Automation of Aircraft Fatigue Life Estimation

Gajek, Stanisław

Automation of Aircraft Fatigue Life Estimation

Fatigue of Aircraft Structures

Volume 2022 (2022): Issue 14 (December 2022)

By:

Stanisław Gajek

Open Access

|Nov 2023

Figures & Tables

Example of logged data before [Frame 1] and after [Frame 2] normalization.

Example of logged data after transformation to load levels.

Block flow diagram of extreme values filter.

Example of extreme values filtration results.

Block flow diagram of the Rainflow Cycle Counting method.

Example of stream generation in the Rainflow Cycle Counting method.

Approximation process of the number of cycles N for uncharacteristic argument.

Global view on third test zone of generated streams.

Visualization of filtered load levels in function of time.

Example of telemetry log used in calculations

Date	Time	Hdg(@)	Ptch	Roll	AccX(g)	RSSI(dB)	AccY(g)	AccZ(g)
2021-10-10	16:27:29.650	178.60	65.6	-17.0	-0.06	82	-0.02	0.05
2021-10-10	16:27:29.850	178.60	65.6	-17.0	-0.06	87	-0.02	0.05
2021-10-10	16:27:30.050	186.60	49.7	0.5	-0.09	70	-0.02	0.05
2021-10-10	16:27:30.250	186.60	49.7	0.5	-0.09	70	-0.09	0.14
2021-10-10	16:27:30.450	202.10	49.7	0.5	-0.09	80	-0.09	0.14
2021-10-10	16:27:30.650	202.10	28.9	8.5	-0.07	85	-0.11	0.21
2021-10-10	16:27:30.850	202.10	28.9	8.5	-0.07	85	-0.11	0.21
2021-10-10	16:27:31.050	233.70	23.1	28.5	-0.02	90	-0.08	0.19
2021-10-10	16:27:31.250	233.70	23.1	28.5	-0.02	90	-0.08	0.19
2021-10-10	16:27:31.450	273.10	40.2	28.5	-0.02	87	-0.08	0.19
2021-10-10	16:27:31.650	273.10	40.2	44.1	0.00	87	-0.03	0.17
2021-10-10	16:27:31.850	273.10	40.2	44.1	0.00	80	-0.03	0.17
2021-10-10	16:27:32.050	295.70	54.7	41.5	0.00	87	-0.01	0.09
2021-10-10	16:27:32.250	295.70	54.7	41.5	0.00	87	-0.01	0.09
2021-10-10	16:27:32.450	328.70	59.7	34.9	0.00	90	-0.01	0.09

Active zone of matrix_

LL	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27
27	1,456	0	1,199	0	0,942	0,814	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
26	0	1,456	0	0	0	0,942	0,814	0,685	0	0	0	0,171	0	0	-0,214	0	0	0	0	0	0	0	0
25	0	0	0	1,327	0	1,071	0	0	0,685	0,557	0	0	0	0	0	0	0	-0,471	0	0	0	0	0
24	0	1,713	0	1,456	1,327	1,199	1,071	0	0,814	0,685	0,557	0	0,300	0	0	0	0	0	-0,471	0	0	0	0
23	0	0	0	1,584	1,456	0	1,199	1,071	0,942	0,814	0,685	0,557	0	0	0	0,043	0	0	0	0	-0,599	-0,728	0
22	0	0	0	0	0	1,456	1,327	0	1,071	0,942	0,814	0,685	0,557	0,428	0,300	0,171	0,043	0	-0,214	-0,343	0	0	0
21	0	0	0	0	1,713	0	1,456	1,327	0	1,071	0,942	0,814	0,685	0,557	0,428	0,300	0	0,043	-0,086	0	0	0	0
20	0	0	0	0	1,841	0	0	1,456	0	0	1,071	0,942	0,814	0,685	0,557	0	0,300	0,171	0,043	0	-0,214	0	0
19	0	0	0	0	0	1,841	1,713	1,584	1,456	0	1,199	1,071	0,942	0,814	0	0,557	0,428	0,300	0	0	0	-0,214	0
18	0	0	0	0	0	1,970	0	0	0	0	1.327	1,199	1,071	0	0.814	0.685	0,557	0,428	0,300	0	0	0	0
17	0	0	0	0	0	0	0	0	0	0	0	1,327	0	1,071	0,942	0,814	0,685	0,557	0,428	0,300	0	0	0
16	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,071	0,942	0,814	0,685	0,557	0,428	0,300	0	0
15	0	0	0	0	0	0	0	0	0	0	0	0	1,456	1,327	1,199	1,071	0,942	0,814	0,685	0,557	0	0,300	0
14	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,327	0	1,071	0,942	0,814	0	0,557	0	0
13	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,327	0	1,071	0,942	0,814	0,685	0	0
12	0	0	3,126	0	0	0	0	0	0	0	0	0	0	0	0	0	1,327	1,199	0	0,942	0,814	0	0
11	0	0	0	0	0	0	0	2,612	0	0	0	0	0	0	0	0	0	1,327	0	1,071	0,942	0,814	0
10	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,327	0	1,071	0,942	0,814
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,456	0	1,199	0	0,942
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,584	0	1,327	0	0
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,327	1,199
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,713	0	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,713	0	0

