Increase in Stability of an X-Configured AUV through Hydrodynamic Design Iterations with the Definition of a New Stability Index to Include Effect of Gravity

Round 1

Reviewer 1 Report

The paper can be accepted in the present form.

Author Response

Dear Reviewer,

Thank you very much. Minor changes have been made on the second reviewer's comments.

Regards

Lakshmi

Reviewer 2 Report

1. The paper has had quite a few improvements, and I am very pleased with the way that the reviewers have responded to my comments.

2. My only major concern is that the details of the various shapes are still not given. I respect the authors’ point that these details can’t be given for commercial reasons, however, in general I think that all such details ought to be provided for a paper which is published in a journal.  In this case there are plenty of other useful pieces of information, so I am very tempted to suggest that it be published in any case – but that is really up to the editor.

3. Table 2 is good, but comes before table 1, and before any discussion of the third line in it in the text. I recommend moving it further back in the paper, to be after table 1.

4. I like the addition of table 1. However, I think that the parameters ought to be non-dimensionalised.  I think that the speed ought to be given as Froude number based on length, and the value of C_BC_G ought to be non-dimensionalised by either hull diameter, or length.  This would make that table of much greater interest to the reader, without giving away any confidential information.

5. And, I don’t understand the comment in the caption for table 1, which states that the green areas are applicable for the assumption of high speed. But surely for this to be the case the values given in the table ought to be zero, or close to that?  However, the green shading includes lots of places where the value is one.  ie G_V  is equal to G_Vgrav and so surely it is not possible for the value of G_Vgrav to be ignored?  Perhaps I am missing something here?  Could the authors better explain that?

6. And, it is important to recognise that it is not possible to identify which area is shaded green when the paper is reproduced in B & W.

Author Response

Dear Reviewer,

Thank you for your review. Please find an address of your most recent comments in the attached file.

Regards

Lakshmi

Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

This is a very interesting paper, and should be published.

However, I have a few comments which I believe need to be taken into account first.

1. The symbols section needs to be more comprehensive, to include all the symbols (many are not included), and the non-dimensionalisation methods for those parameters which have been non-dimensionalised needs to be given.

2. There also needs to be a list of abbreviations. There are many abbreviations used throughout the paper, but no list of what they mean.

3. The distance defined as C_BC_G is the vertical distance between the centre of buoyancy and the centre of gravity – not the “directional distance”. This is important.  But, I don’t understand why the authors have not used the more conventional symbol for this used in the submarine community: “BG”.

4. Equation 1 first appears on page 4, and has not been referred to, or introduced in any way (at that stage). I believe that this would come a lot better later when this is being discussed.  I don’t believe that it needs a derivation, simply acknowledgement of Spencer, where this has come from.

5. Equations 8 – 15 are all a bit basic, and I question whether it is necessary to include them here. The point is that it leads to equation 16, which is well acknowledge in the community (both surface ship and submarine communities).

6. I like the approach that the authors have made to introducing the hydrostatic term into the stability in the vertical plane. I think that this is an important aspect of this paper.  However, I think that the denominator in equation 19 should be: “u²” not: “u”.  I’m certainly happy for the authors to correct me here, but I’m pretty sure that I’m right.  I suspect that this is simply a typo in this equation, but if not, and it continues into the analysis (there is no way that I can tell whether it does, or not) then that needs to be fixed.

7. Equation 22, whilst being correct, is a bit confusing with the mix of dimensionless and non-dimensional terms (see my comment above about how it is necessary to explain how all the terms are non-dimensionalised). In addition, I believe that: “9.81” ought to be replaced with “g” as this is the acceleration due to gravity, which only happens to be 9.81 if using metric units!

8. The reference to many tables is incorrect. It seems to me that the authors have moved the tables around a bit, and forgotten to change the references to them in the paper.  For example, at the bottom of page 7 there is reference to table 4, which is not correct.  There are quite a few of these incorrect references, and I believe that the authors need to go through the paper carefully checking them all.

