Stealth Unmanned Aerial Vehicle Penetration Efficiency Optimization Based on Radar Detection Probability Model
David Sziroczak
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
The paper investigates an indeed interesting subject. The methodology is reasonable, but the discussion of the results is somehow unclear and not supported by adequate plots, both in terms of type and quality.
Some of the optimization figures are not provided, as an example how long it took the optimizer to achieve convergence.
In addition to that, GA is affected by certain degree of randomness; to mitigate this, usually the results from multiple runs are compared statistically to demonstrate that the achieved configuration is neither the result of good luck (e.g. early convergence to the optimal configuration) or bad luck (local minima). This is not investigated in this paper. Please explain why it was/was not necessary to take this action.
Figure 12 is counterintuitive, the baseline model that passes through the DOE to achieve or feed data to the Parametric model is not informative. It is the parametric model they started with that can handle both the baseline and the DOE and generate UAV geometries.
The study neglects the impact of the geometry changes on the UAV stability, maneuverability and handling characteristics. It is acceptable for a preliminary or foundation study but should be stated properly.
27-28 In the situation without winning the air control power, the viability of combat aircraft 27 used for attacking enemy radar and combat aircraft fighting for air control is affected by the stealth capability of radar.
Grammar, sentence not clear
36 However, optimization with a single objective of aerodynamic or stealth per-36 formance often results in vastly different aircraft shapes.
Aerodynamic optimization is already multi-objective, could be re-phrased as Optimization tailored on the requirements from a single discipline []
39 only served 25 years even with a high loss exchange ratio ?? very unclear, exchange or loss of what?
parameter is usually reserved for the design variables, the inputs of the optimization, as design parameters. Target may be called objective, KPI key performance indicator and so on
47 the contradictory in the optimization process
contradiction not contradictory. The concept could be better described with a pareto front.
48 to 51, without a plot this is cumbersome to figure out.
The research showed 56 that the Pareto solution can fully demonstrate the optimization boundary,
Not clear
58 to 60 how pareto optimality works it is well known, reference from different applications does not seem to be required in this case.\
62 to cater the
to counter?
Additional remarks on English will be mostly omitted, the paper will be marked as lacking from this point of view.
107 the use of optimization model is not intuitive.
What you are describing is an optimization procedure with a penetration efficiency model (this is a model because you implemented an algorithm that gives you the results) with a single objective which is the results of the weighted combination of several performance indicators.
110 weighted problem, not weight
sec 2.1, is chord a design parameter? and the angle of the part of the wing between the trailing edge turning points?
142 Benchmark Radar Targets for the Validation of Computa-142 tional Electrical Programs proposed by NASA in 1993 for validation.
please add reference
What is the non-tip direction?
160 AN/SPY-1 radar
add reference
Section 2.3.1 is significantly better in terms on English, and quality of the explanations, than the previous one
Still, 255, ”too far to detect”, not “to detected”, the same applies to the second part of the sentence.
ALTIUS-600M please provide a reference or clarify, according to Google, the Anduring Altius-600M is a small loitering ammunition with a range of at best 240km (4h autonomy x 60kmh cruise speed).
278 why estimated hit probability is a function of distance? enemy defensive actions? Please explain.
275 onwards. Is the return travel included in the calculation of the expected number of sorties?
Furthermore, is the turnback maneuver accounted for?
309 is it not clear if the airfoil itself is a design parameter or not. at line 310 is clearly excluded from the list, but at line 186 it is labelled as the wing configuration as something being optimized.
Several plots, especially Figure 7, have a low resolution/quality
316 Please provide a reference for the GA.
Optimizer's parameters would be of interest, e.g. population size, and convergence criteria.
wing-span is not constrained, but as a result of the wing surface being preserved, the UAV's wing can stretch. Usually, span is limited to prevent issues like hangar accessibility.
If the DOE highlighted that no configuration was going to exceed a practical value, therefore there was no added gain in constraining the span, please specify.
Otherwise explain why it was left unbounded.
Table 5, Max flight sorties decreased, but Penetration efficiency increased. Please justify/explain.
The penetration efficiency seems to be linear with wing aspect ratio. But how have the plots in figure 14 been generated? In terms of convergence history, they provide no information.
It would be interesting to have the experiments associated to the different iterations colored differently, as to highlight the optimization trend.
Additionally, as the penetration efficiency is the combination of the effect of all the design parameters, it is not easy to distinguish the single influences.
A different type of plot, like parallel coordinates, could improve the readability.
Same applies to a convergence plot with penetration efficiency with respect to experiment number.
