physics report

\documentclass[5p,sort&compress]{elsarticle} \usepackage{amssymb} % Mathematical symbols \usepackage{amsmath} % More options for mathematics \usepackage{subfigure} % More options for figures \usepackage{epstopdf} % Convert eps to pdf \usepackage[separate-uncertainty=true]{siunitx} % Proper formatting of units in math mode \usepackage{color} % Supports text color if needed \usepackage{soul} % https://ctan.org/pkg/soul \usepackage{lmodern} % Loading fonts \usepackage{hyperref} % To insert clickable references/urls \usepackage{listings} % To input code in the text \usepackage{amsmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage{graphicx} \usepackage{epstopdf} \usepackage{booktabs} \setlength{\parskip}{2em} \definecolor{green}{rgb}{0,0.6,0} \newcommand{\stirlingii}{\genfrac{\{}{\}}{0pt}{}} % Choose the style of the reference list (do not change) \bibliographystyle{elsarticle-num} \journal{supervisor} % Begin the document \begin{document} \begin{frontmatter} \title{Title of the Report } \author{A. Partner, B. Partner, and C. Partner} \date{\today} % \address{[email protected]} \begin{abstract} The report abstract is a short summary of the report. It is usually one paragraph (100-200 words) and should include about one or two sentences on each of the following main points: \begin{enumerate} \item Purpose of the experiment \item Key results \item Major points of discussion \item Main conclusions \end{enumerate} Tip: It may be helpful if you complete the other sections of the report before writing the abstract. You can basically draw these four main points from them. \\ \textcolor {green} {example: In this experiment a very important physical effect was studied by measuring the dependence of a quantity $V$ of the quantity $X$ for two different sample temperatures. The experimental measurements confirmed the quadratic dependence $V = kX^2$ predicted by Someone's first law. The value of the mystery parameter $k = 15.4\pm 0.5$~s was extracted from the fit. This value is not consistent with the theoretically predicted $k_{theory}=17.34$~s. This discrepancy is attributed to low efficiency of the $V$-detector.} \end{abstract} \end{frontmatter} %% How to make a heading and divide the documents into different sections \section{Introduction} This section is also often referred to as the purpose or plan. It includes two main categories: \ \textbf {Purpose:} It usually is expressed in one or two sentences that include the main method used for accomplishing the purpose of the experiment. \textcolor {green} {Ex: The purpose of the experiment was to determine the mass of an ion using the mass spectrometer. } \textbf {Background and theory:} related to the experiment. This includes explanations of theories, methods or equations used, etc.; for the example above, you might want to explain the theory behind mass spectrometer and a short description about the process and setup you used in the experiment. It is important to remember that report needs to be as straightforward as possible. You should comprise only as much information as needed for the reader to understand the purpose and methods. Your should also provide additional information such as a hypothesis (what is expected to happen in the experiment based on the theory) or safety information. The main focus of the introduction mainly focuses on supporting the reader to understand the purpose, methods, and reasons for these particular methods.Purpose of the experiment \\ \textcolor {green} {Example:} \subsubsection*{Calculation of the pressure coefficient $C_{p}$} From the lectures notes, $C_{p}$ can be obtained by the eq. (1) \begin{equation} -C_{p}= \frac{P-P_{\infty}}{\frac{1}{2}*\rho*U_{\infty}^2} \end{equation} Where $P $ and $P_{\infty}$ are respectively the local pressure and the atmosphere pressure far away. $U_{\infty}$ is the wind velocity of the wind tunnel. \subsubsection*{Calculation of the lift coefficient $C_{L}$} First, the expression for the pressure force acting normal to the chord line is given in the lecture notes as eq.(2), \begin{equation} C_{n} = \oint C_{p}(-\hat{n}*\hat{y})dl, \end{equation} with $C_{p}$ the coefficient of lift and $\hat{n}$ the unit normal vector pointing out of the surface, $\hat{y}$ is the unit vector in the direction normal to the chord line. dl is the length of an infinitesimal line element. Similarly, the axial component can be express as eq.(3) \begin{equation} C_{a} = \oint C_{p}(-\hat{n}*\hat{x})dl, \end{equation} \section {Method} This is a short (half a page or so) passage in your report which should include the experimental process exactly as it was done in the laboratory. The procedure should be written in paragraph form. You should not copy the lab manual. It is possible that the experiment you have done has slightly difference procedures than in the manual. You should not include any results (things happened during the procedure). A good rule of thumb for complete but brief experimental procedures is to provide enough information so that the reader of your report would be able to repeat the experiment.