Study of the viability of a glider drone for the return of experiments carried by weather balloons

Bachelor s Degree in Aerospace Vehicle Engineering Study of the viability of a glider drone for the return of experiments carried by weather balloons Appendices Author: Albert Gassol Baliarda Director: Manel Soria Guerrero Co-Director: Josep Oriol Lizandra Dalmases June 12 th, 2015

Contents List of Figures List of Tables ii iii A International Standard Atmosphere 1 A.1 Temperature modeling.......................... 1 A.2 Pressure modeling............................ 2 A.2.1 Pressure above the tropopause................. 3 A.3 Density modeling............................. 3 A.4 Computational implementation and tabulated data.......... 3 B Jet streams study 7 B.1 Definition of the study.......................... 7 B.2 Results................................... 8 B.2.1 Warm months........................... 9 B.2.2 Cold months........................... 10 B.3 Conclusions................................ 11 B.4 Numerical data extracted from the jet streams maps......... 12 C Airfoil HQ 2.5/12 data 21 Bibliography 25 Albert Gasssol Baliarda i

LIST OF FIGURES List of Figures a.1 Temperature variation with altitude in the ISA............ 2 a.2 Small atmosphere element........................ 2 b.1 Jet streams map corresponding to February 3, 2015.......... 8 b.2 Relative frequencies of the jet stream speeds during the warm months 9 b.3 Relative frequencies of the jet stream speeds equals and majors than 60 kt during the warm months..................... 10 b.4 Relative frequencies of the jet stream speeds during the cold months 10 b.5 Relative frequencies of the jet stream speeds equals and majors than 60 kt during the cold months...................... 11 ii Albert Gasssol Baliarda

List of Tables a.1 International Standard Atmosphere, MSL conditions.......... 1 a.2 ISA tabulated data from the MSL up to 20000 m........... 5 b.1 Results of the analysis of the warm months.............. 9 b.2 Global results of the analysis of the warm months........... 9 b.3 Results of the analysis of the cold months............... 10 b.4 Global results of the analysis of the cold months........... 11 b.5 Numerical data of the wind speeds at 300 mbar over the Spanish territory.................................. 20 c.1 Airfoil HQ 2.5/12 data corresponding to simulations at Re = 500000 23 Albert Gasssol Baliarda iii

Appendix A International Standard Atmosphere The International Standard Atmosphere (ISA) is a mathematical model employed to know the vertical distribution of air properties such as pressure, temperature, density and speed of sound. The ISA is published by the International Organization of Standardization (ISO) as an international standard, ISO 2533:1975. The ISA is also defined in the ICAO Document 7488/2. Since the real atmosphere does not remain constant at any particular time or place, a hypothetical model must be employed as an approximation to what may be expected, so in the ISA the air is considered as a perfect gas and assumed to be devoid of dust, moisture and water vapour. It is considered to be at rest with respect to the Earth as well (that is, no winds or turbulence). The ISA considers the mean sea level (MSL) conditions as given in Table a.1. Temperature T o = 288, 15 K Pressure P o = 101325 Pa Density ρ o = 1, 225 kg/m 3 Speed of sound a o = 340, 294 m/s Acceleration of gravity g o = 9, 807 m/s 2 Table a.1: International Standard Atmosphere, MSL conditions. A.1 Temperature modeling Figure a.1 represents the temperature variation with altitude in the ISA. As it is seen, temperature decreases with altitude at a constant rate of 6.5 K/1000 m up to the tropopause, placed at an altitude of 11000 m. Therefore, the air temperature within the troposphere is given by this expression: T = T o 6.5 h 1000 (a.1) Albert Gasssol Baliarda 1

