23.3 |
121335.9 |
0.033704448 |
|
658 |
24.5 |
134155.9 |
0.037265551 |
|
659 |
25.3 |
143060.1 |
0.039738953 |
|
660 |
25.6 |
146473 |
0.040686966 |
|
661 |
26 |
151086 |
0.041968367 |
|
662 |
26.1 |
152250.4 |
0.042291821 |
|
663 |
26.2 |
153419.3 |
0.042616517 |
|
664 |
26.2 |
153419.3 |
0.042616517 |
|
665 |
26.4 |
155770.6 |
0.043269635 |
|
666 |
26.5 |
156952.9 |
0.043598056 |
|
667 |
26.5 |
156952.9 |
0.043598056 |
|
668 |
26 |
151086 |
0.041968367 |
|
669 |
25.5 |
145330.9 |
0.04036972 |
|
670 |
23.6 |
124480.6 |
0.034577961 |
|
671 |
21.4 |
102354.1 |
0.028431706 |
|
672 |
18.5 |
76492.88 |
0.021248038 |
|
673 |
16.4 |
60112.56 |
0.016697947 |
|
674 |
14.5 |
46990.88 |
0.013053031 |
|
675 |
11.6 |
30074.16 |
0.00835394 |
|
676 |
8.7 |
16916.72 |
0.004699091 |
|
677 |
5.8 |
7518.54 |
0.002088485 |
|
678 |
3.5 |
2737.875 |
0.000760521 |
|
679 |
2 |
894 |
0.000248334 |
|
680 |
0 |
0 |
0 |
|
681 |
0 |
0 |
0 |
|
682 |
0 |
0 |
0 |
|
683 |
0 |
0 |
0 |
|
684 |
0 |
0 |
0 |
|
685 |
0 |
0 |
0 |
|
686 |
0 |
0 |
0 |
|
687 |
0 |
0 |
0 |
|
688 |
0 |
0 |
0 |
|
689 |
0 |
0 |
0 |
|
690 |
0 |
0 |
0 |
|
691 |
0 |
0 |
0 |
|
692 |
0 |
0 |
0 |
|
693 |
0 |
0 |
0 |
|
694 |
1.4 |
438.06 |
0.000121683 |
|
695 |
3.3 |
2433.915 |
0.000676088 |
|
696 |
4.4 |
4326.96 |
0.001201934 |
|
697 |
6.5 |
9442.875 |
0.002623023 |
|
698 |
9.2 |
18917.04 |
0.005254738 |
|
699 |
11.3 |
28538.72 |
0.007927427 |
|
700 |
13.5 |
40732.88 |
0.011314697 |
|
701 |
14.6 |
47641.26 |
0.013233694 |
|
702 |
16.4 |
60112.56 |
0.016697947 |
|
703 |
16.7 |
62331.92 |
0.017314435 |
|
704 |
16.5 |
60847.88 |
0.016902201 |
|
705 |
16.5 |
60847.88 |
0.016902201 |
|
706 |
18.2 |
74032.14 |
0.0205645 |
|
707 |
19.2 |
82391.04 |
0.022886418 |
|
708 |
20.1 |
90296.24 |
0.025082308 |
|
709 |
21.5 |
103312.9 |
0.028698044 |
|
710 |
22.5 |
113146.9 |
0.031429713 |
|
711 |
22.5 |
113146.9 |
0.031429713 |
|
712 |
22.1 |
109159.6 |
0.030322145 |
|
713 |
22.7 |
115167.3 |
0.031990946 |
|
714 |
23.3 |
121335.9 |
0.033704448 |
|
715 |
23.5 |
123427.9 |
0.034285548 |
|
716 |
22.5 |
113146.9 |
0.031429713 |
|
717 |
21.6 |
104276.2 |
0.028965623 |
|
718 |
20.5 |
93925.88 |
0.026090542 |
|
719 |
18 |
72414 |
0.020115016 |
|
720 |
15 |
50287.5 |
0.013968761 |
|
721 |
12 |
32184 |
0.008940007 |
|
722 |
9 |
18103.5 |
0.005028754 |
|
723 |
6.2 |
8591.34 |
0.002386485 |
|
724 |
4.5 |
4525.875 |
0.001257189 |
|
725 |
3 |
2011.5 |
0.00055875 |
|
726 |
2.1 |
985.635 |
0.000273788 |
|
727 |
0.5 |
55.875 |
1.55208E-05 |
|
728 |
0.5 |
55.875 |
1.55208E-05 |
|
729 |
3.2 |
2288.64 |
0.000635734 |
|
730 |
6.5 |
9442.875 |
0.002623023 |
|
731 |
9.6 |
20597.76 |
0.005721605 |
|
732 |
12.5 |
34921.88 |
0.009700529 |
|
733 |
14 |
43806 |
0.012168343 |
|
734 |
16 |
57216 |
0.015893346 |
|
735 |
18 |
72414 |
0.020115016 |
|
736 |
19.6 |
85859.76 |
0.023849952 |
|
737 |
21.5 |
103312.9 |
0.028698044 |
|
738 |
23.1 |
119261.8 |
0.033128314 |
|
739 |
24.5 |
134155.9 |
0.037265551 |
|
740 |
25.5 |
145330.9 |
0.04036972 |
|
741 |
26.5 |
156952.9 |
0.043598056 |
|
742 |
27.1 |
164140.6 |
0.045594657 |
|
743 |
27.6 |
170253.4 |
0.047292638 |
|
744 |
27.9 |
173974.6 |
0.048326326 |
|
745 |
28.3 |
178998.9 |
0.049721961 |
|
746 |
28.6 |
182814.1 |
0.050781724 |
|
747 |
28.6 |
182814.1 |
0.050781724 |
|
748 |
28.3 |
178998.9 |
0.049721961 |
|
749 |
28.2 |
177736.1 |
0.049371189 |
|
750 |
28 |
175224 |
0.048673372 |
|
751 |
27.5 |
169021.9 |
0.046950558 |
|
752 |
26.8 |
160526.6 |
0.044590769 |
|
753 |
25.5 |
145330.9 |
0.04036972 |
|
754 |
23.5 |
123427.9 |
0.034285548 |
|
755 |
21.5 |
103312.9 |
0.028698044 |
|
756 |
19 |
80683.5 |
0.022412101 |
|
757 |
16.5 |
60847.88 |
0.016902201 |
|
758 |
14.9 |
49619.24 |
0.013783132 |
|
759 |
12.5 |
34921.88 |
0.009700529 |
|
760 |
9.4 |
19748.46 |
0.005485688 |
|
761 |
6.2 |
8591.34 |
0.002386485 |
|
762 |
3 |
2011.5 |
0.00055875 |
|
763 |
1.5 |
502.875 |
0.000139688 |
|
764 |
1.5 |
502.875 |
0.000139688 |
|
765 |
0.5 |
55.875 |
1.55208E-05 |
|
766 |
0 |
0 |
0 |
|
767 |
3 |
2011.5 |
0.00055875 |
|
768 |
6.3 |
8870.715 |
0.002464089 |
|
769 |
9.6 |
20597.76 |
0.005721605 |
|
770 |
12.9 |
37192.64 |
0.010331296 |
|
771 |
15.8 |
55794.54 |
0.015498496 |
|
772 |
17.5 |
68446.88 |
0.019013036 |
|
773 |
18.4 |
75668.16 |
0.02101895 |
|
774 |
19.5 |
84985.88 |
0.023607206 |
|
775 |
20.7 |
95767.52 |
0.026602109 |
