2015年高教社杯全国大学生数学建模A题太阳影子定位（Matlab代码）

数据库 2023-04-09 07:27:53 阅读次数: 0

文章目录

一、第一问

（一）经度与影长关系

clc;
clear;

% Φ -> A   纬度
% δ -> F   太阳赤道纬度夹角
% ω -> C   太阳时角
%  h -> Oh  太阳高度角
% λ -> D   经度
%

% 10月22日北京时间9:00-15:00

% 10月22日是一年的第 295 天
n = 295.0;

% 纬度
W = 39 + 54/60 + 26/3600;

Jm = 120;

JArr = [70 75 80 85 90 95 100 105 110 115 120 125 135 140 145 150 155 160 165 170 175];
LsArr = [];

m = 11;
nn = 30;

% T0： m 时 n 分  
% 9:00-15:00
% m = [9, 15]  n = [0, 59]
for i = 1:21
    % 太阳赤纬夹角（度）
    F = 23.45*sin(2*pi*(284+n)/365);

    % 太阳时
    B = 2*pi*(n -81)/364;
    E = 9.87*sin(2*B) - 7.53*cos(B) - 1.5*sin(B); 
        
    J = JArr(i);
    %A = WArr(i);
    T0 = m + nn/60;
    Ts = T0 + E/60 + (J - Jm)/15;
    % 太阳时角（度）
    C = 15*(Ts - 12);


    % 太阳高度角
    Oh = asin(sin(W*pi/180)*sin(F*pi/180) + cos(W*pi/180)*cos(F*pi/180)*cos(C*pi/180));

    % 杆长 L = 3 m
    L = 3;

    % 影长 Ls
    Ls = L/tan(Oh);
    LsArr(i) = Ls;

end

plot(JArr, LsArr);
%axis([1 12 0 7]);
xlabel('经度（°E）');
ylabel('影长（米）');
title('不同经度与影长关系曲线');

在这里插入图片描述

（二）维度与影长关系

clc;
clear;

% Φ -> A   纬度
% δ -> F   太阳赤道纬度夹角
% ω -> C   太阳时角
%  h -> Oh  太阳高度角
% λ -> D   经度
%

% 10月22日北京时间9:00-15:00

% 10月22日是一年的第 295 天
n = 295.0;

%地理位置 北纬39度54分26秒,东经116度23分29秒
% 纬度
W = 39 + 54/60 + 26/3600;
% 经度
J = 116 + 23/60 + 29/3600;
% 时区经度
Dm = 120;

LArr = [1 2 3 4 5 6 7 8 9 10 11 12];
JArr = [70 75 80 85 90 95 100 105 110 115 120 125 135 140 145 150 155 160 165 170 175];
WArr = [15 20 25 30 35 40 45 50 55 60 65 70];
DateArr = [1 32 60 91 121 152 182 213 244 274 305 335];
LsArr = [];

m = 11;
nn = 30;

% T0： m 时 n 分  
% 9:00-15:00
% m = [9, 15]  n = [0, 59]
for i = 1:12
    
    W = WArr(i);
    
    % 太阳赤纬夹角（度）
    F = 23.45*sin(2*pi*(284+n)/365);

    % 太阳时
    B = 2*pi*(n -81)/364;
    E = 9.87*sin(2*B) - 7.53*cos(B) - 1.5*sin(B); 

    %A = WArr(i);
    T0 = m + nn/60;
    Ts = T0 + E/60 + (J - Dm)/15;
    % 太阳时角（度）
    C = 15*(Ts - 12);
    
    % 太阳高度角
    Oh = asin(sin(W*pi/180)*sin(F*pi/180) + cos(W*pi/180)*cos(F*pi/180)*cos(C*pi/180));

    % 杆长 L = 3 m
    L = 3;

    % 影长 Ls
    Ls = L/tan(Oh);
    LsArr(i) = Ls;

end

plot(WArr, LsArr);
%axis([1 12 0 7]);
xlabel('纬度（°E）');
ylabel('影长（米）');
title('不同纬度与影长关系曲线');

在这里插入图片描述

（三）日期与影长关系

clc;
clear;

% Φ -> A   纬度
% δ -> F   太阳赤道纬度夹角
% ω -> C   太阳时角
%  h -> Oh  太阳高度角
% λ -> D   经度
%