Appendix A Figure a.1: Temperature variation with altitude in the ISA [1]. From the troposphere up to 20000 m the temperature remains at a constant value of 216.65 K. A.2 Pressure modeling Pressure variations for the ISA are calculated using the hydrostatic equation, the perfect gas law and Equation (a.1). Figure a.2 shows a small atmosphere element and the forces acting on it. Figure a.2: Small atmosphere element [1]. Assuming that the atmosphere is in equilibrium, if one applies the first Newton s law it results: dp = ρgdh The equation of state for a perfect gas is: (a.2) P = ρrt (a.3) 2 Albert Gasssol Baliarda

where R = 287 J/kgK is the real gas constant for the air. Introducing (a.3) in (a.2) gives: dp P = g RT dh (a.4) Then, the relationship amongst pressure and altitude in the troposphere is obtained by integrating Equation (a.4) between h o = 0 and h: P P o dp h P = g h o RT dh = g h dh R h o T o 6.5 10 3 h P = P o (1 6.5 10 3 h T o ) 5.2561 (a.5) A.2.1 Pressure above the tropopause Temperature is constant at altitudes above the tropopause up to 20000 m, so that integrating Equation (a.4) from the tropopause to an altitude above it results in: P P 11 dp P = g RT 11 h h 11 dh P = P 11 e g RT 11 (h 11 h) (a.6) where the parameters with the subscript 11 correspond to the values at the tropopause, so T 11 = 216.65 K, P 11 = 22632.07 Pa and h 11 = 11000 m. A.3 Density modeling Since the pressure and temperature are known for a given altitude, the density is easily calculated from the perfect gas equation of state, Equation (a.3): ρ = P RT (a.7) A.4 Computational implementation and tabulated data The ISA model can be implemented as a MATLAB function, which with the altitude as the only input, returns the atmospheric parameters T, a, P and ρ corresponding to this altitude. Following it is shown the code of this MATLAB function, which is used for the model developed in Chapter 4. 1 function [ T, a, P, rho ] = ISA ( h ) 2 % ISA r e t u r n s t h e temperature (T), speed o f sound ( a ), p r e s s u r e (P) and 3 % d e n s i t y ( rho ) o f t h e Earth s atmosphere corresponding to a g i v e n 4 % a l t i t u d e, according to t h e I n t e r n a t i o n a l Standard Atmosphere ( ISA ) 5 % model. A l l t h e magnitudes are e x p r e s s e d in SI u n i t s. 6 % The f u n c t i o n i s v a l i d f o r a l t i t u d e s between 0 m and 32000 m. For n e g a t i v e Albert Gasssol Baliarda 3

Appendix A 7 % a l t i t u d e s, t h e f u n c t i o n r e t u r n s t h e MSL c o n d i t i o n s. For a l t i t u d e s majors 8 % than 32000 m t h e f u n c t i o n might r e t u r n i n c o r r e c t v a l u e s. 9 10 % MSL Conditions 11 T0 = 2 8 8. 1 5 ; % [K] 12 a0 = 3 4 0. 2 9 4 ; % [m/ s ] 13 P0 = 101325; % [ Pa ] 14 rho0 = 1. 2 2 5 ; % [ kg /mˆ3] 15 16 % Constants 17 g = 9. 8 0 6 6 5 ; % Gravity a c c e l e r a t i o n, [m/ s ˆ2] 18 Ma = 28.9644 e 3; % Molar mass o f air, [ kg /mol ] 19 R = 8. 3 1 4 4 7 2 ; % U n i v e r s a l gas constant, [ J /( mol*k) ] 20 Ra = R/Ma; % S p e c i f i c gas c o n s t a n t o f a i r [ J /( kg *K) ] 21 gam = 1. 4 ; % A d i a b a t i c gas c o n s t a n t o f t h e a i r 22 LR = 6.5e 3; % Lapse rate, [K/m] 23 LR2 = 1e 3; % Lapse rate, [K/m] 24 25 switch l o g i c a l ( t r u e ) 26 c a s e h <= 0 27 T = T0 ; % [K] 28 a = a0 ; % [m/ s ] 29 P = P0 ; % [ Pa ] 30 rho = rho0 ; % [ kg /mˆ3] 31 32 c a s e h > 0 && h <= 11000 33 T = T0+LR*h ; % [K] 34 a = sqrt (gam*ra*t) ; % [m/ s ] 35 P = P0*(1+LR*h/T0)ˆ( g/lr/ra ) ; % [ Pa ] 36 rho = P/Ra/T; % [ kg /mˆ3] 37 38 c a s e h > 11000 && h <= 20000 39 T11 = T0+LR*11 e3 ; % [K] 40 P11 = P0*(1+LR*11 e3 /T0)ˆ( g/lr/ra ) ; % [ Pa ] 41 42 T = T11 ; % [K] 43 a = sqrt (gam*ra*t) ; % [m/ s ] 44 P = P11*exp( g/ra/t11 *(h 11e3 ) ) ; % [ Pa ] 45 rho = P/Ra/T; % [ kg /mˆ3] 46 47 o t h e r w i s e 48 T11 = T0+LR*11 e3 ; % [K] 49 T20 = T11 ; % [K] 50 P11 = P0*(1+LR*11 e3 /T0)ˆ( g/lr/ra ) ; % [ Pa ] 51 P20 = P11*exp( g/ra/t11 *(20 e3 11e3 ) ) ; % [ Pa ] 52 53 T = T20+LR2*(h 20e3 ) ; % [K] 54 a = sqrt (gam*ra*t) ; % [m/ s ] 55 P = P20*(1+LR2*(h 20e3 )/ T20)ˆ( g/lr2/ra ) ; % [ Pa ] 56 rho = P/Ra/T; % [ kg /mˆ3] 4 Albert Gasssol Baliarda

