A. VALIDACIÓN DE LOS ESCENARIOS DE MANEJO DE VISITANTES
4. Evaluación de escenarios
For the three-dimensional cases, all of the single step ice shapes have been compared to their multistep and experimental counterparts, using both the hybrid comparison method and the cosine similarity method. For the cosine similarity the results are given in tabel 7.1, and for the hybrid comparison method the results
are given in table 7.2. When comparing both tables it can be seen that the results of both tables are very con- sistent, i.e. if the hybrid comparison model gives a low value, the cosine similarity will also give a low value. This is obviously preferable, given that the cosine similarity method should serve as an indicator to the hy- brid comparison method. It is clear however, that the values of the cosine similarity method are generally much lower than the values of the hybrid comparison method. This usually is due to the large different in back extent of the ice, which is the result of the unshedded water, as mentioned in section 6.2. For future research it is possible to give a different weight to each parameter given in 7.3.4, which will allow the user to specify which parameter is most important for a specific case.
The results in table 7.2 show that the values of the cosine similarity method rarely exceed 0.2, which only happens on three seperate occasions. In both multi-element aerofoils, the ice shape on the body is not predicted very well, as both visualized in appendix C and discussed in section 6.2. Furthurmore in case 16, which has two very distinct horns growing vertically, it also matches quite badly. The reason for these, generally, low values is that overall the ice shapes are reasonably similar, having generally the same shape and only vary in specific locations around the aerofoil. It can therefore be concluded that values over 0.2 predict a rather big mismatch in ice shape, but that the lower values should not be discarded as being small, neglible, differences.
1v2 step 1v4 step 2v4 step 1 step v
experimental 2 step v experimental 4 step v experimental C5 0.0013 — — 0.1426 0.1516 — C6 0.0425 — — 0.0523 0.0698 — C7 0.0414 0.0817 0.1048 0.0516 0.0880 0.0979 C8 0.0012 — — 0.1179 0.1278 — C9 0.0054 — — 0.0990 0.1144 — C10 0.0586 — — 0.1488 0.1722 — C11 slat 0.0014 — — 0.0122 0.0116 — C11 body 0.1203 — — 0.4599 0.6914 — C11 flap 0.0086 — — 0.1178 0.0980 — C12 slat 0.0010 — — 0.0155 0.0125 — C12 body 0.0719 — — 0.5820 0.6487 — C12 flap 0.0163 — — 0.1044 0.0978 — C13 0.0063 0.0171 0.0136 0.1176 0.1342 0.1354 C14 0.0287 0.0076 0.0352 0.1804 0.1265 0.1972 C15 — — — 0.2611 — — C16 0.0394 0.0426 0.0413 0.4321 0.3537 0.3316 C17 0.0422 0.0600 0.0529 0.1911 0.2077 0.1817 C18 0.0337 — — 0.0515 0.0594
Table 7.1: Results of the cosine similarity method
When looking at the results in table 7.2, it is clear that overall the hybrid comparison method gives lower values than the geometric parameters alone. This is due to the fact that the geometric parameters are lim- ited to the specified 6, whereas the Fourier parameters that are compared will take the entire ice shape into account. Two ice shapes that have a profound difference in stagnation thickness for instance, will have a larger geometric value, however when the overall ice shapes are similar, the Fourier parameters will lower the average of the hybrid comparison method. Furthermore it can be seen that the experimental ice shapes usually are largely different from both the single step, aswell as the multistep methods. This is mostly due to a large different in back extent of the ice and, in case of the multi element aerofoils, the point where the ice will achieve its maximum thickness.
As previously mentioned, the values coming from the geometric parameters, and therefore the hybrid com- parison method, are quite sensitive for large changes in a single parameter. In order to come up with a decent set of parameters which will vary more linearly, it is necessary to specify which of the geometric and Fourier features are important to the user. This model is presented with an equal weighting to all features, purely for the purpose of demonstrating the method. It is therefore advised for each user to check in what way the parameters are important for a specific case, adjusting the method to the needs of each user.
