From 45f18adf080a83cccb5ebb0b277af5929648b5c5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= Date: Mon, 13 Jun 2022 23:34:53 +0200 Subject: geografska predstavitev --- .gitignore | 2 + fiz/naloga/obdelava.md | 19 +- "fiz/naloga/poro\304\215ilo/Makefile" | 5 + "fiz/naloga/poro\304\215ilo/dokument.bib" | 36 + "fiz/naloga/poro\304\215ilo/dokument.tex" | 249 + "fiz/naloga/poro\304\215ilo/numeri\304\215no.c" | 1 + fiz/naloga/predstavitev/Makefile | 9 +- fiz/naloga/predstavitev/dokument-figure0.dep | 4 +- fiz/naloga/predstavitev/dokument-figure0.md5 | 2 +- fiz/naloga/predstavitev/dokument.tex | 150 +- fiz/naloga/predstavitev/dokument.tex.old | 308 - fiz/naloga/relacije/2A.tsv | 27304 +++++++++++----------- fiz/naloga/relacije/2Aos.tsv | 19551 ++++++++-------- fiz/naloga/relacije/3A.tsv | 21802 ++++++++--------- fiz/naloga/relacije/3Aos.tsv | 12669 +++++----- fiz/naloga/relacije/grafi.sh | 9 + fiz/naloga/relacije/mm2Aos.tsv | 4033 ++++ fiz/naloga/relacije/mm3Aos.tsv | 1672 ++ "fiz/naloga/su\305\276enjstvo/lokacije.c" | 19 +- "fiz/naloga/su\305\276enjstvo/transformiraj.sh" | 1 + fiz/naloga/transformirane/2A1.tsv | 5322 ++--- fiz/naloga/transformirane/2A3.tsv | 3424 +-- fiz/naloga/transformirane/2A4.tsv | 6880 +++--- fiz/naloga/transformirane/2A6.4.tsv | 8040 +++---- fiz/naloga/transformirane/2A7.1.tsv | 7878 +++---- fiz/naloga/transformirane/3A1.tsv | 7638 +++--- fiz/naloga/transformirane/3A2.1.tsv | 7900 +++---- fiz/naloga/transformirane/3A3.1.tsv | 7938 +++---- geo/predstavitev/Makefile | 33 + geo/predstavitev/dokument.bib | 58 + geo/predstavitev/dokument.tex | 252 + geo/predstavitev/sinhr.txt | 20 + 32 files changed, 74879 insertions(+), 68349 deletions(-) create mode 100644 "fiz/naloga/poro\304\215ilo/Makefile" create mode 100644 "fiz/naloga/poro\304\215ilo/dokument.bib" create mode 100644 "fiz/naloga/poro\304\215ilo/dokument.tex" create mode 120000 "fiz/naloga/poro\304\215ilo/numeri\304\215no.c" delete mode 100644 fiz/naloga/predstavitev/dokument.tex.old create mode 100755 fiz/naloga/relacije/grafi.sh create mode 100644 fiz/naloga/relacije/mm2Aos.tsv create mode 100644 fiz/naloga/relacije/mm3Aos.tsv create mode 100644 geo/predstavitev/Makefile create mode 100644 geo/predstavitev/dokument.bib create mode 100644 geo/predstavitev/dokument.tex create mode 100644 geo/predstavitev/sinhr.txt diff --git a/.gitignore b/.gitignore index 831c461..f912df8 100644 --- a/.gitignore +++ b/.gitignore @@ -25,6 +25,8 @@ *.o *.mkv *.png +*.gif +*.svg *# core # datoteke .jpeg so trackane, .jpg pa ne diff --git a/fiz/naloga/obdelava.md b/fiz/naloga/obdelava.md index 299d908..0784212 100644 --- a/fiz/naloga/obdelava.md +++ b/fiz/naloga/obdelava.md @@ -28,7 +28,22 @@ sedaj imamo v mapi relacije datoteki 2A.tsv (11208 podatkov/vrstic) in 3A.tsv (1 ``` cd relacije -./lušči.php y 0.05 < 2A.tsv > 2Aos.tsv -./lušči.php y 0.05 < 3A.tsv > 3Aos.tsv +./grafi.sh +cd .. +``` + +# generiranje predstavitve + +``` +cd predstavitev +make +cd .. +``` + +# generiranje poročila + +``` +cd poročilo +make cd .. ``` diff --git "a/fiz/naloga/poro\304\215ilo/Makefile" "b/fiz/naloga/poro\304\215ilo/Makefile" new file mode 100644 index 0000000..30318d0 --- /dev/null +++ "b/fiz/naloga/poro\304\215ilo/Makefile" @@ -0,0 +1,5 @@ +.NOTPARALLEL: +default: + pdflatex -shell-escape dokument.tex + biber dokument + pdflatex -shell-escape dokument.tex diff --git "a/fiz/naloga/poro\304\215ilo/dokument.bib" "b/fiz/naloga/poro\304\215ilo/dokument.bib" new file mode 100644 index 0000000..842a43d --- /dev/null +++ "b/fiz/naloga/poro\304\215ilo/dokument.bib" @@ -0,0 +1,36 @@ +@online{c4, + url = {http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c4}, +} +@online{c3, + url = {http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c3}, +} +@online{ha, + url = {http://sl.wikipedia.org/wiki/Hallov_pojav}, +} +@online{td, + url = {http://invensense.tdk.com/wp-content/uploads/2015/02/PS-MPU-9250A-01-v1.1.pdf}, +} +@online{he, + url = {http://en.wikipedia.org/wiki/Helmholtz_coil}, +} +@online{fe, + url = {http://lbm.fe.uni-lj.si/oe/OE2/LabVaja/Priprave%20za%201VAJO%20OE2%20V2.docx}, +} +@online{bs, + url = {http://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law}, +} +@online{in, + url = {http://sl.wikipedia.org/wiki/Infinitezimala}, +} +@online{lo, + url = {http://en.wikipedia.org/wiki/Lorentz_force}, +} +@online{c1, + url = {http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/Biosav.html#c1}, +} +@online{am, + url = {http://en.wikipedia.org/wiki/Ampere#Former_definition_in_the_SI}, +} +@online{ro, + url = {http://en.wikipedia.org/wiki/Rotation_matrix}, +} diff --git "a/fiz/naloga/poro\304\215ilo/dokument.tex" "b/fiz/naloga/poro\304\215ilo/dokument.tex" new file mode 100644 index 0000000..3c30347 --- /dev/null +++ "b/fiz/naloga/poro\304\215ilo/dokument.tex" @@ -0,0 +1,249 @@ +% do-vimlatex-onwrite +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage[alsoload=hep]{siunitx} % high energy physics +\usepackage[slovene]{babel} +\usepackage[inline]{enumitem} +\usepackage[a4paper]{geometry} +\usepackage{hologo} +\usepackage[hidelinks,unicode]{hyperref} +\usepackage{datetime} +\usepackage{amssymb} +\usepackage{multicol} +\usepackage{listings} +\usepackage{xcolor} +\usepackage{csquotes} +\usepackage[siunitx,europeanresistors]{circuitikz} +\usepackage[makeroom]{cancel} +\usepackage[backend=biber,style=iso-authoryear,sortlocale=cs_CZ]{biblatex} +\addbibresource{dokument.bib} +\usepackage{pgfplots} +\usepackage{float} +\usepackage{tkz-euclide} +\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development +\sisetup{output-decimal-marker = {,}, quotient-mode=fraction, output-exponent-marker=\ensuremath{\mathrm{e}}} % per-mode=fraction/symbol +\settimeformat{hhmmsstime} +\makeatletter +\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname} +\newcommand{\@xslalph}[1]{% + \ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i% + \or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}% + \or t\or u\or v\or z\or \v{z} + \else\@ctrerr\fi% +} +\AddEnumerateCounter{\xslalph}{\@xslalph}{m} +\makeatother +\definecolor{codegreen}{rgb}{0,0.6,0} +\definecolor{codegray}{rgb}{0.5,0.5,0.5} +\definecolor{codepurple}{rgb}{0.58,0,0.82} +\definecolor{backcolour}{rgb}{0.95,0.95,0.92} +\lstdefinestyle{mystyle}{ + backgroundcolor=\color{backcolour}, + commentstyle=\color{codegreen}, + keywordstyle=\color{magenta}, + numberstyle=\tiny\color{codegray}, + stringstyle=\color{codepurple}, + basicstyle=\ttfamily\footnotesize, + breakatwhitespace=false, + breaklines=true, + captionpos=b, + keepspaces=true, + numbers=left, + numbersep=5pt, + showspaces=false, + showstringspaces=false, + showtabs=false, + tabsize=2 +} +\lstset{style=mystyle} +\newcommand{\cm}[1]{ + \SI[parse-numbers=false]{#1}{\centi\meter} +} +\newcommand{\m}[1]{ + \SI[parse-numbers=false]{#1}{\meter} +} +\newcommand{\kvm}[1]{ + \SI[parse-numbers=false]{#1}{\meter\squared} +} +\newcommand{\kvcm}[1]{ + \SI[parse-numbers=false]{#1}{\centi\meter\squared} +} +\title{Poročilo: Magnetno polje Helmholtzove tuljave (23. naloga)} +\author{Anton Luka Šijanec, 3. a} +\date{V petek, 3. junija 2022} +\newcommand\vektor{\overrightarrow} +\begin{document} +\maketitle +\begin{abstract} + Poročilo merjenja magnetnega polja Helmholtzove tuljave vzdolž dveh geometrijskih osi in primerjave rezultatov s teoretično napovedjo pri fiziki na Gimnaziji Bežigrad. +\end{abstract} +\tableofcontents +\paragraph{Opomba} Uvod in teorija, z izjemo numerične obdelave, sta enaka kot v opisu projekta. +\section{Uvod} +Helmholtzova tuljava oziroma Helmholtzov par je poimenovana po nemškemu fiziku devetnajstega stoletja Hermannu Ludwigu Ferdinandu von Helmholtzu in predstavlja pripravo za izdelavo umetnega lahko dostopnega homogenega magnetnega polja visoke kvalitete. Solenoidi, torej dolge in ozke tuljave, pod električnim poljem sicer delajo kvalitetno, z vstavljenim feromagnetom tudi močno magnetno polje, vendar je le-to težko dostopno, saj se nahaja znotraj navojev. Helmholtzova tuljava pa je sestavljena iz dveh tokovnih zank oziroma magnetnih dipolov, to sta dve ravninsko vzporedni enaki kratki in široki med seboj za polmer oddaljeni tuljavi. Ob prisotnosti enako velikega in enako usmerjenega električnega toka v vodnikih se v sredini med njima pojavi veliko območje s homogenim magnetnim poljem, kar je uporabno za mnoge elektrotehnične probleme, denimo natančno kalibracijo merilnikov in nasprotovanje vplivu Zemljinega magnetnega polja na instrumente. + +Maxwellova tuljava škotskega fizika Jamesa Clerka Maxwella je dodatek Helmholtzovi tuljavi. Z dodatnimi pravilno postavljenimi navitji za ceno dodatnega materiala in kompleksnosti dodatno poveča območje in homogenost magnetnega polja. +\section{Teorija} +Navodilo zahteva meritev in teoretično napoved vrednosti magnetnega polja na oseh tuljave. Če je radij $R$, število navojev $n$ in tok $I$, je jakost magnetnega polja $B$ na sredini +$$B=\left(\frac{4}{5}\right)^{3/2}\frac{\mu_0nI}{R}\text{,}$$ +kjer je $\mu_0$ indukcijska/magnetna konstanta. +($\SI{\pi4e-7}{\volt\second\per\ampere\per\meter}$). +\subsection{Razlaga enačbe} +\subsubsection{Biot-Savartov zakon} +Z Biot-Savartovim zakonom predstavimo vektor $B$ magnetnega polja, ki se pojavi zaradi stalnega električnega polja $I$ v vodniku na poti $C$. Predstavi relacijo magnetnega polja na jakost, smer, dolžino in bližino električnega toka z enačbo +$$B(r)=\frac{\mu_0}{4\pi}\oint_C\frac{Id\ell\times\hat{r}^\prime}{{|r^\prime|}^2}\text{,}$$ +kjer je $d\ell$ vektor na poti elektronov $C$ (krožnica), katerega velikost je infinitezimalno majhen del vodnika v smeri električnega toka, $\ell$ je torej točka na $C$, $\hat{r}^\prime$ je enotski vektor (množen z obratno vrednostjo svoje velikosti --- $\hat{r}^\prime=r^\prime\cdot{|r^\prime|}^{-1}$) vektorja $r^\prime=r-\ell$ --- vektorja premika od vodnika ($d\ell$ oz. $\ell$) do točke $r$, katere vektor magnetnega polja želimo izračunati. Od prej je $\mu_0$ še vedno indukcijska/magnetna konstanta. + +Čeprav se zakon povečini, kot v našem primeru, uporablja na zankah, v katerih teče električni tok, velja tudi za neskončno dolge vodnike. Na tak način je bil z Biot-Savartovim in Lorentzovim zakonom na primer do leta 2019 SI amper definiran kot konstantani tok, ki v vakuumu, ko teče po dveh eden od drugega za en meter oddaljenih vzporednih vodnikih neskončne dolžine z zanemarljivim premerom, povzroči nastanek sile $\SI{2e-7}{\newton}$ na vsak meter dolžine vodnika. +% \subsection{Polje v središču zanke} % TODO +\subsection{Polje na osi zanke skozi obe navitji} +% http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c4 +Biot-Savartov zakon poenostavimo in izračunamo vektorja $B$ za na osi zanke s polmerom $R$ vodnika, po katerem teče tok $I$, poljubno točko $T$, oddaljeno $z$ od središča zanke $S$. + +Zanima nas samo z osjo vzporedna komponenta $B_z$ vektorja magnetnega polja, ker na os pravokotne komponente v homogenem polju sploh ne bo, ko bomo računali jakost polja znotraj Helmholtzove tuljave. + +Kot med na os pravokotno in z osjo vzporedno komponento vektorja $B$ je enak kotu $(\ell,T,S)$. Torej je +$$\sin\theta=\frac{R}{r = \sqrt{z^2+R^2}} \wedge dB_Z=dB\sin\theta \Longrightarrow dB_Z=\frac{\mu_0Id\ell}{4\pi}\cdot\frac{R}{\left(z^2+R^2\right)^{3/2}}\text{.}$$ +% http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c3 +Vse vrednosti, razen infinitezimale dolžine na zanki $d\ell$, so konstantne, integriranje $d\ell$ pa predstavlja obseg zanke $2\pi R$. Tako je velikost z osjo zanke vzporedne komponente vektorja magnetenega polja v točki $T$ izračunana z enačbo +$$B_Z=\frac{\mu_0I}{\cancelto{2}{4\pi}}\cdot\frac{\cancel{2\pi}R^2}{\left(z^2+R^2\right)^{3/2}}\text{.}$$ +Ker so vse točke $d\ell$ na zanki enako oddaljene od točke $T$, je za točke $z$ na osi tuljav $B_Z(z)=B(z)$. +\subsubsection{Dodajanje zank} +Da dobimo enačbo za polje enega navitja Helmholtzove tuljave, enačbo za eno zanko preprosto zmnožimo s številom zank $n$: +$$B_1(z)=\frac{n\mu_0R^2I}{{2\left(z^2+R^2\right)}^{3/2}}\text{.}$$ +Zanima nas taka vrednost $z$, ki je v središču med obema navitjema. To je, kot je zgoraj opisano, $z=R/2$: +$$B_1\left(\frac{R}{2}\right)=\frac{n\mu_0R^2I}{2\left(\left(\frac{R}{2}\right)^2+R^2\right)^{3/2}}\text{.}$$ +Jakost magnetnega polja med obema simetričnima navitjema je enaka dvakratniku $B_1$. +$$B\left(\frac{R}{2}\right)=2{B_1}_Z\left(\frac{R}{2}\right)=$$ +$$=\frac{\cancel{2}n\mu_0R^2I}{\cancel{2}\left(\left(\frac{R}{2}\right)^2+R^2\right)^{3/2}} +=\frac{n\mu_0R^2I}{\left(\frac{1}{4}R^2+R^2\right)^{3/2}=\left(\frac{5}{4}R^2\right)^{3/2}} +=\left(\frac{4}{5}\right)^{3/2}\frac{n\mu_0\cancel{R^2}I}{R\cancel{^3}} +=\left(\frac{8}{5\sqrt{5}}\right)\frac{n\mu I}{R}\text{.