57 58 end 59 60 end In Table a.2 it has been tabulated the ISA parameters from the MSL up to an altitude of 20000 m. Altitude (m) Altitude (ft) Temperature (K) Pressure (Pa) Density (kg/m 3 ) θ = T/T o δ = P/P o σ = ρ/ρ o 0 0 288,15 101325 1,225 1 1 1 500 1640,42 284,90 95461 1,167 0,9887 0,9421 0,9529 1000 3280,84 281,65 89875 1,112 0,9774 0,8870 0,9075 1500 4921,26 278,40 84556 1,058 0,9662 0,8345 0,8637 2000 6561,68 275,15 79495 1,0063 0,9549 0,7846 0,8216 2500 8202,10 271,90 74683 0,957 0,9436 0,7371 0,7811 3000 9842,52 268,65 70109 0,909 0,9323 0,6919 0,7421 3500 11482,94 265,40 65764 0,863 0,9210 0,6490 0,7047 4000 13123,36 262,15 61640 0,819 0,9098 0,6083 0,6687 4500 14763,78 258,90 57728 0,777 0,8985 0,5697 0,6341 5000 16404,20 255,65 54020 0,736 0,8872 0,5331 0,6009 5500 18044,62 252,40 50507 0,697 0,8759 0,4985 0,5691 6000 19685,04 249,15 47181 0,660 0,8647 0,4656 0,5385 6500 21325,46 245,90 44035 0,624 0,8534 0,4346 0,5093 7000 22965,88 242,65 41061 0,590 0,8421 0,4052 0,4812 7500 24606,30 239,40 38251 0,557 0,8308 0,3775 0,4544 8000 26246,72 236,15 35600 0,525 0,8195 0,3513 0,4287 8500 27887,14 232,90 33099 0,495 0,8083 0,3267 0,4042 9000 29527,56 229,65 30742 0,466 0,7970 0,3034 0,3807 9500 31167,98 226,40 28524 0,439 0,7857 0,2815 0,3583 10000 32808,40 223,15 26436 0,413 0,7744 0,2609 0,3369 10500 34448,82 219,90 24474 0,388 0,7631 0,2415 0,3165 11000 36089,24 216,65 22632 0,364 0,7519 0,2234 0,2971 11500 37729,66 216,65 20916 0,336 0,7519 0,2064 0,2746 12000 39370,08 216,65 19330 0,311 0,7519 0,1908 0,2537 12500 41010,50 216,65 17865 0,287 0,7519 0,1763 0,2345 13000 42650,92 216,65 16510 0,265 0,7519 0,1629 0,2167 13500 44291,34 216,65 15259 0,245 0,7519 0,1506 0,2003 14000 45931,76 216,65 14102 0,227 0,7519 0,1392 0,1851 14500 47572,18 216,65 13033 0,210 0,7519 0,1286 0,1711 15000 49212,60 216,65 12045 0,194 0,7519 0,1189 0,1581 15500 50853,02 216,65 11131 0,179 0,7519 0,1099 0,1461 16000 52493,44 216,65 10287 0,165 0,7519 0,1015 0,1350 16500 54133,86 216,65 9508 0,153 0,7519 0,0938 0,1248 17000 55774,28 216,65 8787 0,141 0,7519 0,0867 0,1153 17500 57414,70 216,65 8121 0,131 0,7519 0,0801 0,1066 18000 59055,12 216,65 7505 0,121 0,7519 0,0741 0,0985 18500 60695,54 216,65 6936 0,112 0,7519 0,0685 0,0910 19000 62335,96 216,65 6410 0,103 0,7519 0,0633 0,0841 19500 63976,38 216,65 5924 0,095 0,7519 0,0585 0,0778 20000 65616,80 216,65 5475 0,088 0,7519 0,0540 0,0719 Table a.2: ISA tabulated data from the MSL up to 20000 m. Albert Gasssol Baliarda 5

