Universal Scaling Law for the Velocity of Dominoes Toppling Motion

Bohua Sun

doi:10.20944/preprints201912.0017.v3

Preprint Article Version 3 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 2 December 2019 / Approved: 3 December 2019 / Online: 3 December 2019 (05:28:53 CET)
Version 2 : Received: 8 December 2019 / Approved: 9 December 2019 / Online: 9 December 2019 (03:36:12 CET)
Version 3 : Received: 28 February 2020 / Approved: 29 February 2020 / Online: 29 February 2020 (10:55:12 CET)
Version 4 : Received: 16 March 2020 / Approved: 17 March 2020 / Online: 17 March 2020 (04:24:39 CET)

By using directed dimensional analysis and data fitting, an explicit universal scaling law for the velocity of dominoes toppling motion is formulated. The scaling law shows that domino propagational velocity is linearly proportional to the $1/2$ power of domino separation and thickness, and $-1/2$ power of domino height and gravitation. The study also proved that dominoes width and mass have no influence on the domino wave traveling velocity. The scaling law obtained in this Letter is very useful to the dominoes game and will help the domino player to place the dominoes for fast speed and have a quick estimation on the speed without doing complicated multi-bodies dynamical simulation.

dominoes; toppling motion; velocity; height; thickness; separation

Physical Sciences, Mathematical Physics

Comment 1

Received: 29 February 2020
Commenter: Bohua Sun
Commenter's Conflict of Interests: Author

Comment: One section, ie., DIRECTED DIMENSIONAL ANALYSIS II, is deleted and a section of DIRECTED DIMENSIONAL ANALYSIS I has been rewritten. Abstract and conclusion have been edited.

+ Respond to this comment

Not displayed online.

Please leave your comment to this article below.

Mathematical equations can be typed in either LaTeX formats \\[ ... \\] or $$ ... $$, or MathML format <math> ... </math>. Try the LaTeX or MathML example.

Type equation:

Preview:

Copy equation into message below

Close menu

Please click a symbol to insert it into the message box below:

Please enter the link here:

Optionally, you can enter text that should appear as linked text:

Copy link into message below

Close menu

Please enter or paste the URL to the image here (please only use links to jpg/jpeg, png and gif images):

Copy image into message below

Close menu

Type author name or keywords to filter the list of references in this group (you can add a new citation under Bibliography):

No existing citations in Discussion Group

Wikify editor is a simple editor for wiki-style mark-up. It was written by MDPI for Sciforum in 2014. The rendering of the mark-up is based on Wiky.php with some tweaks. Rendering of mathematical equations is done with MathJax. Please send us a message for support or for reporting bugs.

Close menu

Please declare any conflicts of interest you may have with this paper, financial or otherwise.

I do not have a conflict of interest

I would like to declare a conflict of interest

Display my name on the website

Captcha

Renew

I accept the following conditions:

Comments must follow the standards of professional discourse and should focus on the scientific content of the article. Insulting or offensive language, personal attacks and off-topic remarks will not be permitted. Comments must be written in English. Preprints reserves the right to remove comments without notice. Readers who post comments are obliged to declare any competing interests, financial or otherwise.

* All users must log in before leaving a comment

Notify me about updates to this article or when a peer-reviewed version is published.

Universal Scaling Law for the Velocity of Dominoes Toppling Motion

Abstract

Keywords

Subject

Comments (1)