Figure 17, same comment as for Figure 14.
A correlation plot using Pearson or Spearman coefficients could also better explain the influence of the design parameters on the efficiency.
362, "thickness of the outer wing" not clear, I assume this implies the chord of the outer wing section, however thickness is usually associated with the distance upper-lower skin.
Considering the optimization results, wing sweep angle has relatively lower upper 383 boundary. Clarify, better English needed.
387 please explain what that obvious convergence would be.
Comments on the Quality of English Language
The paper is discontinuous in terms of quality.
The main body of the paper requires a few correction/rephases, and so does the result one.
The introduction includes quite a few grammar mistakes, i.e. nouns used as adjectives and vice versa, and sentences that are either hard to interpretate or without any meaning at all.
A review from someone whose native language is English is advisable.
Author Response
Comments 1: The paper investigates an indeed interesting subject. The methodology is reasonable, but the discussion of the results is somehow unclear and not supported by adequate plots, both in terms of type and quality. Some of the optimization figures are not provided, as an example how long it took the optimizer to achieve convergence.
Response 1: Thank you for your review of this manuscript. It is my honor to have a reviewer as meticulous and professional as you. Details have been added to the beginning of Chapter3.
Comments 2: In addition to that, GA is affected by certain degree of randomness; to mitigate this, usually the results from multiple runs are compared statistically to demonstrate that the achieved configuration is neither the result of good luck (e.g. early convergence to the optimal configuration) or bad luck (local minima). This is not investigated in this paper. Please explain why it was/was not necessary to take this action.
Response 2: The data selected in this paper is the optimal solution from multiple runs. I believe the focus of this paper is on transforming the multi-objective problem of aerodynamic-stealth optimization into a single-objective problem. The comparison of multiple runs deviates from this main topic. Therefore, I only added a description of multiple runs at the beginning of Chapter 3.
Comments 3: Figure 12 is counterintuitive, the baseline model that passes through the DOE to achieve or feed data to the Parametric model is not informative. It is the parametric model they started with that can handle both the baseline and the DOE and generate UAV geometries.
Response 3: The flow chart has been corrected.
Comments 4: The study neglects the impact of the geometry changes on the UAV stability, maneuverability and handling characteristics. It is acceptable for a preliminary or foundation study but should be stated properly.
Response 4: The sentence is added before 2.3chapter. “This paper mainly studies the lift-drag and stealth characteristics of the Lambda wing during the cruise state. However, changes in configuration will also affect the UAV stability, maneuverability and handling characteristics, which will not be considered.”
Comments 5: 27-28 In the situation without winning the air control power, the viability of combat aircraft 27 used for attacking enemy radar and combat aircraft fighting for air control is affected by the stealth capability of radar. Grammar, sentence not clear.
Response 5: This sentence has changed to “Without achieving air supremacy, the survivability of combat aircraft is influenced by its radar stealth capabilities.”
Comments 6: 36 However, optimization with a single objective of aerodynamic or stealth performance often results in vastly different aircraft shapes. Aerodynamic optimization is already multi-objective, could be re-phrased as Optimization tailored on the requirements from a single discipline
Response 6: This sentence has changed to “Optimization tailored to the requirements of a single discipline often leads to significantly different aircraft shapes depending on the optimization objective.”
Comments 7: 39 only served 25 years even with a high loss exchange ratio ?? very unclear, exchange or loss of what?
Response 7: My original intention was to express that the combat survivability of F117 is very high. It has corrected to “The F-117, the world's first stealth aircraft, served only 25 years despite its high combat survivability.”.
Comments 8: parameter is usually reserved for the design variables, the inputs of the optimization, as design parameters. Target may be called objective, KPI key performance indicator and so on
Response 8: The wrong word “parameter” has been changed to “objective”.
Comments 9: 47 the contradictory in the optimization process47 .contradiction not contradictory. The concept could be better described with a pareto front.
Response 9: The wrong word “contradictory” has been changed to “contradiction”. And the pareto front is arranged after this paragraph.
Comments 10: 48 to 51, without a plot this is cumbersome to figure out.
Response 10: My original intention was to show how difficult to balance the weight factor. And that’s the reason for the pareto front. The sentence has changed to “When all weight factors prioritize stealth optimization, the lift drag ratio decreased significantly from 26.04 to 16.94. Despite achieving excellent stealth performance, the optimized result proved unacceptable.”
Comments 11: “The research showed that the Pareto solution can fully demonstrate the optimization boundary” Not clear
Response 11: The sentence has been changed to “Their research demonstrated the flexibility and comprehensiveness of Pareto solutions in analyzing multi-objective optimization results.”