1v2 step 1v4 step 2v4 step 1 step v
experimental 2 step v experimental 4 step v experimental C5 g = 0.0281 h = 0.0191 — — g = 0.6305 g = 0.6370 — C6 g = 0.1499 h = 0.1123 — — g = 0.1695 g = 0.2088 — C7 g = 0.1111 g = 0.2300 h = 0.1733 g = 0.2373 g = 0.4106 g = 0.3894 g = 0.3698 C8 g = 0.0125 h = 0.0085 — — g = 0.2596 g = 0.2569 — C9 g = 0.1338 h = 0.0905 — — g = 0.3548 g = 0.3043 — C10 g = 0.1635 — — g = 0.3583 g = 0.2940 — C11 slat g = 0.0679 h = 0.0855 — — g = 0.3820 g = 0.3500 — C11 body g = 0.2883 h = 0.1948 — — g = 0.5927 g = 0.6175 — C11 flap g = 0.2481 h = 0.1670 — — g = 0.2495 g = 0.2028 — C12 slat g = 0.1150 — — g = 0.3461 g = 0.2817 — C12 body g = 0.1562 h = 0.1067 — — g = 0.4886 g = 0.4924 — C12 flap g = 0.1780 h = 0.1205 — — g = 0.4630 g = 0.4646 — C13 g = 0.2561 h = 0.1755 g = 0.2561 h = 0.1760 g = 0.1460 h = 0.1005 g = 0.5316 g = 0.5214 g = 0.5338 C14 g = 0.0959 h = 0.0672 g = 0.1225 h = 0.0845 g = 0.1555 h = 0.1069 g = 0.5734 g = 0.6201 g = 0.6192 C15 — — — g = 0.4901 — — C16 g = 0.0863 h = 0.0629 g = 0.1854 g = 0.1805 g = 0.6842 g = 0.6935 g = 0.4795 C17 g = 0.2665 h = 0.1963 g = 0.3922 g = 0.3436 g = 0.2944 g = 0.4517 g = 0.3482 C18 g = 0.2167 h = 0.1603 — — g = 0.2142 g = 0.3485 —
8. Conclusions
In this study a comparison was made between a single step and a multistep analysis for different flow solu- tions around an aerofoil, resulting in many different ice shapes. When looking at the results of the two step methods, it can be seen that, especially in the case of glaze ice cases, a multistep method generally gives a better numerical approximation of an experimental ice shape than a single step method. This is also true when looking at four step methods, however are a few problems that need solving before a multistep method can be used effectively.
First of all it is important that the produced ice shape is smooth, to encounter both ingrowth and a nu- merically induced peak at the back of the ice. In case of large ice shapes which have an irregular shape, the meshing is very difficult, making this a very important and time consuming step of the analysis. This can also be, partly, prevented by smoothing out the produced ice shape. Secondly, because of the necessity to refine a mesh for it to be able to cope with the extensive ice shapes, the latter steps in a multistep process, especially the third and fourth step in a four step method, will take a very long time to compute. This can be countered by focussing the refinement regions to where they are necessary, i.e. the regions where high gradients occur, greatly reducing the number of cells in the mesh.
With the multistep analyses that were performed in this study the results varied greatly. With the two step method the results were usually better, apart from the strange phenomenom of a very large back extent in the ice. The results show great promise for the use of multistep methods in prediciting difficult to match ice shapes, like glaze ice shapes, they are, however, not necessary to perform on rime ice cases, given that these are already matched very well by single step methods. The results of the four step method, with the exception of case 17, were very similar to the results of the 1 step and 2 step method. From this it may be concluded that performing a multistep ice accretion analysis is preferable, but that the method that was utilized for this report is not very well suited for performing such difficult analyses. It is therefore recom- mended that this topic continues to be one of interest to AeroTex, for it holds great potential to solve glaze ice cases.
For this study three different pieces of Matlab code have been written. The code to repair an ice shape that has grown in on itself is a simple tool that will generally provide the user with a suitable solution. It must however be noted that it is not suitable for repairing very large ingrown ice shapes, although it will be able to find the point of intersection. It is advised to only use this code if the time step, and therefore the ingrowth, is reasonably small. The code to calculate the feature vectors is ready to use, and is a very simple way of comparing two ice shapes quickly, without the need for resampling them, as is necessary in the hy- brid comparison method. The s/c increments however, have to be constant and equal for both compared ice shapes, which is effected by the TAC2 input files.
The error calculation code that calculates the value of the hybrid comparison method, is a very extensive and versatile code, which can take in the different specified geometric and Fourier parameters in any way the user specifies them. In order for this code to be fully operational, the user should define the weight on the different parameters, customizing the code for a specific set of cases. It has been made in such a way that the user can easily allocate weights to the different geometrical and Fourier features, whilst also allowing the user, albeit slightly more difficult, to create completely new parameters to be compared.
