%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This is the document source index.tex.
% Read this and then change it to your needs. But first make sure
% that your editor window is wide enough to show the top line of %
% signs above to its full width without wrapping
% Note that this file is "compiled". In other words, it is turned
% into a pdf file, web pages, or both. What you put in this file
% determines what ends up in the pdf or on the web pages.
% First is the header of the document. The actual document text
% starts further down, below the \begin{document} line. But you must
% get the header right too.
%
% Note that everything following a percent sign is ignored. That
% includes explanatory comments like the ones you are reading right
% now, as well as disabled formatting commands. To enable a disabled
% formatting command, remove the percent sign.
%
% If you still have questions after looking at this example document,
% and you will have, look at the intro_to_latex web page in the l2h
% help-files subfolder next.
% Leave the next two lines alone please:
\def\classline{\documentclass[12pt,oneside,openany]{book}}
%begin{latexonly}
% The next line sets various options appropriate for an FSU Thesis
% (fsuthesis.cls is Copyright (c) 2010 by Bret Whissel):
\def\classline{\documentclass[11pt]{fsuthesis}}
% Some additional options you might conceivably want to add:
% 1) If you want to print a hardcopy, add ",hardcopy" (without the
% quotes) between the square brackets above. That changes the
% margins a bit to allow easier side-stapling or binding.
% 2) Adding ",chapterleaders" puts dotted lines in the table of contents
% for chapter entries.
% 3) Adding ",expanded" makes the line spacing double-spaced (almost).
% Leave the next two lines alone please:
%end{latexonly}
\classline
%%%%%%%%%%%%%%%%%%%%%%%%%% INTERNATIONIZATION %%%%%%%%%%%%%%%%%%%%%%%%%%
% International Characters:
%
% Note: see the "examples.html" web page in the l2h "help-files"
% folder if you need to deal with Greek characters (besides in
% mathematics, where there is no problem) or with nonWestern European
% characters. In particular, you will then need to replace this
% INTERNATIONALIZATION section with the one you find in template #5.
% In that case you will also need to replace {pdflatex} in \pdfengine
% further down by {xelatex}. And you must have xelatex installed.
%
% WARNING: The next two lines MUST be as given, do NOT touch them in ANY way:
%begin{latexonly}
% Start of the internationalization section:
%
% The following package allows latex to recognize various Western
% European UTF-8 characters, like the ñ in Español:
\usepackage[utf8]{inputenc}
%
% An alternative package that seems to have some more characters is
% utf8x. To try it, put % before the \usepackage[utf8]{inputenc} line
% above. And then remove the % from the line below:
%\usepackage[utf8x]{inputenc}
% No, it won't do Greek or nonWestern European.
%
% WARNING: The next two lines MUST be as given, do NOT touch them in ANY way:
% End of the internationalization section.
%end{latexonly}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% BASIC PACKAGES %%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Hyperref is needed for putting active links in pdf files.
%
% Note: you might need to disable this for the final copy you submit, see
% the FSU requirements on web page links. However, active links in the
% initial versions will make life much easier for your committee members.
%
% TO DISABLE ACTIVE LINKS FOR THE FINAL VERSION, PUT A % AT THE START OF
% ALL LINES FROM HERE TO THE BLANK LINE:
\usepackage[final]{hyperref}
\hypersetup{
pdfborder={0 0 0.5},
citebordercolor={0.7 0.7 0.7},
filebordercolor={0.7 0.7 0.7},
linkbordercolor={0.7 0.7 0.7},
menubordercolor={0.7 0.7 0.7},
runbordercolor={0.7 0.7 0.7},
urlbordercolor={0 0 0},
pdfsubject={Dissertation on Miatas},
pdfkeywords={Quantum Mechanics} {Special Relativity} {Miatas} {Doppler effect},
breaklinks
}
%begin{latexonly}
\usepackage[all]{hypcap}[2008/09/08]\renewcommand{\hypcapspace}{1pt}
%end{latexonly}
% Html defines the web-page related commands. It is only needed if
% you want to make web pages of your document.
% TO DISABLE, PUT A % IN FRONT OF THE NEXT LINE:
\usepackage{html}
% BUT THEN REMOVE THE LEADING % FROM THE NEXT TWO LINES:
%\newcommand{\htmlimage}[2]{}
%\newcommand{\latexhtml}[2]{#1}
% This will also clobber the comment environment. So you will also
% need to move \begin{comment}...\end{comment} stuff behind the
% \end{document} line.
% Epsf is a good way to include figures, and is preferred here:
\usepackage{epsf}
% Float is wanted to prevent latex from putting figures wherever it wants:
%\usepackage{float}
% Graphics is needed to manipulate figures (resize, rotate, ...):
\usepackage{graphicx}
% The next package is needed internally for FSU thesis class:
\usepackage[overload]{textcase}
% Unfortunately, latex2html does not support the tocloft package. So
% musical examples will have to be numbered along with the figures.
\latexhtml{}{
\newenvironment{musex}
{\begin{figure}}
{\end{figure}}
% If you have musical examples, you may want to change {List of Figures}
% below to {List of Figures and Musical Examples}:
\renewcommand{\listfigurename}{List of Figures}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%% DOCUMENT OPTIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%
% In general, when you need more information on something done by a
% package, searching the web for the package name is definitely
% something to try. Almost all packages have pdf instructions.
% Usually a thesis does not have an index. If you want to create one
% for your thesis, see index1.txt in the l2h help-files for how to do
% it. You would put \usepackage{makeidx}\makeindex below this
% comment. You would also put code to actually print the index near
% the very end of this file. And you would add index entries inside
% the text using the \index command.
% Natbib takes care of the format of bibliographic references nicely:
\usepackage[square,numbers]{natbib}
% Options in the square brackets must be separated by commas as in the
% example above. Some more important ones are:
% square: uses square brackets instead of parentheses in citations.
% numbers: uses numerical references instead of author-year.
% super: uses superscript numbers for references.
% comma: separates a list of references using commas.
% sort: sorts a list of references in the bibliography order.
% sort&compress: also compresses say 3,4,5,6 into 3-6
% (See the documentation of the natbib package for more details)
% Additional math symbols from the American Mathematical Society (AMS):
%\usepackage{amsfonts} %includes \mathbb{U} for blackboard bold uppercase
%\usepackage{amssymb} %complete AMS symbol definition, includes amsfonts
%\usepackage[mathscr]{eucal} %makes Euler script available as \mathscr
%\usepackage{amsbsy} %allows bolding of additional characters
% Poor man's bold: \pmb{TEXT} will simulate bold face if the
% characters in TEXT are not available in bold face. Use only if
% \textbf{TEXT}, or \mathbf{TEXT} in math, does not work.
\newcommand{\pmb}[1]{\setbox0=\hbox{#1}\kern-.025em\copy0\kern-\wd0%
\kern.05em\copy0\kern-\wd0\kern-.025em\raise.0433em\box0}
% Note: the AMS packages above will normally give you *real* bold
% characters. Find their documentation on the web.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FORMATTING %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Important note: pdf readers like Adobe Acrobat tend to shrink the
% page when printing it. You need to select an option in the print
% menu to avoid that. Or live with a shrunken page.
