• ### Remove ads and support GameDev.net for only $3. Learn more: The New GDNet+: No Ads! • # The Physics of Racing Series, FAQ Math and Physics This FAQ was written by Brian Beckman, with updates by Robert Keller . • What is the PhORS? It is a series of articles about the physics of racing cars. It is decidedly slanted toward autocrossing (my favorite sport), but sidebars from other forms of racing appear when relevant. I start with the fundamentals (Newton's Laws, for example) and am slowly but surely building up complexity and covering more advanced topics. I cover all aspects of racing where physics applies, from driving to car setup to computer simulations. I am trying hard to make the articles useful and enjoyable for the non-technical reader who knows that physics is important for racing but needs some help understanding it. So, you don't have to be a physicist, engineer, etc. to understand the articles. The series started in our local-area autocrosser's newsletter in June '90. I started posting them to Team.Net not long thereafter. To date (27 July 91) there are nine articles. There is no end in sight. (There are now twelve articles in total -rck 1995) • What are your sources for info in the articles? The analyses in the articles are totally original. I'm figuring out the physics as I go along, as part of figuring out autocrossing and trying to get better at it. I'm a professional physicist (actually doing computer science, these days), and an amateur racer. The articles are kind of a journal of a personal learning process from a physicist's point of view. I avoid reading the "classical" technical texts (Smith, Puhn, Taruffi, etc.) before writing an article (though I *sometimes* cross-check my results with them). I do this on purpose for several reasons: • It would be of little value to you to see mere regurgitations of material you can read yourself in those sources, • I want the depth of understanding that can come only from figuring out the physics from first principles, • "peeking at the answer" would spoil the fun for me, • I hope and can give a somewhat fresh outlook on things. As time goes on, I am working into more accurate approximations at the cost of greater complexity. The earlier articles are easier to understand but less accurate. • How can I get copies of the series? The articles are stored in electronic form for anonymous ftp on ftp://ftp.team.net/autocross thanks to the generosity of Mark Bradakis, one of the founders of Team.net. Ask your local network guru for help with ftp and the decoding procedures outlined below. The articles are free for the taking for personal use, though they are copyrighted by me (more about that below). The following describes the format of the files by giving the example of Physics09.tar.Z, the file that contains the ninth physics article on "Straights." First, download the file to your favorite machine using anonymous ftp. On my unix machine, I would do the following: [font="Courier New"]$ ftp ftp.team.net
Name: ftp
:
230 Guest login ok, access restrictions apply.
ftp> binary
200 Type set to I.
ftp> cd autocross
ftp> ls P*
150 Opening ASCII mode data connection for /bin/ls.
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]37152 Dec[nbsp][nbsp]4[nbsp][nbsp]1991 Physics-12.tar.Z
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 245929 May 10[nbsp][nbsp]1991 Physics01.tar.Z
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 119451 May 10[nbsp][nbsp]1991 Physics02.tar.Z
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 128571 May 10[nbsp][nbsp]1991 Physics03.tar.Z
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 136700 May 10[nbsp][nbsp]1991 Physics04.tar.Z
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 207627 May 10[nbsp][nbsp]1991 Physics05.tar.Z
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 138705 May 10[nbsp][nbsp]1991 Physics06.tar.Z
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 194927 May 10[nbsp][nbsp]1991 Physics07.tar.Z
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 136828 Jun 21[nbsp][nbsp]1991 Physics08.tar.Z
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 262933 Jul[nbsp][nbsp]9[nbsp][nbsp]1991 Physics09.tar.Z
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 131816 Aug 19[nbsp][nbsp]1991 Physics10.tar.Z
-r--r--r--[nbsp][nbsp] 1 0[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]3[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 256133 Oct[nbsp][nbsp]9[nbsp][nbsp]1991 Physics11.tar.Z
226 Transfer complete.
ftp> get Physics09.tar.Z
ftp> quit
$[/font] Then, uncompress the file, as in the following: [font="Courier New"]$ zcat Physics09.tar.Z[/font]

That results in Physics09.tar, which is a virtual "Tape ARchive." Extract the files from it as follows:
[font="Courier New"]
\$ tar xvf Physics09.tar[/font]

A directory "09" containing three files will appear. The files are:

[font="Courier New"]-rw-r--r--[nbsp][nbsp]1 brian[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]354692 Jul[nbsp][nbsp]9 09:54 09-Straights.PS[/font]

This is a file containing PostScript input for any PostScript printer. The file was made and tested on an Apple LaserWriter, but should work on anything. Notice it is very large. The reason is that the Apple Macintosh software that produces it is kind of dumb. The articles are usually five or six pages when printed.

[font="Courier New"]-rw-r--r--[nbsp][nbsp]1 brian[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp]126102 Jul[nbsp][nbsp]9 10:05 09-Straights.self.sit.hqx[/font]

This contains original Macintosh files. The files are encoded in "binhex" format. This file is straight ASCII. Get it over to your Mac, run Stuffit 1.5.1 or 1.6, select "decode binhex" from a menu, and decode the file. An application program will result. This application program is a so-called "self-unstuffing archive." Just execute it (by double clicking, for example). It will extract its contents automagically.

There is always a "Textures" file. Textures is a Mac implementation of TeX, Donald Knuth's technical typesetting software package, with extensions for pictures. Textures allows me to put figures in the articles. I know of no UNIX implementation of TeX that makes it easy to put in pictures, so I use the Mac implementation.

Sometimes there are other supporting files such as Excel spreadsheets or original artwork files.

[font="Courier New"]-rw-r--r--[nbsp][nbsp]1 brian[nbsp][nbsp][nbsp][nbsp][nbsp][nbsp] 13176 Jul[nbsp][nbsp]9 06:28 09-Straights.tex[/font]

This is the TeX source for the article. It is a human-readable, ASCII file, so you can still get the gist of an article by reading it if you don't have an implementation of TeX for typesetting the article. **NOTE** if you process this file, you will get the text of the articles and any equations and tables. You will not get the figures. The figures are available only to Mac users via the Textures file or to hardcopy users who print out the PostScript file.
• What are the terms of the copyright?

Anyone can download the files, print them, read them, give copies to your friends, etc. I ask that you do not charge money if you give away copies. I ask that you not change the articles. Essentially, the articles are "copylefted:" use them freely, but do not restrict the access of anyone else to them by charging money or altering them.

You are free to print them in your local autocrossing newsletter if you
• ask me first (email is OK, [email="brianbec@microsoft.com"]brianbec@microsoft.com[/email]),
• make sure you attribute them to me with my name and address and copyright stuff in the printed version (make sure the blame gets to the right person),
• send me copies of your newsletter. These articles are already being published in at least four newsletters around the country and I have gotten generally positive reviews. I've also generated some debates, which is great fun and really brings out the issues.
Hope you enjoy reading them as much as I enjoy writing them!

\brian\

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