9. Recommendations
Whilst doing this study, several points that can be improved in the process were found, along with some work that still needs doing on the research that has been done. It can be seen that in cases where the ex- perimental ice shapes show a large back extent on the upper or lower surface, the numerical ice shapes do not quite match this large back extent. This may be improved by modelling the droplets as a spectrum of small and large droplets, in stead of the mono dispersed spectrum that has been used in the simulations in this study. Because the larger droplets have a larger mass, they will be less affected by changes in the flow velocity, making them impinge furthur back on the aerofoil.
The way that the ice accretion has been calculated in this study was not ideal. The IHB code will have very little nodes on larger deformations, producing very jagged ice shapes in case of glaze ice. AeroTex has a code that is more suited for this purpose, which, due to circumstances, was not ready for use during the period of the internship. It is advised that this will be used in future studies regarding multistep analyses.
For multistep methods it would be preferable to have a smoother ice shape, given that the rapidly varying ice shapes will have a profound effect on both the meshing and the solving of the next step in the process. The current smoothing code, which is embedded in IHB, is capable of smoothing some ice shapes, but the method is crude and will not always produce a sensible smoothed ice shape. As shown briefly in this report, Fourier descriptors can be used to smooth any given two-dimensional curve, by reconstructing it with less than the full number of coefficients. Furthur research should be done to use Fourier descriptors in this way, but the method looks very suitable for smoothing ice shapes.
In order to be able to use the Fourier descriptors as they are described in this report, it is imperative to have a completely even spreading of nodes. SolidWorks has proven to be unsuitable for this, given that a dif- ference of over 10% has been found between the largest and smallest delta in some cases. Should a proper alternative for SolidWorks arise, in terms of resampling, it is advised that this is used for the calculation of the Fourier components.
For the use of the hybrid comparison method it is necessary to furthur investigate the parameters that are being looked in to, as well as the weighting that each of the features should be given. Depending on what is important to AeroTex, certain parameters could be excluded or added within the code. It is advised that there will be some extra research on adjusting these parameters, in order to obtain a comparison method that can be used on every case. This should prevent the user from having to change the parameters before every new case that is run.
Bibliography
[1] Aircraft Owners and Pilots Association (AOPA), Aircraft Icing. Available from:
http://flighttraining.aopa.org/pdfs/SA11_Aircraft_Icing.pdf, 2002. Accessed: March 24, 2014.
[2] Skybrary, reference for aviation safety knowledge. In-flight icing. Available
from:http://www.skybrary.aero/index.php/In-Flight_Icing, 2014. Accessed: March 24, 2014.
[3] Gent, R. W., Dart, N. P., Cansdale, J. T. Aircraft Icing.Philosophical transactions: Mathematical, Physical and Engineering Sciences, Vol. 358, No. 1776, Ice and Snow Accretion on Structures (Nov. 15, 2000), pp. 2873-2911.
[4] Ruff, G. A. Quantitative Comparison of Ice Accretion Shapes on Airfoils.Journal of AircraftVol. 39, No. 3, pp. 418-426, May-June 2002.
[5] Moser, R. J. TAC2 User Guide Issue 2 (Code Issue 2, Rev 1.143), 2012
[6] Gent, R. W. User Guide for computer program: IHB, Icing Heat Balance - An ice accretion prediction design code, 2013
[7] Issa, R. I. Rise of Total Pressure in Frictional Flow.AIAA Journal, Vol. 33, No. 4, pp. 772-774, 1995 [8] Pope, S. B.Turbulent Flows. Cambridge University Press, 2000. ISBN-13: 978-0521598866 [9] Moser, R. J. EWC (Eulerian Water Catch) Software Specification Document, 2012.