% If the last line on a page is the first line of a new paragraph,
% it's called club line. If the first line of a page is the last line
% of a paragraph, it is called a widow line. The thesis guidelines
% say to avoid them. If the below is not enough, in the *final*
% version use a strategically placed \newpage command:
\widowpenalty=9999
\clubpenalty=9999
% Set LateX to number subsubsections.
% To enable, remove the % in front of the next line:
%\setcounter{secnumdepth}{3}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% PICTURES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% IMPORTANT: You normally need to include "pictures", (like data
% plots, photographs, etcetera), in your document. This section tells
% you what format these must be in.
%
\latexhtml{
% The next two lines specify in which format pictures must be for
% the *pdf* version of your document. In particular, they require
% that you provide every picture in "noneps" format (i.e. gif, jpg,
% jpeg, pdf, png, but *not* eps):
\newcommand{\putpicture}[1]{\includegraphics{#1}}
\newcommand{\pdfengine}{pdflatex} % or {xelatex} instead of {pdflatex}
}{
% The next two lines specify in which format pictures must be for
% the *web pages* version of your document. In particular, they
% require that you provide every picture in "eps" format:
\newcommand{\putpicture}[1]{\epsffile{#1.eps}}
\newcommand{\webengine}{latex}
}
% The above is not a big deal:
%
% Suppose that you have, say, a jpg picture, but you need an eps one.
% Well, there is a folder named "convert" inside the l2h folder. It
% has a subfolder "any_eps". Put a copy of your jpg picture inside
% that folder and double-click "convert_jpg". Bingo, an eps version of
% your picture is produced. Just put it in with your document.
%
% Conversely, suppose you have an eps picture, but you need an noneps
% one. Simply put a copy of the eps picture inside the "eps_pdf"
% subfolder and double-click "convert_eps". Bingo, a pdf version will
% be produced.
%
% You can instead use a commercial program like Adobe Photoshop, or a
% free one like the gimp, to turn jpg, gif, png, ... pictures into eps
% ones or vice-versa. See the "images" web page inside the l2h
% "help-files" folder for more.
%
% See the "plots" web page for more on how to make data plots in eps
% format. There are also additional examples in the "plots" subfolder
% of example subfolder. These latter examples show exactly how the
% plots in this document were made using gnuplot.
% A note for these who would want to mess around with the definitions
% of \pdfengine and \webengine above. The first "word", (i.e. up to
% the first space, if any), must be an executable file in your path,
% (as set by init.bat), when l2h is running. Do not use any quotes in
% the definition. Further requirements for MS Windows users: The
% default extension is .exe, so {latex} really means {latex.exe} say.
% If the executable has extension .cmd, it must be specified, like in
% {latex.cmd} say. If the executable has extension .bat, it must be
% specified *and* the executable needs to be preceded by the word
% "call", like in {call latex.bat} say. Also, if there is a path
% name, use the normal \, not /, in it. You cannot have spaces in the
% path name either: say {C:\Program Files\latex.exe} does not work but
% {C:\PROGRA~1\latex.exe} is OK.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% WEB PAGES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% THIS BLOCK DETERMINES THE SETTINGS FOR THE WEB PAGES. IGNORE IT IF
% YOU ARE NOT PLANNING TO CREATE WEB PAGES OF THE DOCUMENT.
% In a \[re]newcommand{\command}{...}, do *NOT* forget the brackets
% around {\command}. (Yes, this is a latex2html quirk.)
% Hthtml simplifies making active url links, see the latex2html web
% page inside the help-files folder. Enable by removing the next %:
%\usepackage{hthtml}
% Then you can also create a \weblink{TEXT}{URL} command for active
% links to the web by removing the % signs from the next 3 lines:
%\latexhtml
%{\newcommand{\weblink}[2]{\href{#2}{#1}\htlink{{}}{#2}}}
%{\newcommand{\weblink}[2]{\htlink{#1}{#2}}}
% and a \weburl{URL} command by doing the same for the next 3 lines:
%\latexhtml
%{\newcommand{\weburl}[1]{\url{#1}}}
%{\newcommand{\weburl}[1]{\hturl{#1}}}
% This defines the form of the web page data command:
\newcommand{\webpages}[2]{}
% Change the language of some titles like "Table of Contents". See
% subfolder "versions" in l2h for what languages are defined:
\webpages{TITLES_LANGUAGE}{english}
% The following lines describe the short strings that go into the top
% and bottom bars of web pages. Change the texts as needed. Note
% that the strings are in html format.
%
% Warning: you cannot use the characters <, >, {, }, or & in the text
% (besides in html code). Instead use < for <, > for >, {
% for {, } for }, and & for &. Note that is blank
% space and © the copyright symbol.
%
% To insert a link named LINKNAME with address LINKURL, in the desired
% place use LINKNAME. See the example
% links below. Omit class=runnerb for a background (page) color bar.
%
% To insert an image NAME.EXT (e.g. mylogo.jpg), put NAME.EXT inside
% the "keep" subfolder of web-pages. (In the web-pages folder itself,
% it is likely to be deleted eventually.) Then below, in the desired
% place, use 
. To find
% the right values of numbers NNN and NN, you can, for example, open
% the image with your web browser. The correct values will be shown
% in the browser top bar.
%
\webpages{TITLE}{Why White Miatas are Faster} % used for the top web page only
\webpages{TOP_LEFT_TEXT}{ Why White Miatas are Faster}
\webpages{TOP_CENTER_TEXT}{ }
\webpages{TOP_RIGHT_TEXT}{© Leon van Dommelen }
\webpages{TOP_BORDER}{4} % use 0 for no border, 1 for a thin frame
\webpages{TOP_CLASS}{class=runner} % omit class=runner for background color
\webpages{BOT_LEFT_TEXT}{ FAMU-FSU College of Engineering}
\webpages{BOT_CENTER_TEXT}{ }
\webpages{BOT_RIGHT_TEXT}{Processed with l2h }
\webpages{BOT_BORDER}{3} % use 0 for no border, 1 for a thin frame
\webpages{BOT_CLASS}{class=runnerb} % omit class=runnerb for background color
\webpages{NAVIGATION_HEIGHT}{80} % navigation frame height in a frames version
% Where people end up if they back out of the document web pages.
% You may want to have this point to your home page:
\webpages{EXTERNAL_UP_LINK}{../index.html} % or your home page url?
\webpages{EXTERNAL_UP_TITLE}{Format selection page} % or: Home page?
% The digit in the next line determines how small the web pages are
% made. If it is 3, a web page contains an entire chapter. If it is
% 4, it contains only a single section, 5 a subsection, etcetera
\webpages{MAX_SPLIT_DEPTH}{4}
% Using \label{sec:NAME} after a sectioning command allows you to refer
% to that sectional unit as \ref{sec:NAME}. Using \secname{NAME}
% does the same, but that also uses NAME as the name of the corresponding
% web page. And you do not have to type the colon. :)
% Do avoid using spaces in NAME.