Active zone of generated half-cycle array [T]_

LL	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
25	1	0	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
24	0	0	1	0	2	0	2	1	0	1	1	0	0	1	0	0	1	1	1	0	0
23	0	1	0	1	2	2	0	1	1	1	1	0	0	0	0	0	0	2	0	1	0
22	0	0	0	1	2	2	1	3	0	4	2	1	0	1	0	0	3	0	2	1	0
21	0	0	0	1	0	0	1	3	5	7	2	1	2	1	1	2	0	3	0	1	0
20	0	0	0	0	0	0	2	0	3	8	10	8	13	10	5	0	2	0	0	0	0
19	0	0	0	0	0	0	0	1	0	3	5	10	30	53	0	5	1	0	0	0	0
18	0	0	0	0	0	0	0	0	1	2	0	7	29	0	52	10	1	1	0	1	0
17	0	0	0	0	0	0	0	0	1	3	3	8	0	29	31	12	3	0	0	0	0
16	0	0	0	0	0	0	0	0	0	0	1	0	8	7	10	8	1	1	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	1	3	0	5	11	2	1	1	1	0
14	0	0	0	0	0	0	0	0	1	0	0	0	3	2	3	8	7	4	1	1	0
13	0	0	0	0	0	0	0	0	0	1	0	0	1	1	0	3	5	0	1	0	0
12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	2	3	2	1	0
11	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	2	1	1	0	2	0
10	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	2	2	0	0
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	3	0	2	2
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	0	1
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0