A. Grid refinement study
Non-layered Layered
Case Grid size Cp Beta Comp. time (s) Convergence Cp Beta Comp. time (s) Convergence
C5 3.1 mm 0.927394 0.939795 4680 1264 0.988176 0.937854 7120 1378 Chord 0.450m 1.6 mm 0.995248 0.947378 19520 2057 1.01169 0.948403 40760 2186 0.8 mm 1.02025 0.949514 114220 2754 1.02293 0.949777 494340 6000 C7 3.1 mm 0.972134 0.865425 9290 1814 1.00892 0.869079 19780 1929 Chord 0.910m 1.6 mm 1.01171 0.873509 58720 3259 1.02175 0.875038 108170 2982 0.8 mm 1.02371 0.874622 410720 6000 1.02543 0.875133 848050 6000 C8 3.1 mm 0.988866 0.632359 15610 2397 1.01206 0.640601 32800 3007 Chord 0.910m 1.6 mm 1.01610 0.643100 89860 4219 1.02231 0.644613 198700 6000 0.8 mm 1.02184 0.645836 483960 6000 1.02292 0.646125 870490 6000 C12 3.1 mm 1.02741 0.634396 36210 6000 1.05391 0.619016 74150 5515 Chord 0.914m 1.6 mm 1.03888 0.635541 171860 6000 1.03973 0.626216 353150 6000 0.8 mm 1.03880 0.634735 775800 6000 1.03855 0.635327 1544136 6000 C13 3.1 mm 0.954689 0.806904 5710 1281 0.988149 0.813910 9850 1373 Chord 0.530m 1.6 mm 1.00187 0.814382 29360 2261 1.01359 0.816323 48450 2003 0.8 mm 1.02250 0.815008 120830 2552 1.02272 0.814889 511090 6000 C14 3.1 mm 0.855962 0.791614 2530 978 0.957285 0.792685 4660 1034 Chord 0.270m 1.6 mm 0.973167 0.803573 10900 1502 1.00862 0.809426 21380 1632 0.8 mm 1.02432 0.810523 72380 3059 1.03737 0.812082 278870 6000 0.4 mm 1.04088 0.811493 589512 6000 1.05682 0.811066 1173720 6000 C16 3.1 mm 0.962457 0.749659 6730 1354 1.00658 0.753266 11530 1411 Chord 0.600m 1.6 mm 1.00333 0.754580 27340 2232 1.01322 0.758019 60410 2290 0.8 mm 1.01075 0.761560 149300 3004 1.01358 0.763600 369520 3995 C17 3.1 mm 1.00134 0.653691 32440 6000 1.01947 0.650280 34280 3388 Chord 0.910m 1.6 mm 1.02540 0.653428 74060 3912 1.02375 0.655399 174130 4141 0.8 mm 1.02901 0.656813 470060 6000 1.02745 0.656744 1013520 6000
Table A.1: Results of the grid refinement study
D. fixIntersect.m Matlab script
1 clear all 2 close all
3 clc
4
5 [filename, pathname] = uigetfile('*.*', 'Pick your text file'); %Inputs a textfile ... by the users own choice
6 DATA = importdata(filename); 7 N = length(DATA); 8 9 figure 10 hold on 11 plot(DATA(:,1),DATA(:,3),'x−') 12 k = 1; 13 m = 1; 14 check = 0; 15 xlim([−0.1 0.15]) 16 while k ≤ N−1 17 while m ≤ N−1 18 a = [DATA(k,1) DATA(k,3)]; 19 b = [DATA(k+1,1) DATA(k+1,3)]; 20 c = [DATA(m,1) DATA(m,3)]; 21 d = [DATA(m+1,1) DATA(m+1,3)]; 22 if a==c 23 elseif a==d 24 elseif b==c 25 elseif b==d 26 else 27 if Intersect(a,b,c,d) == 1 28 intX = ...
((a(2)−c(2)−((b(2)−a(2))/(b(1)−a(1)))*a(1)+((d(2)−c(2))/(d(1)−c(1))) 29 *c(1))/((d(2)−c(2))/(d(1)−c(1))−(b(2)−a(2))/(b(1)−a(1))));
30 intY = ...
a(2)+((b(2)−a(2))/(b(1)−a(1))*intX)−(((b(2)−a(2))/(b(1)−a(1)))*a(1)); 31 fprintf('There is an intersection at (x = %g,y = %g)\n',intX,intY)
32 %%Calculating the area of the collapsed ice
33 p(1,:) = [intX intY];
34 for n = 0:m−(k+1)
35 p(n+2,:)=DATA(k+1+n,1:2:3);
36 end
37 for o = 1:length(p)−2 %there are 2 less triangles than there are ... points (intersect point included)
38 A = sqrt((p(o+1,1)−p(1,1))^2+(p(o+1,2)−p(1,2))^2); 39 B = sqrt((p(o+2,1)−p(o+1,1))^2+(p(o+2,2)−p(o+1,2))^2); 40 C = sqrt((p(o+2,1)−p(1,1))^2+(p(o+2,2)−p(1,2))^2); 41 AREA(o)=0.5*C*sqrt(A^2−((C^2+A^2−B^2)/(2*C))^2); 42 end 43 AREAtot = sum(AREA); 44 AREAnew = 0; 45 q = −1; 46 while AREAtot>AREAnew 47 q = q +1;