% 10月22日北京时间9:00-15:00

% 10月22日是一年的第 295 天

%地理位置 北纬39度54分26秒,东经116度23分29秒
% 纬度
W = 39 + 54/60 + 26/3600;
% 经度
J = 116 + 23/60 + 29/3600;
% 时区经度
Jm = 120;

DateArr = [1 32 60 91 121 152 182 213 244 274 305 335];
Date = [1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1 9.1 10.1 11.1 12.1]
LsArr = [];


m = 11;
nn = 30;

% T0： m 时 n 分  
% 9:00-15:00
% m = [9, 15]  n = [0, 59]
for i = 1:12
    
    n = DateArr(i);
    
    % 太阳赤纬夹角（度）
    F = 23.45*sin(2*pi*(284+n)/365);

    % 太阳时
    B = 2*pi*(n -81)/364;
    E = 9.87*sin(2*B) - 7.53*cos(B) - 1.5*sin(B); 

    T0 = m + nn/60;
    Ts = T0 + E/60 + (J - Jm)/15;
    % 太阳时角（度）
    C = 15*(Ts - 12);


    % 太阳高度角
    Oh = asin(sin(W*pi/180)*sin(F*pi/180) + cos(W*pi/180)*cos(F*pi/180)*cos(C*pi/180));

    Ohh = Oh*180/pi;



    % 杆长 L = 3 m
    L = 3;

    % 影长 Ls
    Ls = L/tan(Oh);
    LsArr(i) = Ls;

end

plot(Date, LsArr);
%axis([1 12 0 7]);
xlabel('日期');
ylabel('影长（米）');
title('不同日期与影长关系曲线');

在这里插入图片描述

（四）时间与影长关系

clc;
clear;

% Φ -> A   纬度
% δ -> F   太阳赤道纬度夹角
% ω -> C   太阳时角
%  h -> Oh  太阳高度角
% λ -> D   经度
%

% 10月22日北京时间9:00-15:00

% 10月22日是一年的第 295 天
n = 295.0;

%地理位置 北纬39度54分26秒,东经116度23分29秒
% 纬度
W = 39 + 54/60 + 26/3600;
% 经度
J = 116 + 23/60 + 29/3600;
% 时区经度
Jm = 120;

% 太阳赤纬夹角（度）
F = 23.45*sin(2*pi*(284+n)/365);

% 太阳时
B = 2*pi*(n -81)/364;
E = 9.87*sin(2*B) - 7.53*cos(B) - 1.5*sin(B); 

ii = 0;

X = [];



% T0： m 时 n 分  
% 9:00-15:00
% m = [9, 15]  n = [0, 59]
for m = 9:1:14
    for nn = 0:10:59
        ii = ii +1;
        X(ii) = m+nn/60;
        Hour(ii) = m;
        Minute(ii) = nn;
        
        T0 = m + nn/60;
        Ts = T0 + E/60 + (J - Jm)/15;
        % 太阳时角（度）
        C = 15*(Ts - 12);
        


        % 太阳高度角
        Oh = asin(sin(W*pi/180)*sin(F*pi/180) + cos(W*pi/180)*cos(F*pi/180)*cos(C*pi/180));

        Ohh = Oh*180/pi;
        
        HH(ii) = Ohh;

        % 杆长 L = 3 m
        L = 3;

        % 影长 Ls
        Ls = L/tan(Oh);
        LsArr(ii) = Ls;
    end
end




plot(X, LsArr, 'red');
%axis([9 15 22 40]);
xlabel('时间');
ylabel('影子长度');
title('时间--影长');

请添加图片描述

（五）杆长与影长关系

clc;
clear;

% Φ -> A   纬度
% δ -> F   太阳赤道纬度夹角
% ω -> C   太阳时角
%  h -> Oh  太阳高度角
% λ -> D   经度
%

% 10月22日北京时间9:00-15:00

% 10月22日是一年的第 295 天
n = 295.0;




%地理位置 北纬39度54分26秒,东经116度23分29秒
% 纬度
W = 39 + 54/60 + 26/3600;
% 经度
J = 116 + 23/60 + 29/3600;
% 时区经度
Jm = 120;

LArr = [1 2 3 4 5 6 7 8 9 10 11 12];
LsArr = [];

m = 11;
nn = 30;

% T0： m 时 n 分  
% 9:00-15:00
% m = [9, 15]  n = [0, 59]
for i = 1:12
    % 太阳赤纬夹角（度）
    F = 23.45*sin(2*pi*(284+n)/365);

    % 太阳时
    B = 2*pi*(n -81)/364;
    E = 9.87*sin(2*B) - 7.53*cos(B) - 1.5*sin(B); 