\\ \textcolor {green} {Example: First, the surface pressure was measured with a pressure scanner (Scanivalve MPS4264). The MATLAB script $get_qinf_T.m$ was used to find the target freestream velocity $U_{\infty}$. A first offset measurement was taken with the pressure scanner, sample at 800 Hz for 10 seconds , while matlab was taking an offset measurement. After the offset measurment done , the wind tunnel VFD RPM was set to reach the target $U_{\infty}$ within $\pm 0.5 m/s$. For each of the following $\alpha$= [-8 -6 -4 -2 0 2 4 6 7 8 9 10 11 12 13 14 16 18], the same procedure was repeated : The turntable was set to the right angle of attack (as shown in fig.(1)). Then the dynamic pressure and the temperature were taken (\emph{1000} Hz for \emph{30} seconds for pressure, and \emph{14} Hz for \emph{10} seconds for the temperature). While Matlab was taking the data , the pressure scanner was run to take measurement at \emph{800} Hz for \emph{60} seconds. After changing the angle, a break of \emph{5} seconds was taken in order to fully settle the flow into a steady state before taking the next set of measurements. The post-experiment calculations were realized with Matlab. First, the pressure offset was computed in order to get the right pressure measurement. With the \emph{2} offset measurements and the getfiledate.m Matlab code, the time of each offset has been taken. A linear interpolation was realized to get the offset at any time. The pressure points were linked to the corresponding measurement value of the scanner and the time of each measurement was obtained with the getfiledate.m code. The new pressure were finally taken by subtraction of each corresponding time offset to the measurement pressure for every angle of attack. The lower and upper $C_{p}$ values were computed with eq.(1). The denominator in the eq.(1) ($P-P_{\infty}$) correspond to the new pressure calculated by subtraction of the offset . As the pressure points does not surround the airfoil entirely, the $C_{p}$ curves had to be closed by interpolation of the data points using piecewises cubic Hermite polynomials (PCHIP) for the last three points to estimate a value for the trailing edge. An example of a $C_{p}$ curve for a certain angle of attack is shown in fig.(5). Next, the $C_{L}$ values for each angle of attack were computed using eq.(6). The coordinate system used in eq.(6) is shown in fig.(2). fig.(5) shows the resulting plot of this calculation. Finally, the errors in the lift coefficient were computed using eq.(9). The different variance values were given in the lab document and calculated using eq.(8). fig.(3) shows the resulting plot of this calculation.} % adding a figure with caption \begin{figure}[h] \centering \includegraphics[width = 3cm]{A.pdf} \caption{Set up of the airfoil experiment} \label{fig:my_label} \end{figure} \section{Results} In this section all the results of the experiment is reported, including: \textbf {\textit {\textcolor{red}{Raw data}}}- in forms of graphs or tables. Each graph, table, or figure should be labeled and titled properly. Making tables and figures is helpful when you refer to and explain each of them in the report. Make sure that you attach the appropriate units to all physical quantities.\\ Assume that the reader has not done the lab; so give clear \textbf {definition of each symbol} that is used in the report. (ex: “L is the length of the pendulum”.)\\ \textbf {Important results} – It is expected to use complete sentences to communicate the main results, which also should be expended to discussion section. (Ex: “The gravitational acceleration was calculated to be 9.98 m/s”) This enables the important results to stand out from all the calculations, tables, and figures.\\ \textbf {Calculations} Normally, one sample of each calculation is necessary. For example, if the speed of an object is calculated for 6 trials, you are expected to write out calculations for only one of them. However, it is important to mention that the calculation was repeated 6 times and give the average of all 6. Significant figures should be considered in all calculations (see appendix of “Significant Figure Rules” as a resource with significant figures). Again, make sure units are included in all calculations. \textcolor {green} {Example:} The resulting slope of the $C_{l}$ for ${\alpha}\in [-8,8] $ is \textit{6.174} rad and \textit{6.209} rad for ${\alpha}\in [-4,4] $\ . This deviates by \textit{0.1090} and \textit{0.0745} respectively from the \textit{$2{\pi}$} value predicted by thin airfoil theory, indicating larger errors for higher AoA's. The max theoretical error $\Delta C_{l}$ was calculated to be \textit{0.0887}, and occurred at ${\alpha=\ang{16}}$, which is in the stall region. Outside of the stall region the max error was calculated to be \textit{0.0391}, at ${\alpha=\ang{8}}$ \begin{figure}[h!] \centering \includegraphics[width = 5cm]{dCl(AoA)3.png} \caption{Resulting