48 A = sqrt((DATA(k−q,1)−intX)^2+(DATA(k−q,2)−intY)^2);
49 B = ...
sqrt((DATA(m+1+q,1)−DATA(k−q,1))^2+(DATA(m+1+q,2)−DATA(k−q,2))^2); 50 C = sqrt((DATA(m+1+q,1)−intX)^2+(DATA(m+1+q,2)−intY)^2);
51 AREAnew=0.5*C*sqrt(A^2−((C^2+A^2−B^2)/(2*C))^2);
52 end
54 N=length(DATA); 55 check = 1; 56 else 57 end 58 end 59 m = m+1; 60 end 61 m=k; 62 k=k+1; 63 end 64 65 if check == 0
66 disp('The ice did not grow in on itself')
67 else
68 plot(DATA(:,1),DATA(:,3),'ro−') 69 hold off
70 end
1 function [intersect] = Intersect(a,b,c,d) 2 if CCW(a,c,d) == CCW(b,c,d)
3 intersect = 0;
4 elseif CCW(a,b,c) == CCW(a,b,d) 5 intersect = 0;
6 else
7 intersect = 1;
8 end
1 function [ccw] = CCW(A,B,C)
2 if (C(2)−A(2))*(B(1)−A(1))>(B(2)−A(2))*(C(1)−A(1))
3 ccw = 1;
4 else
5 ccw = 0;
F. featureVectors.m Matlab script
1 clear all 2 close all
3 clc
4
5 disp('Please select your first geometry sheet')
6 [firstGeoSheet, pathname1] = uigetfile('*.*', 'Pick your text file'); %Inputs ... a textfile by the users own choice
7 DATA1 = importdata(firstGeoSheet); ...
%importing the data from the txt file into matrix DATA. Textfile should be ... arranged as number−tab−number−return and repeat
8 data1 = DATA1.data; %taking ...
the numerical values of the excelsheet, given in the substructure DATA.data 9
10
11 %% Asking user for second geometry sheet
12 disp('Please select your second geometry sheet')
13 [secondGeoSheet, pathname2] = uigetfile('*.*', 'Pick your text file'); %Inputs ... a textfile by the users own choice
14 DATA2 = importdata(secondGeoSheet); ...
%importing the data from the txt file into matrix DATA. Textfile should be ... arranged as number−tab−number−return and repeat
15 data2 = DATA2.data; %taking ...
the numerical values of the excelsheet, given in the substructure DATA.data 16 17 extupp1 = data1(1,2); 18 extlow1 = data1(2,2); 19 extupp2 = data2(1,2); 20 extlow2 = data2(2,2); 21
22 if extupp1 > extupp2 %Finding ...
the largest upper and lower extent of the ice. 23 extupp = extupp1; 24 else 25 extupp = extupp2; 26 end 27 if extlow1 > extlow2 28 extlow = extlow2; 29 else 30 extlow = extlow1; 31 end
32 indupp1 = find(data1(:,4)==extupp); %Marking ...
the nodes where the ice has stopped growing. 33 indlow1 = find(data1(:,4)==extlow);
34 indupp2 = find(data2(:,4)==extupp); 35 indlow2 = find(data2(:,4)==extlow); 36
37 th1 = data1(indlow1:indupp1,8); ...
%Creating 2 thickness vectors 38 th2 = data2(indlow2:indupp2,8); 39
40 eucDis = abs(th1−th2); ...
%Calculating the Euclidian distance 41
42 figure ...
%Plotting the Euclidian distance 43 hold on
44 plot((−(length(th1)/2)+1:(length(th1)/2))*0.0006,th1,'k−−') 45 plot((−(length(th2)/2)+1:(length(th2)/2))*0.0006,th2,'b−−')
46 plot((−(length(eucDis)/2)+1:(length(eucDis)/2))*0.0006,eucDis,'r') 47 legend('first ice shape','second ice shape','Euclidian distance') 48 xlabel('s/c')
49 ylabel('thickness in mm') 50 hold off
51
52 cosSim = 1−dot(th1,th2)/(norm(th1)*norm(th2)); ...