    %A = WArr(i);
    T0 = m + nn/60;
    Ts = T0 + E/60 + (J - Jm)/15;
    % 太阳时角（度）
    C = 15*(Ts - 12);


    % 太阳高度角
    Oh = asin(sin(W*pi/180)*sin(F*pi/180) + cos(W*pi/180)*cos(F*pi/180)*cos(C*pi/180));

    % 杆长 L = 3 m
    L = LArr(i);

    % 影长 Ls
    Ls = L/tan(Oh);
    LsArr(i) = Ls;

end

plot(LArr, LsArr);
%axis([1 12 0 7]);
xlabel('杆长（米）');
ylabel('影长（米）');
title('不同杆长与影长关系曲线');

在这里插入图片描述

（六）北京3米杆长9-15点影长随时间变化曲线

clc;
clear;

% Φ -> A   纬度
% δ -> F   太阳赤道纬度夹角
% ω -> C   太阳时角
%  h -> Oh  太阳高度角
% λ -> D   经度
%

% 10月22日北京时间9:00-15:00

% 10月22日是一年的第 295 天
n = 295.0;

%地理位置 北纬39度54分26秒,东经116度23分29秒
% 纬度
A = 39 + 54/60 + 26/3600;
% 经度
D = 116 + 23/60 + 29/3600;
% 时区经度
Dm = 120;

% 太阳赤纬夹角（度）
F = 23.45*sin(2*pi*(284+n)/365);

% 太阳时
B = 2*pi*(n -81)/364;
E = 9.87*sin(2*B) - 7.53*cos(B) - 1.5*sin(B); 

ii = 0;

LsArr = [];

X = [];

Larr = [3 4 5 6 7 8 9 10]

% T0： m 时 n 分  
% 9:00-15:00
% m = [9, 15]  n = [0, 59]
for m = 9:1:14
    for nn = 0:10:59
        ii = ii +1;
        X(ii) = m+nn/60;
        
        T0 = m + nn/60;
        Ts = T0 + E/60 + (D - Dm)/15;
        % 太阳时角（度）
        C = 15*(Ts - 12);

        % 太阳高度角
        Oh = asin(sin(A*pi/180)*sin(F*pi/180) + cos(A*pi/180)*cos(F*pi/180)*cos(C*pi/180));

        % 杆长 L = 3 m
        L = 3;

        % 影长 Ls
        Ls = L/tan(Oh);
        LsArr(ii) = Ls;
    end
end

plot(X, LsArr, 'red');
%axis([9 15 22 40]);
xlabel('时间');
ylabel('影子长度');
title('北京3米杆长9-15点影长随时间变化曲线');

请添加图片描述

二、第二问

（一）求解

clc;
clear;

% Φ -> A   纬度
% δ -> F   太阳赤道纬度夹角
% ω -> C   太阳时角
%  h -> Oh  太阳高度角
% λ -> D   经度

dB = [0.4555 	0.4409 	0.4247 	0.4136 	0.3986 	0.3919 	0.3777 	0.3656 	0.3582 	0.3481 	0.3438 	0.3305 	0.3264 	0.3169 	0.3120 	0.3069 	0.2987 	0.2928 	0.2876 	0.2853 	];

dLs = [1.1496 	1.1822 	1.2153 	1.2491 	1.2832 	1.3180 	1.3534 	1.3894 	1.4262 	1.4634 	1.5015 	1.5402 	1.5799 	1.6201 	1.6613 	1.7033 	1.7462 	1.7901 	1.8350 	1.8809 	1.9279 ];

% 4月18日是一年的第 108 天
n = 108;

% 太阳赤纬夹角（度）
C = 23.45*sin(2*pi*(284+n)/365);

% 太阳时
B = 2*pi*(n -81)/364;
E = 9.87*sin(2*B) - 7.53*cos(B) - 1.5*sin(B); 

Jm = 120;

hour = [14	14	14	14	14	14	15	15	15	15	15	15	15	15	15	15	15	15	15	15	15];
minutes = [42	45	48	51	54	57	0	3	6	9	12	15	18	21	24	27	30	33	36	39	42];

value1 = 0;
value2 = 0;

min = 100000000;



j = 1;

X = [];
Y = [];

MinArr = ones(12,5);
dFsArr = [];

LsArr = [];

DD = ones(12, 20);

