Vacuum Balloon–A 350-Year-Old Dream
Round 1
Reviewer 1 Report
The manuscript discusses an interesting topic: building a lighter-than-air vacuum balloon. The balloon needs to withstand the pressure from the air and to be very light, which makes it very challenging to design and manufacture the balloon.
The manuscript can be accepted if the following questions can be answered or clarified properly.
- The concept of ‘lighter-than-air vacuum balloon’ should be addressed more as it determines why the current work is important.
- The format of the equations in the manuscript needs to be improved. The font size is not consistent.
- In Line 101, why is the spherical shape the optimal one? Please clarify it.
- The quality of Figure 2 needs to be improved.
- Is h3>>h1? It seems they are in the same order of magnitude according to Figure 2.
- Why does eigenvalue λ3 start to decrease when h3 increases to some extent?
Author Response
Reviewer’s comment
The concept of ‘lighter-than-air vacuum balloon’ should be addressed more as it determines why the current work is important.
Authors’ reply
The following was added in the Introduction:
“Vacuum balloons can find important applications, such as transportation, Internet delivery, and cellular communications, as they have some advantages compared to lighter-than-air gas balloons: they do not need hydrogen, which is hazardous, or helium, which is increasingly expensive and difficult to contain, they do not need constant heating, like hot-air balloons, and they can have simpler altitude control through pumping air in and out.”
Reviewer’s comment
The format of the equations in the manuscript needs to be improved. The font size is not consistent.
Authors’ reply
We were not able to find font inconsistencies in equations – it looks like it is font 10 everywhere. Letter/digit size may be different in subscripts/superscripts or nominators/denominators, but this is what one would expect.
Reviewer’s comment
In Line 101, why is the spherical shape the optimal one? Please clarify it.
Authors’ reply
The wording was adjusted as follows:
“this shape provides the best volume to surface ratio (Ref. [6]) and is believed to be the optimal one to withstand external pressure with minimum weight (Ref. [7]).”
Reviewer’s comment
The quality of Figure 2 needs to be improved.
Authors’ reply
Corrected.
Reviewer’s comment
Is h3>>h1? It seems they are in the same order of magnitude according to Figure 2.
Authors’ reply
Indeed, h3>>h1. The legend to Figure 2 says “not to scale”, but we added the following clarification:
“; note that, e.g., h3>>h1 for the optimal design
Reviewer’s comment
Why does eigenvalue λ3 start to decrease when h3 increases to some extent?
Authors’ reply
Because Figure 5 (of the first version of the article) plots eigenvalues vs. h3 (core thickness) for constant payload, so h1 (face skin thickness) is lesser for greater h3, so there is some optimal value of h3, and for greater h3 eigenvalues are smaller.
Reviewer 2 Report
The manuscripts could be considered interesting, however major issues rose in my opinion. Firstly authors should better state their contributions and completely avoid the inclusion of parts taken from other publications. Secondly, the obtained results cannot be considered as general and valid, because they are not such obtained as a result of an experimental study.
A strong statement of the paper is that the „design is scalable”. In general, any design activity also requires some scalability. But sometimes the statements in this direction seem contradictory. In my opinion a clarification of the statement would be welcomed
e.g.
„We would just like to note that our design, unlike many others, is spherically symmetric and scalable (multiplying all linear dimensions by the same factor provides an equally viable design; see some caveats related to intracell buckling in Section 2.2)”... (lines 115 - 117)
and
„The design is scalable with respect to all of the above modes of failure: an equally successful design can be obtained by multiplying all linear dimensions by the same factor. However, this is not true for another mode of failure – so called intracell buckling (also known as dimpling).”(lines 263 - 265)
The paper addresses both an analysis using the finite element method (FEA) and possible manufacturing solutions. Closely related to this FEA only a 2D model was used - In the case of buckling studies it is well known that at least for a limited area, an analysis on a 3D model is recommended. I think it is interesting to present in the first phase the mesh of the structure (taking into account the fact that we are dealing with a multilayer model).
Especially since we have continuous surfaces in contact with honeycomb surfaces, captures from the analysis that present the FEA results with emphasis on the interface areas (at the boundary between the layers) would increase the importance of the article.
