Characterisation of the Contact between Cross-Country Skis and Snow: A Macro-Scale Investigation of the Apparent Contact

Round 1

Reviewer 1 Report

Kalliorinne et al present a multi-scale and multi-method analysis of the contact mechanics occurring at the interface between cross-country skis and ice. The two methods used are an artificial neural network (ANNs) and a boundary-element method (BEM). In principle, this is a promising approach, but after reading the manuscript I was rather confused.

 

Since I have no expertise in ANNs, I cannot really comment on that part of the paper beyond the point that I did not even get a rough idea of what  was done with ANNs. It seems like the ANN is trained to turn three scalars (x, m, x_m) into one scalar (h). I am sorry, but I cannot imagine this to be a super complicated exercise, in particular as the dependence of h on the three variables should be rather smooth. But perhaps I completely misunderstand the complexity of the problem?  At this point, I would expect that a few physically motivated functions should span the problem and then only few coefficients need to be adjusted. Or insted of physically motivated function use h(x) for four extreme pairs of the number pair (m, x_m) and interpolate in between?

 

Regarding the BEM, I am also utterly confused. Wouldn't the semi-infinite body approximation only be applicable if the height or depth of the object(s) exceeds the (longest) characteristic length scales of where pressure is applied, which would be the two points where the ski touches the snow. On that scale, the ski should act like a thin beam and not like a semi-infinite body. Even the snow is not necessarily of the order of 1m deep. Depending on the depth of the snow and the elastic modulus of the foundation, different load distributions might be obtained. Or is the BEM only conducted in local contact, smaller in lateral dimension than the height of the ski? Then, it's not clear to me if anything useful can be learned from an elastic model if there for a skier-on-snow problem.

 

What I also find confusing is the factor of two with which E' is multiplied in Eq. (2). Isn't the series coupling of two springs always softer than the softer of the two springs? So perhaps, I am pulling a blank, but this appears to be a quite sloppy mistake. But then, the "Poisson ratio" has a unit.

 

Finally, the inset of the schematic in Fig. 1 shows a small-scale calculation, which, actually does not look schematic too me. In the later parts of the manuscript, I see no analysis of such detailed contact-mechanics calculations and find this somewhat strange. Well, yes, there are statements about relative contact areas but no height profiles of the underlying surfaces. And even, if there are height profiles, in order to get values for the real contact area from an elastic calculation, don't we simply need to know the root-mean-square gradient of the height profiles and the local pressure? There is no need to do a length calculation.

 

The writing strikes me as rather sloppy. There are numerous grammatical mistakes and typos, which make me wonder if the senior researchers, whom I hold in high esteem, have read the draft carfully and if it was them who drafted it, I wonder about their state of being during the moment of writing. They have produced much, much clearer work before.

 

I must confess that I only read the manuscript up to page 11. At this point, it was a succession of sentences to me, to which I could not assign much meaning but I simply could get no grip of what the authors meant to say. Reading many sentences of the nature if we change parameter x from a to b than property p changes its value from m to n i and if we change parameter x' from m' to a' then p tskes the value n' and if we change ...  You might get the point. I understand the need to narrate numerical graphs, but aren't there better ways?

 

So, I would hate to reject a manuscript by these authors. Nonetheless, before I am motivated to read this manuscript again and to eventually endorse it, I would need a completely new, less sloppy, and most importantly better digestable write-up.

 

Author Response

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Reviewer 2 Report

This work is very interesting and it was my pleasure to review it. The authors applied an ANN method to train the measured data set and predicted the topography of the ski camber under different loads. The numerical method, reasons for the choice of surface topography parameters and material parameters, and results are all very well described in the manuscript.

I only have  a few questions as follows:

1. In the method section, the authors collect the data set under different loads, so what is the difference between the topographies under varied loads? Does it affect the results?

2. In Fig.5, the pressure distribution with different loads is studied. However, if I am not misunderstood, the topography applied in the simulation under different loads is different as well. The authorS maybe need to make it clear.

3. Besides the prediction of the topography by application of ANN, is any extension of ANN to apply in contact mechanics, such as predicting the contact area, mean gap or etc?

 

Author Response

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Reviewer 3 Report

Dear authors,

Submitted manuscript is at high level and doesn't needs any improvement!