Comments 12: 58 to 60 how pareto optimality works it is well known, reference from different applications does not seem to be required in this case.
Response 12: 58-60 has been removed
Comments 13: 62 to cater the 62 to counter?
Response 13: Corrected now.
Comments 14: Additional remarks on English will be mostly omitted, the paper will be marked as lacking from this point of view. 107 the use of optimization model is not intuitive.107 What you are describing is an optimization procedure with a penetration efficiency model (this is a model because you implemented an algorithm that gives you the results) with a single objective which is the results of the weighted combination of several performance indicators.
Response 14: I’m sorry that I mistakenly took the optimization procedure as the optimization model. My original intention was to express the integration of the penetration efficiency model and the optimization model. And the sentence has changed to “This paper introduces a penetration efficiency model into an optimization frame-work to nonlinearly transform a multi-objective optimization model into a single-objective optimization model.”
Comments 15: 110 weighted problem, not weight
Response 15: The wrong word “weight” has been changed to “weighted”.
Comments 16: sec 2.1, is chord a design parameter? and the angle of the part of the wing between the trailing edge turning points?
Response 16: The characteristic of the Lambda wing described in this paper is that the leading and trailing edges remain parallel. This configuration can reduce the number of radar wave echoes. The chord length is determined by the wing area and the wing sweep angle due to this rule.
“And C refers to chord length which is determined by the wing area, aspect ratio and wing sweep angle.” This sentence is added now.
Comments 17: 142 Benchmark Radar Targets for the Validation of Computational Electrical Programs proposed by NASA in 1993 for validation.1993年，NASA。please add reference
Response 17: Reference [23] is added now.
Comments 18: What is the non-tip direction?
Response 18: Quote the Wiki” The physical optics method is an intermediate method between geometric optics, which ignores wave effects and full wave electromagnetism, which is a precise theory.”
The calculation accuracy of physical optics (PO) method will decrease in objects with sharp tip close to the wavelength. The smooth surfaces described in this paper are suitable for physical optics methods.
The sentence has changed to “According to the test result, CEM method (based on PO) shows high accuracy for RCS simulation, especially for non-tip objects where the fit is extremely high.”
Comments 19: 160 AN/SPY-1 radar 160 AN/SPY-1 add reference
Response 19: Reference [24] is added now.
Comments 20: Section 2.3.1 is significantly better in terms on English, and quality of the explanations, than the previous one Still, 255, ”too far to detect”, not “to detected”, the same applies to the second part of the sentence.
Response 20: The sentence has changed to “Filtered radars are shown in Figure 9: green dots represent to radars too distant to detect, red dots represent to radars that have fully captured the UAV, and blue dots rep-resent to radars filtered out due to RCS peaks.”
Comments 21: ALTIUS-600M please provide a reference or clarify, according to Google, the Anduring Altius-600M is a small loitering ammunition with a range of at best 240km (4h autonomy x 60kmh cruise speed).
Response 21: Please check this link: https://www.armyrecognition.com/news/army-news/2023/united-states-delivers-altius-600m-loitering-munitions-to-ukraine
As an author, I hope to provide academic papers from a neutral perspective. Therefore, the radars and weapons I chose are all made in the United States. The Anduring Altius-600M is a weapon system that is more suitable for this UAV in terms of size. For real UAV design, enemy radar and own weapon systems should be chosen.
Comments 22: 278 why estimated hit probability is a function of distance? enemy defensive actions? Please explain.
Response 22: Explanation has been added: “In actual combat, air defense weapon systems are very complex. Probability calculations necessitate extensive experimentation with air defense systems, which is nearly impossible during preliminary design phases. This article simplifies the calculation when considering the enemy air defense system, linking missile hit probability to launch distance. This paper selects ALTIUS-600M as the reference missile and sets hit probability to four levels: impossible, low probability, high probability and inevitable. Estimated hit probability is listed in Figure 10.”
Comments 23: 275 onwards. Is the return travel included in the calculation of the expected number of sorties? Furthermore, is the turnback maneuver accounted for?
Response 23: This paper does not consider the flight process after launching, which will make the calculation process more complicated. The turnback maneuver will make the maneuverability and control performance of the rudder surface necessary to consider, which will further increase the burden of the preliminary design.
In addition, I am currently optimizing the design of the seamlessly control surface for this optimized lambda wing configuration, with the aim of reducing the lateral RCS peak caused by the control surface.
Comments 24: 309 is it not clear if the airfoil itself is a design parameter or not. at line 310 is clearly excluded from the list, but at line 186 it is labelled as the wing configuration as something being optimized.