LsArrr = ones(12, 21);
% 杆长
for L = 0:0.1:3
    % 纬度
    for W = 15:0.1:25
        % 经度
        for J = 105:0.1:115
            % 时间
            for i = 1:1:21
                
                T0 = hour(i) + minutes(i)/60;
                Ts = T0 + E/60 + (J - Jm)/15;
            
                % 太阳时角（度）
                S = 15*(Ts - 12);

                % 太阳高度角
                Oh = asin(sin(W*pi/180)*sin(C.*pi/180) + cos(W*pi/180)*cos(C*pi/180)*cos(S*pi/180));

                % 太阳方位角
                if(S <0)
                    Fs = acos(  (sin(C*pi/180) - sin(Oh)*sin(W*pi/180)) / (cos(Oh)*cos(W*pi/180)));
                    FsArr(i) = Fs;
                else
                    Fs = 2*pi - acos(  (sin(C*pi/180) - sin(Oh)*sin(W*pi/180)) / (cos(Oh)*cos(W*pi/180)));
                    FsArr(i) = Fs;
                end
                
                if(i >= 2)
                    value1 = value1 + (  FsArr(i-1) - FsArr(i) - dB(i - 1) )^2;
                    dFsArr(i-1) = FsArr(i-1) - FsArr(i);
                end
                
                % 影长 Ls
                Ls = L / tan(Oh);
                
                LsArr(i) = Ls;
                
                value2 = value2 + (Ls - dLs(i))^2;


                i = i +1;
                
            end
            
            value = value1/20*value2/21;
            %if(value < min)
                %min = value;
                %MinArr = [L W J]
            %end
            
            if (value < 0.0000003)
                X(j) = j;
                j
                Y(j) = value;
                LsArrr(j, :) = LsArr;
                DD(j, :) = dFsArr*180/pi;
                MinArr(j , 1:5) = [j L W J value];
                j = j+1;
            end
            
            
            
            value1 = 0;
            value2 = 0;
            value = 0;
            
               
        end
    end
end




plot(X, Y,'*');

（二）经度灵敏度

clc;
clear;

% Φ -> A   纬度
% δ -> F   太阳赤道纬度夹角
% ω -> C   太阳时角
%  h -> Oh  太阳高度角
% λ -> D   经度
%

% 10月22日北京时间9:00-15:00

% 10月22日是一年的第 295 天
n = 295.0;




%地理位置 北纬39度54分26秒,东经116度23分29秒
% 纬度
A = 40;
% 经度

D2 = 116;
D1 = D2 - 2;
D3 = D2 + 2;
% 时区经度
Dm = 120;

% 太阳赤纬夹角（度）
F = 23.45*sin(2*pi*(284+n)/365);

% 太阳时
B = 2*pi*(n -81)/364;
E = 9.87*sin(2*B) - 7.53*cos(B) - 1.5*sin(B); 

i = 0;

LsArr1 = [];
LsArr2 = [];
LsArr3 = [];



% T0： m 时 n 分  
% 9:00-15:00
% m = [9, 15]  n = [0, 59]
for m = 9:1:14
    for nn = 0:10:59
        i = i +1;
        I(i) = m+nn/60;
        
        T0 = m + nn/60;
        
        Ts1 = T0 + E/60 + (D1 - Dm)/15;
        Ts2 = T0 + E/60 + (D2 - Dm)/15;
        Ts3 = T0 + E/60 + (D3 - Dm)/15;
        % 太阳时角（度）
        C1 = 15*(Ts1 - 12);
        C2 = 15*(Ts2 - 12);
        C3 = 15*(Ts3 - 12);


        % 太阳高度角
        Oh1 = asin(sin(A*pi/180)*sin(F*pi/180) + cos(A*pi/180)*cos(F*pi/180)*cos(C1*pi/180));
        Oh2 = asin(sin(A*pi/180)*sin(F*pi/180) + cos(A*pi/180)*cos(F*pi/180)*cos(C2*pi/180));
        Oh3 = asin(sin(A*pi/180)*sin(F*pi/180) + cos(A*pi/180)*cos(F*pi/180)*cos(C3*pi/180));



        % 杆长 L = 3 m
        L = 3;
        
        
        
        L3 = 3.1;

        % 影长 Ls
        Ls1 = L/tan(Oh1);
        Ls2 = L/tan(Oh2);
        Ls3 = L/tan(Oh3);
        LsArr1(i) = Ls1;
        LsArr2(i) = Ls2;
        LsArr3(i) = Ls3;
    end
end


plot(I, LsArr1);
hold on;
plot(I, LsArr2);
hold on;
plot(I, LsArr3);
%axis([9 15 22 40]);
xlabel('时间');
ylabel('影子长度');
title('经度灵敏度分析');
legend('114°E' ,'116°E','118°E');

