Aerodynamic Design and Strength Analysis of the Wing for the Purpose of Assessing the Influence of the Bell-Shaped Lift Distribution
Round 1
Reviewer 1 Report
The manuscript is good overall. Some minor writing change can be made. For example, in page 1 line 24, the word "probably" is not appropriate in technical writing. It can be changed to Wing is one of the most important parts of a common airplane. In page 2 line 69, the number 0.5x10^6 can be changed with the exponential power format.
Author Response
Dear reviewer,
I would kindly thank you for your review. Edits based on your comments are included in the edited manuscript.
best regards,
Pavel HospodáÅ™
Reviewer 2 Report
Dear authors, my comments can be found in the attached PDF.
Comments for author File: 
Comments.pdf
Author Response
Dear reviewer,
thank you kindly for your review and inspiring comments.
The authors present a very interesting work on wings with bell shaped lift distributions, which goes back to an almost forgotten 6-page work of Prandtl, which in recent years have caught the attention of the aerodynamic community again, like Bowers from NASA in his Prandtl-D project. Besides of the lift to be achieved, they apply the bending moment and weight constraint, solve the structural problem
to have an estimation of the wing weight and with it also predict the flight performance and fuel consumption. This work is very interesting since it is showing the whole picture. However, some improvements must be done, before it can be considered on an archival journal level. In general, the results are very interesting, but the design and optimization method should be described in some
points with more details. The skilled reader should be able to reproduce this method. Therefore, a revision with rebuttal letter is needed.
1. In general, although the text is well understandable, there are many grammatical mistakes, in particular the authors omit many prepositions. Therefore, the grammar of the paper MUST be revised by a native speaker.
>> Grammar correction has been performed and is given in the modified manuscript.
The list of symbols is missing, the paper MUST have a complete list of symbols. For example: SFC = Specific Fuel Consumption
>> List of abbreviation is added.
Line 35: This lifting line theory that was developed in the beginning of the 19th century [2], [3] => To the knowledge of this reviewer Lanchester formulated his Vortex Trunk theory in 1891-4 and Prandtl published his LLT in 1915, see Anderson, “History of Aerodynamics”. The authors should revise this
affirmation carefully and correct or explain where necessary. Or did they mean beginning of 20th century? Remember, 20th century goes from 1901 till 2000.
>> This reminder is incorporated into the revised manuscript.
Line 36: and Prandtl also derived optimal lift distribution for minimum induced drag for a given lift, wing span and bending moment, entitled as elliptical lift distribution, which became a basis for the design of the wing. => Prandtls theory of the elliptic lift distribution requires a constant span but not a given bending moment and total lift, see Anderson, Fundamentals of Aerodynamics. The bell-shaped lift distribution on the other side does not require a constant wingspan. Its this condition that is substituted by bending moment and total lift (weight) and lets the wingspan variable in the case of the bell-shaped lift distribution. The authors should carefully revise this passage. As mentioned also by Anderson: the primary design factor for minimizing induced drag is not the closeness to an elliptical lift distribution, but rather, the ability to make the aspect ratio as large as possible
>> The original article erroneously stated that the elliptical lift distribution is optimal for a given lift, bending moment and wing span. This error has been corrected and is no longer in the corrected manuscript.
Line 53: That is calculated due to wing-span load integration, and it results to 6% less induced drag and 15% more wingspan. Previous work has only looked at the shape of the lift distribution and has not dealt with how this distribution will be realistically achieved. => This formulation might lead the reader to the conclusion that increasing the span and reducing so the induced drag is a new result. The
relation between span and induced drag is a general and well-known result also predicted by the classical wing theory also already by Prandtl, weather with a bell-shaped lift distribution or any other one, see for instance Anderson “Fundamentals of Aerodynamics” or Prandtl. As described in the original 6-page work of Prandtl “Über Tragflügel kleinsten induzierten Widerstandes” the elliptical lift distribution is the one with the least induced drag only if the wingspan is kept constant. It’s exactly this constraint, which is substituted now by structural (bending moment) and weight constraint (total lift), leading to the bell-shaped lift
distribution. It seems to me as the reviewer that from line 53 on this is not clearly stated and hence the authors should point this out in a very clear way throughout the paper to avoid any misunderstanding. It is clear to the reviewer that the authors are fully aware of these facts, but in some passages, it’s not formulated in a very clear way, in particular not if the reader is not so proficient in aerodynamics. Therefore please revise the text in this sense to have these concepts very clear throughout the paper to make it better readable.