Connected with the above I think should be clarified the afirmation „In terms of manufacturing, such shells can be attractive as they can be assembled using flat sandwich panels.” (lines 314, 315) For this case, the statements related to scaling and how to transpose the FEA for this situation must be detailed.
In my opinion, it is mandatory to group and highlight all the simplifying hypotheses considered for this study. This is especially necessary because there is no experimental support and it is highlighted in the fragment between lines 200 - 206 the approximation of the values ​​obtained by the simplified method in relation to those obtained as a result of the FEA study.
Additionally, between lines 163 - 171, the authors state that:
„The validity limits of this formula are not clear, in particular, it is not clear how this formula should be modified to take into account manufacturing imperfections when they are different from those in the shells of Ref. [16]. The results of the above approach were verified and optimized by a finite element analysis (FEA) using ANSYS, which enabled us to compute the stress and strain in the shell components and to perform the eigenvalue buckling analysis (which is actually a classical Euler buckling analysis). The results of the FEA analysis confirmed that the analytical approach provides reasonable estimates and a good starting point for optimization in our case. However, we base the conclusions of this article on the results of the FEA analysis, not on the results of the analytical approach”
In my opinion, I think the „minor” word in line 340 should be removed
Author Response
Reviewer’s comment:
authors should better state their contributions
Authors’ reply:
We believe we clearly stated our contribution in the Discussion as follows:
“We showed that a lighter-than-air rigid vacuum balloon can theoretically be built using commercially available materials.”
Reviewer’s comment:
authors should … completely avoid the inclusion of parts taken from other publications.
Authors’ reply:
We respectfully disagree. The only “other publication” whose results we use after significant rework is our patent application (Ref. 4), which was declined, so no parts of other peer-reviewed work are used in this article. Would the reviewer also deny us the right to use any preprinted material in a peer-reviewed article?
Reviewer’s comment:
Secondly, the obtained results cannot be considered as general and valid, because they are not such obtained as a result of an experimental study.
Authors’ reply:
We respectfully disagree, as otherwise no theoretical/computational work could be “considered as general and valid”. Such approach would not be reasonable. Of course, a lot of experimental work will be needed to achieve a major breakthrough and build a prototype vacuum balloon, but it cannot be done realistically without theoretical/computational work.
Reviewer’s comment:
A strong statement of the paper is that the „design is scalable”. In general, any design activity also requires some scalability. But sometimes the statements in this direction seem contradictory. In my opinion a clarification of the statement would be welcomed
e.g.
„We would just like to note that our design, unlike many others, is spherically symmetric and scalable (multiplying all linear dimensions by the same factor provides an equally viable design; see some caveats related to intracell buckling in Section 2.2)”... (lines 115 - 117)
and
„The design is scalable with respect to all of the above modes of failure: an equally successful design can be obtained by multiplying all linear dimensions by the same factor. However, this is not true for another mode of failure – so called intracell buckling (also known as dimpling).”(lines 263 - 265)
Authors’ reply:
We do not just state “some scalability”, we clearly explain what kind of scalability we have in mind: “multiplying all linear dimensions by the same factor provides an equally viable design”. For example, there is no such scalability for gas balloons, where the area of the envelope increases as radius squared, whereas the volume of the balloon increases as radius cubed. We also immediately mention the caveat and clearly state that intracell buckling limits this scalability (the design is not equally viable for radius below 2.11 m).
Reviewer’s comment:
Closely related to this FEA only a 2D model was used - In the case of buckling studies it is well known that at least for a limited area, an analysis on a 3D model is recommended.
Authors’ reply:
We agree that “an analysis on a 3D model is recommended”, however, so far, trying to reply to the reviewer’s comment, we have only performed such 3D analysis using a coarse mesh. We added the following in Section 2.1:
“We also performed some preliminary buckling analysis using a 3D model with a coarse mesh and obtained the minimum eigenvalue of 3.0. This result is subject to adjustments after a better mesh is used. We used the optimal linear dimensions obtained for the 2D model with the payload fraction of 0.1.”
Reviewer’s comment:
I think it is interesting to present in the first phase the mesh of the structure (taking into account the fact that we are dealing with a multilayer model).