\newcommand{\secname}[1]{\label{sec:#1}}
% \webpagename{sec_title}{NAME} is for unnumbered sectional units:
\newcommand{\webpagename}[2]{}
% If you do NOT want to use this naming scheme, and revert to
% latex2html default web page names node0001.html, node0002.html, ...,
% you need to remove the stuff inside the next latexonly block:
%begin{latexonly}
\newwrite\wpnames\immediate\openout\wpnames=index.pl
\makeatletter\catcode`\~=12
\renewcommand{\secname}[1]{\def\ls{$fnam =~ s/^}\def\lsb{$/#1/;}%
\immediate\write\wpnames{\ls\@currentlabel\lsb}\label{sec:#1}}
\renewcommand{\webpagename}[2]{%
\def\ls{$fname =~ s/^#1$/#2/;}\immediate\write\wpnames{\ls}}
\catcode`\~=\active\makeatother
%end{latexonly}
% Use \picfrbox inside "picture" environments instead of \framebox.
% (Yes, this is a latex2html quirk.)
\def\picfrbox(#1,#2){\framebox(#1,#2)}
\begin{imagesonly}
\def\picfrbox(#1,#2){\framebox(#1,#2)}
\end{imagesonly}
% If you are planning to hyphenate your web pages, here are some
% things that might be useful.
%
% To prevent a part of your document from being hyphenated, (maybe
% because it is in a different language), enclose it between \nowebhypbeg
% and \nowebhypend tags. Make sure the enclosed part does not extend from
% one web page to the other or neither web page will be hyphenated at all.
\newcommand{\nowebhypbeg}{\latexhtml{}
{\begin{rawhtml}\end{rawhtml}}}
\newcommand{\nowebhypend}{\latexhtml{}
{\begin{rawhtml}\end{rawhtml}}}
%
% To explicitly create a potential web-page hyphenation point somewhere
% use \1 (\0 through \9 do not produce erroneous space in latex2html):
\newcommand{\1}{\latexhtml{\-}{\begin{rawhtml}\end{rawhtml}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%% PLEASE FILL IN THE BASIC DOCUMENT DATA %%%%%%%%%%%%%%%%
% Enter your legal name between the curly brackets:
\author{Leonard Louis van Dommelen}
% In case your name contains a letter, call it a, with an accent,
% write it as \`a, \'a, \^a, \"a, \~a, \=a, \.a, \u{a}, \v{a}, \H{a},
% \t{aa}, \c{a}, \d{a}, or \b{a} for grave, acute, circumflex,
% umlaut, tilde, macron, dot, breve, check, long-umlaut, tie-after,
% cedilla, dot-under, or bar-under respectively. To get rid of the
% normal dot above an accented i, write the i as \i.
% To accomodate search engines, the thesis title should be in *words*,
% *not* mathematics, chemical symbols, Greek letters, etcetera.
% Enter the title of your thesis or dissertation between the curly
% brackets. Use "\protect\\" to start a new line:
\title{
A Theoretical Investigation Into \protect\\
The Increased Speed Of White Miatas \protect\\
Due To Surface-Photon Interaction
}
% Remember: to force a new line in plain text, use \\, \newline, or
% \linebreak[4]. Similarly use \newpage or \pagebreak[4] to force a
% new page. (The difference is whether or not LaTeX will stretch the
% broken line to the right margin, or the broken page to the bottom of
% the page. The 4 means you really insist; use less if not.)
%
% As long as I mention page breaking: If you ever have to change a
% page number to, say, 24, use \setcounter{page}{24} just before where
% latex "cuts the page" in question.
%
% Also, if latex starts "hoarding" figures and tables, instead of
% placing them, use \clearpage to stop it.
% For simplicity, the stuff below will be restricted to the pdf version.
\latexhtml{
% Also enter the formal name of your department:
\department{Department of Mechanical Engineering} % omit this line if none.
% Also enter the formal name of your school or college:
\college{FAMU-FSU College of Engineering}
% Also enter the correct defense date:
\defensedate{April 1, 2013} % or {April 1 2031}
% Also enter the correct graduation semester (Spring, Summer, Fall)
\semester{Spring} % or {Fall} or {Summer}
% and year:
\degreeyear{2013} % or {2032} or so
% Also enter the correct manuscript type:
\manuscripttype{Dissertation} % or {Thesis} or {Treatise}.
% and the correct degree:
\degree{Doctor of Philosophy} % or {Master of Science}
% Your committee (make sure they have the proper graduate directive
% status):
\committeeperson{Jane I{.} Doe}{Professor Directing Dissertation}
\committeeperson{John E{.} Don}{University Representative}
\committeeperson{Doug E{.} Do}{Committee Member}
\committeeperson{Dop E{.} Duck}{Committee Member}
\committeeperson{Hu M{.} I}{Committee Member}
% Also correct your defense date below for the web page version if any:
}{\date{April 1, 2013}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
% Here we start the actual document! :)
% Fix to get the math images properly scaled on the web pages:
\latexhtml{}{\setlength{\textheight}{8.42361in}\setlength{\textwidth}{5.625in}
\setlength{\vsize}{8.42361in}\setlength{\hsize}{5.625in}}
% When running a spell check, you want to avoid having the spell
% checker try to spell-check every LaTeX command. The easiest way is
% to use an LaTeX editor like TeXstudio that has spell and grammar
% checking build in. If using emacs, use M-x ispell-buffer for a
% LaTeX-aware spell check. In gedit, the best is to select "Highlight
% Misspelled Words" in the tools menu. Or highlight the paragraph(s)
% that you want to have spell-checked with the mouse and select "Check
% Spelling".
% Establish small roman numeral numbering
\frontmatter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TITLE PAGE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\nowebhypbeg
\maketitle
\nowebhypend
%%%%%%%%%%%%%%%%%%%%%%%%%%%% SIGNATURE PAGE %%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Create the committee page using the data in the customization section:
\latexhtml{\makecommitteepage}{}
% Note: it appears that FSU now has a special form in GradSpace for this.
%%%%%%%%%%%%%%%%%%%%%%%%%%%% DEDICATION PAGE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% See the FSU requirements whether you should have this page:
\latexhtml{\begin{dedication}}{\chapter*{Dedication}}
\centering
To a future where more people drive a Miata and less people drive an SUV.
\latexhtml{\end{dedication}}{}
%%%%%%%%%%%%%%%%%%%%%%%%%%% ACKNOWLEDGEMENTS %%%%%%%%%%%%%%%%%%%%%%%%%%%
\latexhtml{\begin{acknowledgments}}{\chapter*{Acknowledgments}}
% Do not forget your contract or grant.
% The ~ tildes below prevents LaTeX from thinking the point is the end
% of a sentence. (LaTeX would insert additional space behind such a
% point.) It also prevents a line break at that point. If you really
% want to prevent LaTeX from breaking, say, a title line, replace
% every space in it by a tilde. But rewriting more concisely is a
% better idea. If you do want to allow line breaking at the point,
% replace ".~" by "{.} ".
Thanks are due to many people. I particularly want to thank my
major advisor, Prof.~Jane Doe. Without her constant guidance and
support, this thesis would not have obtained the high quality that
it has. I also thank Profs.~Don, Do, Duck, and I for serving on my
committee. They are sure to recognize that the level of research in
this paper is fully worthy of a Ph.D. Many thanks. This work was
supported by the U.S. Central Intelligence Agency under a secret
grant.