三、第三问

clc;
clear;

% Φ -> A   纬度
% δ -> F   太阳赤道纬度夹角
% ω -> C   太阳时角
%  h -> Oh  太阳高度角
% λ -> D   经度

Fs = [0.918623526	0.944000767	0.966801009	0.994166838	1.012283158	1.046853791	1.071045389	1.097061852	1.127405199	1.159996144	1.191548883	1.225531726	1.254788569	1.290149918	1.331772011	1.362830448	1.399931432	1.446251384	1.481107264	1.522542777];



FsArr = [
    0.718578797	0.733382552	0.748746948	0.764690387	0.781231337	0.798388226	0.816179307	0.834622505	0.85373524	0.873534213	0.894035175	0.915252647	0.937199616	0.959887176	0.983324139	1.007516588	1.032467392	1.058175659	1.084636143	1.111838606
0.686999211	0.700565716	0.714630377	0.729209006	0.744317502	0.759971765	0.776187602	0.792980606	0.810366025	0.828358609	0.846972426	0.866220667	0.88611541	0.906667363	0.927885568	0.949777079	0.972346592	0.99559605	1.019524197	1.044126097
0.829657201	0.849114698	0.86934603	0.89037576	0.912227884	0.934925534	0.958490635	0.9829435	1.008302366	1.034582864	1.061797418	1.089954562	1.119058177	1.149106647	1.180091918	1.21199848	1.244802264	1.278469465	1.312955298	1.348202726
0.800063833	0.819138381	0.838945312	0.85950628	0.880842244	0.902973178	0.925917744	0.949692908	0.974313511	0.99979177	1.026136729	1.053353631	1.081443225	1.110401007	1.140216378	1.17087174	1.202341526	1.234591166	1.267576022	1.30124028
0.684818578	0.699406344	0.714514576	0.73015869	0.746353979	0.763115498	0.780457935	0.798395452	0.816941513	0.836108683	0.855908404	0.876350733	0.897444063	0.919194799	0.941607003	0.964682006	0.988417975	1.012809451	1.037846841	1.063515882
0.845459627	0.864429717	0.884177401	0.904729656	0.926113254	0.948354504	0.971478948	0.995510999	1.020473525	1.04638736	1.073270745	1.101138694	1.130002259	1.159867724	1.190735681	1.222600021	1.255446825	1.289253149	1.323985733	1.359599629
0.91707391	0.939303965	0.962461544	0.986576913	1.01167935	1.037796685	1.064954767	1.093176835	1.122482798	1.15288841	1.184404326	1.217035044	1.25077772	1.28562085	1.321542832	1.358510409	1.396477005	1.435380979	1.475143833	1.515668408
0.840665072	0.861372223	0.882886199	0.905230081	0.928425862	0.952494065	0.977453309	1.003319803	1.030106783	1.057823865	1.086476318	1.116064263	1.146581781	1.178015936	1.210345717	1.243540912	1.277560903	1.312353428	1.347853307	1.383981179
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0.634959959	0.645491185	0.656426344	0.667779747	0.679566117	0.69180057	0.704498593	0.71767601	0.731348945	0.74553377	0.760247048	0.775505459	0.791325716	0.807724465	0.824718164	0.842322947	0.860554461	0.879427687	0.898956724	0.91915455
0.764273683	0.780977702	0.798314263	0.816302893	0.834962864	0.854313011	0.874371522	0.895155695	0.91668166	0.938964058	0.962015682	0.985847061	1.010466005	1.03587709	1.062081087	1.089074337	1.11684807	1.145387662	1.174671844	1.204671864
0.537005461	0.551603784	0.566662879	0.582195623	0.598214659	0.614732279	0.631760307	0.64930996	0.667391685	0.686014985	0.705188222	0.724918386	0.74521086	0.766069137	0.787494527	0.809485832	0.832038987	0.855146682	0.878797954	0.902977756
0.722573362	0.737452521	0.752890203	0.768904309	0.785512749	0.802733324	0.820583594	0.839080715	0.858241254	0.878080974	0.898614593	0.919855503	0.941815452	0.964504193	0.987929081	1.012094629	1.037002019	1.062648557	1.089027091	1.116125365