Active zone of the fatigue level matrix [D]_

LL	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
25	0.000198	0	0,000103	7.17E-05	4,86E-05	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
24	0	0	0,000101	0	9.35E-05	0	3,79E-05	1,14E-05	0	3,53E-06	1,79E-06	0	0	1,33E-07	0	0	1,76E-09	1,54E-10	2,75E-12	0	0
23	0	0,000143	0	6,82E-05	8.99E-05	5,73E-05	0	1,03E-05	5,69E-06	2,96E-06	1,43E-06	0	0	0	0	0	0	1,58E-11	0	2,75E-12	0
22	0	0	0	6,67E-05	8,56E-05	5,41E-05	1,62E-05	2,76E-05	0	9,76E-06	2,21E-06	4,46E-07	0	4,26E-08	0	0	6,82E-11	0	1,58E-11	1,54E-10	0
21	0	0	0	6,55E-05	0	0	1.48E-05	2.44E-05	2.08E-05	1,37E-05	1,64E-06	2,96E-07	1,73E-07	1,83E-08	2,17E-09	1.31E-10	0	6.82E-11	0	1,76E-09	0
20	0	0	0	0	0	0	2,70E-05	0	1,03F-05	1,20F-05	5,68F-06	1,41F-06	5,19F-07	5,25F-08	9,37F-10	0	1,31E-10	0	0	0	0
19	0	0	0	0	0	0	0	6,09E-06	0	3,27E-06	1,79E-06	8,72E-07	3,80E-07	2,85E-08	0	9.37E-10	2.17E-09	0	0	0	0
18	0	0	0	0	0	0	0	0	2,10E 06	l,45E06	0	2,14E07	4,49E 08	0	2,80E08	5,25E08	1,83E08	4,26E08	0	l,33E07	0
17	0	0	0	0	0	0	0	0	1,47E-06	1,25E-06	2,22E-07	3,55E-08	0	4,49E-08	3,93E-07	4,79E-07	2,60E-07	0	0	0	0
16	0	0	0	0	0	0	0	0	0	0	1,28E-08	0	3,55E-08	2,14E-07	8,72E-07	1,41E-06	2,96E-07	4,46E-07	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	1,28E-08	2,22E-07	0	1,79E-06	6,25E-06	1,64E-06	1,11-06	1,43E-06	1,79E-06	0
14	0	0	0	0	0	0	0	0	1,05E-07	0	0	0	1,25E-06	1,45E-06	3,27E-06	1,20E-05	1,37E-05	9,76E-06	2,96E-06	3,53E-06	0
13	0	0	0	0	0	0	0	0	0	1,05E-07	0	0	1,47E-06	2,10E-06	0	1,03E-05	2,08E-05	0	5,69E-06	0	0
12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	6,09E-06	0	1,63E-05	2,76E-05	2,05E-05	1,14E-05	0
11	0	0	0	0	0	2,49E-06	0	0	0	0	0	0	0	0	0	2,70E-05	1,48E-05	1,62E-05	0	3,79E-05	0
10	0	0	0	0	0	0	2,49E-06	0	0	0	0	0	0	0	0	0	0	5,41E-05	5.73E-05	0	0
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0,000130	0	9,35E-05	9.73E-05
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	06,55E-05	6,67E-05	6,82E-05	0	7,71E-05
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.000101	0.000103
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.000143	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.000200	0	0

Active zone of [na] matrix_

LL	5	6	7	8	9	10	11	12	13	14	15	16	17	la	19	20	21	22	23	24	25	26	27
27	2.826	0	2,569	0	2,312	2,184	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
26	0	2,569	0	0	0	2,055	1,927	1,798	0	0	0	1,285	0	0	0,899	0	0	0	0	0	0	0	0
25	0	0	0	2,184	0	1,927	0	0	1,542	1,413	0	0	0	0	0	0	0	0,385	0	0	0	0	0
24	0	2,312	0	2,055	1,927	1,798	1,670	0	1,413	1,285	1,156	0	0,899	0	0	0	0	0	0,128	0	0	0	0
23	0	0	0	1,927	1,798	0	1,542	1,413	1,285	1,156	1,028	0,899	0	0	0	0,385	0	0	0	0	0,257	0,385	0
22	0	0	0	0	0	1,542	1,413	0	1,156	1,028	0,899	0,771	0,642	0,514	0,385	0,257	0,128	0	0,128	0,257	0	0	0
21	0	0	0	0	1,542	0	1,285	1,156	0	0,899	0,771	0,642	0,514	0,385	0,257	0,128	0	0,128	0,257	0	0	0	0
20	0	0	0	0	1,413	0	0	1,028	0	0	0,642	0,514	0,385	0,257	0,128	0	0,128	0,257	0,385	0	0,642	0	0
19	0	0	0	0	0	1,156	1,028	0,899	0,771	0	0,514	0,385	0,257	0,128	0	0,128	0,257	0,385	0	0	0	0,899	0
18	0	0	0	0	0	1,028	0	0	0	0	0,385	0,257	0,128	0	0,128	0,257	0,385	0,514	0.642	0	0	0	0
17	0	0	0	0	0	0	0	0	0	0	0	0,128	0	0,128	0,257	0,385	0,514	0,642	0,771	0,899	0	0	0
16	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0,385	0,514	0,642	0,771	0,899	1,028	1,156	0	0
15	0	0	0	0	0	0	0	0	0	0	0	0	0,257	0,385	0,514	0,642	0,771	0,899	1,028	1,156	0	1,413	0
14	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0,642	0	0,899	1,028	1,156	0	1,413	0	0
13	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0,899	0	1,156	1,285	1,413	1,542	0	0
12	0	0	0,642	0	0	0	0	0	0	0	0	0	0	0	0	0	1,156	1,285	0	1,542	1,670	0	0
11	0	0	0	0	0	0	0	0,128	0	0	0	0	0	0	0	0	0	1,413	0	1,670	1,798	1,927	0
10	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,670	0	1,927	2,055	2,184
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,798	0	2,055	0	2,312
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1,927	0	2,184	0	0
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2,441	2,569
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2,312	0	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2,569	0	0