9. I don’t understand the following sentence at the bottom of page 7: “The drag optimized shape of the craft has led to less than optimum positioning of the appendages close to the separation of the hull boundary layer.” Can the authors please rephrase this to explain better what it is that they’re getting at?

10. Table 2 gives the position of the critical point. But, as the authors know, the position of the critical point will depend on the speed.  So, what speed has this critical point been obtained for?

11. I agree with conducting “captive” CFD to obtain the coefficients. However, in chapter 4 there is reference to three different captive motions, all of which are in the horizontal plane.  But, much of the later work is in the vertical plane, so surely captive motions in the vertical plane must have been used to obtain these coefficients?

12. Table 5 has the following caption: “Stability index values for selected designs”. But this is a table of the value of C_f for three designs.  Unfortunately, the way in which C_f has been non-dimensionalised is not given.   However, if this is done using the wetted surface then the wetted surface of each of these different designs needs to be provided.

13. There needs to be a bit more information about the shape of the baseline design. CAD images in three D are all very well, but a large-scale technical drawing would be a lot more helpful.  I can’t even tell which is “up” from these figures!  And, the dimensions of the strakes/control fins for each configuration should be given.

14. Table 10 is quite useful, however, I don’t understand why the % difference has been given for all these coefficients, rather than their actual values. Wouldn’t the actual values have been more interesting to the reader?

15. The values of the stability indices are shown in bar charts. But it is actually difficult to determine the values from these charts.  I think that in addition to the charts a table of the values should be given.  Note also that the way these charts are presented they need to be in colour to be of use.  I recommend that in addition to using colour there should be a very different type of hashing on the bars, so that when printed out in B&W it is possible to work out which is which.

16. Won’t the value of G_Vgrav depend on the speed? If that is the case then the speed needs to be given prominently, and the authors need to discuss this.  What would the values be if this were a different speed?

17. I think that it would be a lot easier to read if the great long paragraph in section 8.1 were broken up into smaller paragraphs!

18. The wording regarding the change in the stability index G_V in the fifth sentence in section 8.1 is a bit misleading. It is stated that there is a 39.6% increase, but I think that this is actually a decrease in the negative value – ie it is coming closer to zero.  Am I correct in my interpretation of this sentence?  If so, then perhaps it could be worded a bit differently?  (And is it really realistic to talk about a three significant figure accuracy here?)

19. I don’t understand enough of the geometry of the different fins to follow the logic in much of section 8.1. This is why we need a much better description of these different fin arrangements.  Three D sketches are all very well, but nothing beats dimensioned technical drawings for this purpose!

20. On line 260 (section 8.1) it is mentioned that: “…for all the designs considered except Designs 6.” I think that this should be: “… Designs 6 and 7”?

21. I don’t understand why the presence of the sail has such a bit influence on the value of G_V. Am I missing something here?  Surely the sail will not have much influence on the manoeuvring coefficients in the vertical plane?  Can the authors explain in more detail why they think that this is the case?  It is certainly counter-intuitive to me.  Could it be something to do with the change in the longitudinal centre of buoyancy and/or mass?  The values of the positions of the longitudinal centre of buoyancy and total volume need to be given, along with the technical drawings, for each of these different designs.
    

22. I think that in line 306 the word: “highers” should be replaced with: “highest”.

23. But, more importantly, I don’t understand why the skates have such an influence on the stability in the vertical plane. Perhaps this is because I don’t understand the geometry sufficiently well – my reading of this is that they are all vertical, so should have negligible influence on the manoeuvring in the vertical plane (whereas they will have a big influence on the manoeuvring in the horizontal plane).

24. I don’t understand what is meant by: “hybrid triangle”. Can the authors give more information on what is meant by this?

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

Thank you for your insightful comments. Please find the attached file with responses.