\latexhtml{\end{acknowledgments}}{}
%%%%%%%%%%%%%%% TABLES OF CONTENTS, FIGURES, AND TABLES %%%%%%%%%%%%%%%%
% Table of contents:
\clearpage
\phantomsection % fix to get active links in the pdf to work properly
\tableofcontents
% A list of tables (if you have more than one):
\clearpage
\phantomsection
\listoftables
% A list of figures (if you have more than one):
\clearpage
\phantomsection
\listoffigures
% A list of musical examples can be enabled by removing the percent
% signs in front of the two lines below.
%\clearpage
%\phantomsection
%\latexhtml{\listofmusex}{}
% If you want a list of symbols, put a % sign in front of the
% \begin{comment} and \end{comment} lines surrounding the example
% below. Then change the table to your needs.
\begin{comment}
\clearpage
\phantomsection
\latexhtml{\begin{listofsymbols}}{\chapter*{List of Symbols}}
The following short list of symbols are used throughout the
document. The symbols represent quantities that I tried to use
consistently.
\begin{center}
\begin{tabular}{ll}
% Note the use of & to separate colums, and \\ to end rows.
% Putting things between $ signs makes them being type-set
% in the mathematics font, and with mathematical spacings.
$\pi$ & $3.1415926\ldots$ \\
$e$ & Base of Natural Logarithms, $e\approx 2.71828\ldots$ \\
$E$ & $mc^2$ \\
$F$ & $ma$
\end{tabular}
\end{center}
\latexhtml{\end{listofsymbols}}{}
\end{comment}
% If you want a list of abbreviations, or a list of other stuff, put
% a % sign in front of the \begin{comment} and \end{comment} lines
% surrounding the example below. Then change the table to your needs.
\begin{comment}
\clearpage
\phantomsection
% If this is *not* a list of abbreviations, change the name appropriately
% in the second set of brackets:
\renewcommand{\listabbrevname}{List of Abbreviations}
% and inside *{...}
\latexhtml{\begin{listofabbrevs}}{\chapter*{List of Abbreviations}}
\begin{center}
\begin{tabular}{ll}
Emacs & Escape-Meta-Alt-Control-Shift- \\
UNCTAD & Under No Condition, Take Any Decision
\end{tabular}
\end{center}
\latexhtml{\end{listofabbrevs}}{}
\end{comment}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ABSTRACT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The thesis abstract is normally no longer than 750 words.
\clearpage
\phantomsection
\latexhtml{\begin{abstract}}{\chapter*{Abstract}}
A theoretical investigation is conducted to understand why white
Miatas, (and more generally white sports cars), are faster than cars
of other colors. It is shown that under conditions of thermal
equilibrium, white Miatas experience reduced photon drag. Under
nonequilibrium conditions, in particular on sunny days, white Miatas
may actually experience enhanced propulsion depending on the
position of the sun.
\latexhtml{\end{abstract}}{}
%%%%%%%%%%%%%%%%%%%%%% START OF THE MAIN DOCUMENT %%%%%%%%%%%%%%%%%%%%%%
% Start normal arabic page numbering
\mainmatter
% First chapter title and its label:
\chapter{Introduction}\secname{intro}
% Note: if you put a latex command inside a sectional title, or a
% figure or table caption, you may sometimes have to precede it by
% \protect. So if you get into trouble with a title or caption,
% try that.
\begin{figure}[htbp]\latexhtml{\par}{}
\centering
% Image bozo.jpg was made by my digital camera. To create bozo.eps,
% I put a copy of bozo.jpg in the "any_eps" folder, inside the l2h
% "convert" folder, and double-clicked "convert.jpg". See web-page
% "images", inside the l2h "help-files" folder, for more details:
\resizebox{1in}{!}{\putpicture{bozo}}
% The next line puts in 1 inch of horizontal space:
\hspace{1in}
% Modified version of the image:
\resizebox{1in}{!}{\putpicture{nobozo}}
% Do not use multiple captions in the same figure; latex2html does
% not handle it correctly:
\caption{A white Miata and a nonwhite one.}
% The \label below creates a mnemonic "fig:bozo" for this figure.
% The actual numbers are put in by latex. That means that you do not
% have to change hundreds of numbers when you add or delete a figure,
% equation, or whatever in a big dissertation. It also cuts down on
% mistakes:
\label{fig:bozo}
\end{figure}
% Note: if your figure is really a musical example, use the musex
% environment instead of figure. In other words, replace {figure}
% above with {musex}.
% Note the use of the mnemonic "fig:bozo" as defined in the figure above:
The Miata is a sports car developed by the Japanese car manufacturer
Mazda. Figure \ref{fig:bozo} shows a white and a nonwhite Miata.
% Use \footnote{...} for footnotes:
The Miata\footnote{Mazda refers to the Miata commonly as the MX-5.
% Use \emph{...} for emphasis (italics) and similarly \textbf{...} for bold:
The designation \emph{Miata} has been dropped altogether in recent
years.} was introduced in the USA market in 1990. It is definitely
important to recognize that the Miata was primarily designed for the
USA market. However, it was also very successful in other markets.
Here are some languages in which the praises of the Miata were sung:
\begin{center}
English
\\ (Spanish) Español
\latexhtml
{% This is for the pdf version of the document:
% See the Internationalization part at the start of this file for more.
\\ (Greek) % not supported by the utf8 and utf8x packages
\\ (Russian) % not supported by the utf8 and utf8x packages
\\ (CJK) % not supported by the utf8 and utf8x packages
\\ (High UTF-8) % not supported by the utf8 and utf8x packages
}
{% And this is for the web pages version of the document:
% Note that unicode characters simply pass through to the web pages.
% (Unfortunately, that is no longer true if you put the characters
% inside mathematics, or inside figures other than in the captions.)
% See the Internationalization part at the start of this file for more.
\\ (Greek) Ελληνικά
\\ (Russian) Русский
\\ (CJK) 中日韓
\\ (High UTF-8) 𐑍𐑎𐑏
}
\end{center}
Needless to say, white was a Miata color from the beginning. However,
early white Miatas had a problem where the paint would peel off the
cars. This was the stage at which the issue of Miata-photon
interaction first received significant popular attention. Owners with
peeling paint noticed that their cars did not only look worse. The
cars also became very noticeably slower when the paint peeled off.
Since then, the increased speed of white Miatas became well known
among knowledgeable owners. However, some others doubted the
association and acquired grey, black, and even red Miatas. While
these Miatas would still drive at reasonable speeds, they had
difficulty competing with the white ones when maximum performance was
an issue.
% Example table. The table environment merely allows the position of
% the table to be changed from h (here) to t (top of page), b (bottom
% of page), or to p (a separate page with just tables and figures).
\begin{table}[htbp]
\centering
\caption[First-generation Miata colors produced, in cars.]{First-generation
Miata colors produced, in cars. Data compiled by John Emerson. Figures
provided by Marketing Division of Mazda Corporation, Irvine, CA. Posted
on miata.net. Data are resorted in order of increasing car speed, scaled
with rated engine power. Data for 1990-1991 white Miatas are applicable
until the paint peels off.}
\label{tab:colors}
\vspace*{.15in} % 0.15 inch of blank space
% The tabular environment produces the actual table. Inside
% mathematics, a table (like say a matrix), is called an array. But
% the idea is the same.