Response 24: Sorry, this is my mistake. Line186 should not include airfoil. the This paper focus on wing configuration.
In addition, I also tried the optimization with airfoil parameters. The airfoil parameters will greatly slow down the optimization speed to an unacceptable level. Optimization of airfoils requires separation from configuration.
Comments 25: Several plots, especially Figure 7, have a low resolution/quality
Response 25: Figures have been updated. Please check them in the new manuscript.
Comments 26: 316 Please provide a reference for the GA.
Response 26: Reference [29] is added now.
Comments 27: Optimizer's parameters would be of interest, e.g. population size, and convergence criteria.
Response 27: Details have been added to the beginning of Chapter3.
Comments 28: wing-span is not constrained, but as a result of the wing surface being preserved, the UAV's wing can stretch. Usually, span is limited to prevent issues like hangar accessibility. If the DOE highlighted that no configuration was going to exceed a practical value, therefore there was no added gain in constraining the span, please specify. Otherwise explain why it was left unbounded.
Response 28: The Lambda wing proposed in this paper is limited by the parallelism of the leading and trailing edges and the wing area, both of which are fixed. The upper limits of the wing span and chord length in this paper are actually hidden in the aspect ratio and the parallelism of the leading and trailing edges of the Lambda wing. This sentence has added to 2.3.2: “These parameters can be combined to determine geometric properties such as wing span and chord length.”
Comments 29: Table 5, Max flight sorties decreased, but Penetration efficiency increased. Please justify/explain.
Response 29: Sorry, the max flight sorties of baseline in my first manuscript was reversed from the optimized result. Now, the data has been corrected.
Comments 30: The penetration efficiency seems to be linear with wing aspect ratio. But how have the plots in figure 14 been generated? In terms of convergence history, they provide no information. It would be interesting to have the experiments associated to the different iterations colored differently, as to highlight the optimization trend. Additionally, as the penetration efficiency is the combination of the effect of all the design parameters, it is not easy to distinguish the single influences. A different type of plot, like parallel coordinates, could improve the readability. Same applies to a convergence plot with penetration efficiency with respect to experiment number. Figure 17, same comment as for Figure 14.
Response 30: In the new manuscript, the Figure14 has changed to figure with convergence history information by color bar.
The penetration efficiency is not linear with wing aspect ratio. You can see the next set of figures. Lift-to-drag ratio is more strongly related to aspect ratio. However, when the aspect ratio increases, the radar detection probability does not decrease linearly. This paper performs a decomposition analysis of various parameters, which distinguishes the proposed model from widely used models. By decomposing the parameters, the impact of each parameter on aerodynamic and stealth performance can be observed, thereby enhancing the feasibility of the model. I hope you will understand.
Comments 31: 362, "thickness of the outer wing" not clear, I assume this implies the chord of the outer wing section, however thickness is usually associated with the distance upper-lower skin.
Response 31: This paper uses the same airfoil, so as the chord length increases, the thickness will increase proportionally. It is generally agreed that wing thickness is related to drag force, so I chose thickness as the word here.
Comments 32: A correlation plot using Pearson or Spearman coefficients could also better explain the influence of the design parameters on the efficiency. Considering the optimization results, wing sweep angle has relatively lower upper 383 boundary. Clarify, better English needed. 387 please explain what that obvious convergence would be.
Response 32: Thank you for your suggestions. I added a Pearson heat map in the new manuscript, which can visualize the influence of each parameter.
And the next paragraph has changed to “From the results, the optimized configuration is closer to the upper limit of the wing sweep angle. A larger wing sweep angle disperses the RCS peak angle. This will increase the proportion of radars below the threshold, which is equivalent to increasing the proportion of blue dots in Figure 9. The influence of the wing sweep angle is moderate compared to the other four parameters. Increasing either the upper bound of the wing sweep angle or the radar scanning threshold, the proportion of blue dots will increase, and the wing sweep angle will have a stronger influence.”
Comments on the Quality of English Language: The paper is discontinuous in terms of quality. The main body of the paper requires a few correction/rephases, and so does the result one. The introduction includes quite a few grammar mistakes, i.e. nouns used as adjectives and vice versa, and sentences that are either hard to interpretate or without any meaning at all. A review from someone whose native language is English is advisable.
Response on the Quality of English Language: Most of the content in this manuscript has been revised in English. Please check~
Reviewer 2 Report
Comments and Suggestions for AuthorsDear authors,
thank you for submitting your manuscript. Based on my review, I am recommending revision as there are many points which should be clarified before publication. Please see my comments/points of concern below.
