Accuracy Analysis of the Measurement of Centre of Gravity and Moment of Inertia with a Swing
Round 1
Reviewer 1 Report
Section 1:
Literature review is rather brief.
L 33 define “CG” on first use in main text
L 38 “dependant” -> “dependent”
L 38 suggest “accurate” rather than “exact”
L 42 add “the properties of rigid bodies” after “analyse”
L 44 suggest “objects” rather than “articles”
L 46 “But similar” -> “Similar”
L 48-49 “including each” -> “each including”
L 51 “those applications” -> “vehicle applications,”
L 62 “if CG” -> “if the CG”
L 66 new paragraph then “The paper”
L 79 “weight” -> “mass”
Table 1 title: “Moment of inertia I base on theoretical calculations.” -> “Moment of inertia I is based on theoretical calculations.”
Section 2: It is unclear how the support frame was designed to have sufficient rigidity and secure, level floor anchoring to ensure that no parasitic motion affects the estimation process. Figure 1 images are somewhat cluttered and it is difficult to see key design features such as the knife edge pivot. The 50 g difference could well be simply due to the weld bead, as mentioned. Density variation could be determined, and so should not be speculated. A modal analysis of the swing structure would be a good addition to its characterisation, to ensure that the rigid body assumption is not prone to error. It is a bit ironic that the reported MI values are based on theoretical calculations.
The inclinometer time constant should be reported. The rationale for the data acquisition rate should also be provided.
L 122 “smaller” -> “less than”
L 134 what is referred to by “them”? Different angle estimation measurement methods?
L 137 “weight” -> “mass” (occurs other places as well…)
L 148 what kind of tape?
L 149 “allows to lift “ -> “allows for lifting of”
L 150 “investigates” -> “investigation of”
L 151 “1.3 m the” -> “1.3 m; and the”
At this point, I stopped pointing out style errors. The entire manuscript will benefit from additional editing for grammar, punctuation, and style.
L 161 is is unclear why the angle is measured for 64 seconds
L 162 why are control measurements advisable and how should they be performed?
L 171 under what circumstances would “If the changes are too fast” occur, and how would one know?
L 184 this sounds more like Newton’s first law
Figure 3 arrows are hard to see. Angle should be labeled alpha rather than 10.00 degrees
L 198 please avoid the use of dots to indicate multiplication in all equations. This is non standard notation that could be misinterpreted as dot products of vectors.
L 215 “osculating” -> “oscillating”
The derivation in section 2.4 does not explain how constants lambda and phi are determined, nor does it explain how the estimate for the total system of swing plus object is then used to extract the parameters for the object itself. (This is not explained until much later in the manuscript, which affects readability)
Section 3
L 242 it is unclear why 54 seconds worth of data are used and how that limits the influence of vibration and disturbances.
L 249 please either provide equations or Matlab code, not a mixture
L 251 avoid the use of the word prove
What is the factor fac and how is it determined? This is an issue for other implementations of there are empirical parameters unless there is a calibration procedure.
Figure 4 should state the number of data in each set of trials
Figure 6 lacks explanation of the variability in the data for case C1
Figure 7 C1 case appears to have a bias at Fw = 0 and a slightly higher fitted slope that the data indicate. Is the function forced to go through the origin?
Section 3.3
L 304 it is still not clear how the damping is estimated
L 321 of course fitting results depend on the function used. Which is the best to use and under what conditions might that change?
Discussion notes issues of vibration of the swing. Effect on the estimation should be discussed. Some statements about the mechanical design benefits need to be substantiated. There is no comparative assessment of the accuracy of this approach compared to other methods.
Conclusions are rather vague and qualitative. Clearer descriptions of the limitations of the apparatus to date and specific recommendations for improvements would enhance the contribution. The last sentence is unsubstantiated.
Author Response
We thank the reviewer for his/her comments and suggestions. Each point is addressed in a separate document for both reviewers together. We provide a pdf and a Word version. Thank you!
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The present paper shows a so interesting and more accurate method to define the centre of gravity and the moment of inertia of an element based on an experimental pendulum analysis. In this sense, the results showed a better accuracy with respect to theoretical values and the error defined in previous case studies. This is an interesting research work with possible application in naval architecture, for instance. Despite this, there are some points that must be revised and improved.
First of all, one of the main information reflected in the paper is the percentual error defined in other research works is a little bit higher than that defined in this paper but it depends on the precision of the process. This precision is defined by the number of decimal points employed and the accuracy (calibration) and sampling frequency of the sensors. In this sense, there are a different number of the decimal point for the same variable in the paper like in table 4 at the time to define distances (dm and dw). In consequence, it is highly recommended to revise all the tables and decimal points employed for the same variable, in accordance with the accuracy of the sampling device or the mathematical precision employed.
On the other hand, the sampling frequency seems to be adequate and it is validated with different sampling methods.
Another pending task to define a really applied idea is to define the moment of inertia in more than one direction at a time. It would be of interest to improve this with a possible explanation about how it can be reached, what may help the paper to increase the interest of readers.
What is more, a little description of possible applications of this methodology may help to increase the interest of readers in this paper.
Despite all the previous comments, the paper is well organised and describe in a scientific way interesting original results so, after minor changes, I consider the paper adequate for publication.
Author Response
We thank the reviewer for his/her comments and suggestions. Each point is addressed in a separate document for both reviewers together. We provide a pdf and a Word version. Thank you!
Author Response File: 
Author Response.docx
Round 2
Reviewer 1 Report
The manuscript is much improved, by responding to specific comments from the previous review; but the quality of the writing remains below average, and the manuscript would still benefit from some editing for style.
Author Response
We thank the reviewer for her/his valuable time and work. We checked the manuscript again and corrected minor mistakes. Thank you again!