% The string lrrrrrrrrr means that there is a left-aligned column,
% followed by 9 right-aligned ones. A centered column would be a c.
{\setlength{\tabcolsep}{3.3pt}% reduces space between columns
\begin{tabular}{lrrrrrrrrr}
% \hline is a horizontal line. You could put | characters in the
% lrrrrrrrrr string above to produce vertical lines. That is ugly.
% Refrain.
\hline\hline
% Note that table columns are separated by & and the line ended by \\.
Year: &1990 &1991 &1992 &1993 &1994 &1995 &1996 &1997 &all~~~\\
\hline
% classic red
Classic red &29195 &16000 &11729 &8415 &6013 &4888 &4006 &3950 &84196 \\
% brilliant black, but always dirty:
Black & & &4626 &6111 &5741 &4877 &4063 &3702 &29120 \\
% british racing green, dark:
BRG green & &3997 & & & & & & &3997 \\
% 1997 marina green, dark:
Marina green & & & & & & & &3000 &3000 \\
% 1996 starlight blue, very dark:
Starlight blue& & & & & & &3000 & &3000 \\
% 1995 merlot, dark purple:
Merlot & & & & & &3500 & & &3500 \\
% 1997 twilight blue, dark:
Twilight blue & & & & & & & &1500 &1500 \\
% montego blue, darkish:
Montego blue & & & & &3003 &2818 &5742 &4571 &16134 \\
% sunburst yellow, light:
Yellow & & &1515 & & & & & &1515 \\
% mariner blue, quite light:
Mariner blue &6540 &3633 &2096 &1082 & & & & &13351 \\
% laguna blue, light:
Laguna blue & & & & &1788 &440 & & &2228 \\
% silver stone metallic:
Silver stone &3481 &5802 &1475 & & & & & &10758 \\
% chaste white:
Chaste white & & & & &3565 &2945 &2160 &1929 &10599 \\
% crystal white:
Crystal white &12420 &8855 &5195 &5874 & &122 & & &32466 \\
\hline
Totals &51636 &38287 &26636 &21482 &20110 &19590 &18971 &18652 &215364\\
\hline\hline
\end{tabular}}
\end{table}
Table \ref{tab:colors} lists the various colors in which the
first-generation Miata was produced. They are sorted by car speed,
relative to engine power. (Table \ref{tab:colors2} shows the same
data sorted by total cars produced.)
At first, some features of table \ref{tab:colors} may seem surprising.
For example, you might reasonable assume that black Miatas would be
slower than red ones. After all, black will absorb all colors of
light, while red absorbs only nonred ones. However, black Miatas are
notoriously difficult to keep clean. Because of the great variations
in surface temperatures, dirt gets \lq\lq{}baked\rq\rq{} on. So black
Miatas reflect a good deal of light due to the dirt.
\begin{table}[htbp]
\centering
\caption{Like the first table, but sorted by total cars produced.}
\label{tab:colors2}
\latexhtml{\vspace*{.15in}}{}%
\setlength{\unitlength}{1pt}\setlength{\tabcolsep}{3.3pt}%
% In my opinion, LaTeX tables look better than html ones. To force
% latex2html to use an image of the LaTeX table, it can be put
% inside a picture environment like here. See the next figure for
% more on this environment.
\begin{picture}(405,237)(-202,0)%\htmlimage{scale=1.6}{}%
%\put(-202,0){\framebox(405,237){}} % used for testing picture size
\put(0,0){\makebox(0,0)[b]{\begin{tabular}{lrrrrrrrrr}\hline\hline
Year: &1990 &1991 &1992 &1993 &1994 &1995 &1996 &1997 &all~~~\\
\hline
% 1997 twilight blue, dark:
Twilight blue & & & & & & & &1500 &1500 \\
% sunburst yellow, light:
Yellow & & &1515 & & & & & &1515 \\
% laguna blue, light:
Laguna blue & & & & &1788 &440 & & &2228 \\
% 1997 marina green, dark:
Marina green & & & & & & & &3000 &3000 \\
% 1996 starlight blue, very dark:
Starlight blue& & & & & & &3000 & &3000 \\
% 1995 merlot, dark purple:
Merlot & & & & & &3500 & & &3500 \\
% british racing green, dark:
BRG green & &3997 & & & & & & &3997 \\
% chaste white:
Chaste white & & & & &3565 &2945 &2160 &1929 &10599 \\
% silver stone metallic:
Silver stone &3481 &5802 &1475 & & & & & &10758 \\
% mariner blue, quite light:
Mariner blue &6540 &3633 &2096 &1082 & & & & &13351 \\
% montego blue, darkish:
Montego blue & & & & &3003 &2818 &5742 &4571 &16134 \\
% brilliant black, but always dirty:
Black & & &4626 &6111 &5741 &4877 &4063 &3702 &29120 \\
% crystal white:
Crystal white &12420 &8855 &5195 &5874 & &122 & & &32466 \\
% classic red
Classic red &29195 &16000 &11729 &8415 &6013 &4888 &4006 &3950 &84196 \\
\hline
Totals &51636 &38287 &26636 &21482 &20110 &19590 &18971 &18652 &215364\\
\hline\hline
\end{tabular}}}
\end{picture}
\end{table}
You might also wonder why the slower colors, and especially red, sold
quite a large number of cars. The reason is psychological. A
significant number of owners are somewhat wary of the speed of their
Miatas. In private communications, Miata owners have told me that it
feels \lq\lq{}somewhat scary, so without a roof in a small, fast,
car.\rq\rq{} The reduced speed of red Miatas provides some sense of
reassurance. Many red Miata owners also end up installing a hardtop
on a semi-permanent basis.
At the other side of the list, you find the hard-core enthusiasts who
go for speed. (To be sure, some white Miata owners might also be
attracted by the fact that the white Miatas do not need much effort to
look clean. But surely, that is a small minority.)
Another observation that may be surprising at first is why a yellow
Miata might best several blue ones. After all, photon energy
increases from red to yellow to green to blue. Actually, the
yellow Miata has a lot of white thrown in. And various blue Miatas
are really dark. While they do emit some blue, they absorb colors
of all wavelengths.
\begin{figure}[htbp]\latexhtml{\par}{}
\centering
\setlength{\unitlength}{1pt} % 72 pt = 1 inch
%
% The picture environment allows you to put labels, arrows, circles,
% etcetera, in your figures. While gnuplot will put in labels, these
% tend to clash with the style of the document fonts and with the
% document font sizes.
%
% Using a picture environment allows you to put every label just
% where you want it. And put every plot where you want it.
% But it does require some trial and error to get the positions of
% the labels just right.
%
% (If you think it is too much work, just let gnuplot put in the
% labels and then position plots "curves" and "stretch" just like
% "bozo" and "nobozo" were put in figure 1.)
