multiple simultaneuous equations solver gives error

%Initial seed values for solve block
C_L = 0.7;
C_L_w = 0.5;
C_D = 0.02;
C_tau = 0.4;
alpha_e = 0.1;
C_LT = 0.1;
i = [0 1 2 3 4 5 6 7 8 9 10];
V_knots = 100 + 15*i; %True airspeed range (knots)
V_i = V_knots*0.515; %true airspeed (m/s)
syms C_L C_D C_tau alpha_e C_LT C_LW

% eqn1 = C_L*sin(alpha_e) - C_D*cos(alpha_e) + C_tau*cos(kappa) - 2*m*g/(rho*V_i^2*S)*sin(alpha_e+gamma_e) == 0;
% eqn2 = C_L*cos(alpha_e) + C_D*sin(alpha_e) + C_tau*sin(kappa) - 2*m*g/(rho*V_i^2*S)*cos(alpha_e+gamma_e) == 0;
% eqn3 = C_tau*z_tau/c_w - V_T*C_LT + (C_m0 + (h-h_0)*C_L_w) == 0;
% eqn4 = C_L - C_LT*S_T/S - C_L_w == 0;
% eqn5 = K*C_L^2 - C_D + C_D0 == 0;
% eqn6 = a*(alpha_e + alpha_wr - alpha_w0) - C_L_w == 0;
for i = V_i
    eqns = [C_L*sin(alpha_e) - C_D*cos(alpha_e) + C_tau*cos(kappa) == 2*m*g/(rho*V_i(i)^2*S)*sin(alpha_e+gamma_e),
        C_L*cos(alpha_e) + C_D*sin(alpha_e) + C_tau*sin(kappa) == 2*m*g/(rho*V_i(i)^2*S)*cos(alpha_e+gamma_e),
        C_tau*z_tau/c_w - V_T*C_LT + (C_m0 + (h-h_0)*C_L_w) == 0,
        C_L - C_LT*S_T/S - C_L_w == 0,
        K*C_L^2 - C_D + C_D0 == 0,
        a*(alpha_e + alpha_wr - alpha_w0) - C_L_w == 0];
    S(i) = vpasolve(eqns, [C_L(i), C_D(i), C_tau(i), alpha_e(i), C_LT(i), C_LW(i)])
end

gives the error:

Array indices must be positive integers or logical values.

Error in aeroTrim (line 153)

eqns = [C_L*sin(alpha_e) - C_D*cos(alpha_e) + C_tau*cos(kappa) == 2*m*g/(rho*V_i(i)^2*S)*sin(alpha_e+gamma_e),

Please advise on how i can fix this and find the values for the variables. Thank you

[Torsten]

You use

for i = V_i

and V_i is complex-valued.

So you can't index arrays with i.

Answer 1

[Star Strider]

‘Array indices must be positive integers or logical values.’

The ‘V_1’ are not integers.

Try something like this instead —

V_iv = V_knots*0.515; %true airspeed (m/s)

then —

for i = 1:numel(V_iv)

V_i = V_iv(i);

...

end

Note that in the posted code, several variables are neither defined nor declared. Declating them —

%Initial seed values for solve block
C_L = 0.7;
C_L_w = 0.5;
C_D = 0.02;
C_tau = 0.4;
alpha_e = 0.1;
C_LT = 0.1;
i = [0 1 2 3 4 5 6 7 8 9 10];
V_knots = 100 + 15*i; %True airspeed range (knots)
V_iv = V_knots*0.515; %true airspeed (m/s)
syms C_L C_D C_tau alpha_e C_LT C_LW 
syms kappa m g rho S gamma_e z_tau c_w V_T C_m0 h h_0 S_T K C_D0 a alpha_wr alpha_w0 
    