Appendix B Jet streams study Jet streams are narrow fast flowing air currents, located at an altitude near the tropopause. There are mainly two jet streams in the Earth that go over the planet from West to East: the polar jet and the subtropical jet. Europe (and Spain) is mostly affected be the polar jet, which is usually located between latitudes 50 N and 60 N at altitudes around 7 12 km, and can reach speeds greater than 100 km/h. Due to the high speeds of the air at these altitudes, it is necessary to have an idea of the order of these air speeds to see the conditions at which the drone will be subjected. B.1 Definition of the study This study consists on a statistical analysis of the jet streams maps to determine how jet streams usually are in the regions of interest. To do this, it has been employed the California Regional Weather Server 1 resource from the San Francisco State University (SFSU), where there is available, amongst others, an archive with the jet streams maps of several regions of the planet and some other meteorological data of the last four years. These jet streams maps are elaborated using the Global Forecast System 2 (GFS) model and are always calculated at the altitude corresponding to 300 mbar, this means, about 9150 m. Figure b.1 shows how these maps look. Following it is explained the considerations that it have been done and how the analysis has been carried out: ˆ The analysis is done since the 1 st of March of 2014 till the 28 th of February of 2015, this means, it covers a period of one year. ˆ The data that is considered in the study belongs to the Spanish territory, concretely the north-eastern zone. 1 the resource can be found in [2]. 2 Global numerical weather prediction system containing a global computer model and variational analysis run by the US National Weather Service (NWS). Albert Gasssol Baliarda 7

Appendix B Figure b.1: Jet streams map corresponding to February 3 rd, 2015. Extracted from [2]. ˆ The maps from the California Regional Weather Server display the overall velocity field with vector arrows, but only gives a numerical value to the velocities exceeding 60 kt. Due to this fact, it is treated apart the days at which wind speeds majors than 60 kt were detected from the days at which wind speeds were less than 60 kt (values that can be considered as usual values). ˆ Initially, it is considered apart the data belonging to warm months (April, May, June, July, August and September) from the belonging to cold months (March, October, November, December, January and February) to see if there exists or not a significant difference amongst them. ˆ The data was extracted from the maps twice daily, at 12am and 12pm local time. It was done to see if the sun affects or not in the jet stream intensity. B.2 Results In this section there are shown the results of the numerical data extracted from the jet streams maps. The numerical data can be seen in Table b.5 of Section B.4. 8 Albert Gasssol Baliarda

B.2.1 Warm months Table b.1 and Figure b.2 show the results obtained from the analysis of the previously called warm months (April, May, June, July, August and September), separating the data extracted at 12am and 12pm. 12am 12pm % Speeds < 60 kt 55,74% 50,82% % Speeds > 60 kt 44,26% 49,18% Average > 60 kt(kt) 70,62 70,78 Standard deviation (kt) 11,66 12,20 Table b.1: Results of the analysis of the warm months. Figure b.2: Relative frequencies of the jet stream speeds during the warm months. It does not exist any clear difference between the values taken at 12am and the ones taken at 12pm, so it will be better considered together. Table b.2 gathers all the results, and Figure b.3 considers only the registered wind speeds equals and majors than 60 knots and represents their relative frequencies. Total % speeds < 60 kt 53,28% % speeds > 60 kt 46,72% Average > 60 kt(kt) 70,7 Standard deviation (kt) 11,91 Table b.2: Global results of the analysis of the warm months. Albert Gasssol Baliarda 9

