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 =[707580859095100105110115120125135140145150155160165170175];
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([11207]);xlabel('经度(°E)');ylabel('影长(米)');title('不同经度与影长关系曲线');
(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 =[123456789101112];
JArr =[707580859095100105110115120125135140145150155160165170175];
WArr =[152025303540455055606570];
DateArr =[1326091121152182213244274305335];
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([11207]);xlabel('纬度(°E)');ylabel('影长(米)');title('不同纬度与影长关系曲线');
(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 =[1326091121152182213244274305335];
Date =[1.12.13.14.15.16.17.18.19.110.111.112.1]
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([11207]);xlabel('日期');ylabel('影长(米)');title('不同日期与影长关系曲线');
(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 =9:1:14for 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([9152240]);xlabel('时间');ylabel('影子长度');title('时间--影长');
(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 =[123456789101112];
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([11207]);xlabel('杆长(米)');ylabel('影长(米)');title('不同杆长与影长关系曲线');
(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 =[345678910]% T0: m 时 n 分
%9:00-15:00% m =[9,15] n =[0,59]for m =9:1:14for 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([9152240]);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');
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 =[0.45550.44090.42470.41360.39860.39190.37770.36560.35820.34810.34380.33050.32640.31690.31200.30690.29870.29280.28760.2853];
dLs =[1.14961.18221.21531.24911.28321.31801.35341.38941.42621.46341.50151.54021.57991.62011.66131.70331.74621.79011.83501.88091.9279];%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 =[141414141414151515151515151515151515151515];
minutes =[42454851545703691215182124273033363942];
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 =9:1:14for 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([9152240]);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 =[0.9186235260.9440007670.9668010090.9941668381.0122831581.0468537911.0710453891.0970618521.1274051991.1599961441.1915488831.2255317261.2547885691.2901499181.3317720111.3628304481.3999314321.4462513841.4811072641.522542777];
FsArr 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1.0999985151.1287792831.158125250.6403508080.6585627580.6773920460.6968544740.7169650040.7377375260.7591845820.7813170590.8041438460.8276714490.8519035630.8768405970.9024791590.9288114940.9558248760.9835009591.0118150921.0407356061.0702230751.1002295740.5712279890.5890280480.6074291170.626448260.646101960.666405910.6873747740.7090219240.7313591250.7543961970.7781406230.8025971240.8277671790.8536485040.8802344820.9075135450.9354685150.9640759010.9933051641.023117964];%10月22日北京时间9:00-15:00%2851.4-3269
NLWJ =[2851.4-3269651.3-31741141.734772451.63077851.32774261.8-398019924081581.7-3182175242792711.2-29672571.427732831.3-3267761.5-26792261.83580421.1-3865921.23070341.9-37833081.7-37722981.3-36641201.636742681.1-2965781.4-2677711.2-30723061.9-36761862.241831041.333702811.1-33622351.136642471.23268631.2-3271531-37641921.3-4752991.6-3571551.3-34731461.3-573891.130683641.51782291.834802291.336692641.4-2573711.223741141.236651021.432732851.1-34612711.5-2774761.2-28722441.730792651.127662981.8-34751411.3-6731971.5-37932.2-41831001.332712321.43572771.225731191.138611591.4-275601-35652721.521751061.13564871.5-2279281.1-4062246134622931.2-35622411.532751371.2-871601.4-32763612-42791581.3-3733051.5-37682461.431731351.73974257131632921.6-33721331.938782431.332702161.638752251.63676251.28752281.63576581.5-32782741.421731621.5-1773361.52751211.736761911.4-3772641.3-26712771.42073601.8-30841141.535732791.3-3168891.4-2277391.410801521.4-3752341.3-15752871.3-33662091.140602741.322713001.7-357310213562971.1-22703241.8-40731001.1-21702601.2-2569261.37771021.830812241.736783581.60792601.327713301.44731261.73775421.213761431.5-4773341.34712461.13365781-3067591.6-31801341.5-677];
nArr =NLWJ(:,1);
LArr =NLWJ(:,2);
WArr =NLWJ(:,3);
JArr =NLWJ(:,4);%247
ii =24;
Fsi =FsArr(ii,:);
n =199;
L =2;
W =40.1;
J =81.1;
hour =[121212121212121313131313131313131313131313];
minutes =[414447505356592581114172023262932353841];
dLs =[1.2472562051.222794591.1989214861.1754289641.1524395731.129917471.107835481.0862542061.0650810721.0444462651.0242641261.0046403140.9854909080.9667904940.9485847350.9309278810.913751750.8971090510.8809737620.8654922590.850504468];% 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')