0.903358781	0.924363784	0.946246334	0.969036441	0.992763546	1.017456145	1.04314136	1.069844417	1.097588063	1.126391873	1.156271464	1.187237608	1.219295215	1.252442218	1.286668314	1.321953603	1.358267104	1.395565171	1.433789833	1.472867072
0.52471407	0.540646665	0.557102218	0.574096427	0.591644736	0.609762192	0.628463296	0.647761816	0.667670585	0.68820127	0.709364107	0.731167606	0.753618228	0.776720017	0.8004742	0.824878746	0.849927892	0.875611623	0.901915123	0.928818187
0.738216613	0.752740489	0.767841684	0.78354109	0.799859931	0.816819677	0.834441934	0.852748313	0.871760275	0.891498947	0.911984905	0.933237923	0.955276678	0.978118419	1.001778576	1.026270326	1.051604097	1.077787011	1.104822266	1.132708445
0.727947641	0.74324618	0.759111219	0.775560177	0.792610355	0.810278805	0.828582177	0.847536534	0.867157148	0.887458262	0.908452823	0.930152171	0.9525657	0.975700472	0.999560787	1.024147712	1.049458562	1.075486331	1.102219082	1.12963929
0.801949296	0.818987352	0.836724157	0.85518531	0.874396606	0.894383874	0.915172776	0.936788574	0.959255847	0.982598162	1.006837695	1.031994785	1.058087421	1.085130662	1.113135975	1.142110484	1.172056139	1.202968786	1.234837151	1.26764173
0.602895061	0.612540658	0.622509254	0.632809824	0.643451445	0.654443272	0.665794499	0.677514325	0.689611908	0.702096317	0.714976471	0.728261078	0.741958558	0.756076961	0.770623874	0.785606317	0.801030628	0.816902333	0.833226007	0.850005117
0.787679545	0.805526389	0.824077736	0.843356863	0.863386833	0.884190276	0.905789141	0.928204394	0.951455681	0.97556093	1.0005359	1.026393667	1.053144041	1.080792916	1.109341542	1.13878572	1.169114922	1.200311335	1.232348837	1.265191903
0.889590505	0.910994068	0.933281137	0.956480548	0.980620315	1.00572723	1.031826388	1.058940638	1.087089945	1.116290664	1.146554704	1.177888597	1.210292444	1.243758749	1.278271138	1.313802964	1.350315817	1.387757941	1.426062597	1.465146402
0.67511432	0.688132594	0.70164298	0.715662252	0.730207443	0.745295784	0.76094463	0.777171362	0.793993286	0.811427503	0.82949076	0.848199282	0.867568572	0.887613185	0.908346467	0.929780269	0.95192461	0.974787311	0.998373579	1.022685553
0.76960631	0.785356263	0.801742766	0.818789078	0.836518747	0.854955488	0.874123037	0.894044969	0.914744494	0.936244206	0.958565797	0.981729714	1.005754779	1.030657737	1.056452746	1.083150806	1.110759107	1.139280302	1.168711709	1.199044423
0.786177323	0.80301502	0.820519161	0.838712384	0.857617297	0.877256316	0.897651458	0.918824097	0.940794692	0.963582456	0.987204988	1.011677846	1.037014058	1.063223577	1.090312662	1.118283195	1.147131922	1.176849617	1.20742018	1.238819666
0.537061665	0.551661764	0.566722686	0.582257308	0.598278269	0.614797862	0.631827909	0.649379622	0.667463447	0.686088883	0.705264284	0.724996639	0.745291319	0.766151812	0.78757942	0.809572932	0.832128271	0.855238115	0.878891487	0.90307332
0.781140457	0.798175226	0.81588968	0.834307313	0.853451624	0.873345951	0.894013254	0.915475873	0.937755237	0.960871533	0.984843321	1.009687085	1.035416735	1.062043032	1.089572948	1.118008944	1.147348181	1.177581642	1.208693183	1.240658509