}$$ +\subsection{Potreben tok za dosego željenega homogenega toka} +Zgornjo enačbo preuredimo v +$$I=\left(\frac{5}{4}\right)^{3/2}\left(\frac{BR}{\mu_0n}\right)\text{,}$$ +kjer je $\mu_0$ malo drugače zapisana ista indukcijska/magnetna konstanta ($=\SI{\pi4e-7}{\tesla\meter\per\ampere}$), in s tem izračunamo potreben tok za stalno homogeno magnetno polje v središču tuljave. +% \subsection{Izmenična napetost} % TODO +% Napajanje tuljave za dosego željenega stalnega magnetnega polja je torej preprosto, saj bo magnetno polje v vseh točkah linearno raslo s tokom skozi obe tuljavi, malo težje pa je izdelati nihajoče magnetno polje, saj je tuljava induktor, čigar impedanca se z višanjem frekvence veča, torej je za dosego enake jakosti magnetnega polja na dvakrat višji frekvenci potrebna dvakrat višja napetost na navitjih. +\subsection{Polje na simetrijski osi} +% Polje na simetrijski osi je bilo težko izračunati, zato sem uporabil vnaprej integrirano enačbo iz dopolnila k projektni nalogi: +% $$ +% B\left(z\right)=\frac{\mu_0NIR^2}{2}\left[ +% \left(R^2+\left(z-\frac{R}{2}\right)^2\right)^{\displaystyle-\frac{3}{2}} +% + +% \left(R^2+\left(z+\frac{R}{2}\right)^2\right)^{\displaystyle-\frac{3}{2}} +% \right] +% $$ +Druge osi nisem znal izračunati, zato bom teoretično napoved izračunal numerično - predstavljal si bom, da je namesto okrogle zanke tam mnogokotnik in uporabil Biot-Savartov zakon v iteraciji z računalnikom. +\subsection{Grafi} +Kot primer vzemimo šolsko Helmholzovo tuljavo s 320 navoji na vsakem navitju, katerega radij je enak $\SI{6,8}{\centi\meter}$, skozi katera teče stalen enosmerni tok \SI{250}{\milli\ampere}. + +\begin{tikzpicture} +\begin{axis}[legend style={at={(1.2,1)}}, anchor=north west, +ylabel = {jakost magnetnega polja}, +xlabel = {razdalja na osi}, +x = 21cm +] +\addplot gnuplot [raw gnuplot, id=test, mark=none]{ +m = pi*4e-7; +R = 0.068; +N = 320; +I = 0.25; +plot [-3*R:3*R] N*m*R**2*I/(2*((x-R/2)**2+R**2)**(3/2)); +}; +\addlegendentry{os skozi središči navitij (L)} +\addplot gnuplot [raw gnuplot, id=test, mark=none]{ +m = pi*4e-7; +R = 0.068; +N = 320; +I = 0.25; +plot [-3*R:3*R] N*m*R**2*I/(2*((x+R/2)**2+R**2)**(3/2)); +}; +\addlegendentry{os skozi središči navitij (D)} +\addplot gnuplot [raw gnuplot, id=test, mark=none]{ +m = pi*4e-7; +R = 0.068; +N = 320; +I = 0.25; +plot [-3*R:3*R] N*m*R**2*I/(2*((x-R/2)**2+R**2)**(3/2)) + N*m*R**2*I/(2*((x+R/2)**2+R**2)**(3/2)); +}; +\addlegendentry{os skozi središči navitij (L+D)} +\end{axis} +\end{tikzpicture} +\subsection{Numerična analiza} +Numerična analiza je preprosta; namesto zanke v obliki kroga seštejemo vrednosti na odsekih vodnika, ki predstavlja mnogokotnik v 3D prostoru. Program za numerično analizo je priložen dokumentu in, v kolikor generira za mojo eksperimentalno tuljavo (\texttt{./numerično.c 0.088 3 17 0.0002 1000 30 pgm > izhod.pgm}), izdela sledeč graf: + +\begin{figure}[H] +\center +\includegraphics[width=0.7\textwidth]{out.png} +\caption{Teoretični model tuljave} +\end{figure} +\section{Praktične meritve} +Kot je napisano v opisu projekta, sem uporabil TDKjev MPU9250 merilnik in mikrokrmilnik Espressif 8266, ki je vsakih nekaj milisekund izmeril absolutno jakost magnetnega polja. Za določanje pozicije merilnika ob danem času sem uporabil funkcijo \textit{Motion Tracking} v programu Blender. Korelacija podatkov iz dveh virov s stališča fizike ni pomembna, vendar je vseeno bežno opisana v predstavitvi. + + \begin{circuitikz} \draw + (0,0) to[battery] (0,4) + to[ammeter, l_=3<\ampere>] (4,4) to[resistor=1.65<\ohm>] (4,0) + to[cute inductor] (0,0) + ; + \end{circuitikz} + +\subsection{Pripomočki} + +\begin{itemize} + \item \SI{3}{\ampere} \SI{5}{\volt} napajalnik + \item štirje \SI{10}{\watt} \SI{2,2}{\ohm} uporniki za nadomestno upornost vsaj \SI{1,65}{\ohm} in zmožnost porabe \SI{20}{\watt} -- v resnici je bila teoretična poraba \SI{15}{\volt\ampere} + \item lakirana bakrena žica za navitji s polmerom \SI{8,8}{\centi\meter}, pridobljena iz toroidnega transformatorja + \item kamera prenosnega telefona za videoanalizo + \item Hallov merilnik mangnetnega polja +\end{itemize} + +\subsection{Opis rezultatov} + +Dobil sem tabelo s 24553 vrsticami. Opravil sem osem uspelih meritev, od tega tri na troamperskem toku, pet pa na dvoamperskem toku. Tabeli meritev sta dostopni na \url{http://git.sijanec.eu/sijanec/sola-gimb-3/src/branch/master/fiz/naloga/relacije}. + + +\subsection{Slike grafov rezultatov} +\begin{figure}[H] + \center + \includegraphics[width=0.8\textwidth]{3A.png} + \caption{Graf magnetnega polja v odvisnosti od pozicije pri triamperskem toku} +\end{figure} +\begin{figure}[H] + \center + \includegraphics[width=0.8\textwidth]{2A.png} + \caption{Graf magnetnega polja v odvisnosti od pozicije pri dvoamperskem toku} +\end{figure} + +\subsection{Primerjava s teoretično napovedjo} +Podatke sem uvozil v LoggerPro in izdelal prilagoditveno krivuljo. Iz meritev sem izluščil najprej centimeterski in nato še milimetrski pas okoli osi. + +\begin{figure}[H] + \center + \includegraphics[width=0.8\textwidth]{1cm.png} + \caption{Grafa meritev in prilagoditvene krivulje, če je pas centimetrski} +\end{figure} +\begin{figure}[H] + \center + \includegraphics[width=0.8\textwidth]{1mm.png} + \caption{Grafa meritev in prilagoditvene krivulje, če je pas milimetrski} +\end{figure} + +\section{Viri} +\nocite{*} +\printbibliography[title={Internetni viri}] +\section{Zaključek} +Prilagoditvena krivulja v programu LoggerPro je ustrezno natančna. +% https://en.wikipedia.org/wiki/Helmholtz_coil +% http://lbm.fe.uni-lj.si/oe/OE2/LabVaja/Priprave%20za%201VAJO%20OE2%20V2.docx +% https://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law +% https://sl.wikipedia.org/wiki/Infinitezimala +% https://sl.wikipedia.org/wiki/Hermann_Ludwig_Ferdinand_von_Helmholtz +% https://en.wikipedia.org/wiki/Lorentz_force +% http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/Biosav.html#c1 +% https://en.wikipedia.org/wiki/Ampere#Former_definition_in_the_SI +\section{Priloge} +\subsection{Program za teoretičen izris magnetnega polja okoli tuljave} +Animaciji dveh tuljav, ki se premikata po prostoru: \url{http://video.arnes.si/?q=helmholtz}. Ena je izdelana s hitrejšim programom (in večjim, da ga res nima smisla vključevati v dokument) v OpenGL, druga pa s tem programom. +\lstinputlisting{numerično.c} +\end{document} diff --git "a/fiz/naloga/poro\304\215ilo/numeri\304\215no.c" "b/fiz/naloga/poro\304\215ilo/numeri\304\215no.c" new file mode 120000 index 0000000..919ad63 --- /dev/null +++ "b/fiz/naloga/poro\304\215ilo/numeri\304\215no.c" @@ -0,0 +1 @@ +../numerično.c \ No newline at end of file diff --git a/fiz/naloga/predstavitev/Makefile b/fiz/naloga/predstavitev/Makefile index 88f2b90..769b5b2 100644 --- a/fiz/naloga/predstavitev/Makefile +++ b/fiz/naloga/predstavitev/Makefile @@ -2,8 +2,15 @@ default: wget -c of/sfu/potrebščine.jpg wget -c t/z/track.png - wget -c t/z/pro.png + wget -c of/sfu/toroid.jpg + wget -c of/sfu/upornik.jpg + wget -c t/z/1cm_okvirček.png + wget -c t/z/1mm_okvirček.png + wget -c t/z/1cm.png + wget -c t/z/1mm.png c -Ofast ../numerično.c -lm ./a.out 0.088 3 17 0.0002 1000 30 pgm > out.pgm convert out.pgm out.png + ./png.gnuplot 3A.png ../relacije/3A.tsv + ./png.gnuplot 2A.png ../relacije/2A.tsv pdflatex -shell-escape dokument.tex diff --git a/fiz/naloga/predstavitev/dokument-figure0.dep b/fiz/naloga/predstavitev/dokument-figure0.dep index e6613d9..dc7edfb 100644 --- a/fiz/naloga/predstavitev/dokument-figure0.dep +++ b/fiz/naloga/predstavitev/dokument-figure0.dep @@ -1,3 +1,3 @@ dokument-figure0.pdf: