Exploring Benefits of Using Blending Splines as Transition Curves

Round 1

Reviewer 1 Report

The paper describes the use of blending splines as transition curves. The aim of the work is to define a “new” type of transition curve, which allows continuity of first and second derivative of the curvature function in the connection points. These two properties are in fact not allowed by clothoid transitions. The work proposes an ERB-function and two different types of local functions, used to create the blending splines. The first type of local functions proposed to build the blending splines are circular arcs. In this case the authors show that circular arcs as local functions allow to guarantee a very smooth behaviour towards the end points but generate high oscillations of the curvature within the transition. Also changing the ERB parameters oscillations cannot be damped. For this reason, the authors proposed to adopt Bezier curves as local functions. In this case a quite good smoothing is still allowed towards the end points and curvature oscillations can be reduced by means of the ERB parameters.

The paper is in general very well written, clear, and easy to read also for people, which not work in this field. In my opinion the paper is good from the point of view of the mathematical description, but some more description should be added by the authors relative to technical implementation. First, the authors should clarify and demonstrate why the proposed transition curve should improve jerk and profile wear. This is not described in the paper, but I think that this aspect is the core of the work. Second, the authors should demonstrate that the proposed transition curve can be realized from the technical point of view and if it is in accordance with current railway standards.

 

Minor corrections:

Considering line 34 page 1 please replace "i an" with "in"

Considering lines 87-89 page 3 “The task of the transition curve is to gradually 88 decrease/increase the radius of the curvature from radius, R1 to R2, and to provide a change in 89 superelevation following the same behaviour as the curvature.”. The variation of superelevation is usually made using linear, Bloss, sine or cosine functions. Usually the clothoid function is adopted to realize the curve transition in the horizontal plane.

Author Response

The authors would like to thank the reviewer for taking the time to consider our work.
We have found the feedback and suggestions to be especially helpful in the process of bringing the paper to a more final version.

Please see the attachment for a point by point answer to the comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

1. The paper has to be structured as follow: introduction, literature review, methodology, results and discussion, conclusions. In methodology you have to be written the model of research, the steps, i.e. detailed and clear methodology of the study.
2. What the research questions the authors have addressed? Include them in the introduction. What are the differences between this study and the previous studies in related areas, the novelty of this work, key research questions, and so on.
3. The aim of the study given in introduction has to be in the new row.
4. In the conclusion have to be given what the model is useful, what are the contributions of research in the field of science, the main results. Give numerical results in conclusions.
5. The abstract needs to be corrected. It has to summarize the contents of the paper. The abstract should include a short introduction of the problem, an outline of the research presented in the paper, and a short conclusion based on the results. Give some numerical results.
6. It is better points 2.1 and 2.2 to be presented in methodology.
7. What is k in Figures 14-18; k-der – Figure 13, 19?
8. Please explain what are the applicability of this research.
9. Which software is used?
10. The Ofotbanen railway is marked in abstract and concussions, but in the text of the research no example or comment is given. Please provide clarification on this issue. The experiment about this railway have to be added in the research – give the parameters, haw the methodology has been used and so on.
11. There are many literature sources that are from the last century, [1-5; 19-23]. Please use more contemporary sources. Add new contemporary literature sources.

Comments for author File: Comments.pdf

Author Response

The authors would like to thank the reviewer for taking the time to consider our work.
We have found the feedback and suggestions to be especially helpful in the process of bringing the paper to a more final version.

Please see the attachment for a point by point answer to the comments.

Author Response File: Author Response.pdf

Reviewer 3 Report

The manuscript presents a study on investigating potential benefits of using blending splines as transition curves. Selected blending splines adopted as transition curves between two existing circular arc segments from the Ofotbanen railway were presented. The manuscript is well-written and I find the study is interesting and will be useful for readership.

I provide my comments below for the authors to consider and further improve the manuscript. Note that while most of the comment are relatively minor, the others are the most compulsory to be attended.

• Introduction: I suggest the authors to carry out a more comprehensive critical review of available literature and determine a Research Gap. Typical track problems associated with the transition curves should be discussed together with related available case studies and field measurements.
• Figure 2: a legend is needed for different curves.
• Figure 3 is not required. A proper reference to original source is sufficient.
• The legends are required for Figure 9, 10, 11
• Table 2: it is not clear to me how those values in the Table selected? Were they from literature (if so, references required) or based on measurements? Please provide more information and explanation on parameters adopted.
• Why only 3 specific lengths of L=60m, 120m, and 180m were selected? Please elaborate on these values.
• The conclusion should be re-written covering the main findings/outcomes of the study. I would suggest to list them into dot point for the benefit of readers

 

Author Response

The authors would like to thank the reviewer for taking the time to consider our work.
We have found the feedback and suggestions to be especially helpful in the process of bringing the paper to a more final version.

Please see the attachment for a point by point answer to the comments.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The paper can be accepted in the current form.

Author Response

Thank you

Reviewer 2 Report

 

This reviewer has read the new revised manuscript presented by the author. In general terms, the corrections proposed in the review report have been taken into account. The authors took note of the comments. The abstract has been modified. New literature sources are added. New comments are added. The introduction and conclusion are extended according to the remarks

Now the article has been improved and can be published.

 

 

Comments for author File: Comments.docx

Author Response

Thank you

Reviewer 3 Report

The Authors have satisfactorily attended my comments. I have now recommended for the publication of the manuscript in the Applied Sciences.

Author Response

Thank you