Analytic Derivation of Ascent Trajectories and Performance of Launch Vehicles

Round 1

Reviewer 1 Report

This submission introduces a novel analytic method to define multistage launcher trajectories, which is inherently useful. The submission also contains several helpful aspects such as a comparison between the analytical model and more accurate numerical computations, as well as specific examples of three-stage and four-stage rocket launchers (e.g. in Section 6), and the difference between equations with and without gravity loss (Eq. 17).   However, there are some important issues which need to be addressed before the submission can be reconsidered for publication:   (1) There is no conclusion or summary section, which is necessary for any reputable academic paper. The authors must write this section. When writing this section, I suggest that the authors specify (i) the "punchline" equations that they have derived, (ii) the inputs and outputs for those equations, (iii) how those equations differ from those in the previous literature, and (iv) how accurate these equations are.   (2) The novelty of the proposed work needs to be better distinguished from previous investigations. The number of references in the introduction is sparse; surely there are many more that derive or use equations which maximize the performance of multistage space rockets.   (3) The figures lack sufficient explanation. Below I list issues which should be addressed in a revised manuscript.   --The Fig. 1 caption should state the meaning of the dark blue circle and the reference plane, and identify the origin of the coordinate system. Further, the caption should describe the meaning of each angle given in the figure. Also, the figure does not include all the variables in Eq. (2), despite the main text suggesting otherwise.   --The Fig. 3 y-axis labels should feature full stops rather than commas.   --Fig. 4 is somewhat sparse. Additional lines may be drawn for different latitudes in order to demonstrate the effect of that parameter on the results.   --In Fig. 6, in the caption there needs to be a specification of the meaning of the blue line, the orange line and the two thick black arcs.   --In Fig. 7, the analytic and numerical curves need to be identified in the caption.   --In Fig. 8, the analytic and numerical curves need to be identified in the caption.   --In Fig. 9, the blue and orange portions of each curve need to be identified in the caption.   --In Fig. 10, the blue and orange portions of each curve need to be identified in the caption.   --In Fig. 12, the analytic and numerical curves need to be identified in the caption.   (4) Other formatting issues:   --The format of the equation which is two equations after Eq. (3) looks ugly because "log" is italicized just as the other variables. Hence, the "l", "o" and "g" in "log" each looks like a separate variable.   --The penultimate paragraph of Section 6 highlights other general issues with the formatting of this submission. Some units are italicized and others are not. There are strange variations in the amount of whitespace between characters. There is also an uncompiled reference. The next paragraph then features a spelling mistake; there are many throughout the document that a spell check would have caught. This lack of care reflects poorly on the submission.

Author Response

Dear Reviewer 1 , please find enclosed the letter ReviewRemarks where you will find answer to each of your questions.

Author Response File: Author Response.pdf

Reviewer 2 Report

A non standard way of presenting a very difficult field,. However, since this review is so rare (I mean how many people actually DO reviews in this field of scholarship) I would give overall reasonably solid kudos

The article is encouraging me to review what I do and do NOT know as of this highly specialized field. 

Only one criticism. I note this

Quote

Figure (12) shows the payload mass evaluation for polar circular orbits of
different altitudes obtained by the analytic (green curve) and numerical (red curve) algorithms. Of course bigger differences are for orbits of lower altitude, however the reduction in the payload mass does not exceeds 10% of the value found analitically

end of quote

Aside from the misspell of the last word in this paragraph, a reader is left wondering exactly WHAT this paragraph means in terms of rocketry . In the introduction, the figure of 10% is also bandied about. What is so revolutionary as to this finding and how does it improve the state of the art of this field ?

I recommend that the writers try to go to the stated intro as to the objectives of the paper, and then conclude with an extension of this particular paragraph as to try to join explicitly the stated initial objectives of the paper (abstract) with the findings and to try to sell the conclusion of this paper as a solid improvement of the state of the art of launch payloads, and all that, for optimal performance

Author Response

Dear Reviewer2 please find enclosed the letter ReviewRemarks where you will find the answer to your comments

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

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