dokument-figure0.test.table -dokument-figure0.pdf: dokument-figure0.test.table -dokument-figure0.pdf: dokument-figure0.test.table +dokument-figure0.pdf: dokument-figure0.test2.table +dokument-figure0.pdf: dokument-figure0.test3.table diff --git a/fiz/naloga/predstavitev/dokument-figure0.md5 b/fiz/naloga/predstavitev/dokument-figure0.md5 index 9272261..da632f2 100644 --- a/fiz/naloga/predstavitev/dokument-figure0.md5 +++ b/fiz/naloga/predstavitev/dokument-figure0.md5 @@ -1 +1 @@ -\def \tikzexternallastkey {F8C196E0132D71A5EC0C9D118B8D9EAF}% +\def \tikzexternallastkey {BAF72873D95C97FEF7A4720976C882DF}% diff --git a/fiz/naloga/predstavitev/dokument.tex b/fiz/naloga/predstavitev/dokument.tex index d2d865b..63ef03a 100644 --- a/fiz/naloga/predstavitev/dokument.tex +++ b/fiz/naloga/predstavitev/dokument.tex @@ -20,25 +20,23 @@ \usepackage[normalem]{ulem} \usepackage{pgfplotstable} \usepackage[slovene]{babel} -% \usepackage[backend=biber,style=iso-authoryear,sortlocale=cs_CZ]{biblatex} % \usepackage[ddMMyyyy]{datetime} \usepackage{ccicons} \usepackage{textcomp} \usepackage{animate} \usepackage{cancel} -% \addbibresource{dokument.bib} +\usepackage[siunitx,europeanresistors]{circuitikz} \usetheme{Madrid} \setbeamertemplate{itemize items}[ball] \setbeamertemplate{caption}[numbered] \usetikzlibrary{calc} %% not really needed............. idk. -\usetikzlibrary{external} -\tikzexternalize +% \usetikzlibrary{external} % hitreje +% \tikzexternalize % hitreje, multiprocess % \usepackage{xcolor} \sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol \newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}} \newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development \newcommand\shortlink[1]{\href{https://xn--jha/#1}{\texttt{https://ž.ga/#1}}} -\newcommand{\razhroscevanje}{0} \def\@maketitle{% \newpage \null @@ -86,7 +84,7 @@ \subtitle{Projektna naloga pri fiziki} \author{Anton Luka Šijanec, 3. a} \institute{Gimnazija Bežigrad} -\date{V sredo, 1. junija 2022} +\date{V petek, 3. junija 2022} \newcommand\vektor{\overrightarrow} % \titlegraphic{\includegraphics[width=\textwidth,height=.5\textheight]{img/jangce.jpg}} @@ -173,16 +171,16 @@ N = 320; I = 0.25; plot [-3*R:3*R] N*m*R**2*I/(2*((x-R/2)**2+R**2)**(3/2)); }; -\addlegendentry{os skozi središči navitij (L)} -\addplot gnuplot [raw gnuplot, id=test, mark=none]{ +\addlegendentry{os skozi središči navitij (L)}; +\addplot gnuplot [raw gnuplot, id=test2, mark=none]{ m = pi*4e-7; R = 0.068; N = 320; I = 0.25; plot [-3*R:3*R] N*m*R**2*I/(2*((x+R/2)**2+R**2)**(3/2)); }; -\addlegendentry{os skozi središči navitij (D)} -\addplot gnuplot [raw gnuplot, id=test, mark=none]{ +\addlegendentry{os skozi središči navitij (D)}; +\addplot gnuplot [raw gnuplot, id=test3, mark=none]{ m = pi*4e-7; R = 0.068; N = 320; @@ -207,7 +205,7 @@ plot [-3*R:3*R] N*m*R**2*I/(2*((x-R/2)**2+R**2)**(3/2)) + N*m*R**2*I/(2*((x+R/2) \begin{figure}[H] \centering \includegraphics[width=0.5\textwidth]{out.png} - % \caption{Simulacija površinskega prereza s programom: \texttt{./a.out 0.088 3 17 0.0002 1000 30 pgm > out.pgm}} + \caption{Simulacija površinskega prereza s programom: \texttt{./a.out 0.088 3 17 0.0002 1000 30 pgm > out.pgm}} \end{figure} \end{multicols} \end{frame} @@ -215,71 +213,140 @@ plot [-3*R:3*R] N*m*R**2*I/(2*((x-R/2)**2+R**2)**(3/2)) + N*m*R**2*I/(2*((x+R/2) \section{Praktična meritev} \begin{frame} \frametitle{\secname} + \begin{multicols}{2} \begin{itemize} \item Osem relativno uspelih meritev, od teh tri na troamperskem toku, ostale na dvoamperskem. \item Videoanaliza z \textit{autotracking} funkcijo programa Blender za pozicijo merilnika v odvisnosti od časa. \item 24553 merilnih mest. Podatki so po obdelavi predstavljeni v obliki $B$ v odvisnosti od $(x;y)$ pri dveh različnih tokovih. \end{itemize} + \begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{upornik.jpg} + \caption{Nadomestni upornik $\SI{1,65}{\ohm}$ iz štirih $\SI{2,2}{\ohm}$ upornikov.} + \end{figure} + \end{multicols} \end{frame} \subsection{Izluščene vrednosti na osi tuljave} \begin{frame} \frametitle{\secname} \framesubtitle{\subsecname} + \begin{multicols}{2} \begin{itemize} \item Programsko izluščene vrednosti v pasu $\pm\SI{0,5}{\centi\meter}$ okoli osi. \item Takih meritev je 15919. - \item Primerjava z grafom. - \item Prilagoditvena krivulja. \end{itemize} + \begin{circuitikz} \draw + (0,0) to[battery] (0,4) + to[ammeter, l_=3<\ampere>] (4,4) to[resistor=1.65<\ohm>] (4,0) + to[cute inductor] (0,0) + ; + \end{circuitikz} + \begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{toroid.jpg} + \caption{Lakirano bakreno žico sem vzel iz nekega toroidnega transformatorja} + \end{figure} + \end{multicols} \end{frame} \section{Posnetki zaslona} -\subsection{LoggerPro} +\subsection{LoggerPro, sredinski pas \SI{1}{\centi\meter}} \begin{frame} \frametitle{\secname} \framesubtitle{\subsecname} \begin{figure}[H] \centering - \includegraphics[width=0.5\textwidth]{pro.png} - \caption{LoggerPro} + \includegraphics[width=0.7\textwidth]{1cm.png} + \caption{LoggerPro, sredinski pas \SI{1}{\centi\meter}} + \end{figure} +\end{frame} +\subsection{LoggerProjev okvirček, sredinski pas \SI{1}{\centi\meter}} +\begin{frame} + \frametitle{\secname} + \framesubtitle{\subsecname} + \begin{figure}[H] + \centering + \includegraphics[width=1\textwidth]{1cm_okvirček.png} + \caption{LoggerProjev okvirček, sredinski pas \SI{1}{\centi\meter}} + \end{figure} +\end{frame} +\subsection{LoggerPro, sredinski pas \SI{1}{\milli\meter}} +\begin{frame} + \frametitle{\secname} + \framesubtitle{\subsecname} + \begin{figure}[H] + \centering + \includegraphics[width=0.7\textwidth]{1mm.png} + \caption{LoggerPro, sredinski pas \SI{1}{\milli\meter}} + \end{figure} +\end{frame} +\subsection{LoggerProjev okvirček, sredinski pas \SI{1}{\milli\meter}} +\begin{frame} + \frametitle{\secname} + \framesubtitle{\subsecname} + \begin{figure}[H] + \centering + \includegraphics[width=1\textwidth]{1mm_okvirček.png} + \caption{LoggerProjev okvirček, sredinski pas \SI{1}{\milli\meter}} \end{figure} \end{frame} - -\section{Posnetki zaslona} \subsection{gnuplot} \begin{frame} \frametitle{\secname} \framesubtitle{\subsecname} \begin{figure}[H] \centering - \includegraphics[width=0.5\textwidth]{gnuplot.png} - \caption{LoggerPro} + \includegraphics[width=0.8\textwidth]{3A.png} + \caption{gnuplot} \end{figure} \end{frame} -%\subsection{Formula \sim} -%\begin{frame} -% \frametitle{\secname} -% \framesubtitle{\subsecname} -% \begin{multicols}{2} -% \begin{itemize} -% \item Enačba Ciolkovskega ali enačba idealne rakete -% -% \end{itemize} -% \end{multicols} -%\end{frame} +\section{Zanimivost} +\subsection{Postopek pridobitve $B(x,y)$ iz surovih