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\title{The Effect of Supersonic Flows on Different Profiles of Aircraft Wings}
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\begin{document}

             \author[1]{Ahmed Soliman  M.Sherif}

             \affil[1]{  Novosibirsk State Technical University}

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\date{\small \em Received: 9 December 2016 Accepted: 31 December 2016 Published: 15 January 2017}

\maketitle


\begin{abstract}
        


When a supersonic stream flows around a thin profile, the pressure acting on the surface element does not depend on the shape of the rest of the profile, but depends only on the slope of the element itself, that is, on the local angle of attack. The local angle of attack is the angle between the surface element and the velocity vector of the undisturbed flow Coefficient of pressure. 

\end{abstract}


\keywords{CAE, frequencies, dynamic, stress, deformation, CNC.}

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\let\tabcellsep& 	 	 		 \par
Fig.  {\ref 1} It can be seen from the graph 1. that the most advantageous angle of attack of an airplane is greater than the most advantageous angle of attack of the wing by (2º÷3º). 
\section[{I. Introduction}]{I. Introduction}\par
The aim of my research is Determining the coefficient of profile-wave resistance for the four profiles which shown with relative thickness ??? =5\% , With the number M?=2.5. Construct the pressure distribution diagram for each profile at angles of attack ?? = 0,?5º,+5º.    The coefficient of profile-wave resistance:? ? = ? 2 ? ? ?? ?? ? 2 ? 1 = ? 2 ? (?0.0499584) ?2.5 2 ? 1 = 0.0436 Area BD ? ?? = ? + ? 2 = 0 + ? ?? = ?? ?? = 0.049958 rad=2.862405°=2°51 ? 45 ?? ? ? = ? 2 ? ? ?? ?? ? 2 ? 1 = ? 2 ? 0.0499584 ?2.5 2 ? 1 = ?0.0436 Area AC ? ?? = ?? ?? = ?0.04996 rad= ? 2.86241°= ? 2°51 ? 45 ?? ? ? = ? 2 ? ? ?? ?? ? 2 ? 1 = ? 2 ? (?0.0499584) ?2.5 2 ? 1 = 0.0436 Area CD ? ?? = ?? ?? = 0.049958 rad=2.862405°=2°51 ? 45 ?? ? ? = ? 2 ? ? ?? ?? ? 2 ? 1 = ? 2 ? (0.0499584) ?2.? ? = ? 2 ? ? ?? ?? ? 2 ? 1 = ? 2 ? (?0.13722486) ?2..71059°=?0°42 ? 38 ?? 2 ? ? ?? 2 ? (?0.01240219) ? = ? = ? = 0.0108 ? ?? ? 2 ? 1 ? 2.5 2 ? 1 Area AC ? ?? = ?? = ?0.08727 ???= ? 5°? ? = ? 2 ? ? ?? ?? ? 2 ? 1 = ? 2 ? (?0.08726646) ?2.5 2 ? 1 = 0.0762 Area BC ? ?? = ? + ? = 0.08726646 + 0.09966865 = 0.186935 rad=10.71059°=10°42 ? 38 ?? ? ? = ? 2 ? ? ?? ?? ? 2 ? 1 = ? 2 ? (0.18693511) ?2.5 2 ? 1 = ?0.1632 ?ð??" ( ? 2 ) =\textbf{5}? ? = 4 ? ? 2 ?? ? 2 ? 1 + ? 1 ? ?? 2 ?? ? 2 ? 1\par
Parameter K1 depends on the shape of the profile: ? 1 = 2 ? [( ?? u ? ??? ) 2 + ( ?? L ? ??? ) 2 ] ??? 1 0 ?? U ? ??? = 1 ?? ? ?? U ?? ?? ?? ? ??ð??"??L L U ? ?? ?? = 2 ???? U ???? = ?? 2 , ???? U ??? ????? = 1 ? ?????? ????? ???????????????? ???? ???? U ???? = ? ?? 2 , ???? U ??? ????? = ?1 ? ?????? ????? ???????????????? ???? ???? L ???? = ? ?? 2 , ???? L ??? ????? = ?1 ? ?????? ????? ???????????????? ???? ???? L ???? = ?? 2 , ???? L ??? ????? = 1 ? ?????? ????? ???????????????? ???? Year\par
Then the parameter K1 for profile 1 will be equal to? 1 = 2 ? (1 2 ? 0.5 + (?1) 2 ? 0.5 + (?1) 2 ? 0.5 + 1 2 ? 0.5) = 2 ? 2 = 4\par
Defining the value of the parameter K1 for profile 2:\par
Defining the value of the parameter K1 for profile 4:\par