Stealth UAV Penetration efficiency optimization based on radar detection probability model
page numbers refer to the pdf numbering
General
English is difficult to understand in many parts of the article, revision of language is necessary.
Images quality is varied, some are very good quality, some are rather poor. Please consider the notes under the specific section to improve.
Based on the manuscript, L/D is ultimately used as a proxy for range, as speed, vehicle mass, altitude, etc. is fixed for the mission. However, isn't aircraft range a constraint in this case, rather than an optimization variable? As long as the UCAV is able to strike at the assumed 1000km radius area, the surplus range is meaningless, do you agree?
Specific
Fig 1: it took me some time to interpret the bottom half of the figure, it is very small and low resolution. Please consider providing a better quality version.
Fig 2: the difference between mesh, and the mesh overall for that matter is difficult to see due to the small size. Perhaps consider if it is necessary to show both meshes, and whether 1 larger sized image would show the point better.
Table 1. reference is not provided, although the text mentions that data refer to a specific radar
Equation 2 and followup text: if the terms in he equation are explained, then all terms should be included, for example u' or F1, Beta, etc. please check and revise.
Figure 6: is this figure necessary? If so, what is shown on the axes? Consider removing or revising.
p7: 1×10^5 radars are scattered: is this a reasonable number for radar units? Wouldn't this result in unrealistically high weight on stealth in an optimization process, as this is not a scenario that would be encountered in real life?
p8: . "This paper calculates the RCS of incident angle within ± 60° forward, which are the main factors effecting the radar detection probability. Radars corresponding to other angles will be included in radars within ± 60° forward." not sure what the authors mean here, please provide additional explanation. Also as a related matter, why are radars over 60° angle excluded from detection? this assumption removes most of the generated radars, wouldn't that artificially lower the detection probability? Also this configuration begs the question, why not consider just a slice of the area in the simulation?
fig8 : It is not clear how to interpret this plot, is it rectangular or polar? how can one interpret and read values off the blue curve? Please revise/explain/correct
p9L253: "UAV which is scanned 4 times is considered as the threshold of locking by missiles." is there any reference or study available to substantiate this assumption?
either table 3 or figure 11 is redundant
Table 5/Figure 13: is it reasonable, that the optimization process drives towards a larger aircraft size? As radar detection is positively correlated to the overall area of the aircraft, this seems like a counterintuitive result. Please provide discussion on the matter. As a related question, does the model consider the change in angle of attack due to a larger wing planform, and/or varying aircraft mass due to different size? Please at least provide a discussion.
P17L403: it would be very interesting to see what effects the radar parameters have on the optimised aircraft shape. As the data shown in fig 22 and 23 are essentially the inputs for the optimization process, I believe it would be more meaningful to show the effects on the results.
Comments on the Quality of English Language
English is difficult to understand in many parts of the article, revision of language is necessary.
Author Response
Comments 1: English is difficult to understand in many parts of the article, revision of language is necessary. Images quality is varied, some are very good quality, some are rather poor. Please consider the notes under the specific section to improve.
Response 1: Thank you for your review of this manuscript. It is my honor to have a reviewer as meticulous and professional as you. Some English revisions have been done in the new manuscript. Please check.
Comments 2:Based on the manuscript, L/D is ultimately used as a proxy for range, as speed, vehicle mass, altitude, etc. is fixed for the mission. However, isn't aircraft range a constraint in this case, rather than an optimization variable? As long as the UCAV is able to strike at the assumed 1000km radius area, the surplus range is meaningless, do you agree?
Response 2: I understand your confusion. The aircraft range is often used as a constraint when determining the overall parameters in the earliest stage of aircraft design. However, in actual combat, a longer range often represents the combat range that the aircraft can cover. There is also a demand for increasing the range in many aircraft modifications. Therefore, improving the range during the optimization phase is definitely not meaningless. You can check the 14th formula (Breguet formula) in the manuscript:
Comments 3: Fig 1: it took me some time to interpret the bottom half of the figure, it is very small and low resolution. Please consider providing a better quality version. Fig 2: the difference between mesh, and the mesh overall for that matter is difficult to see due to the small size. Perhaps consider if it is necessary to show both meshes, and whether 1 larger sized image would show the point better.
Response 3: Higher resolution Figure 1 and Figure 2 are provided in the new manuscript. Figure 1 has changed the bottom half of the figure. Figure 2 has added the meshing details
Comments 4: Table 1. reference is not provided, although the text mentions that data refer to a specific radar
Response 4: Reference [24] is added now.
