## SciPost Submission Page

# The friction of tilted skates on ice

### by J. M. J. van Leeuwen

### Submission summary

As Contributors: | J.M.J. van Leeuwen |

Arxiv Link: | https://arxiv.org/abs/1910.13802v2 |

Date submitted: | 2020-02-05 |

Submitted by: | van Leeuwen, J.M.J. |

Submitted to: | SciPost Physics Core |

Discipline: | Physics |

Subject area: | Fluid Dynamics |

Approach: | Theoretical |

### Abstract

The friction felt by a speed skater is calculated as function of the velocity and tilt angle of the skate. This calculation is an extension of the more common theory of friction of upright skates. Not only in rounding a curve the skate has to be tilted, but also in straightforward skating small tilt angles occur, which turn out to be of noticeable influence on the friction. As for the upright skate the friction remains fairly insensitive of the velocities occurring in speed skating.

###### Current status:

### Author comments upon resubmission

The first referee states that the paper is not very original and difficult

to read. Indeed the extension of the computation of the friction of an

upright skate to an inclined skate is not very original, but the technical

aspects of this calculation are far from trivial.

The paper was set up in a compact way since the author did not

want to repeat himself in the used material of the first publication.

In view of the criticism of the first referee the paper has been

rewritten paying attention to the detailed points raised by the first

referee. Concerning the role of the contact length,

it is not clear to the author what the referee means by the question

that the dependence on the contact length seems to be absent.

The contact length is THE important parameter in the calculation

determining the forces. Rather than plotting the friction as function

of the contact length, the contact length is determined by

the weight of the skater, which is the practical input parameter.

That requires an iterative procedure. This point has been stressed

stronger in the new version.

The second referee rightfully points to a very relevant paper

(of Lozowski et al.) which has been overlooked in the present study.

The author thanks the referee for this remark. The relation of the

present work to this earlier is worked out in detail in the new version.

The author disagrees with the second referee that the paper is

``almost identical to the paper mentioned''.

The difference with the papers of Lozowski et al. concerns the

rheology of ice with respect to external pressure and the boundary

conditions on the pressure in the layers of water between skate

and ice, in particular with respect to the forces on the side of the

blade. These differences are extensively elaborated in the new

version of the paper. That the outcome of the theory gives a lower

value of the friction (and therefore a larger difference with the

measurements) is in the opinion of the author not a drawback of the

new approach, given the uncertainty in the

hardness and response of ice and the idealisations of the model

(perfectly smooth skate and ice and omission of heatleaks in the ice).

### List of changes

- In the Introduction the commentary on the rheology is made more explicit.

- The justification of the used boundary conditions is given in the Introduction and the separate Section on the boundary conditions is rewritten such as to make it more explicit.

- The role of the contact length is stressed and elaborated.

- The discussion of the geometry (Fig. 3) is hopefully made more clear.

- References to the previous paper are made more complete.

- The missed publication of Lozowski et al. (new reference [6]) is extensively discussed both in the Introduction and the Conclusions, explaining the differences between this paper and the present paper.

- Fig. 5 has been extended with one more curve and Fig. 6 has been corrected (horizontal axis).

- Together these changes have extended the first version with two more pages.