|
776 |
22 |
108174 |
0.030048357 |
|
777 |
23.2 |
120296.6 |
0.03341576 |
|
778 |
25 |
139687.5 |
0.038802114 |
|
779 |
26.5 |
156952.9 |
0.043598056 |
|
780 |
27.5 |
169021.9 |
0.046950558 |
|
781 |
28 |
175224 |
0.048673372 |
|
782 |
28.3 |
178998.9 |
0.049721961 |
|
783 |
28.9 |
186669.4 |
0.051852662 |
|
784 |
28.9 |
186669.4 |
0.051852662 |
|
785 |
28.9 |
186669.4 |
0.051852662 |
|
786 |
28.8 |
185379.8 |
0.051494441 |
|
787 |
28.5 |
181537.9 |
0.050427228 |
|
788 |
28.3 |
178998.9 |
0.049721961 |
|
789 |
28.3 |
178998.9 |
0.049721961 |
|
790 |
28.3 |
178998.9 |
0.049721961 |
|
791 |
28.2 |
177736.1 |
0.049371189 |
|
792 |
27.6 |
170253.4 |
0.047292638 |
|
793 |
27.5 |
169021.9 |
0.046950558 |
|
794 |
27.5 |
169021.9 |
0.046950558 |
|
795 |
27.5 |
169021.9 |
0.046950558 |
|
796 |
27.5 |
169021.9 |
0.046950558 |
|
797 |
27.5 |
169021.9 |
0.046950558 |
|
798 |
27.5 |
169021.9 |
0.046950558 |
|
799 |
27.6 |
170253.4 |
0.047292638 |
|
800 |
28 |
175224 |
0.048673372 |
|
801 |
28.5 |
181537.9 |
0.050427228 |
|
802 |
30 |
201150 |
0.055875045 |
|
803 |
31 |
214783.5 |
0.059662131 |
|
804 |
32 |
228864 |
0.063573384 |
|
805 |
33 |
243391.5 |
0.067608804 |
|
806 |
33 |
243391.5 |
0.067608804 |
|
807 |
33.6 |
252322.6 |
0.070089656 |
|
808 |
34 |
258366 |
0.071768391 |
|
809 |
34.3 |
262945.5 |
0.073040479 |
|
810 |
34.2 |
261414.5 |
0.072615208 |
|
811 |
34 |
258366 |
0.071768391 |
|
812 |
34 |
258366 |
0.071768391 |
|
813 |
33.9 |
256848.4 |
0.071346845 |
|
814 |
33.6 |
252322.6 |
0.070089656 |
|
815 |
33.1 |
244868.8 |
0.068019175 |
|
816 |
33 |
243391.5 |
0.067608804 |
|
817 |
32.5 |
236071.9 |
0.065575573 |
|
818 |
32 |
228864 |
0.063573384 |
|
819 |
31.9 |
227435.8 |
0.063176671 |
|
820 |
31.6 |
223178.2 |
0.061993983 |
|
821 |
31.5 |
221767.9 |
0.061602237 |
|
822 |
30.6 |
209276.5 |
0.058132397 |
|
823 |
30 |
201150 |
0.055875045 |
|
824 |
29.9 |
199811.2 |
0.055503165 |
|
825 |
29.9 |
199811.2 |
0.055503165 |
|
826 |
29.9 |
199811.2 |
0.055503165 |
|
827 |
29.9 |
199811.2 |
0.055503165 |
|
828 |
29.6 |
195821.8 |
0.054394977 |
|
829 |
29.5 |
194500.9 |
0.054028064 |
|
830 |
29.5 |
194500.9 |
0.054028064 |
|
831 |
29.3 |
191872.5 |
0.053297963 |
|
832 |
28.9 |
186669.4 |
0.051852662 |
|
833 |
28.2 |
177736.1 |
0.049371189 |
|
834 |
27.7 |
171489.3 |
0.047635959 |
|
835 |
27 |
162931.5 |
0.045258786 |
|
836 |
25.5 |
145330.9 |
0.04036972 |
|
837 |
23.7 |
125537.7 |
0.034871615 |
|
838 |
22 |
108174 |
0.030048357 |
|
839 |
20.5 |
93925.88 |
0.026090542 |
|
840 |
19.2 |
82391.04 |
0.022886418 |
|
841 |
19.2 |
82391.04 |
0.022886418 |
|
842 |
20.1 |
90296.24 |
0.025082308 |
|
843 |
20.9 |
97627.04 |
0.027118643 |
|
844 |
21.4 |
102354.1 |
0.028431706 |
|
845 |
22 |
108174 |
0.030048357 |
|
846 |
22.6 |
114154.9 |
0.031709709 |
|
847 |
23.2 |
120296.6 |
0.03341576 |
|
848 |
24 |
128736 |
0.035760029 |
|
849 |
25 |
139687.5 |
0.038802114 |
|
850 |
26 |
151086 |
0.041968367 |
|
851 |
26.6 |
158139.7 |
0.043927718 |
|
852 |
26.6 |
158139.7 |
0.043927718 |
|
853 |
26.8 |
160526.6 |
0.044590769 |
|
854 |
27 |
162931.5 |
0.045258786 |
|
855 |
27.2 |
165354.2 |
0.04593177 |
|
856 |
27.8 |
172729.7 |
0.047980522 |
|
857 |
28.1 |
176477.8 |
0.04902166 |
|
858 |
28.8 |
185379.8 |
0.051494441 |
|
859 |
28.9 |
186669.4 |
0.051852662 |
|
860 |
29 |
187963.5 |
0.052212125 |
|
861 |
29.1 |
189262 |
0.05257283 |
|
862 |
29 |
187963.5 |
0.052212125 |
|
863 |
28.1 |
176477.8 |
0.04902166 |
|
864 |
27.5 |
169021.9 |
0.046950558 |
|
865 |
27 |
162931.5 |
0.045258786 |
|
866 |
25.8 |
148770.5 |
0.041325183 |
|
867 |
25 |
139687.5 |
0.038802114 |
|
868 |
24.5 |
134155.9 |
0.037265551 |
|
869 |
24.8 |
137461.4 |
0.038183764 |
|
870 |
25.1 |
140807.2 |
0.039113152 |
|
871 |
25.5 |
145330.9 |
0.04036972 |
|
872 |
25.7 |
147619.5 |
0.041005454 |
|
873 |
26.2 |
153419.3 |
0.042616517 |
|
874 |
26.9 |
161726.8 |
0.044924157 |
|
875 |
27.5 |
169021.9 |
0.046950558 |
|
876 |
27.8 |
172729.7 |
0.047980522 |
|
877 |
28.4 |
180266.2 |
0.050073973 |
|
878 |
29 |
187963.5 |
0.052212125 |
|
879 |
29.2 |
190565 |
0.052934776 |
|
880 |
29.1 |
189262 |
0.05257283 |
|
881 |
29 |
187963.5 |
0.052212125 |
|
882 |
28.9 |
186669.4 |
0.051852662 |
|
883 |
28.5 |
181537.9 |
0.050427228 |
|
884 |
28.1 |
176477.8 |
0.04902166 |
|
885 |
28 |
175224 |
0.048673372 |
|
886 |
28 |
175224 |