podatkov} +\begin{frame} + \frametitle{\secname} + \framesubtitle{\subsecname} + \begin{multicols}{2} + \begin{enumerate} + \item \textit{Motion Tracking} funkcija programa Blender za $x,y(t)$. + \item \textit{MPU9250} za $B(t)$ + \item Vsakemu podatku iz točke 1 priredimo časovno najbližjo vrednost podatka iz točke 2 + \item S programom \textit{GIMP} izluščimo kalibracijske točke + \begin{itemize} + \item središče koordinatnega sistema + \item točko za določanje kotnega zasuka slike + \item stranice \SI{10}{\centi\meter} merila + \end{itemize} + \vfill\null\columnbreak + \item S številom pikslov in $\alpha = atan2(K_y-S_y, K_x-S_x)$ najprej transformiramo velikosti krajevnih vrednosti meritev, nato pa še pozicijo (zasučemo): + \def\V{ + \begin{bmatrix} + T_x \\ + T_y + \end{bmatrix} + } + \def\R{ + \begin{bmatrix} + \cos\alpha & -\sin\alpha \\ + \sin\alpha & \cos\alpha + \end{bmatrix} + } + $$ + \vektor{T_n} = \V\cross\R + $$ + \end{enumerate} + \end{multicols} +\end{frame} \section{Viri} \begin{frame}{\secname} - %\nocite{*} - %\printbibliography[title={Viri}] - Viri so navedeni v opisu projekta. + Viri so navedeni v poročilu. \end{frame} \subsection*{Licence slik} \begin{frame}{\secname}{\subsecname} \begin{itemize} % \setcounter{enumi}{-1} % \item \href{https://xn--jha.ga/raydevlin}{Ray Devlin} \href{https://w.wiki/nbq}{\textit{Wanzhou City Slums}} \ccLogo\ccAttribution\ CC-BY 2.0 Generic (\shortlink{ccby20g}) - \item Vse slike so \copyright Anton Luka Šijanec 2021 + \item Vse slike so moje avtorsko delo. \end{itemize} \end{frame} \section{Zaključek} @@ -292,18 +359,7 @@ plot [-3*R:3*R] N*m*R**2*I/(2*((x-R/2)**2+R**2)**(3/2)) + N*m*R**2*I/(2*((x+R/2) \item Hvala Adrianu Sebastianu Šiški in Oliverju Wagnerju za pomoč pri videoanalizi. %Ta dokument je informativne narave in se lahko še spreminja. % Najnovejša različica, to je \hologo{LaTeX} izvorna koda in PDF dokumenti, je na voljo v mojem šolskem Git repozitoriju na naslovu \url{https://git.sijanec.eu/sijanec/sola-gimb-3/}. % Povezava za prenos zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/fiz/naloga/predstavitev/dokument.pdf}. +\item Predstavitev in opis projekta sta objavljena na \url{http://git.sijanec.eu/sijanec/sola-gimb-3/src/branch/master/fiz/naloga} \end{itemize} \end{frame} -\if\razhroscevanje1 - \subsection*{Razhroščevalne informacije} - \begin{frame}{\secname}{\subsecname} - \begin{itemize} - \item Konec generiranja dokumenta: \today\ ob \currenttime. - \item Grafi imajo natančnost \functionSamples\space točk na graf. - %\item Dokument se je generiral R0qK1KR2 \SI{}{\second}. - \item Doument se je generiral aaasecgeninsaaa \SI{}{\second}. - \item Pred objavo izklopite razhroščevanje. To storite tako, da v glavi dokumenta nastavite ukaz \texttt{razhroscevanje} na 0. - \end{itemize} - \end{frame} -\fi \end{document} diff --git a/fiz/naloga/predstavitev/dokument.tex.old b/fiz/naloga/predstavitev/dokument.tex.old deleted file mode 100644 index 87eaf79..0000000 --- a/fiz/naloga/predstavitev/dokument.tex.old +++ /dev/null @@ -1,308 +0,0 @@ -% do-vimlatex-onwrite -\documentclass[aspectratio=1610]{beamer} -\usepackage[utf8]{inputenc} -\usepackage{etoolbox} -% \usepackage[hidelinks]{hyperref} -% \usepackage[a4paper, total={7in, 10in}]{geometry} -\usepackage{graphicx} -\usepackage{hologo} -\usepackage{amssymb} -\usepackage{pgfplots} -% \usepackage[inline]{enumitem} -\usepackage{amsmath} -\usepackage{siunitx} -\usepackage{multicol} -\usepackage{tabularcalc} -\usepackage{mathtools} -\usepackage{float} -\usepackage{tasks} -\usepackage{environ} -\usepackage[normalem]{ulem} -\usepackage{pgfplotstable} -\usepackage[slovene]{babel} -% \usepackage[backend=biber,style=iso-authoryear,sortlocale=cs_CZ]{biblatex} -% \usepackage[ddMMyyyy]{datetime} -\usepackage{ccicons} -\usepackage{textcomp} -\usepackage{animate} -\usepackage{cancel} -% \addbibresource{dokument.bib} -\usetheme{Madrid} -\setbeamertemplate{itemize items}[ball] -\setbeamertemplate{caption}[numbered] -\usetikzlibrary{calc} %% not really needed............. idk. -\usetikzlibrary{external} -\tikzexternalize -% \usepackage{xcolor} -\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol -\newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}} -\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development -\newcommand\shortlink[1]{\href{https://xn--jha/#1}{\texttt{https://ž.ga/#1}}} -\newcommand{\razhroscevanje}{0} -\def\@maketitle{% - \newpage - \null - \vskip 2em% - \begin{center}% - \let \footnote \thanks - {\LARGE \@title \par}% - \vskip 1.5em% - {\large - \lineskip .5em% - \begin{tabular}[t]{c}% <------ - \@author% <------ Authors - \end{tabular}\par}% <------ - \vskip 1em% - {\large \@date}% - \end{center}% - \par - \vskip 1.5em} -%opening - -\makeatletter -\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname} -\newcommand{\@xslalph}[1]{% - \ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or %f\or g\or h\or i% - \or j\or k\or l\or m\or n\or o\or p\or r\or s\or %\v{s}% - \or t\or u\or v\or z\or \v{z}%% - \else\@ctrerr\fi% -} -%\AddEnumerateCounter{\xslalph}{\@xslalph}{m}\\ -\providecommand\@enhook{} -\g@addto@macro\@enhook{% - \ifx *\@entemp\def\@tempa{\@enLabel\xslalph}% - \fi} -\makeatother - -\newcommand*\textfrac[2]{ - \frac{\text{#1}}{\text{#2}} -} -\renewcommand\abstractname{Povzetek} -\renewcommand\contentsname{Kazalo vsebine} -\renewcommand\figurename{Slika} -\renewcommand\abstractname{Povzetek} -\newcommand{\iic}{I\textsuperscript{2}C } -\title{Magnetno polje Helmholtzove tuljave --- 23. naloga} -\subtitle{Projektna naloga pri fiziki} -\author{Anton Luka Šijanec, 3. a} -\institute{Gimnazija Bežigrad} -\date{V sredo, 1. junija 2022} -\newcommand\vektor{\overrightarrow} -% \titlegraphic{\includegraphics[width=\textwidth,height=.5\textheight]{img/jangce.jpg}} - -% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260 -\begin{document} - - -\begin{frame} - \titlepage -\end{frame} - -\begin{frame} - \frametitle{Vsebina predstavitve} - \begin{multicols}{2} - \tableofcontents - \end{multicols} -\end{frame} - -\section{Helmholtzova tuljava} -\begin{frame} - \frametitle{\secname} - \begin{multicols}{2} - \begin{itemize} - \item $d=R$ - \item Homogeno in dostopno magnetno polje znotraj dveh navitij - \item Cilj poizkusa: izračunati teoretične vrednosti polja tuljave v prostoru in jih primerjati z izmerjenimi praktičnimi vrednostmi. - \item Pripomočki za praktični preizkus: \SI{3}{\ampere} napajalnik in \SI{10}{\watt} \SI{2,2}{\ohm} uporniki, lakirana bakrena žica za navitja, kamera za videoanalizo s programom Blender, Hallov merilnik magnetnega polja MPU9250 in mikrokrmilnik ESP8266. - \end{itemize} - \begin{figure}[H] - \centering - \includegraphics[width=.5\textwidth]{potrebščine.jpg} - \caption{Tuljava in potrebščine za poizkus} - \end{figure} - \end{multicols} -\end{frame} - -\section{Teorija} -\subsection{Biot-Savartov zakon} -\begin{frame} - \frametitle{\secname} - \framesubtitle{\subsecname} - \begin{multicols}{2} - \begin{itemize} - \item Biot-Savartov zakon: $$B(r)=\frac{\mu_0}{4\pi}\oint_C\frac{Id\ell\times\hat{r}^\prime}{{|r^\prime|}^2}\text{,}$$ - \item Izpeljava: $$\sin\theta=\frac{R}{r = \sqrt{z^2+R^2}} \wedge dB_Z=dB\sin\theta \Longrightarrow$$$$dB_Z=\frac{\mu_0Id\ell}{4\pi}\cdot\frac{R}{\left(z^2+R^2\right)^{3/2}}\text{.