Active zone of [N] matrix

11	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27
27	5016	0	9323	0	18880	27888	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
26	0	6867	0	0	0	29520	45552	72734	0	0	0	739650	0	0	8777566	0	0	0	0	0	0	0	0
25	0	0	0	13948	0	31222	0	0	135688	242254	0	0	0	0	0	0	0	1238567291	0	0	0	0	0
24	0	6971	0	14323	21400	33011	52788	0	153650	283687	559374	0	2816397	0	0	0	0	0	363061881753	0	0	0	0
23	0	0	0	14668	22239	0	57012	97452	175690	337414	699601	1595342	0	0	0	260105776	0	0	0	0	15664059809	2702740887	0
22	0	0	0	0	0	36956	61809	0	203528	409747	903678	2239961	6489824	23452051	119196963	1112010656	44006761878	0	126400861458	6485934196	0	0	0
21	0	0	0	0	23955	0	67384	122768	0	511886	1220828	3379409	11549092	54623608	460444357	15321059277	0	44006761878	2685596385	0	0	0	0
20	0	0	0	0	24864	0	0	140556	0	0	1759740	5687415	25032002	190653754	5334063388	0	15321059277	1112010656	260105776	0	45963108	0	0
19	0	0	0	0	0	44669	82322	164245	362646	0	2800799	11471251	78942989	1857066911	0	5334063388	460444357	119196963	0	0	0	8777566	0
18	0	0	0	0	0	48215	0	0	0	0	5256855	32687505	646542282	0	1857066911	190653754	54623608	23452051	12463071	0	0	0	0
17	0	0	0	0	0	0	0	0	0	0	0	225095240	0	646542282	78942989	25032002	11549092	6489824	4109855	2816397	0	0	0
16	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	11471251	5687415	3379409	2239961	1595342	1194495	927346	0
15	0	0	0	0	0	0	0	0	0	0	0	0	13534742	5256855	2800799	1759740	1220828	903678	699601	559374	0	381954	0
14	0	0	0	0	0	0	0	0	0	0	0	0	0	0	916340	0	511886	409747	337414	0	242254	0	0
13	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	289957	0	203528	175690	153650	135688	0	0
12	0	0	9513	0	0	0	0	0	0	0	0	0	0	0	0	0	122768	108806	0	87954	79823	0	0
11	0	0	0	0	0	0	0	1151365	0	0	0	0	0	0	0	0	0	61809	0	52788	49000	45552	0
10	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	34910	0	31222	29520	27888
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	22239	0	20563	0	18880
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	14668	0	13948	0	0
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	9535	9323
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	6971	0	0	0
5	0	0	0	0	0	0	0	0	0	j	0	1	0	0	0	0	0	0	0	0	5058	0	0

Material fatigue characteristics of aluminum used in analyzed component_

σ_m	lg(N)	(lg(σ_a)
0	3,3	2,2551
0	7	1,4699
34	3,3	2,1954
34	7	1,228
69	3,3	2,1138
69	7	1,1087
103	3,3	2,0761
103	7	1,0333
138	3,3	2,0384
138	7	0,9516
207	3,3	1,9913
207	7	0,8323