Regards

Lakshmi 

Author Response File: Author Response.pdf

Reviewer 2 Report

This work describes a design procedure for autonomous underwater vehicle (AUV), aimed at improving its passive stability characteristics, even before active control is considered. The main aspect of novelty is represented by including hydrostatic contributions in the vertical plane stability analysis. Hydrostatic terms are typically dropped in the identification of important stability indices, possibly leading to inaccurate stability assessment. As the authors reasonably point out, this is particularly true in the case for moderate surge speeds, in which the hydrostatic forces are still comparable to the hydrodynamic ones. After optimizing the appendage design of an AUV to obtain target values of the gravity term enhanced stability index, the authors present results of Lumped Parameter Model simulations confirming the improved stability of the optimized design. The problem investigated, the methodologies used and the results presented can all be considered interesting for the engineering community. The overall scientific approach appears sound, as the design of the numerical experiments proposed is clearly appropriate. Also the results mainly support the conclusions presented.

The paper is written in good English although some occasional paragraphs or sentences are not completely clear. The main problem however, is the overall organization of the manuscript is quite confusing. Text referencing to tables or images is often characterized by wrong numbering, and in some occasions the text references to non existing tables or figures.

 For such reasons, in this reviewer's opinion, a series of issues must be addressed by the authors if the paper can be accepted for publication.  Here follows a list of the most important ones:

- Considering the gravitational/hydrostatic term in the evaluation of stability indices for AUVs developed by authors like Renilson, Fossen Lewis et al., is a clear enrichment of the physical model upon which the linear dynamic stability analysis is based. However, the authors seem to assume that the acceptable range of values for index G_v indicated by Renilson (and reported in Table 3) is to be considered unaltered when considering gravity corrected index G_Vgrav. This is not obvious, so a proper justification should be provided. Maybe --- if possible within the confined framework of a journal article --- the authors should consider including main features of Renilson determination of G_v acceptable range, and highlight the reasons why such a range is the same even considering the gravity term.

- In the result section, the authors should make an effort to highlight in a clearer way the impact of the considering G_Vgrav rather than G_V. Is the new/corrected index helping to identify stable configurations that would be otherwise discarded because they would be considered unstable based on G_V? In a way, the variation trends of both G_Vgrav and G_V throughout the appendages optimization campaign is similar. Both indices increase moving from the unstable range towards the stable one (0.5-0.8). Apparently, the values reported in Figure 5 seem to suggest that G_Vgrav values of design iteration 8 indeed is barely in the stable range suggested by Renilson and reported in Table 2. Yet, the authors state (line 244) "It is important to note that though the value of stability index GVgrav for the Design 8 does not fall within the recommended range (Table 2)." Aside from the fact that the sentence appears incomplete, it somehow suggests that the value presented in Figure 5 is instead just shy of the stable range. The LPM simulations appear to confirm this, as also design iteration 8 appears unstable although considerably closer to stability with respect to the base design. Of course, the paper message would be more powerful if, as said, the final iteration could be sitting in the stable range if computed with G_Vgrav and not with G_V, and this could be confirmed with LPM. If creating new results is not possible, the authors should at least stress in a clearer way the superiority of G_Vgrav in identifying LPM-stable configurations, which is a particularly important point for this contribution. In addition, they should probably point out more clearly that, given that design iteration 8 leads to a nearly null value of G_V, it would be disregarded being quite far from the target range. instead, such configuration appears on the verge of stability.