}$$ - \item Konstante izpišemo, ostane $d\ell$, kar integriramo v $2\pi R$: $$B_Z=\frac{\mu_0I}{\cancelto{2}{4\pi}}\cdot\frac{\cancel{2\pi}R^2}{\left(z^2+R^2\right)^{3/2}}\text{.}$$ - \end{itemize} - \begin{figure}[H] - \centering - \includegraphics[width=0.5\textwidth]{track.png} - \caption{Avtomatizirano sledenje merilniku v programu Blender} - \end{figure} - \end{multicols} -\end{frame} - -\subsection{Vrednost v središču med navitjema} -\begin{frame} - \frametitle{\secname} - \framesubtitle{\subsecname} - \begin{multicols}{2} - \begin{itemize} - \item Magnetno polje je premo sorazmerno z $I$ in $n$: $$B_1(z)=\frac{n\mu_0R^2I}{{2\left(z^2+R^2\right)}^{3/2}}\text{.}$$ - \item $z=R/2$ je središče med navitjima:$$B_1\left(\frac{R}{2}\right)=\frac{n\mu_0R^2I}{2\left(\left(\frac{R}{2}\right)^2+R^2\right)^{3/2}}\text{.}$$ - \item Iščemo torej $2B_1$. Nekaj korakov kasneje (opisani so v opisu projekta): - $$B(R/2)=\left(\frac{8}{5\sqrt{5}}\right)\frac{n\mu I}{R}$$ - \end{itemize} - \end{multicols} -\end{frame} - -\subsection{Vrednost v središču med navitjema} -\begin{frame} - \frametitle{\secname} - \framesubtitle{\subsecname} -\begin{tikzpicture} -\begin{axis}[legend style={at={(1.2,1)}}, anchor=north west, -ylabel = {jakost magnetnega polja}, -xlabel = {razdalja na osi}, -x = 21cm -] -\addplot gnuplot [raw gnuplot, id=test, mark=none]{ -m = pi*4e-7; -R = 0.068; -N = 320; -I = 0.25; -plot [-3*R:3*R] N*m*R**2*I/(2*((x-R/2)**2+R**2)**(3/2)); -}; -\addlegendentry{os skozi središči navitij (L)} -\addplot gnuplot [raw gnuplot, id=test, mark=none]{ -m = pi*4e-7; -R = 0.068; -N = 320; -I = 0.25; -plot [-3*R:3*R] N*m*R**2*I/(2*((x+R/2)**2+R**2)**(3/2)); -}; -\addlegendentry{os skozi središči navitij (D)} -\addplot gnuplot [raw gnuplot, id=test, mark=none]{ -m = pi*4e-7; -R = 0.068; -N = 320; -I = 0.25; -plot [-3*R:3*R] N*m*R**2*I/(2*((x-R/2)**2+R**2)**(3/2)) + N*m*R**2*I/(2*((x+R/2)**2+R**2)**(3/2)); -}; -\addlegendentry{os skozi središči navitij (L+D)} -\end{axis} -\end{tikzpicture} - -\end{frame} - -\subsection{Numerična obdelava} -\begin{frame} - \frametitle{\secname} - \framesubtitle{\subsecname} - \begin{multicols}{2} - \begin{itemize} - \item Predstavljamo si, da je krog tridesetkotnik, tedaj lahko integral spremenimo v $\Sigma$. - \item Simulacija površinskega prereza s programom: \texttt{./numerično.c 0.088 3 17 0.0002 1000 30 pgm > izhod.pgm}. - \end{itemize} - \begin{figure}[H] - \centering - \includegraphics[width=0.5\textwidth]{out.png} - % \caption{Simulacija površinskega prereza s programom: \texttt{./a.out 0.088 3 17 0.0002 1000 30 pgm > out.pgm}} - \end{figure} - \end{multicols} -\end{frame} - -\section{Praktična meritev} -\begin{frame} - \frametitle{\secname} - \begin{itemize} - \item Osem relativno uspelih meritev, od teh tri na troamperskem toku, ostale na dvoamperskem. - \item Videoanaliza z \textit{autotracking} funkcijo programa Blender za pozicijo merilnika v odvisnosti od časa. - \item 24553 merilnih mest. Podatki so po obdelavi predstavljeni v obliki $B$ v odvisnosti od $(x;y)$ pri dveh različnih tokovih. - \end{itemize} -\end{frame} -\subsection{Izluščene vrednosti na osi tuljave} -\begin{frame} - \frametitle{\secname} - \framesubtitle{\subsecname} - \begin{itemize} - \item Programsko izluščene vrednosti v pasu $\pm\SI{0,5}{\centi\meter}$ okoli osi. - \item Takih meritev je 15919. - \item Primerjava z grafom. - \item Prilagoditvena krivulja. -\end{frame} - -\section{Posnetki zaslona} -\subsection{LoggerPro} -\begin{frame} - \frametitle{\secname} - \framesubtitle{\subsecname} - \begin{frame} - \centering - \includegraphics[width=0.5\textwidth]{pro.png} - \caption{LoggerPro} - \end{figure} -\end{frame} - -\section{Posnetki zaslona} -\subsection{gnuplot} -\begin{frame} - \frametitle{\secname} - \framesubtitle{\subsecname} - \begin{frame} - \centering - \includegraphics[width=0.5\textwidth]{gnuplot.png} - \caption{LoggerPro} - \end{figure} -\end{frame} -%\subsection{Formula \sim} -%\begin{frame} -% \frametitle{\secname} -% \framesubtitle{\subsecname} -% \begin{multicols}{2} -% \begin{itemize} -% \item Enačba Ciolkovskega ali enačba idealne rakete -% -% \end{itemize} -% \end{multicols} -%\end{frame} - -\section{Viri} -\begin{frame}{\secname} - %\nocite{*} - %\printbibliography[title={Viri}] - Viri so navedeni v opisu projekta. -\end{frame} -\subsection*{Licence slik} -\begin{frame}{\secname}{\subsecname} - \begin{itemize} - % \setcounter{enumi}{-1} - % \item \href{https://xn--jha.ga/raydevlin}{Ray Devlin} \href{https://w.wiki/nbq}{\textit{Wanzhou City Slums}} \ccLogo\ccAttribution\ CC-BY 2.0 Generic (\shortlink{ccby20g}) - \item Vse slike so \copyright Anton Luka Šijanec 2021 - \end{itemize} -\end{frame} -\section{Zaključek} -\begin{frame}{\secname} -\begin{itemize} -\item Hvala za pozornost! - -\item Vprašanja? - -\item Hvala Adrianu Sebastianu Šiški in Oliverju Wagnerju za pomoč pri videoanalizi. %Ta dokument je informativne narave in se lahko še spreminja. -% Najnovejša različica, to je \hologo{LaTeX} izvorna koda in PDF dokumenti, je na voljo v mojem šolskem Git repozitoriju na naslovu \url{https://git.sijanec.eu/sijanec/sola-gimb-3/}. -% Povezava za prenos zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/fiz/naloga/predstavitev/dokument.pdf}. -\end{itemize} -\end{frame} -\if\razhroscevanje1 - \subsection*{Razhroščevalne informacije} - \begin{frame}{\secname}{\subsecname} - \begin{itemize} - \item Konec generiranja dokumenta: \today\ ob \currenttime. - \item Grafi imajo natančnost \functionSamples\space točk na graf. - %\item Dokument se je generiral R0qK1KR2 \SI{}{\second}. - \item Doument se je generiral aaasecgeninsaaa \SI{}{\second}. - \item Pred objavo izklopite razhroščevanje. To storite tako, da v glavi dokumenta nastavite ukaz \texttt{razhroscevanje} na 0. - \end{itemize} - \end{frame} -\fi -\end{document} diff --git a/fiz/naloga/relacije/2A.tsv b/fiz/naloga/relacije/2A.tsv index 846fcd2..8b390c4 100644 --- a/fiz/naloga/relacije/2A.tsv +++ b/fiz/naloga/relacije/2A.tsv @@ -1,13652 +1,13652 @@ -0 -0.008132 -0.018770 30.93 207.45 4.85 209.79916563228 0.000102 -0.007 -0.008082 -0.018774 30.93 207.45 4.85 209.79916563228 0.000102 -0.093 -0.008025 -0.018789 30.93 207.45 4.85 209.79916563228 0.000102 -0.102 -0.008019 -0.018843 29.49 210.34 6.59 212.49942070509 