0.048673372 |
|
887 |
27.6 |
170253.4 |
0.047292638 |
|
888 |
27.2 |
165354.2 |
0.04593177 |
|
889 |
26.6 |
158139.7 |
0.043927718 |
|
890 |
27 |
162931.5 |
0.045258786 |
|
891 |
27.5 |
169021.9 |
0.046950558 |
|
892 |
27.8 |
172729.7 |
0.047980522 |
|
893 |
28 |
175224 |
0.048673372 |
|
894 |
27.8 |
172729.7 |
0.047980522 |
|
895 |
28 |
175224 |
0.048673372 |
|
896 |
28 |
175224 |
0.048673372 |
|
897 |
28 |
175224 |
0.048673372 |
|
898 |
27.7 |
171489.3 |
0.047635959 |
|
899 |
27.4 |
167794.9 |
0.046609721 |
|
900 |
26.9 |
161726.8 |
0.044924157 |
|
901 |
26.6 |
158139.7 |
0.043927718 |
|
902 |
26.5 |
156952.9 |
0.043598056 |
|
903 |
26.5 |
156952.9 |
0.043598056 |
|
904 |
26.5 |
156952.9 |
0.043598056 |
|
905 |
26.3 |
154592.7 |
0.042942455 |
|
906 |
26.2 |
153419.3 |
0.042616517 |
|
907 |
26.2 |
153419.3 |
0.042616517 |
|
908 |
25.9 |
149926 |
0.041646154 |
|
909 |
25.6 |
146473 |
0.040686966 |
|
910 |
25.6 |
146473 |
0.040686966 |
|
911 |
25.9 |
149926 |
0.041646154 |
|
912 |
25.8 |
148770.5 |
0.041325183 |
|
913 |
25.5 |
145330.9 |
0.04036972 |
|
914 |
24.6 |
135253.3 |
0.03757038 |
|
915 |
23.5 |
123427.9 |
0.034285548 |
|
916 |
22.2 |
110149.7 |
0.030597174 |
|
917 |
21.6 |
104276.2 |
0.028965623 |
|
918 |
21.6 |
104276.2 |
0.028965623 |
|
919 |
21.7 |
105243.9 |
0.029234444 |
|
920 |
22.6 |
114154.9 |
0.031709709 |
|
921 |
23.4 |
122379.7 |
0.033994377 |
|
922 |
24 |
128736 |
0.035760029 |
|
923 |
24.2 |
130890.5 |
0.036358512 |
|
924 |
24.4 |
133063 |
0.036961963 |
|
925 |
24.9 |
138572.2 |
0.038492318 |
|
926 |
25.1 |
140807.2 |
0.039113152 |
|
927 |
25.2 |
141931.4 |
0.039425432 |
|
928 |
25.3 |
143060.1 |
0.039738953 |
|
929 |
25.5 |
145330.9 |
0.04036972 |
|
930 |
25.2 |
141931.4 |
0.039425432 |
|
931 |
25 |
139687.5 |
0.038802114 |
|
932 |
25 |
139687.5 |
0.038802114 |
|
933 |
25 |
139687.5 |
0.038802114 |
|
934 |
24.7 |
136355.1 |
0.037876451 |
|
935 |
24.5 |
134155.9 |
0.037265551 |
|
936 |
24.3 |
131974.5 |
0.036659617 |
|
937 |
24.3 |
131974.5 |
0.036659617 |
|
938 |
24.5 |
134155.9 |
0.037265551 |
|
939 |
25 |
139687.5 |
0.038802114 |
|
940 |
25 |
139687.5 |
0.038802114 |
|
941 |
24.6 |
135253.3 |
0.03757038 |
|
942 |
24.6 |
135253.3 |
0.03757038 |
|
943 |
24.1 |
129811 |
0.03605865 |
|
944 |
24.5 |
134155.9 |
0.037265551 |
|
945 |
25.1 |
140807.2 |
0.039113152 |
|
946 |
25.6 |
146473 |
0.040686966 |
|
947 |
25.1 |
140807.2 |
0.039113152 |
|
948 |
24 |
128736 |
0.035760029 |
|
949 |
22 |
108174 |
0.030048357 |
|
950 |
20.1 |
90296.24 |
0.025082308 |
|
951 |
16.9 |
63833.84 |
0.017731635 |
|
952 |
13.6 |
41338.56 |
0.011482943 |
|
953 |
10.3 |
23711.12 |
0.006586426 |
|
954 |
7 |
10951.5 |
0.003042086 |
|
955 |
3.7 |
3059.715 |
0.000849922 |
|
956 |
0.4 |
35.76 |
9.93334E-06 |
|
957 |
0 |
0 |
0 |
|
958 |
0 |
0 |
0 |
|
959 |
0 |
0 |
0 |
|
960 |
2 |
894 |
0.000248334 |
|
961 |
5.3 |
6278.115 |
0.001743922 |
|
962 |
8.6 |
16530.06 |
0.004591687 |
|
963 |
11.9 |
31649.84 |
0.008791628 |
|
964 |
15.2 |
51637.44 |
0.014343745 |
|
965 |
17.5 |
68446.88 |
0.019013036 |
|
966 |
18.6 |
77322.06 |
0.021478367 |
|
967 |
20 |
89400 |
0.024833353 |
|
968 |
21.1 |
99504.44 |
0.027640143 |
|
969 |
22 |
108174 |
0.030048357 |
|
970 |
23 |
118231.5 |
0.03284211 |
|
971 |
24.5 |
134155.9 |
0.037265551 |
|
972 |
26.3 |
154592.7 |
0.042942455 |
|
973 |
27.5 |
169021.9 |
0.046950558 |
|
974 |
28.1 |
176477.8 |
0.04902166 |
|
975 |
28.4 |
180266.2 |
0.050073973 |
|
976 |
28.5 |
181537.9 |
0.050427228 |
|
977 |
28.5 |
181537.9 |
0.050427228 |
|
978 |
28.5 |
181537.9 |
0.050427228 |
|
979 |
27.7 |
171489.3 |
0.047635959 |
|
980 |
27.5 |
169021.9 |
0.046950558 |
|
981 |
27.2 |
165354.2 |
0.04593177 |
|
982 |
26.8 |
160526.6 |
0.044590769 |
|
983 |
26.5 |
156952.9 |
0.043598056 |
|
984 |
26 |
151086 |
0.041968367 |
|
985 |
25.7 |
147619.5 |
0.041005454 |
|
986 |
25.2 |
141931.4 |
0.039425432 |
|
987 |
24 |
128736 |
0.035760029 |
|
988 |
22 |
108174 |
0.030048357 |
|
989 |
21.5 |
103312.9 |
0.028698044 |
|
990 |
21.5 |
103312.9 |
0.028698044 |
|
991 |
21.8 |
106216.1 |
0.029504507 |
|
992 |
22.5 |
113146.9 |
0.031429713 |
|
993 |
23 |
118231.5 |
0.03284211 |
|
994 |
22.8 |
116184.2 |
0.032273426 |
|
995 |
22.8 |
116184.2 |
0.032273426 |
|
996 |
23 |
118231.5 |
0.03284211 |
|
997 |
22.7 |
115167.3 |
0.031990946 |
|
998 |
22.7 |
115167.3 |
0.031990946 |
|
999 |
