-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathgetDrag2.m
296 lines (244 loc) · 7.45 KB
/
getDrag2.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
function [Cd] = getDrag2(rocket,v,a,nu)
%% Rocket's dimensions
d = rocket.geo.body.D; %[in]
L = rocket.data.length.L; %total length [in]
Sb = pi*(d)*L; %body surface area [in^2]
Cr = rocket.geo.fin.c*12; %fin root chord [in]
lambda = rocket.geo.fin.TR;
tc = rocket.geo.fin.ThR; %nondimensional fin thickness []
nf = rocket.geo.fin.n;%number of fins
Sf = rocket.geo.fin.S*144; %fin surface area [in^2]
Lp = 0; %launch lug length [in]
Lap = 0; %nose to launch lug length [in]
Ap = 0; %maximum cross section area of launch lug [in^2]
Sp = 3; %wetted surface area of proturbance [in^2]
Ln = rocket.data.length.nosecone; %nose length [in]
L0 = L - Ln; %body length [in]
xTc = 0.3*Cr; %Location of maximum thickness of wing/chord
db = d; %[in]
Sn = rocket.geo.nc.S*144;% area of the nosecone [in^2]
% Incompressible Skin Friction Coeff. w/ roughness
K = 0.00008; % polished metal/wood
%K = 0.00025; % smooth matte paint, carefully applied
%% Speed of Sound ft/s
% if h < 37000 % Less than 37,000 ft
% a = -0.004*h + 1116.45;
% elseif h <= 64000
% a = 968.08;
% else
% a = 0.0007*h + 924.99;
% end
if abs(v) < 20
Cd = 0.3;
return;
elseif v < 0
v = abs(v);
end
% % Mach Number
M = abs(v/a);
%% Kinematic Viscosity ft^2/s
% if h < 15000
% nu = 0.000157*exp(2.503e-5*h);
% elseif h <= 30000
% nu = 0.000157*exp(2.76e-5*h - 0.03417);
% elseif h <= 248160
% nu = 0.000157*exp(4.664e-5*h - 0.6882);
% else
% nu = 5;
% end
%% Body's Friction Drag
CdB = bodyFrictionDrag(M,L,d,Sb,K,a,nu);
%% Fins'Friction Drag
CdF = finFrictionDrag(M,Cr,nu,K,xTc,tc,nf,Sf,d,lambda,a);
%% Interference Drag
CdP = interferenceDrag(M,Lp,nu,K,Lap,Ap,d,Sp);
%% Drag due to rivets, joints,....
Sr = Sb + Sf + Sp + Sn; % Total Wetted Area of Rocket
Cde = excrescenciesDrag(M,Sr,d);
%% Total Skin Friction Drag
Kf = 1.04; % Interference Factor
CdFriction = CdB + Kf*CdF + Kf*CdP + Cde;
%% Base Drag Coeff.
Kb = 0.0274*atan(L0/d + 0.0116);
n = 3.6542*(L0/d)^-0.2733;
% get base drag at Mach 0.6
CdB06 = bodyFrictionDrag(0.6,L,d,Sb,K,a,nu);
CdF06 = finFrictionDrag(0.6,Cr,nu,K,xTc,tc,nf,Sf,d,lambda,a);
CdP06 = interferenceDrag(0.6,Lp,nu,K,Lap,Ap,d,Sp);
Cde06 = excrescenciesDrag(0.6,Sr,d);
CdFriction06 = CdB06 + Kf*CdF06 + Kf*CdP06 + Cde06;
CdBase06 = Kb*(db/d)^n/sqrt(CdFriction06);
if M <= 0.6
CdBase = Kb*(db/d)^n/sqrt(CdFriction);
elseif M < 1
fb = 1 + 215.8*(M - 0.6)^6;
CdBase = CdBase06 * fb;
elseif M <= 2
fb = 2.0881*(M - 1)^3 - 3.7938*(M - 1)^2 ...
