pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · the length of each spoke is...

11
Chapter Chapter 3 Mathematics in daily life Mathematics in daily life Part Part 2 1 Dr.Weerakaset Suanpaga (D.Eng.) Department of Civil Engineering Faculty of Engineering , Kasetsart University Bangkok, Thailand http://pirun.ku.ac.th/~fengwks/mathcomp 3 3.4 2 3.5 !

Upload: others

Post on 26-Oct-2020

3 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction

Chapter Chapter 33Mathematics in daily lifeMathematics in daily life

Part Part 22

������������ � ������

11

������������ � ������Dr.Weerakaset Suanpaga

(D.Eng.)

Department of Civil EngineeringFaculty of Engineering , Kasetsart University

Bangkok, Thailand

http://pirun.ku.ac.th/~fengwks/mathcomp

����� 3

���� ����������������3.4 �����������

22

�3.5 ������ �����!

Page 2: pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction

3.4 ����������� (Convolution)

��������������� ����������������������������������� �!����"��� ��"��#"������$������%������������������������&�� ���$�������&���������� �!����&'%�������$���� ��������(����������������(��&��&'����

�� ���� ������ � "������#�������)����*��+��,!&�)$�%��-����� � ��$���&�����&��&'���������������� �!��� �!�� ��(����'�(����������*&�� �(�����

(� � ( # + (� � ( �� # � ��

33

)$�$)� *�(��%&��%$��(�����#"+� �' *�(��%&��%$��(������$)� ���#")$"$��'��� ��&�������#��&')������'�(�������!�������%&�� . !���������� � /����&'����'%�������(����� ��(��-,���')$� � �����������&'����� � �����0���� ��������&'������� �(�����)��%&��%$��(���"1�)&���$ ������)$��'�(�������� �*&����� ��0���

��"��#$%�������&����"'���() ���� �*���+ �����&� �����������2�� 1. *�(��%&��%$��(���������)������'�(����� �$)� ���#"����&��&'����

���)*�+ �����������

,������&+�� ������ ����-��.������ � (,.�.�.) �&+�� ����1���(2�3��4� ��� $5-�&5��'���$'�� ��$�� �$�������+ ���%5-%��&�� ���16�+�$7

44

� 7 &�(28�"�� 1 #�& �2��+���16����+���"$��+�:+5-%1���(��+���*����� 1 #�&$�+��8

Page 3: pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction

+�,��� ��)-�� ������.+� (���)

1 ;28�(��,�(2�����++��1��� 1,000

2 ;28�(��,�(2�1���;&�� 500

3 ? 6 �&�1AB���������1��*3� ��(2�

55

A �����&��( ��5-%"A�+�$ +�$� 200 *�" 2,000

7 �&���+�D*��������� 500

�$�� &�+�$-&�+��� 1 ��1$�-�

-�� ,.�.�. 5-%"'����"$��+1���(2�3��4� ���8�$�����*&+��A&������ ����16� 3 ��A&� 5-%���'�������� � &�+7 �����1E$5-%� �� %����1���-&�+�����A&�� 1 ��1$�-� �����1����'���� 1 #�& &����*����-�2��$ ��$�

��A&�"�� 1 ������ � 3 ���*����

66

��A&�"�� 1 ����� � 3 ���*������A&�"�� 2 ������ � 4 ���*������A&�"�� 3 ������ � 5 ���*����

������F� $+ ���%"�� ,.�.�. � %�+�&��5-%��*�� ���16��'����"&�#� 5�� &���1$�-�

Page 4: pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction

� �+"�� %�+���"��*�����"��1. !G+��������"'� (Input function) �2�QQQ2. !G+������ �*���+(Response function)�2�QQQ..

77

( p )3. �&�+��� ����A������16�"&�5$

������� ����� 1 2 3 4 5 6 7

0 0 1 0.5 2 2.2 2.4 2.6 0.5 0 0 (*103 ���)

5 4 3 (5*0) + (4*0) + (3*1) = 3 � ����

5 4 3 (5*0) + (4*1) + (3*0.5) = 5.5 � ���� 5 4 3 ….. = 13 * 103 ���

5 4 3 = 17 1 * 103 ���

88

5 4 3 ….. = 17.1 10 ���

5 4 3 ….. = 26 * 103 ���5 4 3 ….. = 28.4 * 103 ���

5 4 3 ….. = 23.9 * 103 ��� 5 4 3 ….. = 15 * 103 ���

5 4 3 ….. = 2.5*103 ���

��� ������ (9 � �����) �.�.�. ������� ��! 134,400 ���

Page 5: pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction

��(��$+��������������!G+�����������"'� �2� �'����+ �"��� %�+�&��5�� &���1$�-� () ���� �*���+ �2� ���5-%+ ���%U�+,����� �$� ��"��#$% �2� �'����+ ����"�� ,.�.�. 5�% 5�� &���1$�-�

25

30

������! ,.�.�. 5�%+*1���.���"���$5�

99

0

5

10

15

20

1 2 3 4 5 6 7 8 9�

������

����

(������

+*1���.���"���A$5���1$�-�"�� 6 ��5�%+*1���.�%��"���A$5���1$�-��A$"%�� (��1$�-�"�� 9)

%&"����

�''34��&�

1010

56���!&����$��� *(�

��������'%��� *(�/����#��*(��&���� 20 � 2548 )$���������%,�%��

"���3���� �&�����'%����(�����&'����/��5��������� �������� �&�"����������� �&�

Page 6: pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction

3.7 ������ �����!�2����+��%�+-�2������+"��

��$+1� ��.�'����U��$��" 3"�+U�+� �+ &�+7

1111

��W����.�"��5�%-Point => � �+�D�7"���'���W-Line => F�� ��&�8'�-polygon =>U�*U (28�"��

������ U�+�**��2�U&�����%�"�+���* ����5�1�"3U�+������* �#"�

1212

Page 7: pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction

1313

/0�1�2����+-�23�+-����4���,����56����+���-��.-7� 8.�. 2536

1414

/0�1�2 �2.<���)23�+ *�����-��,����2����) 36% ,�.<��)� 40% /�����)/�?+ 24%

Page 8: pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction

ExerciseExercise)�� A ��$)�� B ��2���������)$����#������ ���#?

. A

1515

. B

1616

/0�1�2-���-@<��� (rose diagram) 3�+/0�1�2�+-�2/ ,+���25��/������+3�+�@--������8@*+.34�����-

Page 9: pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction

2 ����� !"#$��%���� !&'((�����')��*+�,�-#(

��%���

(��(�����%�.�/&�0�����%�$���&&()����� !� !�(�2*34�

1530

31-60

43

23

61-90

91-120

10

11

121-150 14

1717

151-180 20

181-210

211-240

10

4

241-270

271-300

15

20

301-330

331-360

40

36

� !�� : Watham (1995)

A diagram in which statistical information concerning direction and speed of the wind at a location may be summarized; a line segment is drawn in each of perhaps eight compass directions from a common origin; the length of a particular segment is proportional to the frequency with which winds blow from that direction; thicknesses of a segment indicate frequencies of occurrence of various classes of wind speed.

Interpreting the wind rose •There are a number of different formats which can be used to display wind roses. These wind roses have been constructed in the following way:

Wind rose diagram

1818

•The percentage of calm conditions is represented by the size of the centre circle - the bigger the circle, the higher is the frequency of calm conditions. •Each branch of the rose represents wind coming from that direction, with north to the top of the diagram. Eight directions are used. •The branches are divided into segments of different thickness and colour, which represent wind speed ranges from that direction. Speed ranges of 10km/h are used in these wind roses. The length of each segment within a branch is proportional to the frequency of winds blowing within the corresponding range of speeds from that direction.

Page 10: pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction

1919

Figure 1. Wind roses, showing wind speed, direction, and frequency of occurrence at the Livermore site and Site 300 during 2007.

The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction. Different line widths of each spoke represent wind speed classes. The average wind speed in 2007 at the Livermore site was 2.5 m/s (5.6 mph); at Site 300 it was 6.4 m/s (14.4 mph).It can be seen from this data that the prevailing wind direction is from the southwest. This is the predominant wind direction during the summer. The wind does blow from the northeast and this is primarily during the winter.

Ref: http://www-metdat.llnl.gov/cgi-pub/about.pl

2020

Page 11: pirun.ku.ac.thpirun.ku.ac.th/~fengwks/mathcomp/weerakset_ch3_s2.pdf · The length of each spoke is proportional to the frequency at which the wind blows from the indicated direction

/0�1�2���+H�@���2���,�����2 �2��5��-��,I+�.�J-���

2121

Questions?

�����)�����.-7� ��0-�Weerakaset SuanpagaDepartment of Civil EngineeringFaculty of Engineering , Kasetsart UniversityFaculty of Engineering , Kasetsart UniversityBangkok, Thailand

www.pirun,ku.ac.th/~fengwks/mathcomp

Reference:1. ��$7&���8 ����+!* ��$*$, *��7�%����$*�����������!����"$)���&�,��&�%(�,2549

2. ��$7&���8 ����+!* , Lecture note *��7�%����$*�����������!����"$)���&�,2551,

2�*��!���� �7�%���(��2�2� *$��� �7�%�� ��.3: http://www-metdat.llnl.gov/cgi-pub/about.pl