%Calculating the cosine similarity 53 disp(cosSim)
G. errorCalculation.m Matlab script
1 clear all 2 close all
3 clc
4
5 %% Calculating the Fourier parameters, starting by asking for the first ice shape
6 disp('Please select your first ice shape file')
7 [firstIceShape] = uigetfile('*.*', 'Pick your text file'); %Inputs ... a textfile by the users own choice
8 DATA1 = importdata(firstIceShape); ...
%Importing the data from the txt file into matrix DATA. Textfile should be ... arranged as number−tab−number−return and repeat
9
10 [a1,N1] = calcFparams(DATA1); %Output ...
of the function calcFparams, input is DATA1, output is a1 and N1
11 %% Asking user for second ice shape and performing a check that both files have same N
12
13 disp('Please select your second ice shape file')
14 [secondIceShape] = uigetfile('*.*', 'Pick your text file'); %Inputs ... a textfile by the users own choice
15 DATA2 = importdata(secondIceShape); ...
%Importing the data from the txt file into matrix DATA. Textfile should be ... arranged as number−tab−number−return and repeat
16
17 [a2,N,∆] = calcFparams(DATA2); %Output of ...
the function calcFparams, input is DATA2, output is a2 and N2 18
19 if N1 6= N %Making ...
sure that both input files are of the same length, this is unfortunately still a ... necessity
20 disp('====Please make sure that both input files consist of the same number of ... nodes====')
21 return
22 end
23 %% Calculating the two Fourier parameters
24
25 fs = zeros(length(∆),1); 26 f=zeros(N,1);
27 for k = 1:N−1
28 fs(k) = 1/∆(k); %Calculating ...
the sampling frequency
29 f(k) = ((k−1)/(N−1))*(fs(k)/2); ...
%Calculating the spacial frequency
30 end 31 32 diff = 0; 33 K = 100; 34 for k = 2:K 35 diff = diff + ... abs((abs(a2(k))−abs(a1(k))))/(f(k)*(max((abs(a2(k))),abs(a1(k))))); ... %Calculating the difference in Fourier coefficients, normalized to the ... largest of the two coefficients and adding them up into 1 variable
36 end
37
38 F1 = abs((max(abs(a2))−max(abs(a1))))/(max(max(abs(a2)),max(abs(a1)))); %F1: ... difference in maximum coefficient, normalized by the largest of the two coefficients
39 F2 = diff/(K−1); %F2: ...
difference in all Fourier coefficients divided by the amount of coefficients to ... give an average.
40 %% Calculating the Geometric parameters, starting by asking for the first geometry sheet 41
42 disp('Please select your first geometry sheet')
43 [firstGeoSheet, pathname1] = uigetfile('*.*', 'Pick your text file'); %Inputs ... a textfile by the users own choice
44 DATA1 = importdata(firstGeoSheet); ...
%importing the data from the txt file into matrix DATA. Textfile should be ... arranged as number−tab−number−return and repeat
45 data1 = DATA1.data; %taking ...
the numerical values of the excelsheet, given in the substructure DATA.data 46
47 [p1] = calcGparams(data1); %Output ...
of the function calcGparams, input is data1, output is p1
48 %% Asking user for second geometry sheet
49 disp('Please select your second geometry sheet')
50 [secondGeoSheet, pathname2] = uigetfile('*.*', 'Pick your text file'); %Inputs ... a textfile by the users own choice
51 DATA2 = importdata(secondGeoSheet); ...
%importing the data from the txt file into matrix DATA. Textfile should be ... arranged as number−tab−number−return and repeat
52 data2 = DATA2.data; %taking ...
the numerical values of the excelsheet, given in the substructure DATA.data 53
54 [p2] = calcGparams(data2); %Output ...
of the function calcGparams, input is data2, output is p2
55 %% Calculating all 6 geometric parameters
56 P = zeros(9,1); 57 for i = 1:9
58 P(i) = (abs(p2(i)−p1(i)))/(max(abs(p2(i)),abs(p1(i)))); ... %Calculating the differences in the first 9 geometric Features
59 end
60 G1 = (P(1)+P(2))/2; %G1: ...
difference in upper horn angle and magnitude
61 G2 = (P(3)+P(4))/2; %G2: ...
difference in lower horn angle and magnitude
62 G3 = P(5); %G3: ...
difference in total aera of ice
63 G4 = P(6); %G4: ...
difference in stagnation thickness
64 G5 = (P(7)+P(8)); %G5: ...
difference in back extent on both upper and lower surface