+1.4618*(M - 1) + 1.883917;
CdBase = CdBase06 * fb;
elseif M <= 4
fb = 0.297*(M - 2)^3 - 0.7937*(M -2)^2 ...
- 0.1115*(M - 2) + 1.64006;
CdBase = CdBase06 * fb;
else
fb = 0.6;
CdBase = CdBase06 * fb;
end
%% Transonic Drag
% Transonic Divergence Mach Number
Md = -0.0156*(Ln/d)^2 + 0.136*(Ln/d) + 0.6817;
% Rocket Effective Length Le = L if nose doesn't bulge
% Le = length from nose to end of bulging section
Le = L;
% Mach Number Transonic
if Ln/Le < 0.2
aCoeff = 2.4;
bCoeff = -1.05;
Mf = aCoeff*(Le/d)^bCoeff+1.0175;
else
aCoeff = -321.94*(Ln/Le)^2 + 264.07*(Ln/Le) - 36.348;
bCoeff = 19.634*(Ln/Le)^2 - 18.369*(Ln/Le) + 1.7434;
Mf = aCoeff*(Le/d)^bCoeff+1.0175;
end
% Max Rise in Drag
c = 50.676*(Ln/L)^2 - 51.734*(Ln/L) + 15.642;
g = -2.2538*(Ln/L)^2 + 1.3108*(Ln/L) - 1.7344;
if Le/d >= 6
delCdMax = c*(Le/d)^g;
else
delCdMax = c*(6)^g;
end
% Drag drise for a given M
if (Md <= M) && (M <= Mf)
x = (M - Md)/(Mf - Md);
F = -8.347*x^5 + 24.543*x^4 - 24.946*x^3 + 8.6321*x^2 ...
+ 1.1195*x;
delCdT = delCdMax*F;
else
delCdT = 0;
end
%% Supersonic Drag
if M >= Mf
delCdS = delCdMax;
else
delCdS = 0;
end
%% Total Drag Coeff.
CdF_cor = CdF*Kf;
CdP_cor = CdP*Kf;
Cd = real(CdB + CdF_cor + CdP_cor + Cde + CdBase + delCdT + delCdS);
% if ~isreal(Cd)
% warning("Imaginary Drag Coefficient!")
% Cd = 0.3;
% end
%%%Overwrite instability at high Mach
% if M >= 3.5
% Cd = 0.2;
% end
end
%% Supporting Functions
function CdB = bodyFrictionDrag(M,L,d,Sb,K,a,nu)
% Compressive Reynolds Number
RnBody = (a.*M.*L)./(12.*nu).*(1 + 0.0283.*M - 0.043*M.^2 + 0.2107*M.^3 ...
- 0.03829*M.^4 + 0.002709*M.^5);
% Incompressible Skin Friction Coeff.
CfStarBody = 0.037036*RnBody.^(-0.155079);
% Compressible Skin Friction Coeff.
CfBody = CfStarBody*(1 + 0.00798*M - 0.1813*M.^2 + 0.0632*M.^3 ...
- 0.00933*M.^4 + 0.000549*M.^5);
CfStarRBody = (1.89 + 1.62*log10(L/K))^(-2.5);
% Compressible Skin Friction Coeff. w/ roughness
CfRBody = CfStarRBody/(1 + 0.2044.*M.^2);
% Final Skin Friction Coeff.
if CfBody >= CfRBody
CfFinalB = CfBody;
else
CfFinalB = CfRBody;
end
% Body Drag Coeff. due to friction
CdB = CfFinalB*(1 + 60/(L/d)^3 + 0.0025*(L/d))*4*Sb...
/(pi*d^2);
end
%% Fin Friction Drag
function CdF = finFrictionDrag(M,Cr,nu,K,xTc,tc,nf,Sf,d,lambda,a)
% Compressible Reynolds Number
RnFin = (a.*M.*Cr)./(12*nu).*(1 + 0.0283*M - 0.043*M.^2 ...