Appendix B Figure b.3: Relative frequencies of the jet stream speeds equals and majors than 60 kt during the warm months. B.2.2 Cold months In the same way that it has been done previously, Table b.3 and Figure b.4 show the results of the analysis of the cold months (March, October, November, December, January and February). 12am 12pm % Speeds < 60 kt 51,10% 51,10% % Speeds > 60 kt 48,90% 48,90% Average > 60 kt(kt) 77,08 75,39 Standard deviation (kt) 19,84 18,03 Table b.3: Results of the analysis of the cold months. Figure b.4: Relative frequencies of the jet stream speeds during the cold months. 10 Albert Gasssol Baliarda

As it occurs in the warm months, it does not exist a significant difference between the values from 12am and 12pm, so that it will be assumed that it does not exist any dependence with the hour of the day in any of the two cases. According to this, Table b.4 gathers the results in a single table and Figure b.5 represents the relative frequencies of the registered wind speeds equals and majors than 60 kt, as Figure b.3 does. Total % Speeds < 60 kt 51,10% % Speeds > 60 kt 48,90% Average > 60 kt(kt) 76,24 Standard deviation (kt) 18,92 Table b.4: Global results of the analysis of the cold months. Figure b.5: Relative frequencies of the jet stream speeds equals and majors than 60 kt during the cold months. B.3 Conclusions According to the results, wind speeds only exceed the value of 60 knots a half of the times roughly, and when it occurs, the great majority of the registered wind speeds are between 60 kt and 70 kt. Extreme values like 120 150 kt only occur in isolated days and quite randomly, so these values should not be considered as representatives. It is also remarkable that the average of the wind speeds majors than 60 kt is slightly major (5.54%) during the cold months than during the warm months, but the difference is not enough to be worth being considered. Albert Gasssol Baliarda 11

Appendix B B.4 Numerical data extracted from the jet streams maps Table b.5 shows the numerical data extracted from the California Regional Weather Server jet streams maps. Cells containing a hyphen mean that the registered wind speeds were less than 60 kt. Day 12am Velocity (knots) 12pm March 2014 1 110 110 2 70 80 3 110 90 4 90 110 5 90 100 6 80-7 - - 8 - - 9 - - 10 - - 11 70-12 70 60 13-60 14 - - 15-70 16 70-17 - - 18 - - 19 - - 20 - - 21 - - 22 60 70 23 60 70 24 90 60 25 90 90 26 90 70 27 70 70 28 70 70 29 60 60 30 70-31 - 60 April 2014 1 60 60 2 70 70 3 60-4 70 90 5 70 60 12 Albert Gasssol Baliarda

6 - - 7 - - 8 60 70 9 - - 10-60 11 70 60 12 70 70 13 70-14 - - 15 - - 16 60-17 - - 18 - - 19-70 20 70 80 21 70 70 22-70 23 60 60 24 60 80 25 90 80 26 60 70 27 90 90 28 70 70 29 - - 30-60 May 2014 1-70 2 70 100 3 90 90 4 60-5 - - 6 - - 7 - - 8 - - 9 - - 10 - - 11 60 70 12 90 100 13 130 120 14 60 60 15 60 60 16 80-17 - - 18 - - 19-70 20 70 90 Albert Gasssol Baliarda 13

Appendix B 21 80 100 22 100 90 23-60 24 70 60 25-70 26 70 70 27 60 60 28 70 70 29 90 90 30 70 60 31 60 60 June 2014 1 70 60 2 - - 3 70-4 - 70 5 - - 6-60 7 80 60 8 60-9 - - 10 - - 11 - - 12 - - 13 - - 14 - - 15 70 60 16 60-17 - - 18-60 19 70-20 - - 21 - - 22 - - 23-70 24 70 70 25 - - 26-70 27 60 70 28-70 29 70 90 30 60 - July 2014 1-70 2 60 70 3 80 90 14 Albert Gasssol Baliarda

4 70-5 - - 6 - - 7 80 80 8 60 60 9 - - 10 - - 11 - - 12 - - 13-60 14 - - 15 - - 16 - - 17 - - 18 60 70 19 80 90 20 90 90 21 80 60 22 - - 23 - - 24 - - 25-60 26 - - 27 - - 28 - - 29 70 70 30 - - 31 - - August 2014 1-60 2 70 60 3 60 70 4 70 70 5 - - 6 - - 7 - - 8 - - 9 - - 10 - - 11-70 12 70 70 13 80 70 14 70 90 15 90 70 16 70-17 - - Albert Gasssol Baliarda 15