Comments 5: Equation 2 and followup text: if the terms in he equation are explained, then all terms should be included, for example u' or F1, Beta, etc. please check and revise.
Response 5: The equation2 followup text has been revised.
Comments 6: Figure 6: is this figure necessary? If so, what is shown on the axes? Consider removing or revising.
Response 6: Figure 6 has been removed.
Comments 7: p7: 1×10^5 radars are scattered: is this a reasonable number for radar units? Wouldn't this result in unrealistically high weight on stealth in an optimization process, as this is not a scenario that would be encountered in real life?P7：
Response 7: I think you may have misunderstood the assumptions here. The 10,000 radars are used to simulate the possibility of a single radar in the area based on Gaussian distribution. The denominator in Formula 9 is 10,000, and the numerator is the radar that can detect the aircraft. This fraction represents the probability of being detected by this single radar when performing the penetration mission. In addition, the use of 10,000 here is a reasonable choice based on the computer. Actually, increasing this value will help to improve the stability of the calculation of radar detection probability. This value will not influence the weight on stealth.
Comments 8: p8: "This paper calculates the RCS of incident angle within ± 60° forward, which are the main factors effecting the radar detection probability. Radars corresponding to other angles will be included in radars within ± 60° forward." not sure what the authors mean here, please provide additional explanation. Also as a related matter, why are radars over 60° angle excluded from detection? this assumption removes most of the generated radars, wouldn't that artificially lower the detection probability? Also this configuration begs the question, why not consider just a slice of the area in the simulation?
Response 8: Here are my explanations: 1. The lateral stealth performance often has little effect on radar detection during the cruise process. The lateral radar wave crest is perpendicular to the flight speed, and the lateral radar wave crest stays on the radar for very little time. Therefore, it is very difficult to scan the wave crest. The trough of the lateral radar stealth performance covers very few radars and can basically scan the aircraft in the forward direction. In summary, the calculation of the lateral stealth performance wastes some computing resources
- The lateral stealth performance of flying wing aircraft is often affected by the stealth treatment of the wing tip. The optimization of the wing tip is often after the configuration optimization. And the evaluation target of the lateral stealth performance is often the maneuvering process rather than the cruise process. Therefore, when studying the configuration of the cruise process optimization, the lateral stealth is generally not studied.
Comments 9: fig8 : It is not clear how to interpret this plot, is it rectangular or polar? how can one interpret and read values off the blue curve? Please revise/explain/correct
Response 9: Sorry, the description was not enough. In the left plot, the relationship between RCS and incident angle is depicted. Although, from a physical standpoint, the incident angle should ideally be represented in polar coordinates, using Cartesian coordinates for this plot enhances clarity and readability. I hope you will understand.
And the paragraph has been changed to “Conversely, if the radar parameters are determined, the RCS σ corresponds to the detection distance. Figure 7 shows that the conversion of aircraft σ-Phi curve into R-Phi curve. The left plot displays the relationship between the aircraft’s forward RCS and incident angle, measured in [dBsm]. The right schematic illustrates the range where the aircraft can be detected after converting RCS into radar detectable distance. This paper calculates the RCS of incident angles within ± 60° forward, which are the main factors affecting radar detection probability. Radars corresponding to other angles will be included in radars within ± 60° forward.”
Comments 10: p9L253: "UAV which is scanned 4 times is considered as the threshold of locking by missiles." is there any reference or study available to substantiate this assumption?
Response 10: The threshold value of a radar typically depends on its performance and program settings, and is not a fixed value but a range. The threshold value of 4 is a relatively conservative value. The determination of this value is also related to the environmental noise situation. Additionally, the reference for the AN/SPY-1 radar has been updated to [24].
Comments 11: either table 3 or figure 11 is redundant
Response 11: Table 3 now has been deleted.
Comments 12: Table 5/Figure 13: is it reasonable, that the optimization process drives towards a larger aircraft size? As radar detection is positively correlated to the overall area of the aircraft, this seems like a counterintuitive result. Please provide discussion on the matter. As a related question, does the model consider the change in angle of attack due to a larger wing planform, and/or varying aircraft mass due to different size? Please at least provide a discussion.
Response 12: Please allow me to explain to you. The wing area of ​​the UAV studied in this article is fixed. Therefore, when the aspect ratio increases, the chord length will decrease proportionally. Its forward cross-sectional area can be regarded as having little change. The parameters that actually affects the forward cross-sectional area are wing area and airfoil thickness.
Comments 13: P17L403: it would be very interesting to see what effects the radar parameters have on the optimised aircraft shape. As the data shown in fig 22 and 23 are essentially the inputs for the optimization process, I believe it would be more meaningful to show the effects on the results.