+ 0.2107*M.^3 - 0.03829*M.^4 + 0.002709*M.^5);
% Incompressible Skin Friction Coeff.
CfStarFin = 0.037036*RnFin.^(-0.155079);
% Compressible Skin Friction Coeff.
CfFin = CfStarFin*(1 + 0.00798*M - 0.1813*M.^2 + 0.0632*M.^3 ...
- 0.00933*M.^4 + 0.000549*M.^5);
% Incompressible Skin Friction Coeff. w/ roughness
CfStarRFin = (1.89 + 1.62*log10(Cr/K))^(-2.5);
% Compressible Skin Friction Coeff. w/ roughness
CfRFin = CfStarRFin/(1 + 0.2044*M.^2);
% Final Skin Friction Coeff.
if CfFin >= CfRFin
CfFinalF = CfFin;
else
CfFinalF = CfRFin;
end
% Incompressible Reynold Number
Re = (a.*M.*Cr)/(12*nu);
% Average Flat Plate Skin Friction Coeff. for each fin
if lambda == 0
CfLambda = CfFinalF.*(1+ 0.5646./log10(Re));
else
CfLambda = CfFinalF.*(log10(Re)).^(2.6)/(lambda^2 - 1) ...
.*(lambda^2./(log10(Re.*lambda)).^(2.6) - (log10(Re)).^(-2.6) ...
+ 0.5646*lambda^2./(log10(Re.*lambda)).^(3.6) ...
-0.5646.*(log10(Re)).^(-3.6));
end
% Drag Coeff. for all fins
xBar = xTc/Cr; % nondimensional location of maximum thickness
% Drag Coeff. of all fins
CdF = CfLambda.*(1 + 60*tc^4 + 0.8*(1 + 5*xBar^2)*tc)...
*4*nf*Sf/(pi*d^2);
end
function [CdP] = interferenceDrag(M,Lp,nu,K,Lap,Ap,d,Sp)
if Lp ~= 0
% Compressible Reynolds Number
RnP = (a.*M.*Lp)/(12*nu).*(1 + 0.0283*M - 0.043*M.^2 + 0.2107*M.^3 ...
- 0.03829*M.^4 + 0.002709*M.^5);
% Incompressible Skin Friction Coeff.
CfStarP = 0.037036*RnP.^(-0.155079);
% Compressible Skin Friction Coeff.
CfP = CfStarP*(1 + 0.00798*M - 0.1813*M.^2 + 0.0632*M.^3 ...
- 0.00933*M.^4 + 0.000549*M.^5);
% Incompressible Skin Friction Coeff. w/ roughness
CfStarRP = (1.89 + 1.62*log10(Lp/K))^-2.5;
% Compressible Skin Friction Coeff. w/ roughness
CfRP = CfStarRP/(1 + 0.2044*M.^2);
% Final Skin Friction Coeff.
if CfP >= CfRP
CfFinalP = CfP;
else
CfFinalP = CfRP;
end
% Friction Coeff. of Protuberance
CfFinalID = 0.815*CfFinalP.*(Lap/Lp)^-0.1243;
% Wetted Area of Protuberance, Sp
% Drag Coeff. of Protuberance due to Friction
CdP = CfFinalID*(1 + 1.798*(sqrt(Ap)/Lp)^1.5)*4*Sp/(pi*d^2);
else
CdP = 0;
end
end
function Cde = excrescenciesDrag(M,Sr,d)
if M < 0.78
Ke = 0.00038;
Cde = Ke*4*Sr/(pi*d^2);
elseif M <= 1.04
Ke = -0.4501*M^4 + 1.5954*M^3 - 2.1062*M^2 ...
+ 1.2288*M - 0.26717;
Cde = Ke*4*Sr/(pi*d^2);
elseif M <= 3
Ke = 0.0002*M^2 - 0.0012*M + 0.0018;
Cde = Ke*4*Sr/(pi*d^2);
else
Ke = 0;
Cde = 0;
end
end