Author Response

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Round 2

Reviewer 1 Report

“a determined length” in abstract makes no sense to me. Are you sure to have used the proper translation of the Swedish word “bestämd”? 

 

What do you mean with “apparent contact characteristics”? The way, you don’t hyphenate means the characteristics are apparent, but perhaps you mean to talk about the characteristics of the apparent contact area? 

 

In the last sentence of the abstract, the authors mention that elastic properties have a large impact on the apparent contact area. I guess that even uneducated readers should know that softer materials make more contact than stiffer ones, given everything else is identical, except for the flat punch. The abstract remains relatively unclear about how the manuscript will go beyond that. And in the manuscript, it is not clear to me either what additional insight is gained than that obvious insight.

 

First page: It remains unclear to me what apparent contact area means. The sentence “The apparent contact area can be considered being the contact area seen at the macro scale” is not helpful, as people with good eyes might be in a position to see a gap between certain parts of the ski, while others don’t. So, it would help to know if you refer to the entire ski or if you mean the interfacial separation has to exceed 1 mm, or whatever you perceive as “macro scale”. Usually, I would associate the apparent contact area with the entire ski, except perhaps for the fronts that bend up. 

 

I had to read the last paragraph on pg. 3 numerous times, until I could make sense out of it. It might be better if you condensed the first two sentences in this paragraph to “… for determining the pressure profile of cross-country skis on ice …”. (Actually, I had to read numerous sentences many times, but then the other referees had no such trouble. Thus, it must be my fault to have these difficulties.) 

 

The new sentence on pg. 4 makes no sense to me. A pressure cannot be a coupling between the scales. They have different units. It would help if the authors could be more concise there. 

 

Page 6, please correct “within in” in a sentence, which might benefit from more optimization. 

 

When the terms “macro”, “meso”, and “micro” are used.  I suppose, mm, micron, and nano-meters, but it’s not clear. “micro” can also stand for micron. But then what is “meso” if the macro-images have already sub-millimeter resolution. Thus, it would be nice if it could be specified. Would it make sense to use different resolutions for in-plane and out-of-plane direction at each scale? In the figure 6, the “macro” image shows lines at 0.23 and 1.33 mm heights, which to me means that “macro” means a resolution, which I would not want to call macro. 

 

What I don’t understand in this work is whether the results from the contact mechanics calculations in 3.2 can be compared to the measurements made in 3.1? If so, why don’t the authors show a comparison? I mean, they could use the ski profile as initial height and then apply a load near the position of the boot. Using the highly efficient Lulea code, such a calculation should be doable in less than a minute. I must say that I am skeptical that the such produced profiles would be close to the experimental observation, but I could be (hope to be) wrong. 

 

Also, it remains unclear to me the following: The ANN is trained with height profiles. And then a corresponding pressure profile is shown in Fig. 4. How do you convert h(x) into p(x)? By determining u(x) = h(x)-h_0(x) and converting that into p(x) using linear elasticity of a semi-infinite half space? 

 

I guess, the merit of the study lies in how AI was used. Unfortunately, I don’t know much about that even if AI is the big fuss these days. Now, it is not clear to me to what extent the architecture of the neural network is designed specifically for this study, or if this is a standard protocol. 

 

It remains unclear to me to what extent micro-scale calculations in the spirit of those shown in the top row of Figure 1 were conducted. The introduction and the theory section promise such calculations, but I saw no result figures on micro-scale simulations and the term “micro” does not appear between the end of the theory section and reference 12.  But this must be again my problem, as the other referees were perfectly fine with everything in the manuscript. 

 

In a final note, I would like to clarify the following: My comment about the quality of previous work was not meant as an insult on the submitted manuscript. I apologize if it came across that way. I merely wanted to convey that I did not intend to be “mean” to the authors and that I was afraid to have missed merit of the study. Perhaps this work is like “Radio Gaga”. I never understood why this song became so successful, but I yet enjoy listening to other music by Queen. So, with some luck, this manuscript is going to be well received by others (you already have two expert referees on your side) despite my critical take at it. Since I don’t want to impose my opinion, I leave it up to you to what extent you change the manuscript in response to my report.

Author Response

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