%
% In this figure, the picture width is 400 units and the height 140.
% The coordinates of the far left bottom point are 0 and 0. That
% means that in "(x,y)" coordinate pairs, 0 < "x" < 400 and
% 0 < "y" < 140.
%
% For more info, see http://en.wikibooks.org/wiki/LaTeX/Picture
%
\begin{picture}(400,140)(0,0)
% The following \picfrbox command, when uncommented, puts a frame
% around the total picture area. That is helpful when
% experimenting in verifying that everything stays within the
% limits defined above:
%\put(0,0){\picfrbox(400,140){}}
% The next line puts plot 'curves.eps' such that its bottom left
% point ([bl]) is at coordinates 19 horizontally and 0 vertical.
% Taking into account that the plot has a blank margin, this leaves
% enough space below and to the left of the plot to put in labels.
\put(19,0){\makebox(0,0)[bl]{\putpicture{curves}}}
% For the plot 'stretch.eps', it is more convenient to specify the
% location of its bottom right ([br]) point. The "x" value is 410 and
% not 400 since the plot has a 10 point white margin at the right:
\put(410,0){\makebox(0,0)[br]{\putpicture{stretch}}}
% change to a smaller font:
{\small
% put labels on the curves (the [l] causes left-alignment of the label
% to the specified position)
\put(50,110){\makebox(0,0)[l]{$a(t)/a(0)$}}
\put(150,112){\makebox(0,0)[l]{$v_{\rm p,w}(t)$}}
\put(150,61){\makebox(0,0)[l]{$v_{\rm p,r}(t)$}}
% Put in labels for the two left axes ([r] is right alignment):
\put(27,15){\makebox(0,0)[r]{0\%}}
\put(27,135.5){\makebox(0,0)[r]{100\%}}
\put(274.5,15){\makebox(0,0)[r]{0}}
\put(274.5,135.5){\makebox(0,0)[r]{1}}
\put(275,90){\makebox(0,0)[r]{$v_{\rm p}/v_{\rm p,w}$}}
% Put in labels for the two bottom axes (b and t are bottom and
% top alignment; if there are no l or r inside [], these
% labels are horizontally centered around the specified point):
\put(30,3){\makebox(0,0)[b]{0}}
\put(94,3){\makebox(0,0)[b]{10}}
\put(140,0.5){\makebox(0,0)[bl]{$t$ (seconds)}}
\put(276.8,3){\makebox(0,0)[b]{0}}
\put(397,3){\makebox(0,0)[b]{1}}
\put(340,0){\makebox(0,0)[b]{$v_{\rm i}/v_{\rm i,w}$}}
} % end smaller font
\end{picture}
% If you also provide a shortened caption inside [], like the one
% below, make sure there is NO LINEBREAK BETWEEN ] AND {. (Yes, a
% latex2html quirk.)
\caption[Speed difference between a white and a red Miata.]{Left:
Speed difference between a white and a red Miata. This uses plot
units. Right: the nonlinear stretching used to clarify the speed
difference.}
\label{fig:curves}
\end{figure}
% The tilde ~ in "Fig.~" below prevents the abbreviation point from
% being regarded as the end of a sentence. (After such an end point
% additional blank space would be inserted.) You could instead use
% "Fig.\ " if you wanted to allow a line break behind the point.
The left-hand graph in Fig.~\ref{fig:curves} compares the speed $v(t)$
of a red Miata to that of a white one. Here $v$ is the velocity and
$t$ the time in seconds from rest. Subscripts w and r indicate the
white and red Miatas, respectively. The velocity is taken relative to
the terminal velocity of the white Miata. The acceleration $a(t)$,
relative to the initial one $a(0)$, is also plotted. (The relative
acceleration is the same for the Miatas, although the absolute
acceleration of the red Miata is of course less.) For simplicity, CVT
mode is assumed.
To clarify the speed difference, the velocity has been plotted on a
slightly nonlinear scale. The right-hand graph shows this scaling.
In it, $v_{\rm{i}}$ is the indicated speed and $v_{\rm{p}}$ the
plotted speed. Note that this correction is reminiscent of the
difference between indicated airspeed and true airspeed in aviation.
The plotted speed takes here the place of the true airspeed in
aviation.
Mathematically, the velocity correction is given by
\begin{displaymath}
\frac{v_{\rm p}}{v_{\rm p,w}} =
\frac{1+e^{1990^2(v_{\rm i}-v_{\rm i,w})/v_{\rm i,w}}}{2}
\end{displaymath}
Note that 1990 is the model year of the first Miatas. For
convenience, the above curve can be approximated as piecewise linear.
The purpose of this paper is to shed some theoretical light on the
described empirical observations. It will be shown that special
relativity combined with quantum mechanics directly implies the speed
advantage of white Miatas. Therefore, the speed difference is not an
experimental aberration but a scientific fact.
% Do not use mathematics inside section titles. There would be big
% font size issues on the web pages. In the worst case, fake it using
% italics, like in \emph{x}:
\chapter{Theoretical Background}\secname{theory}
% Note the references to sections and the bibliographical citations:
The Miata-light interaction is obviously described by the two pillars
of modern physics, special relativity and quantum mechanics. Since
the reader is surely well aware of quantum electrodynamics, either in
% Use \lq{} and \rq{} for left and right quotes; they look better on
% the web pages:
Feynman\rq{}s path integral approach or in canonical formulation, it
needs no introduction. However, a few key results will be summarized
in subsections \ref{sec:specrel} and \ref{sec:quantum} for ready
reference. For more information, see
% Bibliographical references are inserted using the cite command.
% The key, like Feynman06 here, is whatever you put in the
% references.bib file. (See \bibliography at the end of this file).
\cite[pp.~1-152]{Feynman06}. A more easily accessible source may be
\cite{QMFE}.
\section{Special relativity}
\secname{specrel}
The speed of any Miata is small, but not vanishingly small, compared
to the speed of light. (There are some mathematical issues associated
with the previous statement that will be addressed in a planned second
volume of this book.) Therefore relativistic mechanics must be used.
Einstein\rq{}s famous relation
% Note that ^{...} creates a superscript and _{...} a subscript.
% The \label allows you to refer to this equation elsewhere by the
% mnemonic \ref{eq:emc2}. Do *not* put the \label on a line by
% itself, but *do* put a % behind it, (yes, a latex2html quirk):
\begin {equation}
E = m c^{2} \label{eq:emc2}%
\end {equation}
% If you just want mathematics without an equation number, use
% the displaymath environment. For a multiline equation, see below.
implies that a moving Miata picks up additional mass.
However, the principle of relativity, as first formulated by
Poincar\'e, allows the viewpoint of a driver inside the Miata.
Physics is the same regardless of the relative motion of the
observers. The driver viewpoint will frequently be used in the
current paper to simplify the arguments.
% Note that mathematics inside the text is enclosed between dollar
% signs. Also note \sqrt for square root and \frac for fraction.
The most important relation for the purpose of this paper is the
relativistic Doppler shift. The equation that governs the difference
in observed wavelength $\lambda$ of light, and the corresponding
difference in observed frequency $\omega$, between moving observers is
% The eqnarray environment is good for lining up equations on separate
% lines, or for splitting a long single equation over separate lines.