Appendix B 18-60 19-60 20 60 70 21 70 60 22 70 60 23 - - 24 - - 25 - - 26 - - 27 - - 28 - - 29 - - 30 - - 31 - - September 2014 1 - - 2 - - 3 - - 4 - - 5 - - 6 - - 7 - - 8 - - 9 - - 10-70 11 60-12 - - 13-60 14 60 70 15 70 60 16-60 17 70-18 60 60 19 60 70 20 70 70 21 70 70 22 70 70 23 - - 24 - - 25 80 70 26 70 60 27 60-28 - - 29 - - 30 - - October 2014 16 Albert Gasssol Baliarda

1 - - 2 - - 3 - - 4 - - 5 - - 6 - - 7-60 8 60-9 - 60 10 60 60 11 - - 12 60 60 13 90 70 14 60 100 15-60 16 70 60 17 70-18 - - 19 - - 20 - - 21 - - 22 - - 23 - - 24 - - 25 - - 26 - - 27 - - 28 - - 29 - - 30 - - 31 - - November 2014 1 - - 2 - - 3-60 4 60 80 5 80 80 6 140 110 7 60 60 8 60 60 9 60 90 10 100-11 - 80 12 120 70 13 80-14 70 70 Albert Gasssol Baliarda 17

Appendix B 15 90 70 16 80 90 17 90 110 18 70-19 - - 20 - - 21 - - 22 - - 23 - - 24 - - 25 - - 26 - - 27 - - 28-80 29 70 60 30 60 110 December 2014 1 60 60 2 100 70 3 - - 4 - - 5-70 6-60 7 70 70 8 60 60 9 150 130 10 70-11 60-12 - - 13-60 14 80 70 15-60 16 60 90 17 90 70 18 - - 19 - - 20 - - 21 - - 22 - - 23 - - 24 - - 25 - - 26 - - 27 60 90 28 90 90 29 100-18 Albert Gasssol Baliarda

30 80 70 31 - - January 2015 1 - - 2 60-3 - - 4 - - 5 - - 6 - - 7-60 8 - - 9 - - 10 - - 11-60 12 60-13 60-14 70-15 - - 16 70 70 17 70 70 18 - - 19 100 110 20 - - 21-60 22 70 90 23 70 80 24 60-25 80 70 26 60 60 27 80 70 28 60 60 29 60 70 30 100 150 31 150 80 February 2015 1 70 70 2 70 60 3 60 70 4 70 60 5-60 6 60-7 - 70 8 90 90 9 70-10 - 60 11 70 60 Albert Gasssol Baliarda 19

Appendix B 12 - - 13-60 14 70 90 15 - - 16 60-17 - - 18 - - 19 - - 20 60-21 80 70 22 110 100 23-90 24 90 90 25 100 80 26 - - 27 80 80 28 60 60 Table b.5: Numerical data of the wind speeds at 300 mbar over the Spanish territory extracted from the California Regional Weather Server maps. 20 Albert Gasssol Baliarda