The Then the parameter K1 for profile 3 will be equal to?? 1 = 2 ? ((0.5) 2 ? 1 + (?0.5) 2 ? 1) = 2 ? 0.5 = 1\par
By determining the parameter K1 for each profile, we can calculate the coefficients of the profile-wave resistance for given angles of attack: ? 1 = 16 3 ? 1 = 4 ? = 0°=0 rad ? ? = 4 ? ? 2 ?? ? 2 ? 1 + ? 1 ? ? 2 ?? ? 2 ? 1 = 4 ? 0 2 ?2.5 2 ? 1 + 4 ? 0.05 2 ?2.5 2 ? 1 = 0.0044 ? = ±5°=±0.087266 rad ? ? = 4 ? ? 2 ?? ? 2 ? 1 + ? 1 ? ? 2 ?? ? 2 ? 1 = 4 ? 0.08726646 2 ?2.5 2 ? 1 + 4 ? 0.05 2 ?2.5 2 ? 1 = 0.0177 ? 1 = 8 ? = 0°=0 rad ? ? = 4 ? ? 2 ?? ? 2 ? 1 + ? 1 ? ? 2 ?? ? 2 ? 1 = 4 ? 0 2 ?2.5 2 ? 1 + 8 ? 0.05 2 ?2.5 2 ? 1 = 0.0087 ? = ±5°=±0.087266 rad ? ? = 4 ? ? 2 ?? ? 2 ? 1 + ? 1 ? ? 2 ?? ? 2 ? 1 = 4 ? 0.08726646 2 ?2.5 2 ? 1 + 8 ? 0.05 2 ?2.5 2 ? 1 = 0.022 ? 1 = 1 ? = 0°=0 rad? ? = 4 ? ? 2 ?? ? 2 ? 1 + ? 1 ? ? 2 ?? ? 2 ? 1 = 4 ? 0 2 ?2.5 2 ? 1 + 1 ? 0.05 2 ?2.5 2 ? 1 = 0.0011 ? = ±5°=±0.087266 rad ? ? = 4 ? ? 2 ?? ? 2 ? 1 + ? 1 ? ? 2 ?? ? 2 ? 1 = 4 ? 0.08726646 2 ?2.5 2 ? 1 + 1 ? 0.05 2 ?2.5 2 ? 1 = 0.0144 ? 1 = 16 3 = 5.333 ? = 0°=0 rad ? ? = 4 ? ? 2 ?? ? 2 ? 1 + ? 1 ? ? 2 ?? ? 2 ? 1 = 4 ? 0 2 ?2.5 2 ? 1 + 5.333 ? 0.05 2 ?2.5 2 ? 1 = 0.0058 ? = ±5°=±0.087266 rad ? ? = 4 ? ? 2 ?? ? 2 ? 1 + ? 1 ? ? 2 ?? ? 2 ? 1 = 4 ? 0.08726646 2 ?2.5 2 ? 1 + 5.333 ? 0.05 2 ?2.5 2 ? 1 = 0.0191 IV. Conclusions 1.\par
As the angle of attack increases to a certain value, the aerodynamic quality increases. At a certain angle of attack, the quality reaches a maximum value of ????????. This angle is called the most advantageous angle of attack, ??????? ???????? ??????????????ð??"ð??"????????.\par
2. On the angle of attack of the zero lifting force, where ????=0, the aerodynamic quality will be zero. 3. The effect on the aerodynamic quality of the profile shape is related to the relative thickness and curvature of the profile. The shape of the profile contours, the shape of the sock and the position of the maximum profile thickness along the chord 4. To obtain large values of ????????, the optimum thickness and curvature of the profile, the shape of the contours and the extension of the wing are selected. 5. To obtain the highest quality values, the best shape of the wing is elliptical with a rounded leading edge.\par
6. The zero lifting force angle ?? 0 is at the intersection of the polar with the axis ????. At this angle of attack, the coefficient of lift is zero (????=0). For the wings of modern aircraft, usually (?? 0 =2º÷0º). For modern wings, ??????? ???????? ??????????????ð??"ð??"???????? lies within (?? 0 =4º÷6º). \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Fig. 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-5.png}
\caption{\label{fig_3}?}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_4}A}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-7.png}
\caption{\label{fig_5}2 ?}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-8.png}
\caption{\label{fig_6}Profile 4 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-9.png}
\caption{\label{figure9}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-10.png}
\caption{\label{figure10}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-11.png}
\caption{\label{figure11}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-12.png}
\caption{\label{figure12}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-13.png}