Example of active zone in half-cycle array_

LL	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26
25	1	0	2	0	2	1	0	1	1	0	0	1	0	0	1	1	1	x	0
24	0	1	2	2	0	1	1	1	1	0	0	0	0	0	0	2	x	1	0
23	0	1	2	2	1	3	0	4	2	1	0	1	0	0	3	x	2	1	0
22	0	1	0	0	1	3	5	7	2	1	2	1	1	2	x	3	0	1	0
21	0	0	0	0	2	0	3	8	10	8	13	10	5	x	2	0	0	0	0
20	0	0	0	0	0	1	0	3	5	10	30	53	x	5	1	0	0	0	0
19	0	0	0	0	0	0	1	2	0	7	29	x	52	10	1	1	0	1	0
18	0	0	0	0	0	0	1	3	3	8	x	29	31	12	3	0	0	0	0
17	0	0	0	0	0	0	0	0	1	x	8	7	10	8	1	1	0	0	0
16	0	0	0	0	0	0	0	0	x	1	3	0	5	11	2	1	1	1	0
15	0	0	0	0	0	0	1	x	0	0	3	2	3	8	7	4	1	1	0
14	0	0	0	0	0	0	x	1	0	0	1	1	0	3	5	0	1	0	0
13	0	0	0	0	0	x	0	0	0	0	0	0	1	0	2	3	2	1	0
12	0	0	0	1	x	0	0	0	0	0	0	0	0	2	1	1	0	2	0
11	0	0	0	x	1	0	0	0	0	0	0	0	0	0	0	2	2	0	0
10	0	0	x	0	0	0	0	0	0	0	0	0	0	0	0	3	0	2	2
9	0	x	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	0	1
8	x	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0

DOI: https://doi.org/10.2478/fas-2022-0007 | Journal eISSN: 2300-7591 | Journal ISSN: 2081-7738

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Language: English

Page range: 83 - 103

Published on: Nov 28, 2023

Published by: Institute of Aviation

In partnership with: Paradigm Publishing Services

Publication frequency: 1 times per year

Keywords:

Aircraft Fatigue,

Rainflow Cycle Counting,

Load Spectra,

UAV

Related subjects:

Engineering,

Introductions and overviews,

Engineering, other

© 2023 Stanisław Gajek, published by Institute of Aviation
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Previous article Volume 2022 (2022): Issue 14 (December 2022)Next article

Automation of Aircraft Fatigue Life Estimation

Figures & Tables

Figure 3.1.

Figure 3.2.

Figure 3.3.

Figure 3.4.

Figure 3.5.

Figure 3.6.

Figure 3.7.

Figure 4.1.

Figure 4.2.

Figure 4.3.

Figure 4.4.

Figure 4.5.

Figure 4.6.

Figure 4.7.

Figure 5.1.

Figure 5.2.

Figure 5.2.

Example of telemetry log used in calculations

Active zone of matrix_

Active zone of generated half-cycle array [T]_

Active zone of the fatigue level matrix [D]_

Active zone of [na] matrix_

Active zone of [N] matrix

Material fatigue characteristics of aluminum used in analyzed component_

Example of active zone in half-cycle array_

Paradigm

My account

LL	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
25	1	0	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
24	0	0	1	0	2	0	2	1	0	1	1	0	0	1	0	0	1	1	1	0	0
23	0	1	0	1	2	2	0	1	1	1	1	0	0	0	0	0	0	2	0	1	0
22	0	0	0	1	2	2	1	3	0	4	2	1	0	1	0	0	3	0	2	1	0
21	0	0	0	1	0	0	1	3	5	7	2	1	2	1	1	2	0	3	0	1	0
20	0	0	0	0	0	0	2	0	3	8	10	8	13	10	5	0	2	0	0	0	0
19	0	0	0	0	0	0	0	1	0	3	5	10	30	53	0	5	1	0	0	0	0
18	0	0	0	0	0	0	0	0	1	2	0	7	29	0	52	10	1	1	0	1	0
17	0	0	0	0	0	0	0	0	1	3	3	8	0	29	31	12	3	0	0	0	0
16	0	0	0	0	0	0	0	0	0	0	1	0	8	7	10	8	1	1	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	1	3	0	5	11	2	1	1	1	0
14	0	0	0	0	0	0	0	0	1	0	0	0	3	2	3	8	7	4	1	1	0
13	0	0	0	0	0	0	0	0	0	1	0	0	1	1	0	3	5	0	1	0	0
12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	2	3	2	1	0
11	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	2	1	1	0	2	0
10	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	2	2	0	0
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	3	0	2	2
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	0	1
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0