22.7 |
115167.3 |
0.031990946 |
|
1000 |
23.5 |
123427.9 |
0.034285548 |
|
1001 |
24 |
128736 |
0.035760029 |
|
1002 |
24.6 |
135253.3 |
0.03757038 |
|
1003 |
24.8 |
137461.4 |
0.038183764 |
|
1004 |
25.1 |
140807.2 |
0.039113152 |
|
1005 |
25.5 |
145330.9 |
0.04036972 |
|
1006 |
25.6 |
146473 |
0.040686966 |
|
1007 |
25.5 |
145330.9 |
0.04036972 |
|
1008 |
25 |
139687.5 |
0.038802114 |
|
1009 |
24.1 |
129811 |
0.03605865 |
|
1010 |
23.7 |
125537.7 |
0.034871615 |
|
1011 |
23.2 |
120296.6 |
0.03341576 |
|
1012 |
22.9 |
117205.6 |
0.032557147 |
|
1013 |
22.5 |
113146.9 |
0.031429713 |
|
1014 |
22 |
108174 |
0.030048357 |
|
1015 |
21.6 |
104276.2 |
0.028965623 |
|
1016 |
20.5 |
93925.88 |
0.026090542 |
|
1017 |
17.5 |
68446.88 |
0.019013036 |
|
1018 |
14.2 |
45066.54 |
0.012518493 |
|
1019 |
10.9 |
26554.04 |
0.007376127 |
|
1020 |
7.6 |
12909.36 |
0.003585936 |
|
1021 |
4.3 |
4132.515 |
0.001147922 |
|
1022 |
1 |
223.5 |
6.20834E-05 |
|
1023 |
0 |
0 |
0 |
|
1024 |
0 |
0 |
0 |
|
1025 |
0 |
0 |
0 |
|
1026 |
0 |
0 |
0 |
|
1027 |
0 |
0 |
0 |
|
1028 |
0 |
0 |
0 |
|
1029 |
0 |
0 |
0 |
|
1030 |
0 |
0 |
0 |
|
1031 |
0 |
0 |
0 |
|
1032 |
0 |
0 |
0 |
|
1033 |
0 |
0 |
0 |
|
1034 |
0 |
0 |
0 |
|
1035 |
0 |
0 |
0 |
|
1036 |
0 |
0 |
0 |
|
1037 |
0 |
0 |
0 |
|
1038 |
0 |
0 |
0 |
|
1039 |
0 |
0 |
0 |
|
1040 |
0 |
0 |
0 |
|
1041 |
0 |
0 |
0 |
|
1042 |
0 |
0 |
0 |
|
1043 |
0 |
0 |
0 |
|
1044 |
0 |
0 |
0 |
|
1045 |
0 |
0 |
0 |
|
1046 |
0 |
0 |
0 |
|
1047 |
0 |
0 |
0 |
|
1048 |
0 |
0 |
0 |
|
1049 |
0 |
0 |
0 |
|
1050 |
0 |
0 |
0 |
|
1051 |
0 |
0 |
0 |
|
1052 |
0 |
0 |
0 |
|
1053 |
1.2 |
321.84 |
8.94001E-05 |
|
1054 |
4 |
3576 |
0.000993334 |
|
1055 |
7.3 |
11910.32 |
0.003308423 |
|
1056 |
10.6 |
25112.46 |
0.006975689 |
|
1057 |
13.9 |
43182.44 |
0.01199513 |
|
1058 |
17 |
64591.5 |
0.017942098 |
|
1059 |
18.5 |
76492.88 |
0.021248038 |
|
1060 |
20 |
89400 |
0.024833353 |
|
1061 |
21.8 |
106216.1 |
0.029504507 |
|
1062 |
23 |
118231.5 |
0.03284211 |
|
1063 |
24 |
128736 |
0.035760029 |
|
1064 |
24.8 |
137461.4 |
0.038183764 |
|
1065 |
25.6 |
146473 |
0.040686966 |
|
1066 |
26.5 |
156952.9 |
0.043598056 |
|
1067 |
26.8 |
160526.6 |
0.044590769 |
|
1068 |
27.4 |
167794.9 |
0.046609721 |
|
1069 |
27.9 |
173974.6 |
0.048326326 |
|
1070 |
28.3 |
178998.9 |
0.049721961 |
|
1071 |
28 |
175224 |
0.048673372 |
|
1072 |
27.5 |
169021.9 |
0.046950558 |
|
1073 |
27 |
162931.5 |
0.045258786 |
|
1074 |
27 |
162931.5 |
0.045258786 |
|
1075 |
26.3 |
154592.7 |
0.042942455 |
|
1076 |
24.5 |
134155.9 |
0.037265551 |
|
1077 |
22.5 |
113146.9 |
0.031429713 |
|
1078 |
21.5 |
103312.9 |
0.028698044 |
|
1079 |
20.6 |
94844.46 |
0.026345704 |
|
1080 |
18 |
72414 |
0.020115016 |
|
1081 |
15 |
50287.5 |
0.013968761 |
|
1082 |
12.3 |
33813.32 |
0.009392595 |
|
1083 |
11.1 |
27537.44 |
0.007649294 |
|
1084 |
10.6 |
25112.46 |
0.006975689 |
|
1085 |
10 |
22350 |
0.006208338 |
|
1086 |
9.5 |
20170.88 |
0.005603025 |
|
1087 |
9.1 |
18508.04 |
0.005141125 |
|
1088 |
8.7 |
16916.72 |
0.004699091 |
|
1089 |
8.6 |
16530.06 |
0.004591687 |
|
1090 |
8.8 |
17307.84 |
0.004807737 |
|
1091 |
9 |
18103.5 |
0.005028754 |
|
1092 |
8.7 |
16916.72 |
0.004699091 |
|
1093 |
8.6 |
16530.06 |
0.004591687 |
|
1094 |
8 |
14304 |
0.003973337 |
|
1095 |
7 |
10951.5 |
0.003042086 |
|
1096 |
5 |
5587.5 |
0.001552085 |
|
1097 |
4.2 |
3942.54 |
0.001095151 |
|
1098 |
2.6 |
1510.86 |
0.000419684 |
|
1099 |
1 |
223.5 |
6.20834E-05 |
|
1100 |
0 |
0 |
0 |
|
1101 |
0.1 |
2.235 |
6.20834E-07 |
|
1102 |
0.6 |
80.46 |
2.235E-05 |
|
1103 |
1.6 |
572.16 |
0.000158933 |
|
1104 |
3.6 |
2896.56 |
0.000804601 |
|
1105 |
6.9 |
10640.84 |
0.00295579 |
|
1106 |
10 |
22350 |
0.006208338 |
|
1107 |
12.8 |
36618.24 |
0.010171741 |
|
1108 |
14 |
43806 |
0.012168343 |
|
1109 |
14.5 |
46990.88 |
0.013053031 |
|
1110 |
16 |
57216 |
0.015893346 |
|
1111 |
18.1 |
73220.84 |
0.020339137 |
|
1112 |
20 |
89400 |
0.024833353 |
|
1113 |
21 |
98563.5 |
0.027378772 |
|
1114 |
21.2 |
100449.8 |
0.027902756 |
|
1115 |
21.3 |
101399.7 |
0.02816661 |
|
1116 |
21.4 |
102354.1 |
0.028431706 |
|
1117 |
21.7 |
105243.9 |
0.029234444 |
|
1118 |
22.5 |
113146.9 |
0.031429713 |
|
1119 |
23 |
118231.5 |
0.03284211 |
|
1120 |
23.8 |
126599.3 |
0.035166511 |
|
1121 |
24.5 |
134155.9 |
0.037265551 |
|
1122 |
25 |
139687.5 |
0.038802114 |
|
1123 |
24.9 |
138572.2 |