0.000102 -0.114 -0.008016 -0.018838 29.49 210.34 6.59 212.49942070509 0.000102 -0.131 -0.008012 -0.018850 29.49 210.34 6.59 212.49942070509 0.000102 -0.148 -0.008002 -0.018850 29.49 210.34 6.59 212.49942070509 0.000102 -0.167 -0.007999 -0.018848 29.49 210.34 6.59 212.49942070509 0.000102 -0.185 -0.007994 -0.018846 29.49 210.34 6.59 212.49942070509 0.000102 -0.198 -0.007989 -0.018845 29.49 210.34 6.59 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0.002861 -1.438477 581.233704 -76.628174 586.26492725748 0.000102 +68.051 0.005565 0.003061 -1.438477 581.233704 -76.628174 586.26492725748 0.000102 +68.07 0.007579 0.003266 -1.438477 581.233704 -76.628174 586.26492725748 0.000102 +68.08 0.009624 0.003444 -1.438477 581.233704 -76.628174 586.26492725748 0.000102 +68.099 0.011611 0.003595 -1.438477 581.233704 -76.628174 586.26492725748 0.000102 +68.119 0.013661 0.003742 -1.438477 581.233704 -76.628174 586.26492725748 0.000102 +68.129 0.015745 0.003886 -1.438477 581.233704 -76.628174 586.26492725748 0.000102 +68.148 0.017836 0.004026 -1.078858 577.986572 -76.628174 583.04503976749 0.000102 +68.167 0.019941 0.004115 -1.078858 577.986572 -76.628174 583.04503976749 0.000102 +68.187 0.022076 0.004199 -1.078858 577.986572 -76.628174 583.04503976749 0.000102 +68.196 0.024160 0.004248 -1.078858 577.986572 -76.628174 583.04503976749 0.000102 +68.216 0.026230 0.004282 -1.078858 577.986572 -76.628174 583.04503976749 0.000101 +68.236 0.028283 0.004354 -1.078858 577.986572 -76.628174 583.04503976749 0.000101 +68.254 0.030357 0.004396 -1.078858 577.986572 -76.628174 583.04503976749 0.000101 +68.264 0.032456 0.004417 -3.236573 562.833374 -77.321640 568.12896274112 0.000100 diff --git "a/fiz/naloga/su\305\276enjstvo/lokacije.c" "b/fiz/naloga/su\305\276enjstvo/lokacije.c" index bc9e2e1..1d759cf 100644 --- "a/fiz/naloga/su\305\276enjstvo/lokacije.c" +++ "b/fiz/naloga/su\305\276enjstvo/lokacije.c" @@ -2,6 +2,8 @@ #include // datoteka se mora začeti s prvim frameom - prižgana lučka #include #define STR0(x) (x ? x : "") +#define ŠIR 3840 // moramo vedeti, da GIMP koordinate pretvorimo v blender koo +#define VIŠ 2160 // nisem prepričan. če se ti zdi, da je to nepotrebno => mail int main (int argc, char ** argv) { long double kalibracijske_vrednosti[] = { 14.20, -2.35, 2.25 }; if (argc < 1+1+7) { @@ -12,18 +14,19 @@ int main (int argc, char ** argv) { char * cp; int merilo_leva_šir = strtol(argv[5], &cp, 10); cp++; - int merilo_leva_viš = strtol(cp, NULL, 10); + int merilo_leva_viš = VIŠ-strtol(cp, NULL, 10); int merilo_desna_šir = strtol(argv[6], &cp, 10); cp++; - int merilo_desna_viš = strtol(cp, NULL, 10); + int merilo_desna_viš = VIŠ-strtol(cp, NULL, 10); int središče_šir = strtol(argv[7], &cp, 10); cp++; - int središče_viš = strtol(cp, NULL, 10); + int središče_viš = VIŠ-strtol(cp, NULL, 10); int kotna_točka_šir = strtol(argv[8], &cp, 10); cp++; - int kotna_točka_viš = strtol(cp, NULL, 10); + int kotna_točka_viš = VIŠ-strtol(cp, NULL, 10); long double pikslov_v_1m = 10*sqrtl(powl(labs(merilo_leva_šir-merilo_desna_šir), 2)+powl(labs(merilo_leva_viš-merilo_desna_viš), 2)); - fprintf(stderr, "pikslov v 1m je %Lf\n", pikslov_v_1m); + long double kot = atan2l(kotna_točka_viš - središče_viš, kotna_točka_šir - središče_šir); + fprintf(stderr, "pikslov v 1m je %Lf\tkot je %Lf rad\n", pikslov_v_1m, kot); char buf[512]; fgets(buf, 512, stdin); int i = 0; @@ -53,7 +56,11 @@ int main (int argc, char ** argv) { for (unsigned int j = 0; j <= frame+1; j++) fgets(millis, 512, timestamps); unsigned int milliseconds = strtoul(millis, NULL, 10); - fprintf(stdout, "%lu\t%u\t%Lf\t%Lf\n", frame - starting_frame, milliseconds - starting_milliseconds, piksel_šir, piksel_viš); + + long double točka_šir_ro = piksel_šir*cosl(kot)-piksel_viš*sinl(kot); + long double točka_viš_ro = piksel_šir*sinl(kot)+piksel_viš*cosl(kot); + + fprintf(stdout, "%lu\t%u\t%Lf\t%Lf\n", frame - starting_frame, milliseconds - starting_milliseconds, točka_šir_ro, točka_viš_ro); fgets(buf, 512, stdin); } } diff --git "a/fiz/naloga/su\305\276enjstvo/transformiraj.sh" "b/fiz/naloga/su\305\276enjstvo/transformiraj.sh" index 8b379ac..d0c9aea 100755 --- "a/fiz/naloga/su\305\276enjstvo/transformiraj.sh" +++ "b/fiz/naloga/su\305\276enjstvo/transformiraj.sh" @@ -1,4 +1,5 @@ #!/bin/bash +gcc lokacije.c -lm for i in *.tsv do t=`rev <<<$i | cut -d. -f2- | rev` diff --git a/fiz/naloga/transformirane/2A1.tsv b/fiz/naloga/transformirane/2A1.tsv index 9f8fd08..a09da1a 100644 --- a/fiz/naloga/transformirane/2A1.tsv +++ b/fiz/naloga/transformirane/2A1.tsv @@ -1,2661 +1,2661 @@ -0 0 -0.008132 -0.018770 -1 16 -0.008082 -0.018774 -2 33 -0.008064 -0.018781 -3 50 -0.008042 -0.018787 -4 66 -0.008025 -0.018789 -5 83 -0.008019 -0.018843 -6 100 -0.008019 -0.018843 -7 116 -0.008016 -0.018838 -8 133 -0.008012 -0.018850 -9 150 -0.008002 -0.018850 -10 166 -0.007999 -0.018848 -11 183 -0.007994 -0.018846 -12 200 -0.007989 -0.018845 -13 216 -0.007999 -0.018848 -14 233 -0.007999 -0.018844 -15 250 -0.008000 -0.018839 -16 266 -0.007996 -0.018808 -17 283 -0.007980 -0.018837 -18 300 -0.007982 -0.018836 -19 316 -0.007980 -0.018839 -20 333 -0.007975 -0.018835 -21 350 -0.007945 -0.018832 -22 366 -0.007953 -0.018808 -23 383 -0.007976 -0.018812 -24 400 -0.007974 -0.018808 -25 416 -0.007956 -0.018804 -26 433 -0.007884 -0.018853 -27 450 -0.007838 -0.018849 -28 466 -0.007826 -0.018847 -29 483 -0.007823 -0.018842 -30 500 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32616 0.003349 -0.065067 -1958 32633 0.003276 -0.065379 -1959 32650 0.003743 -0.065025 -1960 32666 0.004980 -0.063631 -1961 32683 0.007016 -0.061127 -1962 32700 0.009475 -0.057960 -1963 32716 0.011616 -0.055010 -1964 32733 0.013260 -0.052292 -1965 32750 0.014350 -0.050197 -1966 32766 0.015202 -0.048442 -1967 32783 0.015991 -0.046971 -1968 32800 0.016779 -0.045871 -1969 32816 0.017478 -0.045202 -1970 32833 0.017724 -0.044753 -1971 32850 0.017670 -0.044669 -1972 32866 0.017303 -0.045488 -1973 32883 0.016479 -0.046833 -1974 32900 0.015802 -0.048005 -1975 32916 0.015599 -0.049234 -1976 32933 0.015501 -0.050294 -1977 32950 0.015410 -0.051149 -1978 32966 0.015370 -0.051525 -1979 32983 0.015459 -0.051198 -1980 33000 0.015622 -0.050607 -1981 33016 0.015844 -0.050077 -1982 33033 0.015989 -0.049853 -1983 33050 0.016051 -0.049904 -1984 33066 0.016111 -0.049975 -1985 33083 0.016111 -0.049956 -1986 33100 0.016062 -0.049960 -1987 33116 0.016013 -0.050011 -1988 33133 0.016031 -0.050007 -1989 33150 0.016083 -0.049972 -1990 33166 0.016111 -0.049955 -1991 33183 0.016117 -0.049956 -1992 33200 0.016119 -0.049955 -1993 33216 0.016099 -0.049928 -1994 33233 0.016108 -0.049905 -1995 33250 0.016139 -0.049899 -1996 33266 0.016172 -0.049926 -1997 33283 0.016175 -0.049892 -1998 33300 0.016174 -0.049875 -1999 33316 0.016176 -0.049866 -2000 33333 0.016182 -0.049870 -2001 33350 0.016191 -0.049907 -2002 33366 0.016218 -0.049899 -2003 33383 0.016230 -0.049878 -2004 33400 0.016230 -0.049873 -2005 33416 0.016231 -0.049872 -2006 33433 0.016233 -0.049869 -2007 33450 0.016235 -0.049867 -2008 33466 0.016248 -0.049859 -2009 33483 0.016259 -0.049852 -2010 33500 0.016268 -0.049865 -2011 33516 0.016272 -0.049827 -2012 33533 0.016279 -0.049802 -2013 33550 0.016295 -0.049797 -2014 33566 0.016294 -0.049795 -2015 33583 0.016294 -0.049794 -2016 33600 0.016303 -0.049816 -2017 33616 0.016308 -0.049819 -2018 33633 0.016311 -0.049815 -2019 33650 0.016305 -0.049808 -2020 33666 0.016304 -0.049802 -2021 33683 0.016320 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31367 0.156344 0.082310 -1883 31383 0.157205 0.082312 -1884 31400 0.158002 0.082255 -1885 31417 0.158802 0.082231 -1886 31433 0.159614 0.082190 -1887 31450 0.160423 0.082152 -1888 31467 0.161233 0.082148 -1889 31483 0.161977 0.082307 -1890 31500 0.162693 0.082346 -1891 31517 0.163421 0.082405 -1892 31533 0.164150 0.082464 -1893 31550 0.164878 0.082523 -1894 31567 0.165606 0.082582 -1895 31583 0.165936 0.082430 -1896 31600 0.166570 0.082272 -1897 31617 0.167152 0.082130 -1898 31633 0.167733 0.081988 -1899 31650 0.167889 0.082272 -1900 31667 0.168219 0.082426 -1901 31683 0.168386 0.081951 -1902 31700 0.168591 0.081643 -1903 31717 0.168797 0.081336 -1904 31733 0.169002 0.081028 -1905 31750 0.168995 0.080507 -1906 31767 0.169043 0.080042 -1907 31783 0.169122 0.079553 -1908 31800 0.169193 0.078004 -1909 31817 0.169264 0.076735 -1910 31833 0.169368 0.075466 -1911 31850 0.169463 0.074198 -1912 31867 0.169558 0.072929 -1913 31883 0.169440 0.071234 -1914 31900 0.169379 0.069651 -1915 31917 0.169540 0.068099 -1916 31933 0.169642 0.066539 -1917 31950 0.169532 0.064126 -1918 31967 0.169675 0.062161 -1919 31983 0.169767 0.060137 -1920 32000 0.169868 0.058547 -1921 32017 0.169983 0.057171 -1922 32033 0.169709 0.055717 -1923 32050 0.169887 0.054118 -1924 32067 0.170186 0.051703 -1925 32083 0.170429 0.049514 -1926 32100 0.170672 0.046471 -1927 32117 0.170996 0.043948 -1928 32133 0.170872 0.042200 -1929 32150 0.171049 0.040562 -1930 32167 0.171198 0.038897 -1931 32183 0.171341 0.037216 -1932 32200 0.171484 0.035534 -1933 32217 0.171202 0.033641 -1934 32233 0.171340 0.031744 -1935 32250 0.171397 0.029011 -1936 32267 0.171454 0.026502 -1937 32283 0.171544 0.023999 -1938 32300 0.171625 0.021494 -1939 32317 0.171493 0.020482 -1940 32333 0.171418 0.019076 -1941 32350 0.171342 0.017671 -1942 32367 0.171266 0.016266 -1943 32383 0.171215 0.014435 -1944 32400 0.171411 0.012664 -1945 32417 0.171388 0.009692 -1946 32433 0.171592 0.007074 -1947 32450 0.171533 0.003807 -1948 32467 0.171606 0.001430 -1949 32483 0.171587 0.000410 -1950 32500 0.171476 -0.000763 -1951 32517 0.171435 -0.002028 -1952 32533 0.170897 -0.004318 -1953 32550 0.170699 -0.006277 -1954 32567 0.170524 -0.007746 -1955 32583 0.170368 -0.008156 -1956 32600 0.170064 -0.008628 -1957 32617 0.169604 -0.009564 -1958 32633 0.169221 -0.010395 -1959 32650 0.168980 -0.011228 -1960 32667 0.168724 -0.011853 -1961 32683 0.168352 -0.012000 -1962 32700 0.167942 -0.012476 -1963 32717 0.167359 -0.013097 -1964 32733 0.166821 -0.013735 -1965 32750 0.166257 -0.014337 -1966 32767 0.165588 -0.015061 -1967 32783 0.164984 -0.015586 -1968 32800 0.164362 -0.016041 -1969 32817 0.163616 -0.016574 -1970 32833 0.162764 -0.017201 -1971 32850 0.161949 -0.017801 -1972 32867 0.161131 -0.018220 -1973 32883 0.160277 -0.018425 -1974 32900 0.159283 -0.018455 -1975 32917 0.158229 -0.018505 -1976 32933 0.157147 -0.018696 -1977 32950 0.155939 -0.019233 -1978 32967 0.154808 -0.019678 -1979 32983 0.153570 -0.020090 -1980 33000 0.152363 -0.020343 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33550 0.108086 -0.014799 -2014 33567 0.106546 -0.014813 -2015 33583 0.104971 -0.014897 -2016 33600 0.103378 -0.014929 -2017 33617 0.101676 -0.014869 -2018 33633 0.099921 -0.014810 -2019 33650 0.098161 -0.014730 -2020 33667 0.096348 -0.014549 -2021 33683 0.094419 -0.014195 -2022 33700 0.092338 -0.013771 -2023 33717 0.090100 -0.013240 -2024 33733 0.087780 -0.012765 -2025 33750 0.085403 -0.012382 -2026 33767 0.082921 -0.011847 -2027 33783 0.080477 -0.011269 -2028 33800 0.078021 -0.010861 -2029 33817 0.075550 -0.010358 -2030 33833 0.073027 -0.009982 -2031 33850 0.070645 -0.009890 -2032 33867 0.068397 -0.009817 -2033 33883 0.066283 -0.009828 -2034 33900 0.064443 -0.009934 -2035 33917 0.064443 -0.009934 -2036 33933 0.064443 -0.009934 -2044 34067 0.046295 -0.007947 -2045 34083 0.046295 -0.007947 -2046 34100 0.044627 -0.008026 -2047 34117 0.042935 -0.008102 -2048 34133 0.041185 -0.008176 -2049 34150 0.039408 -0.008244 -2050 34167 0.037599 -0.008259 -2051 34183 0.035861 -0.008353 -2052 34200 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33384 0.008681 -0.074873 -2004 33400 0.007849 -0.076376 -2005 33417 0.007026 -0.077559 -2006 33434 0.006254 -0.078463 -2007 33450 0.005517 -0.079116 -2008 33467 0.004770 -0.079700 -2009 33484 0.004001 -0.080486 -2010 33500 0.003236 -0.081341 -2011 33517 0.002574 -0.082162 -2012 33534 0.001627 -0.083038 -2013 33550 0.001046 -0.083518 -2014 33567 0.000398 -0.084337 -2015 33584 -0.000181 -0.084507 -2016 33600 -0.000776 -0.084724 -2017 33617 -0.001298 -0.084940 -2018 33634 -0.001812 -0.085135 -2019 33650 -0.002259 -0.085461 -2020 33667 -0.002685 -0.086021 -2021 33684 -0.003098 -0.086678 -2022 33700 -0.003469 -0.087409 -2023 33717 -0.003756 -0.088160 -2024 33734 -0.004085 -0.088669 -2025 33750 -0.004309 -0.089246 -2026 33767 -0.004575 -0.089955 -2027 33784 -0.004849 -0.090616 -2028 33800 -0.005063 -0.090980 -2029 33817 -0.005146 -0.091142 -2030 33834 -0.005125 -0.091170 -2031 33850 -0.005026 -0.091118 -2032 33867 -0.004897 -0.091148 -2033 33884 -0.004699 -0.091289 -2034 33900 -0.004410 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creative commons ni moč uporabljati. + @echo VSEBINE DOKUMENTA nisem izdal pod nobenim dovoljenjem, zato uporaba + @echo slik v dokumentu teoretično pravno ni dovoljena. + @echo + @echo xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx + @echo xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx + @echo xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx + @echo xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx + wget -c upload.wikimedia.org/wikipedia/commons/b/b9/Phase_shift-ru.svg + sed -e s/Фазовый/fazni/g < Phase_shift-ru.svg | sed -e s/сдвиг/zamik/g > zamik.svg + convert zamik.svg zamik.png + wget -c upload.wikimedia.org/wikipedia/commons/6/6d/ElectricityUCTE.svg + convert ElectricityUCTE.svg omrežje.png + wget -c upload.wikimedia.org/wikipedia/commons/a/ab/HVDC_Europe.svg + convert HVDC_Europe.svg hvdc.png + wget -c "`curl -L xn--jha.ga/entsoe | sed -e "s/