- Still related with the previous point, it would be also possible that the effect of considering G_Vgrav rather than G_V is more evident when analyzing the effect of appendage (especially sail) removal, or of the presence of holes in the skates. This because, as pointed out, removing material, along with surface, would in principle alter G_Vgrav  more, as such index should be able to feel the mass subtraction from the front more than G_V is doing. Unfortunately the analysis on sail and skates is completely unclear in the text. The tables referenced seem not to present the data suggested in the text. For instance, in line 292 it is said "The design 5a indicates that the absence of the sail had a decrease in stability from Design 5". But design 5a is reported in Table 7 to present no skates, rather than no sail. In addition, I believe the titles in the plots in Figures 7 and 8 have inverted titles, as the presence or not of each appendage is investigated in designs 5, 5a, 5b, while the presence of holes in skates is investigated through designs 7.5a, 7.5b, 7.5c, 7.5d. Moreover, it is confusing that the plot of Figure 8 includes design 7.5a, which --- albeit considering no sail  --- is not considered in the text description in section 8.2. And what is even more puzzling, is that the G_Vgrav and G_V values presented for design iteration 7.a in Figure 7 do not coincide with the values of the same quantity presented in Figure 8. Also, in Section 8.3 it is said on line 307 that "The entire removal of skates with the sail remaining on the craft in Design 7.5a shows that the stability index G_V is the least in this configuration in comparison to other modifications of the skates". But as of Table 8, Design iteration 7.5a presents the removal of the sail, not the skates (the configuration without skates is 5.a). So, all in all both section 8.2 and 8.3 appear quite out of sync with the Figures and Tables they are meant to comment, which makes it very hard for the reader to extract meaningful information out of them. In this reviewer's opinion, a further, sorted out version of these two sections will make the paper much better and highlight even more the usefulness of G_Vgrav in the stability analysis.

- The authors correctly point out in different occasions that the gravity correction term, being independent of the surge velocity, has more impact for moderate cruise speed. Would it be possible for the authors to have a more quantitative indication of the velocity ranges in which it is advisable to add the correction, and in which instead its use results in no significant gains?

- The problem of text images and tables being somewhat out os sync is not confined to sections 8.2 and 8.3, but is somewhat present throughout the paper. Of course, this could be merely a result of the website submission upload procedure. However, I would advise the authors to look into the problem. For instance, Table 1 referenced in line 215 and 267 should instead probably be Table 2. A citation is missing from line 270. Figure 2 referenced in line 143 does not portray a mesh. Figure 5 referenced in line 165 does not portray a geometry. Table 7 referenced in line 154 does not show Design 1. Table 3 referenced in line 193 should apparently become Table 5 (but the caption of Table 5 refers to stability index, not to drag coefficients, although the stability index is called C_f rather than G_v or G_Vgrav). Also, line 129 refers the drag increase across designs to Table 4, but it should be Table 5.

- Another minor issue is related to Equation (1). Why has it been placed there? Ideally, it is derived right as Equation (16), so it should be placed after Equations (17)and (18).

- A final minor issue. After line 91 the authors state that the BRF equations of motion are written using a generic origin. Which is the one effectively used in this work? Given Figure 2, it seems the origin has bee placed at the center of buoyancy. It is maybe useful to state it more clearly.

Author Response

Dear Reviewer,

Thank you for your insightful comments. Please find the attached document.

Regards

Lakshmi

Author Response File: Author Response.pdf

Reviewer 3 Report

Several typos are present, the text and the formatting should be carefully checked. Some references are missing and the reference to some figures is wrong.

The motivation for using significantly different CFD setups for the different simulations should be provided.

The number of periods for the planar motion mechanism simulation is not specified and assumed to be equal to three. Is the number correct? Since the number appears to be small, can the authors provide a figure to show that the quantities of interest are converged?

Several design modifications are provided. A more detailed discussion about how these are derived is necessary.

Author Response

Dear Reviewer,

Thank you for your insightful words. Please find the attached document.

Regards

Lakshmi

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I confirm that the amended version submitted by the authors appears significantly improved with respect to the original version. In particular, all the points raised in the first review have been addressed in a satisfactory fashion. I thank the authors for their effort.

For such reasons, I am recommending the publication of the paper in its current form.

The only minor problem I found and needs to be fixed, is the presence of a couple of references that seem off on a Table and Figure in page 19 (lines 341 and 346, respectively).