\caption{\label{figure13}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-14.png}
\caption{\label{figure14}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-15.png}
\caption{\label{figure15}}\end{figure}
 			\footnote{© 2017 Global Journals Inc. (US)} 			\footnote{© 2017 Global Journals Inc. (US) ? = 0.099917 rad=5.724822°= 5°43 ? 29 ??} 		 		\backmatter  			  				\begin{bibitemlist}{1}
\bibitem[Byshgens and Studnev ()]{b4}\label{b4} 	 		‘Aerodynamics of aircraft. Dynamics of longitudinal and lateral movement’.  		 			G S Byshgens 		,  		 			R V Studnev 		.  	 	 		\textit{Mechanical Engineering}  		1979.  	 
\bibitem[Kalachev ()]{b6}\label{b6} 	 		‘Airplane, pilot and safety of flight’.  		 			G S Kalachev 		.  	 	 		\textit{Mechanical Engineering}  		1979.  	 
\bibitem[Arzhannikov and Sadekova ()]{b0}\label{b0} 	 		 			N S Arzhannikov 		,  		 			G S Sadekova 		.  	 	 		\textit{Aerodynamics of aircraft},  				 (Moscow)  		1984.  	 
\bibitem[At the points of intersection, we find the angles of attack (?? 1 & ?? 2 ) When flying, where the aerodynamic quality will be the same and necessarily smaller]{b10}\label{b10} 	 		\textit{At the points of intersection, we find the angles of attack (?? 1 \& ?? 2 ) When flying, where the aerodynamic quality will be the same and necessarily smaller},  		 	 	 (Angles of attack with the same aerodynamic quality are carried out from the origin of the coordinates of the secant to the field) 
\bibitem[Bochkarev ()]{b1}\label{b1} 	 		 			A F Bochkarev 		.  		\textit{Aeromechanics aircraft. Mechanical engineering press},  				 (Moscow)  		1985.  	 
\bibitem[Byshgens and Studnev ()]{b2}\label{b2} 	 		‘Dynamics of the plane's spatial motion’.  		 			G S Byshgens 		,  		 			R V Studnev 		.  	 	 		\textit{Mechanical Engineering}  		1967.  	 
\bibitem[Byshgens and Studnev ()]{b3}\label{b3} 	 		‘Dynamics of the plane's spatial motion’.  		 			G S Byshgens 		,  		 			R V Studnev 		.  	 	 		\textit{Mechanical Engineering}  		1967.  	 
\bibitem[Salenko and Obuhovsky ()]{b8}\label{b8} 	 		\textit{Flight Dynamics},  		 			S D Salenko 		,  		 			A D Obuhovsky 		.  		2014. Novosibirsk: NSTU press.  	 
\bibitem[Ostoslavsky and Strazheva ()]{b7}\label{b7} 	 		\textit{Flight dynamics. The trajectories of the summerenforcement apparatus},  		 			I V Ostoslavsky 		,  		 			I V Strazheva 		.  		1969. Moscow: Mechanical engineering press.  	 
\bibitem[Guskov and Zaiganov ()]{b5}\label{b5} 	 		 			Y P Guskov 		,  		 			G I Zaiganov 		.  	 	 		\textit{Airplane flight control},  				 (Moscow)  		1980.  	 
\bibitem[The angle of attack of the zero lifting force (?) of the aircraft is practically no different from the angle of attack of the zero lift of the wing. Since the lifting force is zero on the angle, at this angle of attack only the vertical movement of the aircraft downward, called a vertical dive]{b9}\label{b9} 	 		\textit{The angle of attack of the zero lifting force (?) of the aircraft is practically no different from the angle of attack of the zero lift of the wing. Since the lifting force is zero on the angle, at this angle of attack only the vertical movement of the aircraft downward, called a vertical dive},  		 	 	 (at an angle of 90º is possible) 
\end{bibitemlist}
 			 		 	 
\end{document}