LL	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26
25	1	0	2	0	2	1	0	1	1	0	0	1	0	0	1	1	1	x	0
24	0	1	2	2	0	1	1	1	1	0	0	0	0	0	0	2	x	1	0
23	0	1	2	2	1	3	0	4	2	1	0	1	0	0	3	x	2	1	0
22	0	1	0	0	1	3	5	7	2	1	2	1	1	2	x	3	0	1	0
21	0	0	0	0	2	0	3	8	10	8	13	10	5	x	2	0	0	0	0
20	0	0	0	0	0	1	0	3	5	10	30	53	x	5	1	0	0	0	0
19	0	0	0	0	0	0	1	2	0	7	29	x	52	10	1	1	0	1	0
18	0	0	0	0	0	0	1	3	3	8	x	29	31	12	3	0	0	0	0
17	0	0	0	0	0	0	0	0	1	x	8	7	10	8	1	1	0	0	0
16	0	0	0	0	0	0	0	0	x	1	3	0	5	11	2	1	1	1	0
15	0	0	0	0	0	0	1	x	0	0	3	2	3	8	7	4	1	1	0
14	0	0	0	0	0	0	x	1	0	0	1	1	0	3	5	0	1	0	0
13	0	0	0	0	0	x	0	0	0	0	0	0	1	0	2	3	2	1	0
12	0	0	0	1	x	0	0	0	0	0	0	0	0	2	1	1	0	2	0
11	0	0	0	x	1	0	0	0	0	0	0	0	0	0	0	2	2	0	0
10	0	0	x	0	0	0	0	0	0	0	0	0	0	0	0	3	0	2	2
9	0	x	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	0	1
8	x	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0

LL	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
25	1	0	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
24	0	0	1	0	2	0	2	1	0	1	1	0	0	1	0	0	1	1	1	0	0
23	0	1	0	1	2	2	0	1	1	1	1	0	0	0	0	0	0	2	0	1	0
22	0	0	0	1	2	2	1	3	0	4	2	1	0	1	0	0	3	0	2	1	0
21	0	0	0	1	0	0	1	3	5	7	2	1	2	1	1	2	0	3	0	1	0
20	0	0	0	0	0	0	2	0	3	8	10	8	13	10	5	0	2	0	0	0	0
19	0	0	0	0	0	0	0	1	0	3	5	10	30	53	0	5	1	0	0	0	0
18	0	0	0	0	0	0	0	0	1	2	0	7	29	0	52	10	1	1	0	1	0
17	0	0	0	0	0	0	0	0	1	3	3	8	0	29	31	12	3	0	0	0	0
16	0	0	0	0	0	0	0	0	0	0	1	0	8	7	10	8	1	1	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	1	3	0	5	11	2	1	1	1	0
14	0	0	0	0	0	0	0	0	1	0	0	0	3	2	3	8	7	4	1	1	0
13	0	0	0	0	0	0	0	0	0	1	0	0	1	1	0	3	5	0	1	0	0
12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	2	3	2	1	0
11	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	2	1	1	0	2	0
10	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	2	2	0	0
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	3	0	2	2
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	0	1
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0