Authors’ reply:
A fragment of the mesh is shown in Figure 5 of the new version of the article.
Reviewer’s comment:
Especially since we have continuous surfaces in contact with honeycomb surfaces, captures from the analysis that present the FEA results with emphasis on the interface areas (at the boundary between the layers) would increase the importance of the article.
Authors’ reply:
We added Figure 6 of the new version with some results of FEA.
Reviewer’s comment:
Connected with the above I think should be clarified the afirmation „In terms of manufacturing, such shells can be attractive as they can be assembled using flat sandwich panels.” (lines 314, 315) For this case, the statements related to scaling and how to transpose the FEA for this situation must be detailed.
Authors’ reply:
We just have in mind that the stellated icosahedron has flat edges, whereas a sphere does not. Investigation of a design based on the stellated icosahedron is far beyond the scope of this article.
Reviewer’s comment:
In my opinion, it is mandatory to group and highlight all the simplifying hypotheses considered for this study. This is especially necessary because there is no experimental support and it is highlighted in the fragment between lines 200 - 206 the approximation of the values obtained by the simplified method in relation to those obtained as a result of the FEA study.
Additionally, between lines 163 - 171, the authors state that:
„The validity limits of this formula are not clear, in particular, it is not clear how this formula should be modified to take into account manufacturing imperfections when they are different from those in the shells of Ref. [16]. The results of the above approach were verified and optimized by a finite element analysis (FEA) using ANSYS, which enabled us to compute the stress and strain in the shell components and to perform the eigenvalue buckling analysis (which is actually a classical Euler buckling analysis). The results of the FEA analysis confirmed that the analytical approach provides reasonable estimates and a good starting point for optimization in our case. However, we base the conclusions of this article on the results of the FEA analysis, not on the results of the analytical approach”
Authors’ reply:
We do not quite understand this phrase (or its implications): “it is highlighted in the fragment between lines 200 - 206 the approximation of the values obtained by the simplified method in relation to those obtained as a result of the FEA study”. Yes, we say that the results of FEA are close to those obtained using formulas in Ref. [18, p. 6-6] with a knock-down factor of 1, but we base the design on FEA results, not the results using those formulas. As for “grouping and highlighting all the simplifying hypotheses considered for this study”, we added the following in Section 2.1 (we did not summarize approximations used for standard unity checks for other modes of failure):
“Let us summarize the approximations used to estimate the critical buckling pressure for the design. We used the values of air pressure of 101 kPa and density of 1.29 kg/m3 at the temperature of 0°C, material properties provided by manufacturers, a conservative simplification for honeycomb shear modulus, a 2D linear buckling FEA, a payload fraction value of 0.1. We did not take into account the very small buoyant force reduction due to the shell compression by atmospheric pressure and the weight of adhesives (see the reasoning at the end of Section 2.3). We provided some arguments based on a review of available experimental data suggesting that the safety factor of the linear buckling analysis should be enough to neutralize the knock-down factor due to imperfections and nonlinear effects.”
Reviewer’s comment:
In my opinion, I think the „minor” word in line 340 should be removed
Authors’ reply:
“relatively minor” was replaced by “less essential”.
Reviewer 3 Report
Interesting concept. The reviewer is curious about the manufacturing process, in perticular, if authors can elaborate:
- how/what is used to bond the skin to the honeycomb structure?
- given the skin is so thin, what is the challenge here?
Author Response
Reviewer’s comment:
how/what is used to bond the skin to the honeycomb structure?
Authors’ reply:
We added the following in Section 2.3:
“The face skins can be bonded to the honeycomb core using adhesives. To reduce the weight, the adhesive can be applied only to the tops of the honeycomb cell walls using the approach of Ref. [34].”
Reviewer’s comment:
given the skin is so thin, what is the challenge here?
Authors’ reply:
Working with boron carbide ceramic is challenging. It is difficult to provide the required very thin shape with near full density, and fragility of the thin ceramic is a big issue. Some processes, such as CVD deposition, can facilitate shaping, but are expensive. We believe, however, that these challenges can be overcome with modern technologies.
Round 2
Reviewer 2 Report
No additional comments