0.75752161	0.774057025	0.791225304	0.809046674	0.827541204	0.846728644	0.866628219	0.887258403	0.908636648	0.930779081	0.953700155	0.977412246	1.001925213	1.027245888	1.05337752	1.080319156	1.10806496	1.136603476	1.165916825	1.195979861
0.708072671	0.725546187	0.743635729	0.762357654	0.781727658	0.801760554	0.82247003	0.843868362	0.8659661	0.88877171	0.912291178	0.936527568	0.961480533	0.987145786	1.013514518	1.040572779	1.068300809	1.096672343	1.125653877	1.155203922
0.591932269	0.611390918	0.631527529	0.652361291	0.673910545	0.696192508	0.719222952	0.74301584	0.767582914	0.792933226	0.819072624	0.846003169	0.873722501	0.902223137	0.931491717	0.961508191	0.992244951	1.023665931	1.055725665	1.088368345
0.604877918	0.624484478	0.644771223	0.665756746	0.687458693	0.709893473	0.733075926	0.757018943	0.781733044	0.807225898	0.833501787	0.860561022	0.888399287	0.917006933	0.946368214	0.976460469	1.007253253	1.038707444	1.070774312	1.103394593
0.825920594	0.844607576	0.864040615	0.884244167	0.905242336	0.927058619	0.949715604	0.973234627	0.997635363	1.022935363	1.049149525	1.076289491	1.104362967	1.133372968	1.16331697	1.194185988	1.225963561	1.258624665	1.292134549	1.326447523
0.57593857	0.593798201	0.612253467	0.631320573	0.651015051	0.671351552	0.692343601	0.714003323	0.736341128	0.759365368	0.783081941	0.807493866	0.832600801	0.85839853	0.88487839	0.912026673	0.939823971	0.968244496	0.997255371	1.026815901
0.688982267	0.703900665	0.719340748	0.735317105	0.75184407	0.768935601	0.786605125	0.804865373	0.823728191	0.843204317	0.863303142	0.884032435	0.905398039	0.927403537	0.950049878	0.973334973	0.997253258	1.021795215	1.046946866	1.072689238
0.706396256	0.724041428	0.742301617	0.761192578	0.78072931	0.800925838	0.821794951	0.843347913	0.865594138	0.888540821	0.912192533	0.936550772	0.961613468	0.987374444	1.013822832	1.040942454	1.068711154	1.097100105	1.126073092	1.155585781
0.891551813	0.91482588	0.938998979	0.964092838	0.990127026	1.017118386	1.045080392	1.074022413	1.103948895	1.134858441	1.166742806	1.199585786	1.233362022	1.268035725	1.303559325	1.339872081	1.376898674	1.41454781	1.452710906	1.49126089
0.753335773	0.768866464	0.78500006	0.801756869	0.819157267	0.837221579	0.855969918	0.875422007	0.895596966	0.916513071	0.938187467	0.960635847	0.98387208	1.007907797	1.032751914	1.058410109	1.084884236	1.112171675	1.140264628	1.169149347
0.691765944	0.705440469	0.719612562	0.73429763	0.749511112	0.765268392	0.781584691	0.798474952	0.815953693	0.834034853	0.852731599	0.872056125	0.892019412	0.912630959	0.933898488	0.955827609	0.978421456	1.001680275	1.025600988	1.050176711
0.714031566	0.7313905	0.749361205	0.767959823	0.787201838	0.807101861	0.827673389	0.848928526	0.870877669	0.893529162	0.916888901	0.940959903	0.965741825	0.991230442	1.017417081	1.044288005	1.071823767	1.099998515	1.128779283	1.15812525
0.640350808	0.658562758	0.677392046	0.696854474	0.716965004	0.737737526	0.759184582	0.781317059	0.804143846	0.827671449	0.851903563	0.876840597	0.902479159	0.928811494	0.955824876	0.983500959	1.011815092	1.040735606	1.070223075	1.100229574
0.571227989	0.589028048	0.607429117	0.62644826	0.64610196	0.66640591	0.687374774	0.709021924	0.731359125	0.754396197	0.778140623	0.802597124	0.827767179	0.853648504	0.880234482	0.907513545	0.935468515	0.964075901	0.993305164	1.023117964
];