Parandtl“Über Tragflügel kleinsten induzierten Widerstandes”:
Die Nebenbedingung, daß die Spannweite vorgeschrieben ist, ist dabei aber durchaus wesentlich, und es ist also die Behauptung durchaus unzulässig, daß die elliptische Auftriebsverteilung die beste schlechthin sei. Der induzierte Widerstand ist um so kleiner, je größer die Spannweite gemacht wird. Wenn in einem Sonderfall die Spannweite des Flugzeuges durch die Forderung begrenzt wird, daß das Flugzeug durch ein bestimmtes vorgegebenes Hallentor geschoben werden kann, so ist es am Platz, innerhalb der so vorgeschriebenen Spannweite den Auftrieb elliptisch zu verteilen. Wenn aber eine derartige Begrenzung nicht vorliegt, dann wird man sich nach anderen Gesichtspunkten richten müssen.
Hier soll eine einfachere Aufgabe gestellt werden, diese aber exakt durchgeführt werden. Man kommt nämlich zu einer vernünftigen Begrenzung der Spannweite auch dadurch, daß man neben dem Gesamtauftrieb Ades Flügels das Trägheitsmoment A r2 der Auftriebsverteilung vorschreibt. r ist dann der "Trägheitsradius" der Auftriebsverteilung. Auf das Trägheitsmoment der Auftriebsverteilung wird man geführt, wenn man das Holmgewicht an jeder Stelle proportional dem dort wirkenden Biegungsmoment M setzt.
>> This point is closely related to the previous comment and the introduction to the article has been revised in general in light of this.
Line 160: It is suitable to use airfoil characteristics from Xfoil computation for linear part of
the lift curve at low-speed regime. => Why was this mentioned? It is not clear if Xfoil was used or not and if yes, which results were obtained by XFoil. If XFoil was used to find the airfoil drag it should be described or mentioned in detail or simply stated more clearly in the wing design section, for instance already after line 150.
>> The aerodynamic characteristics calculated by the Xfoil program are only used for the test example and this is now more clearly written in the text.
Line 175: Geometrical sets of analyzed wings were modelled in CATIA program => There are no details of these geometrical sets given. This is, however, one of the central steps in the whole work. Besides of the rectangular wing shape five more shapes where developed. Details on the method, the different constraints and why the wings came out quite different of each other have to be given in some more detail (I know details were given, but add some more information to make it very clear so that a skilled reader can reproduce it). See also the comment below on the block diagram, which might make it more understandable.
>>The description of geometry formation by the CATIA programme is now better described and a tables have been added to the annex showing the distribution of chord and twists over the span of optimised wings.
8. Line 205: Wing optimization procedure - The optimization procedure is aimed at minimizing total aerodynamic drag for having lift force and bending moment. Different optimization methods were used for different wing planform design. Most of wing geometries are optimized by combination of design of experiment and response surface method => The description is this section is not giving much details. In lines 218 – 220 it is not clear if these wings were drafted “by hand” or another method, for instance LTT or response surface method. How these wings were designed in detail should be mentioned. How LLT works with CFD and response surfaces together. The remaining two wings that were designed (lines 221-
222) to investigate the bell shaped lift distribution are described but the details provided up to line 226 are not enough to allow the reader to reproduce these results. The one allows a chord variation and the other an aerodynamic twist. Was this done with LLT only or are there more steps and methods needed? How many iterations with CFD were needed? Or did CFD simply confirm the LLT results? To answer all these questions a block diagram showing the whole process for all cases and how LLT/CFD/Response Surfaces/Optimization loops/constraints and so on work together would be very helpful and should be added to the paper. With the clear block diagram also the explanations in the text will be better
understandable to all readers.
>> This part of the article has been redrafted to make it clear what the sequence of the optimization process is and at which stage the LLT used and where the CFD calculation.
Although the wing forms can be roughly recognized in figures 5 and 6 one plot with all 5 wing shapes (chord lengths against span) in one plot should be added.
>> Comparison of wing shapes are depicted in figure 7(a) and more detail information can be found in added appendix.
Line 279: The x-component of skin friction coefficients can be seen for higher angle of attack in the left side of Figure 6. => The authors should mention exactly at which angle of attack these shear stress countour plots were made. They should mention also that at the positions of zero shear stress the detachment starts, in order to make the paper better readable for all, also for readers not so proficient in aerodynamics.- 11. Line 281: Places of separated flow is bordered by a black line. => How were they identified? Zero shear stress? Please mention carefully.