% Note that the center (equals signs) column is surrounded by & and &,
% and that a new line is started with \\. The \nonumber is used to
% prevent an equation number from being inserted in that line. If you
% do not want equation numbers at all, use the eqnarray* environment
% instead.
{\setlength{\jot}{9pt}% extra space between the rows
\begin{eqnarray}
\lambda_v & = & \lambda_0 \sqrt{\frac{c + v}{c - v}} \nonumber \\
\omega_v & = & \omega_0 \sqrt{\frac{c - v}{c + v}}
\label{eq:relds}%
\end{eqnarray}}
% For equations with a long left-hand side, you sometimes want to allow
% the left hand side to stick out over the right hand side. Use the
% \lefteqn{...} command to do so. To see it in action, remove the
% leading % signs from the next eqnarray:
%\begin{eqnarray*}
% \lefteqn{\langle\Psi_1(\vec r_1,S_{z1},\vec r_2,S_{z2};t)|
% \Psi_2(\vec r_1,S_{z1},\vec r_2,S_{z2};t)\rangle =} \\
% &&\!\!
% \sum_{S_{z1} = \pm\frac12\hbar} \sum_{S_{z2} = \pm\frac12\hbar}
% \int_{{\rm all}\ \vec r_1} \int_{{\rm all}\ \vec r_2}
% \Psi_1^*(\vec r_1,S_{z1},\vec r_2,S_{z2};t)
% \Psi_2(\vec r_1,S_{z1},\vec r_2,S_{z2};t)
% \,{\rm D}^3 \vec r_1 \,{\rm D}^3 \vec r_2
%\end{eqnarray*}
Here the subscript 0 stands for the emitter of the light, and
subscript $v$ for an observer moving with speed $v$ away from the
emitter. If the observer moves towards the emitter, $v$ is negative.
(To be true, the formulae above apply whether the observer 0 is
emitting the light or not. But in most practical applications,
observer 0 is indeed the emitter.)
Of course, Miatas do not drive in vacuum but in the atmosphere.
Fortunately, this effect may be ignored as secondary on light
propagation as long as no
% Note that subscripts, and superscripts, can only be used inside a
% math enclosure:
significant H$_{2}$O in liquid form is present. (In any case,
Miatas are known to disagree with these so-called \lq\lq{}rain\rq\rq{}
conditions.) However, the atmosphere is very important because of
aerodynamic drag. These issues will be addressed further in
subsection \ref{sec:aero}.
\section{Quantum mechanics}
\secname{quantum}
% Note the umlaut:
Schr\"odinger, in his famous equation, associated energy with the
partial time differentiation operator, and linear momentum with the
partial space differentiation operator in a given direction:
% \!, \,, \:, \;, \quad, and \qquad provide increasing amounts of
% blank space in equations (\! is negative!):
\begin{equation}
E\quad\Longleftrightarrow\quad
i\hbar\frac{\partial}{\partial t}
\qquad
p_x\quad\Longleftrightarrow\quad
-i\hbar\frac{\partial}{\partial x} \label{eq:se}%
\end{equation}
Here $\hbar$ is the scaled Planck\rq{}s constant and $i$ is
$\sqrt{-1}$.
The above results are of critical importance for this paper, because
the Miata-light interaction is due to exchange of the energy and
momentum of photons of light. Therefore, it is helpful to make the
above relations specific for photons:
\begin{equation}
E = \hbar\omega \qquad p = \hbar \frac{\omega}{c} \label{eq:photon}%
\end{equation}
These expressions are known as the Planck-Einstein and de Broglie
relations. They may be derived by applying Schr\"odinger\rq{}s
associations on a complex, propagating monochromatic light wave. As
is well known, the first expression is consistent with Einstein\rq{}s
relation (\ref{eq:emc2}) in view of the fact that photons have zero
rest mass.
\section{Aerodynamics}\secname{aero}
The primary factor limiting the maximum speed of a Miata is
aerodynamic resistance. This resistance is related to boundary layers
along the surface of the Miata in which the air is being dragged
along. Going downstream, this air forms a wake behind the Miata. The
wake is the primary cause of resistance,
\cite[see][pp.~570-571]{Prandtl61}.
The wake is always relatively wide because the boundary layer
separates from the surface at some point,
\cite{VanD81,VanD_Shen82,VanD_Cowley90}. This greatly increases the
aerodynamic resistance. Controlling separation remains a difficult
problem, \cite{Shen_Xiao90}.
There is also the problem that the boundary layer is normally
turbulent. By itself, turbulence will increase drag due to its
thermodynamically irreversible mechanics, \cite{Walker88}. However,
often transition to turbulence decreases drag instead because it also
tends to delay separation.
The high speed of, in particular, white Miatas, will also bring in
compressibility effects, \cite{Ackeret_Feldmann_Rott47}. Note that
such effects are largest in elevated speed areas such as near the
top of the windshield header.
\chapter{Photon-Surface Interactions}
\secname{mechanisms}
% If you really, really, want to insist that a figure is placed
% exactly where you put it, uncomment the \usepackage{float} line
% in the header and then replace the [htbp] below with [H]:
\begin{figure}[htbp]\latexhtml{\par}{}
\centering
% For images including bitmaps (photographs, or more general
% pictures in .jpg, .gif, .bmp, etcetera, format) the next line is
% needed for better image quality on the web pages:
\htmlimage{extrascale=3,notransparent}{}
% Compare the quality of this picture on the web pages with the first
% figure. It is better. Look at the noses of the Miatas!
\setlength{\unitlength}{1pt} % 1 pt = 1 inch / 72
% Here the picture width is 400 units and the height 55. The coordinates
% of the far left bottom point are -200 and 0. That means that in "(x,y)"
% coordinate pairs, -200 < "x" < 200 and 0 < "y" < 55.
\begin{picture}(400,55)(-200,0)
\thinlines
%\put(-200,0){\picfrbox(400,55){}}
% The next line puts picture bozo.eps such that its bottom center
% point ([b]) is at coordinates -100 horizontally and 0 vertical.
% So it is centered in the left half of the graph.
\put(-100,0){\makebox(0,0)[b]{\resizebox{1in}{!}{\putpicture{bozo}}}}
% Similarly, the bottom center of nobozo.eps is at +100 and 0:
\put(100,0){\makebox(0,0)[b]{\resizebox{1in}{!}{\putpicture{nobozo}}}}
% Put in the arrows using \put(x,y){\vector(rw,rh){length}} where
% -4 < rw < 4 and -4 < rh < 4 are the relative width and height.
% The values rh and rw must be in whole units with no common divisor.
% The "length" is measured horizontally unless the arrow is vertical,
% (rw = 0), in whih case it is measured vertically.
\put(-150,26){\vector(3,-1){30}}
\put(-120,16){\vector(1,1){20}}
\put(50,26){\vector(3,-1){30}}
\put(80,16){\vector(2,3){10}}
% (For lines without arrow heads, use \line instead of \vector.)