% 10月22日北京时间9:00-15:00

% 285	1.4	-32	69



NLWJ = [285	1.4	-32	69
65	1.3	-31	74
114	1.7	34	77
245	1.6	30	77
85	1.3	27	74
26	1.8	-39	80
199	2	40	81
58	1.7	-31	82
175	2	42	79
271	1.2	-29	67
257	1.4	27	73
283	1.3	-32	67
76	1.5	-26	79
226	1.8	35	80
42	1.1	-38	65
92	1.2	30	70
34	1.9	-37	83
308	1.7	-37	72
298	1.3	-36	64
120	1.6	36	74
268	1.1	-29	65
78	1.4	-26	77
71	1.2	-30	72
306	1.9	-36	76
186	2.2	41	83
104	1.3	33	70
281	1.1	-33	62
235	1.1	36	64
247	1.2	32	68
63	1.2	-32	71
53	1	-37	64
192	1.3	-4	75
299	1.6	-35	71
55	1.3	-34	73
146	1.3	-5	73
89	1.1	30	68
364	1.5	1	78
229	1.8	34	80
229	1.3	36	69
264	1.4	-25	73
71	1.2	23	74
114	1.2	36	65
102	1.4	32	73
285	1.1	-34	61
271	1.5	-27	74
76	1.2	-28	72
244	1.7	30	79
265	1.1	27	66
298	1.8	-34	75
141	1.3	-6	73
197	1.5	-3	79
3	2.2	-41	83
100	1.3	32	71
232	1.4	35	72
77	1.2	25	73
119	1.1	38	61
159	1.4	-2	75
60	1	-35	65
272	1.5	21	75
106	1.1	35	64
87	1.5	-22	79
28	1.1	-40	62
246	1	34	62
293	1.2	-35	62
241	1.5	32	75
137	1.2	-8	71
60	1.4	-32	76
361	2	-42	79
158	1.3	-3	73
305	1.5	-37	68
246	1.4	31	73
135	1.7	39	74
257	1	31	63
292	1.6	-33	72
133	1.9	38	78
243	1.3	32	70
216	1.6	38	75
225	1.6	36	76
25	1.2	8	75
228	1.6	35	76
58	1.5	-32	78
274	1.4	21	73
162	1.5	-1	77
336	1.5	2	75
121	1.7	36	76
191	1.4	-3	77
264	1.3	-26	71
277	1.4	20	73
60	1.8	-30	84
114	1.5	35	73
279	1.3	-31	68
89	1.4	-22	77
39	1.4	10	80
152	1.4	-3	75
234	1.3	-15	75
287	1.3	-33	66
209	1.1	40	60
274	1.3	22	71
300	1.7	-35	73
102	1	35	62
97	1.1	-22	70
324	1.8	-40	73
100	1.1	-21	70
260	1.2	-25	69
26	1.3	7	77
102	1.8	30	81
224	1.7	36	78
358	1.6	0	79
260	1.3	27	71
330	1.4	4	73
126	1.7	37	75
42	1.2	13	76
143	1.5	-4	77
334	1.3	4	71
246	1.1	33	65
78	1	-30	67
59	1.6	-31	80
134	1.5	-6	77

];

nArr = NLWJ(:, 1);
LArr = NLWJ(:, 2);
WArr = NLWJ(:, 3);
JArr = NLWJ(:, 4);
%     24 7
ii = 24;

Fsi = FsArr(ii, :); 

n = 199;

L = 2;

W = 40.1;

J = 81.1;

hour = [12	12	12	12	12	12	12	13	13	13	13	13	13	13	13	13	13	13	13	13	13];
minutes = [41	44	47	50	53	56	59	2	5	8	11	14	17	20	23	26	29	32	35	38	41];

dLs = [1.247256205	1.22279459	1.198921486	1.175428964	1.152439573	1.12991747	1.10783548	1.086254206	1.065081072	1.044446265	1.024264126	1.004640314	0.985490908	0.966790494	0.948584735	0.930927881	0.91375175	0.897109051	0.880973762	0.865492259	0.850504468];

% 时区经度
Jm = 120;

% 太阳赤纬夹角（度）
C = 23.45*sin(2*pi*(284+n)/365);

% 太阳时
B = 2*pi*(n -81)/364;
E = 9.87*sin(2*B) - 7.53*cos(B) - 1.5*sin(B); 

LsArr = [];

X = [];

for i=1:1:21
    
    T0 = hour(i) + minutes(i)/60;
    
    Ts = T0 + E/60 + (J - Jm)/15;
    
    X(i)  = T0;
    
    % 太阳时角（度）
    S = 15*(Ts - 12);


    % 太阳高度角
    Oh = asin(sin(W*pi/180)*sin(C*pi/180) + cos(W*pi/180)*cos(C*pi/180)*cos(S*pi/180));


    % 影长 Ls
    Ls = L/tan(Oh);
    LsArr(i) = Ls;
 
end



plot(X(:, 1:20), Fs, '.');
hold on;
plot(X(:, 1:20), Fsi, 'blue');

xlabel('时间');
ylabel('方位角之差（°）');
title('7月18日 杆长2米 （40.1°N，81.1°E）');

legend('实际值', '预测值')

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