>> Based on these two comments, these figures are described in more detail in the revised manuscript.
Line 282: The right-hand side of Figure 6 shows the aerodynamic load distribution for both calculation methods, and it's noticeable that even here there's a relatively good agreement between the lifting line theory and CFD. => How this can be explained, in particular at which angles of attack? With or without substantial flow detachment? See also comments below.
>> this comment is now better explained in the article
Line 306: With a high degree of probability, this is a phenomenon used by birds during dynamic soaring. => This is not a scientific statement. Either there are examples or citations from the literature, or it is a guess and has still to be investigated. Please reformulate it carefully.
>> corrected
- Line 419: For this glide regime the airplane is engine idling => Typo => For this glide regime the airplane is engine gliding
>> corrected
15. Line 449: Calculated using a lifting line theory, the total aerodynamic drag can be divided into an induced and a viscous part. => The drag of a subsonic aircraft usually is sub divided in three components: pressure drag + skin friction drag + induced drag. See for example Anderson, Fundamentals of Aerodynamics. Please correct and explain accordingly where necessary in the paper.
>> corrected
468: Aerodynamic analysis revealed good match of used lifting line method with CFD calculation both in total values of aerodynamic characteristics and the distribution of lift force over semispan. => See comments below
And finally, it is necessary to note the advantage of the using of lifting line method with the analytical design of the wing’s structure. It is a fast method that give solutions within units of seconds and are thus suitable for preliminary wing designs. => This is truth. The reason is that in this case the Reynolds number Re=3.5x106 is high. This, however, works only well if there
is no flow detachment or still if the flow detached area is small. The authors should justify it accordingly, mentioning also the Reynolds number in this context again, in order not to give the impression to the reader that this is a new finding, since this is actually expected and well known. Therefore, these ideal flow design methods, in particular also the LLT, are treated in all outstanding aerodynamics books till today, like the ones from Prof. J.D. Anderson Jr., “Fundamentals of Aerodynamics”, and similar ones. The authors already mentioned three
books of Prof. Anderson, in this context they might consider also to mention the one on “Fundamentals of Aerodyanamics” (or a similar one like Houghton or Kuethe and so on).
>> The use of the LLT method is possible precisely for the wing regime where there is no flow separation (≈ideal flow). At higher values of the lift coefficient, more complex flow structures are formed and can no longer be credibly calculated by this method. This was also the case for the "test case" where the polar between calculation and measurement corresponded relatively well for the lower lift values. Again, this section is edited in the revised text.
best regards,
Pavel HospodáÅ™
Reviewer 3 Report
The work is good, I recommend it for publication. There are several points:
is it necessary to indicate the affiliation and contacts of the authors in this manner? One email is enough for correspondence. Check the journal's sample.
extra space after [4] on line 41.
line 69 and in the whole text: 10^6 or 106 (like in line 156)? And x or *(like in line 156)? Or . ? Pick one style for all the text. And pay attention to other designations in the manuscript.
line 79: "no one fully explained all the aerodynamic consequences until 2016" can this be stated? There is always a chance that some work might be overlooked. I think that it is incorrect to make such statements, it is better to say something like "the authors do not know about such works", etc.
line 80: Bowers et al. published his article [14] (he is not the one author of [14], there are others).
line 120: Г or Г (like in Eq.1)? Italics or not? Same goes for other letters and symbols in the manuscript.
Table 1: Root Tip
line 189: "desired y+ equals 1" ?
line 190: "-about 40" ?
line 215: tables
line 216: Table 2. Definition
line 267 and in the whole text: isosurface
line 287: Figure 7(a) depicts different...
line 321 (b) - without bold
line 324: 3. Structural...
line 331: ... Table 2 ...
line 381: Estimated ...
line 391: 4. Flight ...
line 456: Table 3. Summary ...
line 464: Comparison ...
Author Response
Dear reviewer,
I would kindly thank you for your review. Edits based on your comments are included in the edited manuscript.
best regards,
Pavel HospodáÅ™
Round 2
Reviewer 2 Report
The authors have addressed well the comments. Bacially the block diagram (or better flow chart) of the design method was not added, wich would improve the readability of the paper substantially, but is not mandatory.