0.038492318 |
|
1124 |
24.8 |
137461.4 |
0.038183764 |
|
1125 |
25 |
139687.5 |
0.038802114 |
|
1126 |
25.4 |
144193.3 |
0.040053715 |
|
1127 |
25.8 |
148770.5 |
0.041325183 |
|
1128 |
26 |
151086 |
0.041968367 |
|
1129 |
26.4 |
155770.6 |
0.043269635 |
|
1130 |
26.6 |
158139.7 |
0.043927718 |
|
1131 |
26.9 |
161726.8 |
0.044924157 |
|
1132 |
27 |
162931.5 |
0.045258786 |
|
1133 |
27 |
162931.5 |
0.045258786 |
|
1134 |
27 |
162931.5 |
0.045258786 |
|
1135 |
26.9 |
161726.8 |
0.044924157 |
|
1136 |
26.8 |
160526.6 |
0.044590769 |
|
1137 |
26.8 |
160526.6 |
0.044590769 |
|
1138 |
26.5 |
156952.9 |
0.043598056 |
|
1139 |
26.4 |
155770.6 |
0.043269635 |
|
1140 |
26 |
151086 |
0.041968367 |
|
1141 |
25.5 |
145330.9 |
0.04036972 |
|
1142 |
24.6 |
135253.3 |
0.03757038 |
|
1143 |
23.5 |
123427.9 |
0.034285548 |
|
1144 |
21.5 |
103312.9 |
0.028698044 |
|
1145 |
20 |
89400 |
0.024833353 |
|
1146 |
17.5 |
68446.88 |
0.019013036 |
|
1147 |
16 |
57216 |
0.015893346 |
|
1148 |
14 |
43806 |
0.012168343 |
|
1149 |
10.7 |
25588.52 |
0.007107927 |
|
1150 |
7.4 |
12238.86 |
0.003399686 |
|
1151 |
4.1 |
3757.035 |
0.001043622 |
|
1152 |
0.8 |
143.04 |
3.97334E-05 |
|
1153 |
0 |
0 |
0 |
|
1154 |
0 |
0 |
0 |
|
1155 |
0 |
0 |
0 |
|
1156 |
0 |
0 |
0 |
|
1157 |
0 |
0 |
0 |
|
1158 |
0 |
0 |
0 |
|
1159 |
0 |
0 |
0 |
|
1160 |
0 |
0 |
0 |
|
1161 |
0 |
0 |
0 |
|
1162 |
0 |
0 |
0 |
|
1163 |
0 |
0 |
0 |
|
1164 |
0 |
0 |
0 |
|
1165 |
0 |
0 |
0 |
|
1166 |
0 |
0 |
0 |
|
1167 |
0 |
0 |
0 |
|
1168 |
0 |
0 |
0 |
|
1169 |
2.1 |
985.635 |
0.000273788 |
|
1170 |
5.4 |
6517.26 |
0.001810351 |
|
1171 |
8.7 |
16916.72 |
0.004699091 |
|
1172 |
12 |
32184 |
0.008940007 |
|
1173 |
15.3 |
52319.12 |
0.014533099 |
|
1174 |
18.6 |
77322.06 |
0.021478367 |
|
1175 |
21.1 |
99504.44 |
0.027640143 |
|
1176 |
23 |
118231.5 |
0.03284211 |
|
1177 |
23.5 |
123427.9 |
0.034285548 |
|
1178 |
23 |
118231.5 |
0.03284211 |
|
1179 |
22.5 |
113146.9 |
0.031429713 |
|
1180 |
20 |
89400 |
0.024833353 |
|
1181 |
16.7 |
62331.92 |
0.017314435 |
|
1182 |
13.4 |
40131.66 |
0.011147692 |
|
1183 |
10.1 |
22799.24 |
0.006333126 |
|
1184 |
6.8 |
10334.64 |
0.002870736 |
|
1185 |
3.5 |
2737.875 |
0.000760521 |
|
1186 |
0.2 |
8.94 |
2.48334E-06 |
|
1187 |
0 |
0 |
0 |
|
1188 |
0 |
0 |
0 |
|
1189 |
0 |
0 |
0 |
|
1190 |
0 |
0 |
0 |
|
1191 |
0 |
0 |
0 |
|
1192 |
0 |
0 |
0 |
|
1193 |
0 |
0 |
0 |
|
1194 |
0 |
0 |
0 |
|
1195 |
0 |
0 |
0 |
|
1196 |
0 |
0 |
0 |
|
1197 |
0.2 |
8.94 |
2.48334E-06 |
|
1198 |
1.5 |
502.875 |
0.000139688 |
|
1199 |
3.5 |
2737.875 |
0.000760521 |
|
1200 |
6.5 |
9442.875 |
0.002623023 |
|
1201 |
9.8 |
21464.94 |
0.005962488 |
|
1202 |
12 |
32184 |
0.008940007 |
|
1203 |
12.9 |
37192.64 |
0.010331296 |
|
1204 |
13 |
37771.5 |
0.010492092 |
|
1205 |
12.6 |
35482.86 |
0.009856358 |
|
1206 |
12.8 |
36618.24 |
0.010171741 |
|
1207 |
13.1 |
38354.84 |
0.010654129 |
|
1208 |
13.1 |
38354.84 |
0.010654129 |
|
1209 |
14 |
43806 |
0.012168343 |
|
1210 |
15.5 |
53695.88 |
0.014915533 |
|
1211 |
17 |
64591.5 |
0.017942098 |
|
1212 |
18.6 |
77322.06 |
0.021478367 |
|
1213 |
19.7 |
86738.12 |
0.02409394 |
|
1214 |
21 |
98563.5 |
0.027378772 |
|
1215 |
21.5 |
103312.9 |
0.028698044 |
|
1216 |
21.8 |
106216.1 |
0.029504507 |
|
1217 |
21.8 |
106216.1 |
0.029504507 |
|
1218 |
21.5 |
103312.9 |
0.028698044 |
|
1219 |
21.2 |
100449.8 |
0.027902756 |
|
1220 |
21.5 |
103312.9 |
0.028698044 |
|
1221 |
21.8 |
106216.1 |
0.029504507 |
|
1222 |
22 |
108174 |
0.030048357 |
|
1223 |
21.9 |
107192.8 |
0.029775811 |
|
1224 |
21.7 |
105243.9 |
0.029234444 |
|
1225 |
21.5 |
103312.9 |
0.028698044 |
|
1226 |
21.5 |
103312.9 |
0.028698044 |
|
1227 |
21.4 |
102354.1 |
0.028431706 |
|
1228 |
20.1 |
90296.24 |
0.025082308 |
|
1229 |
19.5 |
84985.88 |
0.023607206 |
|
1230 |
19.2 |
82391.04 |
0.022886418 |
|
1231 |
19.6 |
85859.76 |
0.023849952 |
|
1232 |
19.8 |
87620.94 |
0.024339169 |
|
1233 |
20 |
89400 |
0.024833353 |
|
1234 |
19.5 |
84985.88 |
0.023607206 |
|
1235 |
17.5 |
68446.88 |
0.019013036 |
|
1236 |
15.5 |
53695.88 |
0.014915533 |
|
1237 |
13 |
37771.5 |
0.010492092 |
|
1238 |
10 |
22350 |
0.006208338 |
|
1239 |
8 |
14304 |
0.003973337 |
|
1240 |
6 |
8046 |
0.002235002 |
|
1241 |
4 |
3576 |
0.000993334 |
|
1242 |
2.5 |
1396.875 |
0.000388021 |
|
1243 |
0.7 |
109.515 |
3.04209E-05 |
|
1244 |
0 |
0 |
0 |
|
1245 |
0 |
0 |
0 |
|
1246 |
0 |