% eqn1 = C_L*sin(alpha_e) - C_D*cos(alpha_e) + C_tau*cos(kappa) - 2*m*g/(rho*V_i^2*S)*sin(alpha_e+gamma_e) == 0;
% eqn2 = C_L*cos(alpha_e) + C_D*sin(alpha_e) + C_tau*sin(kappa) - 2*m*g/(rho*V_i^2*S)*cos(alpha_e+gamma_e) == 0;
% eqn3 = C_tau*z_tau/c_w - V_T*C_LT + (C_m0 + (h-h_0)*C_L_w) == 0;
% eqn4 = C_L - C_LT*S_T/S - C_L_w == 0;
% eqn5 = K*C_L^2 - C_D + C_D0 == 0;
% eqn6 = a*(alpha_e + alpha_wr - alpha_w0) - C_L_w == 0;
for i = 1:numel(V_iv)
    V_i = V_iv(i);
eqns = [C_L*sin(alpha_e) - C_D*cos(alpha_e) + C_tau*cos(kappa) == 2*m*g/(rho*V_i(i)^2*S)*sin(alpha_e+gamma_e),
    C_L*cos(alpha_e) + C_D*sin(alpha_e) + C_tau*sin(kappa) == 2*m*g/(rho*V_i(i)^2*S)*cos(alpha_e+gamma_e),
    C_tau*z_tau/c_w - V_T*C_LT + (C_m0 + (h-h_0)*C_L_w) == 0,
    C_L - C_LT*S_T/S - C_L_w == 0,
    K*C_L^2 - C_D + C_D0 == 0,
    a*(alpha_e + alpha_wr - alpha_w0) - C_L_w == 0];
% S(i) = vpasolve(eqns, [C_L(i), C_D(i), C_tau(i), alpha_e(i), C_LT(i), C_LW(i)])
S = solve(eqns, [C_L(i), C_D(i), C_tau(i), alpha_e(i), C_LT(i), C_LW(i)])
end

S = struct with fields:
        C_L: [0×1 sym]
        C_D: [0×1 sym]
      C_tau: [0×1 sym]
    alpha_e: [0×1 sym]
       C_LT: [0×1 sym]
       C_LW: [0×1 sym]

Index exceeds the number of array elements. Index must not exceed 1.

So the loop problem is solved snd the code executes. It is not possible to go further without numeric values for the undefined constants.

.

[Punit Ahuja]

I've taken your suggestion and included the new code below.

To make it easier, i've equated all of the constants to 1.

%Initial seed values for solve block
C_L = 0.7;
C_L_w = 0.5;
C_D = 0.02;
C_tau = 0.4;
alpha_e = 0.1;
C_LT = 0.1;
i = [0 1 2 3 4 5 6 7 8 9 10];
V_knots = 100 + 15*i; %True airspeed range (knots)
V_iv = V_knots*0.515; %true airspeed (m/s)
kappa = 1; m=1; g=1; rho=1; S=1; gamma_e=1; z_tau=1; c_w=1; V_T=1; C_m0=1; h=1; 
h_0=1; S_T=1; K=1; C_D0=1; a=1; alpha_wr=1; alpha_w0=1;
syms C_L C_D C_tau alpha_e C_LT C_LW
for i = 1:numel(V_iv)
    V_i = V_iv(i);
    eqns = [C_L*sin(alpha_e) - C_D*cos(alpha_e) + C_tau*cos(kappa) == 2*m*g/(rho*V_i(i)^2*S)*sin(alpha_e+gamma_e),
        C_L*cos(alpha_e) + C_D*sin(alpha_e) + C_tau*sin(kappa) == 2*m*g/(rho*V_i(i)^2*S)*cos(alpha_e+gamma_e),
        C_tau*z_tau/c_w - V_T*C_LT + (C_m0 + (h-h_0)*C_L_w) == 0,
        C_L - C_LT*S_T/S - C_L_w == 0,
        K*C_L^2 - C_D + C_D0 == 0,
        a*(alpha_e + alpha_wr - alpha_w0) - C_L_w == 0];
    S = solve(eqns, [C_L(i), C_D(i), C_tau(i), alpha_e(i), C_LT(i), C_LW(i)])
end

Is it now possible to solve these?

Sorry for not including them the first time.

I also get this in the command window after running the code:

S =

struct with fields:

C_L: [0×1 sym]

C_D: [0×1 sym]

C_tau: [0×1 sym]

alpha_e: [0×1 sym]

C_LT: [0×1 sym]

C_LW: [0×1 sym]

Index exceeds the number of array elements. Index must not exceed 1.