Response 13: In the recent manuscript, I added a description of the total calculation time. The optimization of the wing is quite a long-time job. I fixed the parameters of the AN/SPY-1 radar at the beginning of the study. Changing the radar parameters and then optimizing the calculation will cost a large computational cost, which is difficult for me to revise the paper in ten days. I hope you can understand my difficulties.
Comments on the Quality of English Language: English is difficult to understand in many parts of the article, revision of language is necessary.
Response on the Quality of English Language: Most of the content in this manuscript has been revised in English. Please check~
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper made significant progresses with respect to the original draft. The reviewer appreciate the non-negligible efforts put in place by the authors.
I only have few minor comment and not critical remarks.
Flight altitude and profile have a significant impact on the aircraft detectability.
The former limits the maximum distance at which a microwave radar could see the aircraft due to the horizon.
But apparently the simulation domain is flat.
No mention is made on the paper on the UAV flight altitude, can only be inferred from the air density used in CDF simulation to be about 8500m, more or less.
That would put the simplified horizon on a spherical Earth at 330km.
As the minimum detection range is less than that, the authors could specify that the exploitation of a simplified flat-Earth is justified by the fact that the UAV is not going to gain any benefit from Earth's curvature due to it's altitude.
And also specify altitude and profile (constant altitude, straight towards the target) that in terms of survivability represents one the worst possible scenarios.
About the Altius, manufacturer did not provide that many information, and some websites (all second hand sources) list its range as of 276 miles.
I would say that the UAV carries a single loitering ammunition, comparable in terms of mass and performances with the 600M, with a range of 370km and the hit probability according to the metric you defined.
Plots are indeed better and more readable. It was a pity not to include the information on iterations that you had, but it was impossible to see them in the black and white plots.
Author Response
Thank you very much for your meticulous review. Your meticulousness and rigor have been the greatest motivation for me to revise this paper.
Comment 1: Flight altitude and profile have a significant impact on the aircraft detectability. The former limits the maximum distance at which a microwave radar could see the aircraft due to the horizon. But apparently the simulation domain is flat. No mention is made on the paper on the UAV flight altitude, can only be inferred from the air density used in CDF simulation to be about 8500m, more or less. That would put the simplified horizon on a spherical Earth at 330km. As the minimum detection range is less than that, the authors could specify that the exploitation of a simplified flat-Earth is justified by the fact that the UAV is not going to gain any benefit from Earth's curvature due to it's altitude. And also specify altitude and profile (constant altitude, straight towards the target) that in terms of survivability represents one the worst possible scenarios.
Response 1: You may have made a mistake in calculating the altitude. The flight altitude calculated in this paper is 10,000m at a cruising state of 0.65 Mach. Thank you for your comment on the issue of earth curvature. I am deeply touched by your rigorous academic style. I have added the description of the flight altitude (Table 2) and the direct flight target (line230) in the paper. I have also explained the issue of earth curvature. The explanation is as follows:“The flight altitude studied in this paper is 10 km, and the horizon distance calculated using the horizon calculation formula is 357 km. This distance is far greater than the radar detection range for the UAV. Therefore, it ensures the validity of the flat Earth model assumption, thereby guaranteeing the accuracy of the radar detection range equation. This makes the process of flying straight towards the target the worst scenario for survivability in the calculation model.”
Comment 2: About the Altius, manufacturer did not provide that many information, and some websites (all second hand sources) list its range as of 276 miles. I would say that the UAV carries a single loitering ammunition, comparable in terms of mass and performances with the 600M, with a range of 370km and the hit probability according to the metric you defined.
Response 2: The description has been corrected to: “This paper simplifies the calculation when considering the enemy air defense system, linking missile hit probability to launch distance. The UAV carries a single loitering ammunition with an effective range of 350km, comparable in terms of mass and performances with the ALTIUS-600M as the reference missile and sets hit probability to four levels: impossible, low probability, high probability and inevitable. Estimated hit probability is listed in Figure 10.”
Comment 3: Plots are indeed better and more readable. It was a pity not to include the information on iterations that you had, but it was impossible to see them in the black and white plots.
Response 3: This paper uses a genetic algorithm, so it is inevitable that there will be iterative mutations in each generation, which will cause the chart with color bar to not express the iterative information so clearly. However, the convergence trend of each parameter can still be seen through the convergence information of each parameter.