0 |
0 |
|
1247 |
0 |
0 |
0 |
|
1248 |
0 |
0 |
0 |
|
1249 |
0 |
0 |
0 |
|
1250 |
0 |
0 |
0 |
|
1251 |
0 |
0 |
0 |
|
1252 |
1 |
223.5 |
6.20834E-05 |
|
1253 |
1 |
223.5 |
6.20834E-05 |
|
1254 |
1 |
223.5 |
6.20834E-05 |
|
1255 |
1 |
223.5 |
6.20834E-05 |
|
1256 |
1 |
223.5 |
6.20834E-05 |
|
1257 |
1.6 |
572.16 |
0.000158933 |
|
1258 |
3 |
2011.5 |
0.00055875 |
|
1259 |
4 |
3576 |
0.000993334 |
|
1260 |
5 |
5587.5 |
0.001552085 |
|
1261 |
6.3 |
8870.715 |
0.002464089 |
|
1262 |
8 |
14304 |
0.003973337 |
|
1263 |
10 |
22350 |
0.006208338 |
|
1264 |
10.5 |
24640.88 |
0.006844693 |
|
1265 |
9.5 |
20170.88 |
0.005603025 |
|
1266 |
8.5 |
16147.88 |
0.004485524 |
|
1267 |
7.6 |
12909.36 |
0.003585936 |
|
1268 |
8.8 |
17307.84 |
0.004807737 |
|
1269 |
11 |
27043.5 |
0.007512089 |
|
1270 |
14 |
43806 |
0.012168343 |
|
1271 |
17 |
64591.5 |
0.017942098 |
|
1272 |
19.5 |
84985.88 |
0.023607206 |
|
1273 |
21 |
98563.5 |
0.027378772 |
|
1274 |
21.8 |
106216.1 |
0.029504507 |
|
1275 |
22.2 |
110149.7 |
0.030597174 |
|
1276 |
23 |
118231.5 |
0.03284211 |
|
1277 |
23.6 |
124480.6 |
0.034577961 |
|
1278 |
24.1 |
129811 |
0.03605865 |
|
1279 |
24.5 |
134155.9 |
0.037265551 |
|
1280 |
24.5 |
134155.9 |
0.037265551 |
|
1281 |
24 |
128736 |
0.035760029 |
|
1282 |
23.5 |
123427.9 |
0.034285548 |
|
1283 |
23.5 |
123427.9 |
0.034285548 |
|
1284 |
23.5 |
123427.9 |
0.034285548 |
|
1285 |
23.5 |
123427.9 |
0.034285548 |
|
1286 |
23.5 |
123427.9 |
0.034285548 |
|
1287 |
23.5 |
123427.9 |
0.034285548 |
|
1288 |
24 |
128736 |
0.035760029 |
|
1289 |
24.1 |
129811 |
0.03605865 |
|
1290 |
24.5 |
134155.9 |
0.037265551 |
|
1291 |
24.7 |
136355.1 |
0.037876451 |
|
1292 |
25 |
139687.5 |
0.038802114 |
|
1293 |
25.4 |
144193.3 |
0.040053715 |
|
1294 |
25.6 |
146473 |
0.040686966 |
|
1295 |
25.7 |
147619.5 |
0.041005454 |
|
1296 |
26 |
151086 |
0.041968367 |
|
1297 |
26.2 |
153419.3 |
0.042616517 |
|
1298 |
27 |
162931.5 |
0.045258786 |
|
1299 |
27.8 |
172729.7 |
0.047980522 |
|
1300 |
28.3 |
178998.9 |
0.049721961 |
|
1301 |
29 |
187963.5 |
0.052212125 |
|
1302 |
29.1 |
189262 |
0.05257283 |
|
1303 |
29 |
187963.5 |
0.052212125 |
|
1304 |
28 |
175224 |
0.048673372 |
|
1305 |
24.7 |
136355.1 |
0.037876451 |
|
1306 |
21.4 |
102354.1 |
0.028431706 |
|
1307 |
18.1 |
73220.84 |
0.020339137 |
|
1308 |
14.8 |
48955.44 |
0.013598744 |
|
1309 |
11.5 |
29557.88 |
0.008210527 |
|
1310 |
8.2 |
15028.14 |
0.004174487 |
|
1311 |
4.9 |
5366.235 |
0.001490622 |
|
1312 |
1.6 |
572.16 |
0.000158933 |
|
1313 |
0 |
0 |
0 |
|
1314 |
0 |
0 |
0 |
|
1315 |
0 |
0 |
0 |
|
1316 |
0 |
0 |
0 |
|
1317 |
0 |
0 |
0 |
|
1318 |
0 |
0 |
0 |
|
1319 |
0 |
0 |
0 |
|
1320 |
0 |
0 |
0 |
|
1321 |
0 |
0 |
0 |
|
1322 |
0 |
0 |
0 |
|
1323 |
0 |
0 |
0 |
|
1324 |
0 |
0 |
0 |
|
1325 |
0 |
0 |
0 |
|
1326 |
0 |
0 |
0 |
|
1327 |
0 |
0 |
0 |
|
1328 |
0 |
0 |
0 |
|
1329 |
0 |
0 |
0 |
|
1330 |
0 |
0 |
0 |
|
1331 |
0 |
0 |
0 |
|
1332 |
0 |
0 |
0 |
|
1333 |
0 |
0 |
0 |
|
1334 |
0 |
0 |
0 |
|
1335 |
0 |
0 |
0 |
|
1336 |
0 |
0 |
0 |
|
1337 |
0 |
0 |
0 |
|
1338 |
1.5 |
502.875 |
0.000139688 |
|
1339 |
4.8 |
5149.44 |
0.001430401 |
|
1340 |
8.1 |
14663.84 |
0.004073291 |
|
1341 |
11.4 |
29046.06 |
0.008068356 |
|
1342 |
13.2 |
38942.64 |
0.010817409 |
|
1343 |
15.1 |
50960.24 |
0.014155632 |
|
1344 |
16.8 |
63080.64 |
0.017522414 |
|
1345 |
18.3 |
74847.92 |
0.020791104 |
|
1346 |
19.5 |
84985.88 |
0.023607206 |
|
1347 |
20.3 |
92102.12 |
0.025583941 |
|
1348 |
21.3 |
101399.7 |
0.02816661 |
|
1349 |
21.9 |
107192.8 |
0.029775811 |
|
1350 |
22.1 |
109159.6 |
0.030322145 |
|
1351 |
22.4 |
112143.4 |
0.031150958 |
|
1352 |
22 |
108174 |
0.030048357 |
|
1353 |
21.6 |
104276.2 |
0.028965623 |
|
1354 |
21.1 |
99504.44 |
0.027640143 |
|
1355 |
20.5 |
93925.88 |
0.026090542 |
|
1356 |
20 |
89400 |
0.024833353 |
|
1357 |
19.6 |
85859.76 |
0.023849952 |
|
1358 |
18.5 |
76492.88 |
0.021248038 |
|
1359 |
17.5 |
68446.88 |
0.019013036 |
|
1360 |
16.5 |
60847.88 |
0.016902201 |
|
1361 |
15.5 |
53695.88 |
0.014915533 |
|
1362 |
14 |
43806 |
0.012168343 |
|
1363 |
11 |
27043.5 |
0.007512089 |
|
1364 |
8 |
14304 |
0.003973337 |
|
1365 |
5.2 |
6043.44 |
0.001678735 |
|
1366 |
2.5 |
1396.875 |
0.000388021 |
|
1367 |
0 |
0 |
0 |
|
1368 |
0 |
0 |
0 |
|
1369 |
0 |
0 |
0 |
|
Total Braking Energy |
50.95583 |
||
We have asssumed the gross vehicle weight is 1000kg.