LL	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26
25	1	0	2	0	2	1	0	1	1	0	0	1	0	0	1	1	1	x	0
24	0	1	2	2	0	1	1	1	1	0	0	0	0	0	0	2	x	1	0
23	0	1	2	2	1	3	0	4	2	1	0	1	0	0	3	x	2	1	0
22	0	1	0	0	1	3	5	7	2	1	2	1	1	2	x	3	0	1	0
21	0	0	0	0	2	0	3	8	10	8	13	10	5	x	2	0	0	0	0
20	0	0	0	0	0	1	0	3	5	10	30	53	x	5	1	0	0	0	0
19	0	0	0	0	0	0	1	2	0	7	29	x	52	10	1	1	0	1	0
18	0	0	0	0	0	0	1	3	3	8	x	29	31	12	3	0	0	0	0
17	0	0	0	0	0	0	0	0	1	x	8	7	10	8	1	1	0	0	0
16	0	0	0	0	0	0	0	0	x	1	3	0	5	11	2	1	1	1	0
15	0	0	0	0	0	0	1	x	0	0	3	2	3	8	7	4	1	1	0
14	0	0	0	0	0	0	x	1	0	0	1	1	0	3	5	0	1	0	0
13	0	0	0	0	0	x	0	0	0	0	0	0	1	0	2	3	2	1	0
12	0	0	0	1	x	0	0	0	0	0	0	0	0	2	1	1	0	2	0
11	0	0	0	x	1	0	0	0	0	0	0	0	0	0	0	2	2	0	0
10	0	0	x	0	0	0	0	0	0	0	0	0	0	0	0	3	0	2	2
9	0	x	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	0	1
8	x	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0

LL	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
25	1	0	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
24	0	0	1	0	2	0	2	1	0	1	1	0	0	1	0	0	1	1	1	0	0
23	0	1	0	1	2	2	0	1	1	1	1	0	0	0	0	0	0	2	0	1	0
22	0	0	0	1	2	2	1	3	0	4	2	1	0	1	0	0	3	0	2	1	0
21	0	0	0	1	0	0	1	3	5	7	2	1	2	1	1	2	0	3	0	1	0
20	0	0	0	0	0	0	2	0	3	8	10	8	13	10	5	0	2	0	0	0	0
19	0	0	0	0	0	0	0	1	0	3	5	10	30	53	0	5	1	0	0	0	0
18	0	0	0	0	0	0	0	0	1	2	0	7	29	0	52	10	1	1	0	1	0
17	0	0	0	0	0	0	0	0	1	3	3	8	0	29	31	12	3	0	0	0	0
16	0	0	0	0	0	0	0	0	0	0	1	0	8	7	10	8	1	1	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	1	3	0	5	11	2	1	1	1	0
14	0	0	0	0	0	0	0	0	1	0	0	0	3	2	3	8	7	4	1	1	0
13	0	0	0	0	0	0	0	0	0	1	0	0	1	1	0	3	5	0	1	0	0
12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	2	3	2	1	0
11	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	2	1	1	0	2	0
10	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	2	2	0	0
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	3	0	2	2
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	0	1
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0

LL	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26
25	1	0	2	0	2	1	0	1	1	0	0	1	0	0	1	1	1	x	0
24	0	1	2	2	0	1	1	1	1	0	0	0	0	0	0	2	x	1	0
23	0	1	2	2	1	3	0	4	2	1	0	1	0	0	3	x	2	1	0
22	0	1	0	0	1	3	5	7	2	1	2	1	1	2	x	3	0	1	0
21	0	0	0	0	2	0	3	8	10	8	13	10	5	x	2	0	0	0	0
20	0	0	0	0	0	1	0	3	5	10	30	53	x	5	1	0	0	0	0
19	0	0	0	0	0	0	1	2	0	7	29	x	52	10	1	1	0	1	0
18	0	0	0	0	0	0	1	3	3	8	x	29	31	12	3	0	0	0	0
17	0	0	0	0	0	0	0	0	1	x	8	7	10	8	1	1	0	0	0
16	0	0	0	0	0	0	0	0	x	1	3	0	5	11	2	1	1	1	0
15	0	0	0	0	0	0	1	x	0	0	3	2	3	8	7	4	1	1	0
14	0	0	0	0	0	0	x	1	0	0	1	1	0	3	5	0	1	0	0
13	0	0	0	0	0	x	0	0	0	0	0	0	1	0	2	3	2	1	0
12	0	0	0	1	x	0	0	0	0	0	0	0	0	2	1	1	0	2	0
11	0	0	0	x	1	0	0	0	0	0	0	0	0	0	0	2	2	0	0
10	0	0	x	0	0	0	0	0	0	0	0	0	0	0	0	3	0	2	2
9	0	x	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	0	1
8	x	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0