% Put in the "photon gamma" labels (note the use of the \makebox with
% a [r] to right-align the string to the specified (x,y), near the
% start of the arrows):
\put(-152,27){\makebox(0,0)[r]{photon $\gamma$}}
\put(48,27){\makebox(0,0)[r]{photon $\gamma$}}
% In rare cases, some part of your figure might be improperly
% clipped on the web pages. Putting a tiny rule in the problem
% corner can fix that, like say: \put(-200,0){\rule{.2pt}{.2pt}}
\end{picture}
% If you also provide a shortened caption inside [], like the one
% below, make sure there is NO LINEBREAK BETWEEN ] AND {. (Yes, a
% latex2html quirk.)
\caption[Photon-surface interaction mechanisms.]{Photon-surface
interaction mechanisms. They depend on photon wavelength.
Photos \copyright{} Leon van Dommelen.}
\label{fig:bozo2}
\end{figure}
At this stage, the photon-surface interaction can be understood to the
required detail. Figure \ref{fig:bozo2} above shows how an incoming
photon of light, $\gamma$, interacts with a white and a nonwhite
Miata. The white Miata will reflect or emit photons of all colors.
However, a red Miata will mostly emit red photons.
If a red Miata absorbs a blue photon and releases its energy as heat,
the momentum of the photon is gone. The red Miata has effectively
stopped the photon. Because of Newton\rq{}s third law, action equals
minus reaction, the red Miata experiences an opposite force slowing it
down. That would hold even if all the photon energy was emitted again
as omnidirectional infrared radiation.
On the other hand, as illustrated in figure \ref{fig:bozo2},
the white Miata leaves the backward moving momentum of the photon
largely intact, assuming a predominantly specular emission. The
vertical momentum does change more significantly. But that merely
presses the white Miata more strongly onto the road, providing an
additional measure of safety at its higher speeds.
(As the Planck-Einstein and the Broglie relations show, photon energy
is proportional to momentum. It is not proportional to square
momentum, as Newtonian physics would suggest. So if a red Miata
re-emitted all incoming photon energy as radiation, and if that
radiation was predominantly specular with respect to the incoming
photon, then there would not be a difference between the Miatas.
Unfortunately, neither condition is true.)
You might of course wonder whether the advantage of the white Miata
would not be offset by photons coming from other directions. There is
something to that. It should be stressed that a Miata, of any color,
in an equilibrium situation with blackbody radiation coming from all
directions, will \emph{not} experience a net force. Any other
statement would obviously violate the second law of thermodynamics.
And this paper would never suggest it would not. Only the highest
standards of scientific integrity are applied in this work.
However, for a \emph{moving} Miata, the photons coming from the front
are \emph{blue-shifted}. That is described by the relativistic Doppler shift
(\ref{eq:relds}). This increases their energy, and as a result, a
moving Miata on an otherwise equilibrium earth experiences a photon
drag slowing it down. Photons like the example in figure
\ref{fig:bozo2} dominate. As a result, the Miata will experience a
photon drag. But a white Miata will experience less drag because it
slows down the dominant photons less.
It is also interesting to look at nonequilibrium situations. In
particular, on sunny days the photon distribution is far from a
blackbody one. Photons come predominantly from a concentrated source:
the sun. Now if the sun is in front of the Miata, figure
\ref{fig:bozo2} showed that a white Miata experiences less photon
drag.
You might now of course conjecture that if the sun is in the back,
then this advantage could reverse. That in that case, a red Miata
might have an advantage. Unfortunately, that is not true. Figure
\ref{fig:bozo3} shows what happens. In this case, there is a
\lq\lq{}solar sail\rq\rq{} effect. This effect, well established for
interstellar travel, actually provides a propulsive force for the
Miata. Now if a photon is simply absorbed by a red Miata, its
momentum adds to that red Miata. But if a photon is reflected by a
white Miata, \emph{double} its momentum is added to that white Miata.
Of course, the real situation is more complex. A white Miata is not a
perfect reflector, and a red Miata not a perfect absorber. Figure
\ref{fig:bozo3} tries to capture the average situation. Still, the
white Miata experiences a much greater solar sail effect.
\begin{figure}[htbp]\latexhtml{\par}{}
\centering
\htmlimage{extrascale=3,notransparent}{}
\setlength{\unitlength}{1pt}
\begin{picture}(400,55)(-200,0)
\thinlines
%\put(-200,0){\picfrbox(400,55){}}
\put(-100,0){\makebox(0,0)[b]{\resizebox{1in}{!}{\putpicture{bozo}}}}
\put(100,0){\makebox(0,0)[b]{\resizebox{1in}{!}{\putpicture{nobozo}}}}
\put(-58,24){\vector(-3,-1){30}}
\put(-88,14){\vector(4,-1){27}}
\put(142,24){\vector(-3,-1){30}}
\put(112,14){\vector(1,-1){10}}
\put(-56,25){\makebox(0,0)[l]{photon $\gamma$}}
\put(144,25){\makebox(0,0)[l]{photon $\gamma$}}
\end{picture}
\caption{The solar sail effect.}
\label{fig:bozo3}
\end{figure}
There is another important effect that Miata owners often ignore. The
high-energy radiation absorbed by a red Miata comes out primarily as
heat. Now heated air at the surface of the red Miata wants to rise
away from the Miata because it is lighter than the surrounding air at
the same pressure. Clearly, that will promote separation, the primary
effect limiting the speed of a Miata. True, the rising air will also
promote turbulence, which might delay separation a bit. However, it
is to be expected that global buoyancy will dominate and separation
will be promoted. This will greatly increase the aerodynamic drag of
a red Miata.
\begin{figure}[htbp]
\centering
% Here the latex is kept simple. The labels were put in by gnuplot,
% so all we need to do is insert the plot and add a caption.
\putpicture{contour}
\caption[G\"ortler vortex system in the boundary layer on a white
Miata at speed.]{G\"ortler vortex system in the boundary layer on a
white Miata at speed. Inferred from theoretical observations by
Van Dommelen and Yapalparvi.}
\label{fig:contour}
\end{figure}
On the other hand, current work by the author and Yapalparvi, (in
progress), suggests that the lower surface temperatures of a white
Miata will generate a \lq\lq{}G\"ortler\rq\rq{} vortex system that may
be very efficient in delaying separation. Figure \ref{fig:contour}
shows the expected motion of the system. Note that this represents
just a very small segment of the thin boundary layer, looking
upstream.
With the advantageous photon interaction, in addition to the
enhancement of the aerodynamics by the G\"ortler system, the much
higher speed of white Miatas is clearly fully explained.
\chapter{Concluding Remarks}
\secname{conclusion}
The claim that white Miatas are noticeably faster than other ones, and
in particular red ones, is commonly considered with considerable
skepticism. It is often argued that this experimental observation is
due to observational bias of some Miata owners and is not supported by
independent verification. The analysis in this paper, however,
clearly shows that such skepticism is unjustified. For solid
theoretical reasons, white Miatas cannot be anything else than faster
than other colors.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% APPENDICES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% was required or if a copyright approval letter is required.
\chapter{More Details}
\secname{more}
This appendix has deliberately been left empty, to convey the sense of
peace and quiet that comes from driving a Miata.
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The author was born. He is still alive.
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