plot of $\Delta C_{L}$} \label{fig:my_label} \end{figure} \\ The standard deviations presented in tab.1 were used in the result above. $\sigma{q_{inf}}$, and $\sigma{P_{i}}$ were found with eqn (8). However, $\sigma{P_{i}}$ is a vector for all of the pressure ports, and will not be presented. \begin{table}[h!] \caption{Value of variance} \centering \begin{tabular}{lllll} \hline $\sigma_{P_{0}}$ & $\sigma_{\alpha}$ & $\sigma_{q_{\inf}}$ & \\ \hline 3.000 & 0.250 & 0.453 & \\ {[}Pa{]} & {[}deg{]} & {[}Pa{]} & \\ \hline \end{tabular} \end{table} \begin{figure}[h!] \centering \includegraphics[width = 5cm]{Cl(AoA)3.png} \caption{Resulting plot of $C_{L}$ compared to experimental data} \label{fig:my_label} \end{figure} \begin{figure}[h!] \centering \includegraphics[width = 5cm]{Cp(8deg)2.png} \caption{- $C_{p}$ for $\alpha = \ang{8} $} \label{fig:my_label} \end{figure} \section{Discussion} The most important part of your report is the discussion section. Here you explain your results and allow your instructor to see that you have a thorough understanding of the scientific concept of the experiment and the results. In this section you also compare the expected (theoretical) results with actual (experimental) ones. It is possible that your experiment turns out not exactly the way it was supposed to. Analyze and discuss why the results might have been different and try to explain why you obtained the results you did. Be specific what caused the error: faulty equipment, inaccurate measurements or calculation errors. After you have discussed the cause of the error, try to suggest how to avoid the error and how to setup the experiment more effectively (ex: be more careful with measurements, use more precise equipment, etc.)\\ \textcolor{green}{ Example} According to thin airfoil theory, the Cl curve for cambered airfoils should be straight for low angles of attack with a slope of <textit{$2\pi$}. It should also have a positive lift at $\alpha = \ang{0} $. The resulting $C_{L}$ curve clearly follows this trend, albeit not perfectly, especially at higher AoA's. This likely follows from the assumption of a thin airfoil, as the NREL S826 has a non negligible aspect ratio of \textit{5} . Furthermore, the boundary layer acts as a streamline, essentially adding some minute thickness to the airfoil flow. It would therefore experience a higher adverse pressure gradient due to the curvature, and thus earlier separation. This can also be observed in figure \textit{4}, where a high pressure gradient is starting to form already for $\alpha = \ang{8} $ at ~ $\frac{x}{c} \approx 0.2$. Furthermore, stall can be predicted to be about $\alpha = \ang{12} $ from figure 3. This seems to fit well with previous experimental data shown in pink \cite{Airfoiltools.com}, . Larger theoretical errors are expected in this region, as separation and irregular flow further complicates the theory. The discrepancies are also likely to be due to the measurement errors described in the theory section. The max calculated error $\Delta C_{L}$ is \textit{5.93} $\%$ of the total $C_{L}$. \section{Conclusion} This section is a short paragraph that includes one or two sentences. Conclusion summarizes the major result(s) of the experiment. \\ \textcolor{green}{Example} The goal of this lab was experimentally measure pressure around an airfoil for different AoA's and to compare the resulting lift data with theory. This was done with numerical integration of the pressure distrubution, while also adjusting for measurment errors. There seems to be good agreement between the lab data and theory. The resulting slope of the $C_{L}$ curve deviates at a maximum \textit{0.109} from thin airfoil theory outside the stall region. This is probably due to the thickness of the airfoil, as well as the measurement error in the equipment. As expected stall occurs at about $\alpha = \ang{12} $, which can be qualitatively observed in both the $C_{L}$ and $C_{P}$ curves. % htb is a placement option where h = here, t = top of page, b = bottom of page % htb means it first tries to place the figure at this point in the text, then the % next option is the top of the page and the last option is the bottom of the page % Tables and figures are placed by the document compiler, and if the figures end % up all over the place even though the placement options has been set it is usually % a sign that there are too many figures and too little text % Note that siunitx use the number in the parenthesis as the uncertainty in the last digit of the number % Use the *-symbol to remove numbering of section if required \section*{References} \bibliography{references} \begin{thebibliography}{9} \bibitem{pressure scanner} Scanivalve: MPS4264 Miniature Pressure ScannerManual, \\\texttt{http://www-cs-faculty.stanford.edu/\~{}uno/abcde.html} \bibitem{Airfoiltools.com} Airfoil tools: Previous experimental data for the NREL S826, \\\texttt{http://airfoiltools.com/airfoil/details?airfoil=s826-nr} \end{thebibliography} \end{document}