The Brakingenergy can be converted into KWH when multiplied with a factor of 2.77778e-7.
Thus , the total energy consumed for braking is 50.95583 KWH.
Link for USSD Driving cycle Excel sheet:-
Q2:Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated?
Ans:- In case of EV & HEV electric motor con be experienced two type of braking , those are :
1.Mechanical Braking ,
2.Electrical Braking.
Mechanical Braking:-
Mechanical brakes all act by generating frictional forces as two surfaces rub against each other. The stopping power or capacity of a brake depends largely on the surface area of frictional surfaces as well as on the actuation force applied. The friction and wear encountered by the working surfaces are severe. Thus, the durability of a brake or service life between maintenance depends heavily on the type of material used to line the shoe or pad.
Mechanical brakes are assemblies consisting of mechanical elements for the slowing or stopping of shafts in equipment drives. They use levers or linkages to transmit force from one point to another. Braking slows or stops the movement of the coupled shafts.
There are several types of mechanical brakes like,
- Drum Brake:-
A drum brake is a brake in which the friction is caused by a set of shoes or pads that press against a rotating drum-shaped part called a brake drum.
The term "drum brake" usually means a brake in which shoes press on the inner surface of the drum. When shoes press on the outside of the drum, it is usually called a clasp brake. Where the drum is pinched between two shoes, similar to a conventional disk brake, it is sometimes called a "pinch drum brake", although such brakes are relatively rare. A related type of brake uses a flexible belt or "band" wrapping around the outside of a drum, called a band brake. 
Fig:Drum Brake
- Disk Brake:-
The disc brake is a device for slowing or stopping the rotation of a wheel while it is in motion. A brake disc is usually made of cast iron, but may in some cases be made of composites such as reinforced carbon-carbon or ceramic-matrix composites. This is connected to the wheel and/or the axle. To stop the wheel, friction material in the form of brake pads (mounted on a device called a brake caliper ) is forced hydraulically, pneumatically, or electromagnetically against both sides of the disc. Friction causes the disc and attached wheel to slow or stop. Brakes convert the motion to heat, and if the brakes get too hot, they become less effective, a phenomenon known as brake fade. 
Fig: Disc Brake
In case of HEV Special type of Braking technique are can be used for IC engines but not for Electric engine, Those are
Engine Braking:
A compression engine brake is a device that can convert a diesel engine into an air compressor, a power absorbing device. These devices are used in trucking applications to provide a means for retarding the vehicle, supplementing the normal vehicle braking system. The retarding operation is under full control of the vehicle operator and can be used simultaneously with the normal service brakes. Engine brakes can be installed at any time on a new or used vehicle for most applications.
By restricting airflow, When we lift off the accelerator, the throttle valve closes. That creates a vacuum in the intake manifold. The piston will now have to work against this vacuum to continue moving. That is engine braking.
Fig: Engine Braking
Exhaust Braking Mechanism:
An exhaust brake works by restricting the flow of exhaust gases through the engine Heavy goods vehicles can often require increased braking, in situations where friction brakes could overheat and fail. This is achieved by using an exhaust brake. It achieves this by closing a butterfly valve located in the exhaust manifold. This maintains high pressures in the exhaust manifold, and the engine cylinders, which in turn, act as a brake against the engine rotating. This then slows the road wheels through the transmission or power train.
Fig: Exhaust Braking Mechanism
Electrical Braking:-
Brakes are used to reduce or cease the speed of motors.
If the load is removed from an electric motor and supply to it be disconnected, it will continue to run for some time due to inertia. The time elapsing before it stops will be especially long if the motor is massive and has run at high speed.
It is essential, however, in many cases that the motor and its driven machine be stopped quickly (in machine tools, cranes, hoists, etc). In fact, quick stopping of a motor is more essential than quick starting. Delay in starting up a motor only causes the machinery to stand idle; a delay in stopping a motor may result in heavy damage to equipment or to the manufactured products and even the loss of human life.
We know that there are various types of motors available (DC motors, induction motors, synchronous motors, single-phase motors, etc.) and the specialty and properties of these motors are different from each other, hence these braking methods also differ from each other. But we can divide braking into three parts mainly, which are applicable for almost every type of motor.
- Regenerative Braking.
- Plugging type braking.
- Dynamic braking.
Regenerative Braking:
Regenerative braking takes place whenever the speed of the motor exceeds the synchronous speed. This baking method is called regenerative baking because here the motor works as a generator and the supply itself is given power from the load, i.e. motors. The main criteria for regenerative braking is that the rotor has to rotate at a speed higher than synchronous speed, only then the motor will act as a generator and the direction of current flow through the circuit and direction of the torque reverses and braking takes place. The only disadvantage of this type of braking is that the motor has to run at a super synchronous speed which may damage the motor mechanically and electrically, but regenerative braking can be done at sub synchronous speed if the variable frequency source is available.
Fig: Structure of single-axle series regenerative braking system
Plugging Type Braking:
Another type of braking is Plugging type braking. In this method the terminals of supply are reversed, as a result of the generator torque also reverses which resists the normal rotation of the motor, and as a result, the speed decreases. During plugging external resistance is also introduced into the circuit to limit the flowing current. The main disadvantage of this method is that here power is wasted.
Dynamic Braking:
Another method of reversing the direction of torque and braking the motor is dynamic braking. In this method of braking the motor which is at a running condition is disconnected from the source and connected across a resistance. When the motor is disconnected from the source, the rotor keeps rotating due to inertia and it works as a self-excited generator. When the motor works as a generator the flow of the current and torque reverses. During braking to maintain the steady torque sectional resistances are cut out one by one.
