Preprint Article Version 3 Preserved in Portico This version is not peer-reviewed

# Universal Scaling Law for the Velocity of Dominoes Toppling Motion

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)

How to cite: Sun, B. Universal Scaling Law for the Velocity of Dominoes Toppling Motion. Preprints 2019, 2019120017 (doi: 10.20944/preprints201912.0017.v3). Sun, B. Universal Scaling Law for the Velocity of Dominoes Toppling Motion. Preprints 2019, 2019120017 (doi: 10.20944/preprints201912.0017.v3).

## Abstract

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.

## Keywords

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

## Subject

PHYSICAL SCIENCES, General & Theoretical 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.
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