Error in aeroTrim (line 153)

eqns = [C_L*sin(alpha_e) - C_D*cos(alpha_e) + C_tau*cos(kappa) == 2*m*g/(rho*V_i(i)^2*S)*sin(alpha_e+gamma_e),

[Star Strider]

Please do not subscript ‘V_i’ because in each loop iteration it is a scalar —

%Initial seed values for solve block
C_L = 0.7;
C_L_w = 0.5;
C_D = 0.02;
C_tau = 0.4;
alpha_e = 0.1;
C_LT = 0.1;
i = [0 1 2 3 4 5 6 7 8 9 10];
V_knots = 100 + 15*i; %True airspeed range (knots)
V_iv = V_knots*0.515; %true airspeed (m/s)
kappa = 1; m=1; g=1; rho=1; S=1; gamma_e=1; z_tau=1; c_w=1; V_T=1; C_m0=1; h=1; 
h_0=1; S_T=1; K=1; C_D0=1; a=1; alpha_wr=1; alpha_w0=1;
syms C_L C_D C_tau alpha_e C_LT C_LW
for i = 1:numel(V_iv)
    V_i = V_iv(i);
    eqns = [C_L*sin(alpha_e) - C_D*cos(alpha_e) + C_tau*cos(kappa) == 2*m*g/(rho*V_i^2*S)*sin(alpha_e+gamma_e),
        C_L*cos(alpha_e) + C_D*sin(alpha_e) + C_tau*sin(kappa) == 2*m*g/(rho*V_i^2*S)*cos(alpha_e+gamma_e),
        C_tau*z_tau/c_w - V_T*C_LT + (C_m0 + (h-h_0)*C_L_w) == 0,
        C_L - C_LT*S_T/S - C_L_w == 0,
        K*C_L^2 - C_D + C_D0 == 0,
        a*(alpha_e + alpha_wr - alpha_w0) - C_L_w == 0];
%     S = solve(eqns, [C_L(i), C_D(i), C_tau(i), alpha_e(i), C_LT(i), C_LW(i)])
[C_Ls{i}, C_Ds{i}, C_taus{i}, alpha_es{i}, C_LTs{i}, C_LWs{i}] = solve(eqns, [C_L, C_D, C_tau, alpha_e, C_LT, C_LW]);
end

C_Ls 

C_Ls = 1×11 cell array
    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}

C_Ds

C_Ds = 1×11 cell array
    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}

C_taus

C_taus = 1×11 cell array
    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}

alpha_es

alpha_es = 1×11 cell array
    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}

C_LTs

C_LTs = 1×11 cell array
    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}

C_LWs

C_LWs = 1×11 cell array
    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}

I made some slight changes and it runs without error.

The problem is that it does not produce any useful results, at least in its present form. Different values for the other variables (all now set equal to 1) may change that.

.

[Punit Ahuja]

thank you good sir

[Star Strider]

As always, my pleasure!

[Alex Sha]

Numerical Solutions:

i	C_L	C_D	C_TAU	ALPHA_E	C_LT	C_L_W
0	0.821020148353258	1.67407408400201	-1.86495420551723	1.68597435387049	-0.864954205517232	1.68597435387049
1	0.821023762637745	1.67408001881584	-1.86486589916737	1.68588966180511	-0.864865899167367	1.68588966180511
2	0.821026195663131	1.67408401396507	-1.86480635574535	1.68583255140848	-0.864806355745349	1.68583255140848
3	0.821027911515128	1.67408683148689	-1.86476431593763	1.68579222745276	-0.864764315937635	1.68579222745276
4	0.821029166792955	1.67408889272473	-1.86473353548028	1.68576270227323	-0.864733535480275	1.68576270227323
5	0.821030112773441	1.67409044608077	-1.86471032520523	1.68574043797867	-0.864710325205233	1.68574043797867
6	0.821030843345073	1.67409164572392	-1.8646923918575	1.68572323520257	-0.864692391857501	1.68572323520257
7	0.821031419287761	1.67409259145767	-1.86467824909721	1.68570966838497	-0.864678249097213	1.68570966838497
8	0.82103188135886	1.67409335020767	-1.86466689930221	1.68569878066107	-0.86466689930221	1.68569878066107
9	0.821032257718414	1.6740939682142	-1.86465765269067	1.68568991040908	-0.864657652690667	1.68568991040908
10	0.821032568329102	1.67409447825708	-1.86465001998691	1.68568258831601	-0.864650019986908	1.68568258831601