Electric motor can't develop braking torque at high speed similar to starting because the Speed torque characteristics graph of the motor is shown below, 
From the above graph, it is clearly shown in the first graph that till the motor reaches the critical speed it has constant torque and once it reaches the critical speed, the curve is having a downslope which is a constant power region. And this graph denotes the accelerating operation of the motor. For the deceleration or braking operation of the motor, this graph is mirrored down which will be having the speed (+ve) and torque (-ve).
For example,
we can say that an EV can achieve 0-100 kmph in 10 sec. Acceleration operation goes this way, with low speed and high torque constant torque region is achieved which has accelerating power and by reaching the critical speed it shifts to constant power region and thus it is easy for an EV to reach 0-100 kmph.
As said the braking operation graph will be the mirrored image of the above plot. So we cannot say that the motor producing 7 Nm torque for accelerating can also produce -7 Nm for braking. Because we are operating in the field weakening region and operating above the base speed. Thus Peak acceleration torque is greater than the peak deceleration torque. Thus for acceleration, it has a high torque with low speed and for deceleration, it has low torque with high speed.
Coordination of electric and mechanical braking:
There are two types of brake control strategies that are used to coordinate the electrical brake and mechanical.
- Series control strategies
- Parallel control strategies
The comparison of the control strategies is shown in the below figure.
From the above figure, we can clearly see that according to the amount of the brake pedal travel of the vehicle, the mechanical brakes and regenerative brake are applied.
- Series control strategies:
When the brake is applied according to the brake pedal travel the front wheel friction brake, the rear wheel friction brakes, and the regenerative brakes are applied one after another. As the braking requirements increase the frictional brakes are used accordingly.
For the low speed of the vehicle, regenerative braking is used but it may be limited according to the SOC (State of Charge) of the battery. As the speed of the vehicle increases the rear wheel frictional brake will be applied, if the braking requirement is not satisfied yet then the front wheel frictional brake is also used. In this strategy, regenerative brake starts to operate ahead of friction brake.
The regenerative braking system could restore kinetic energy and potential energy to a battery or any other form of power during braking. However, the large current produced by the generator during braking would affect battery performance and shorten battery life. A hybrid-power system is an excellent energy storage system, in which an ultra-capacitor bank and a battery pack are connected through a DC/DC power converter. The ultra-capacitor in this system can store instantaneous large currents quickly, which can protect the battery from large currents, suggesting that the ultra-capacitor can restore the regenerative energy very quickly, which will improve starting and acceleration performance, extend the driving range and increase fuel economy.
The coordination of the series control braking can be done with preference to the comfort of braking or energy storage.
Fig: Series control strategy
- Parallel control strategies:
The regenerative braking system is the own system of Electric and Hybrid Electric vehicles. The system can restore the kinetic energy and potential energy, used during start and accelerating, into the battery through the electrical machine. The total brake force is composed of friction brake force on the front axle, friction brake force on the rear axle, and regenerative brake force when a vehicle is equipped with regenerative braking system brakes.
The parallel brake strategy is not only safe enough but also can restore the largest amount of brake energy.
Fig: Parallel control strategies
An example of parallel control strategies is Nissan's EDIB in Leaf.
The model's features are:
Safe braking: EVs and hybrid vehicles use regenerative braking, which utilizes the motor to convert the kinetic energy during deceleration into electrical energy. With energy regeneration, an EV is able to run on less electricity and a hybrid vehicle on less fuel.
The EDIB (Electric Driven Intelligent Brake) allows and controls optimization of the regenerative brake and regular friction brake (hydraulic brake).
Technology Functionality: After stepping on the brake pedal, the system produces a natural and adequate braking force that corresponds to the operation. The amount of energy regeneration also needs to be increased as much as possible.
EDIB (Electric Driven Intelligent Brake) controls the regenerative brake and friction brake to support both of these requirements. Further, it also controls the reactive force from the pedal in order to unify the feeling when stepping down on the pedal and the sense of deceleration.
Technology Configuration: When the driver steps on the brake pedal, the stroke sensor detects the operation of the brake. That information is communicated to the ECU and controls the motor. The motor engages the piston and amplifies the friction brake's pressure (hydraulic pressure). Through optimum control of the friction brake's hydraulic pressure, the energy regeneration outcome is maximized.
Q3:Make a MATLAB program which plots contour of given motor speed, torque and efficiency values. Attach the code as a .m file attach a screenshot of all the plots.
Ans:-
The matlab code to plot contour of given motor is given below
clear all;
close all;
clc;
% A program for plotting efficiency contours for electric motors
% input speed and torque array of data
% The x-axis corresponding to motor speed (w) in rad/sec
x = linspace(1 , 1000);
% The y-axis corresponding to Torque produced by motor in N.m
y = linspace(1 , 250);
% Allocate motor loss constants
% For copper loss
kc = 0.2;
% For iron loss
ki = 0.008;
% For windage loss
kw = 0.00001;
% For constant motor loss
CLoss = 20;
% Now making motor speed & torque in Matrix
[X,Y] = meshgrid(x,y);
% To calculate output power of electric motor
%Power = Torque x Speed
Po = (X.*Y);
% To find losses
% Equation to find copper losses
B = (Y.^2)*kc;
% Equation to find Iron losses
C = X.*ki;
% Equation to find windage losses
D = (X.^3)*kw;
% Relationship between Input Power and Output Power of electric motor
Pi = Po + B + C + D + CLoss;
% To calculate the effieciency
Z = Po./Pi;
% We now set the efficiencies for which a contour will be plotted
N = [0.70, 0.80, 0.85, 0.90, 0.91, 0.92, 0.925, 0.93];
box off
grid off
contour(X,Y,Z,N);
xlabel('Speed in rad/sec');
ylabel('Torque in N.m');
hold on
% Now plot a contour of the power output of electric motor
% The Output Power in array format has already been calcuated.
% We draw contours at 8 kw and 10 kW.
V = [8000, 10000];
contour(X,Y,Po,V);
title('Plot for efficiency contour, Speed vs Torque')
Code Explanation:
- At first used command clear all, close all, and clc to remove previous
- In the above code Speed and Torque of the motor are defined using the "linspace"
- Then all the loss constants as mentioned above are entered in the code and named accordingly.
- After that, a Matrix is created for Speed and Torque using the "meshgrid"command to help to create Contour Plot.
- Then all the losses, output power, and input power are calculated according to the above-mentioned formulas.
- Next, we created another efficiency matrix so that we can define levels for the Contour.
- At last, we plotted contour using the "contour" command, and once the program runs we get the following results.
Output Contour Plot:
Observation:
- From the above plot, we can observe that the most efficient region in the contour is the innermost elliptical shape with an efficiency of over 93%.
- It is evident from the contour that, the efficiency decreases as values are away from the innermost shape.
- It is optimal for the Motor to operate between the innermost ellipse and its adjacent one for maximum efficiency and performance.
Conclusion:
- The energy required for braking in the UDDS drive cycle was calculated.
- Studied Why electric motor can’t develop braking torque at high speed similar to starting and also studied the coordination of mechanical and electric brakes.
- A Matlab program was written for plotting the contour of given motor speed, torque, and efficiency values.