Appendix C Airfoil HQ 2.5/12 data The following table (Table c.1) contains the numerical information of the aerodynamic airfoil HQ 2.5/12 (available in [3]) from which have been done the airfoil graphs of Chapter 3, Section 3.2. α (deg) C l C d C dp C m Top Xtr Bot Xtr -10,75-0,4130 0,0969 0,0946-0,0433 1 0,0236-10,5-0,5896 0,0503 0,0479-0,0690 1 0,0120-10,25-0,6196 0,0453 0,0428-0,0708 1 0,0118-10 -0,6528 0,0432 0,0407-0,0668 1 0,0117-9,75-0,6799 0,0369 0,0338-0,0675 0,9950 0,0115-9,5-0,6719 0,0298 0,0261-0,0717 0,9869 0,0116-9,25-0,6471 0,0262 0,0219-0,0745 0,9832 0,0119-9 -0,6216 0,0236 0,0190-0,0760 0,9780 0,0123-8,75-0,5920 0,0216 0,0168-0,0777 0,9742 0,0126-8,5-0,5585 0,0204 0,0153-0,0796 0,9714 0,0130-8,25-0,5321 0,0180 0,0127-0,0808 0,9665 0,0141-8 -0,5029 0,0172 0,0118-0,0816 0,9604 0,0150-7,75-0,4719 0,0163 0,0107-0,0827 0,9559 0,0160-7,5-0,4468 0,0155 0,0098-0,0824 0,9475 0,0168-7,25-0,4200 0,0145 0,0087-0,0825 0,9412 0,0181-7 -0,3973 0,0138 0,0079-0,0817 0,9320 0,0199-6,75-0,3707 0,0133 0,0074-0,0815 0,9254 0,0221-6,5-0,3472 0,0127 0,0068-0,0808 0,9168 0,0257-6,25-0,3204 0,0125 0,0066-0,0806 0,9101 0,0302-6 -0,2963 0,0120 0,0060-0,0800 0,9020 0,0357-5,75-0,2694 0,0119 0,0058-0,0798 0,8955 0,0402-5,5-0,2448 0,0114 0,0053-0,0793 0,8876 0,0453-5,25-0,2181 0,0112 0,0050-0,0791 0,8813 0,0499-5 -0,1915 0,0111 0,0048-0,0788 0,8739 0,0531-4,75-0,1661 0,0106 0,0043-0,0784 0,8678 0,0601-4,5-0,1394 0,0105 0,0041-0,0782 0,8605 0,0653-4,25-0,1134 0,0101 0,0037-0,0779 0,8544 0,0740-4 -0,0871 0,0098 0,0034-0,0776 0,8474 0,0867 Albert Gasssol Baliarda 21

Appendix C -3,75-0,0608 0,0094 0,0031-0,0774 0,8411 0,1122-3,5-0,0356 0,0089 0,0029-0,0772 0,8345 0,1845-3,25-0,0104 0,0083 0,0026-0,0770 0,8279 0,2783-3 0,0138 0,0077 0,0024-0,0768 0,8216 0,4196-2,75 0,0395 0,0073 0,0024-0,0764 0,8146 0,5077-2,5 0,0665 0,0072 0,0024-0,0761 0,8085 0,5551-2,25 0,0938 0,0072 0,0023-0,0759 0,8012 0,5841-1,75 0,1490 0,0072 0,0023-0,0755 0,7882 0,6298-1,5 0,1770 0,0072 0,0023-0,0754 0,7823 0,6450-1,25 0,2047 0,0072 0,0023-0,0752 0,7757 0,6602-1 0,2320 0,0072 0,0023-0,0749 0,7685 0,6794-0,75 0,2593 0,0072 0,0023-0,0746 0,7603 0,6937-0,5 0,2869 0,0072 0,0023-0,0744 0,7525 0,7037-0,25 0,3143 0,0072 0,0023-0,0742 0,7436 0,7127 0 0,3420 0,0073 0,0023-0,0740 0,7355 0,7226 0,25 0,3693 0,0073 0,0023-0,0737 0,7265 0,7321 0,5 0,3969 0,0073 0,0023-0,0736 0,7190 0,7405 0,75 0,4246 0,0073 0,0023-0,0735 0,7110 0,7477 1 0,4523 0,0073 0,0023-0,0734 0,7028 0,7544 1,25 0,4797 0,0073 0,0023-0,0732 0,6943 0,7616 1,5 0,5072 0,0074 0,0023-0,0731 0,6848 0,7687 1,75 0,5345 0,0074 0,0023-0,0729 0,6754 0,7762 2 0,5616 0,0074 0,0024-0,0727 0,6655 0,7838 2,25 0,5887 0,0074 0,0024-0,0725 0,6546 0,7920 2,5 0,6155 0,0075 0,0024-0,0722 0,6433 0,8001 3 0,6683 0,0075 0,0026-0,0715 0,6168 0,8184 3,25 0,6942 0,0076 0,0026-0,0710 0,6004 0,8285 3,5 0,7197 0,0077 0,0027-0,0705 0,5819 0,8399 3,75 0,7444 0,0078 0,0028-0,0698 0,5613 0,8527 4 0,7684 0,0079 0,0029-0,0690 0,5380 0,8681 4,25 0,7909 0,0080 0,0030-0,0679 0,5111 0,8899 4,5 0,8149 0,0081 0,0031-0,0670 0,4785 0,9327 4,75 0,8505 0,0085 0,0033-0,0690 0,4390 1 5 0,8731 0,0089 0,0036-0,0683 0,3999 1 5,25 0,8953 0,0094 0,0038-0,0675 0,3621 1 5,5 0,9179 0,0098 0,0041-0,0668 0,3299 1 5,75 0,9402 0,0102 0,0044-0,0660 0,3026 1 6 0,9632 0,0106 0,0047-0,0654 0,2813 1 6,25 0,9863 0,0110 0,0051-0,0647 0,2648 1 6,5 1,0095 0,0114 0,0054-0,0640 0,2502 1 6,75 1,0325 0,0117 0,0057-0,0633 0,2355 1 7 1,0549 0,0121 0,0060-0,0626 0,2189 1 7,25 1,0768 0,0125 0,0063-0,0617 0,2011 1 7,5 1,0988 0,0129 0,0067-0,0609 0,1848 1 7,75 1,1201 0,0133 0,0071-0,0600 0,1679 1 8 1,1405 0,0138 0,0075-0,0590 0,1513 1 22 Albert Gasssol Baliarda