Reviewer 2 Report
Comments and Suggestions for AuthorsDear authors,
thank you for providing your feedback, I agree with all the points not listed here. However I still have a few comments/recommendations based on your answer. Please see them below:
Response 2. Thank you for your explanation, please provide this as an argument in the main text.
Response 4. Extra reference should be added correctly
N. Landry, H. Goodrich, design for the AN/SPY-1 phaSec array
where is it publshed?
Response 7. Thank you for your explanation, I understand the 2D normal spatial distribution part. I am still on the opinion, that the large number of radar units skews the fitness of the stealth evaluation. There are many (I would say the majority) radar units which have no practical chance to observe the aircraft, simply because they are generated too far away or at 60+ degree angle from the aircraft. So in my interpretation it is actually the radar position in most of the cases that gives higher "undetection" chance, not the shape of the aircraft, which in my opinion would skew the optimization results. If you think about it even a less stealthy aircraft has a good chance not to be detected if the radar is far away/at a given angle and due to the generation strategy most radars are actually placed rather far away. Please at least provide a discussion on the reasoning behind this assumption in the text.
Response 8. Please provide this explanation in the main text, with references if available.
Author Response
Thank you very much for your meticulous review. Your meticulousness and rigor have been the greatest motivation for me to revise this paper.
Comment 1: Response 2. Thank you for your explanation, please provide this as an argument in the main text.
Response 1: The explanation has been added: “The aircraft range is often used as a constraint when determining the overall parameters in the earliest stage of aircraft design. However, in actual combat, a longer cruise range often represents a bigger combat range that the aircraft can cover. There-fore, this paper defines as the penetration efficiency coefficient, which represents the sum factor of the maximum cruise range for penetration missions throughout the entire life of the stealth UAV. The penetration efficiency coefficient serves as the optimization objective function”
Comment 2: Response 4. Extra reference should be added correctly N. Landry, H. Goodrich, design for the AN/SPY-1 phaSec arrayN. where is it publshed?
Response 2: Sorry, my previous citation was incorrect. The reference has changed to “N.R. Landry, H.C. Goodrich, H.F. Inacker, L.J. Lavedan, Practical Aspects of Phase-Shifter and Driver Design for a Tactical Multifunction Phased-Array RADAR System, IEEE Transactions on Microwave Theory and Techniques, 22 (1974) 617-625.”
Comment 3: Response 7. Thank you for your explanation, I understand the 2D normal spatial distribution part. I am still on the opinion, that the large number of radar units skews the fitness of the stealth evaluation. There are many (I would say the majority) radar units which have no practical chance to observe the aircraft, simply because they are generated too far away or at 60+ degree angle from the aircraft. So in my interpretation it is actually the radar position in most of the cases that gives higher "undetection" chance, not the shape of the aircraft, which in my opinion would skew the optimization results. If you think about it even a less stealthy aircraft has a good chance not to be detected if the radar is far away/at a given angle and due to the generation strategy most radars are actually placed rather far away. Please at least provide a discussion on the reasoning behind this assumption in the text.
Response 3: To be honest, I had the same confusion when building the model: "There are many radars distributed far away from the aircraft, completely in undetectable positions. Why do we need to distribute so many irrelevant radars in the calculation?" However, in actual combat, there are indeed situations where there is low threat during combat missions (no radar in the flight path). If this task is removed when calculating the detection probability, the probability of being detected by the radar will increase, and the proportion of stealth performance optimization will greatly increase. This will result in the neglect of aerodynamic performance during low threat missions and lead to distortion of the model for calculating the full life cycle. This is why the low threat radar was not removed in this article.
In addition, this article mentions that the radar distribution follows a two-dimensional Gaussian distribution model, which is a model that is closer to the target point and more. Choosing to use a large number of radar units is actually to simulate a continuous probability function (covering area) in a discrete case. As long as the number of radar units is sufficient, the fitting of the probability function will be more accurate. In actual combat, for aircraft with very poor stealth performance, as long as the radar position is very remote, there is indeed a certain probability that they can perform the mission. However, it should be noted that the premise is that the radar location is very remote, and in this article, the probability of remote location will be lower due to spatial distribution issues.
Response 8. Please provide this explanation in the main text, with references if available.
Response 4: The explanation has changed to “When calculating radar cross-section, focus is primarily on the forward direction of the aircraft due to the brief appearance of lateral radar wave crests, which are perpendicular to flight speed and complicate effective scanning. While optimizing wing tips is typically necessary for lateral stealth performance and often follows aerodynamic configuration optimization, this paper does not address wing tip optimization. Therefore, it calculates the RCS for incident angles within ± 60° forward.”
But I haven't found any reference with similar descriptions yet.