8,25 1,1605 0,0143 0,0079-0,0579 0,1367 1 8,5 1,1800 0,0148 0,0083-0,0567 0,1232 1 8,75 1,1983 0,0153 0,0088-0,0553 0,1088 1 9 1,2157 0,0159 0,0093-0,0539 0,0952 1 9,25 1,2314 0,0165 0,0099-0,0521 0,0824 1 9,5 1,2457 0,0171 0,0104-0,0501 0,0705 1 9,75 1,2580 0,0178 0,0111-0,0478 0,0570 1 10 1,2633 0,0190 0,0121-0,0447 0,0310 1 10,25 1,2643 0,0205 0,0134-0,0412 0,0136 1 10,5 1,2730 0,0216 0,0145-0,0388 0,0107 1 10,75 1,2842 0,0225 0,0155-0,0369 0,0096 1 11 1,2940 0,0235 0,0167-0,0349 0,0088 1 11,25 1,3020 0,0247 0,0179-0,0328 0,0083 1 11,5 1,3058 0,0263 0,0196-0,0305 0,0078 1 11,75 1,3135 0,0276 0,0210-0,0288 0,0076 1 12 1,3203 0,0290 0,0225-0,0271 0,0074 1 12,25 1,3252 0,0306 0,0242-0,0255 0,0073 1 12,5 1,3287 0,0324 0,0261-0,0239 0,0071 1 12,75 1,3316 0,0343 0,0281-0,0226 0,0069 1 13 1,3328 0,0364 0,0304-0,0213 0,0068 1 13,25 1,3331 0,0388 0,0328-0,0203 0,0066 1 13,5 1,3324 0,0413 0,0355-0,0195 0,0063 1 13,75 1,3304 0,0441 0,0384-0,0189 0,0063 1 14 1,3273 0,0471 0,0415-0,0185 0,0062 1 14,25 1,3227 0,0504 0,0449-0,0184 0,0061 1 14,5 1,3185 0,0539 0,0485-0,0186 0,0061 1 14,75 1,3125 0,0577 0,0525-0,0191 0,0060 1 15 1,3068 0,0617 0,0566-0,0199 0,0060 1 15,25 1,2968 0,0665 0,0616-0,0212 0,0059 1 15,5 1,2913 0,0709 0,0661-0,0225 0,0059 1 15,75 1,2815 0,0761 0,0713-0,0243 0,0058 1 16 1,2772 0,0806 0,0760-0,0260 0,0059 1 16,25 1,2667 0,0862 0,0817-0,0282 0,0058 1 16,5 1,2612 0,0912 0,0869-0,0304 0,0059 1 Table c.1: Airfoil HQ 2.5/12 data corresponding to simulations at Re = 500000. Extracted from [3]. Albert Gasssol Baliarda 23

Bibliography [1] Mustafa Cavcar. The International Standard Atmosphere (ISA). In: Anadolu University, Turkey (2000), pp. 1 7. [2] San Francisco State University. California Regional Weather Server. 2010. url: http: //squall.sfsu.edu/crws.html (visited on 03/16/2015). [3] HQ 2.5/12 AIRFOIL. url: NoTithttp://airfoiltools.com/airfoil/details? airfoil=hq2512-ille (visited on 04/30/2015). Albert Gasssol Baliarda 25