the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Swinging Motion of a Kite with Suspended Control Unit Flying Turning Manoeuvres
Mark Schelbergen
Roland Schmehl
Abstract. The flexible membrane kite employed by some airborne wind energy systems carries a suspended control unit capable of inducing a characteristic pitch and roll swinging motion during sharp turning manoeuvres. This paper assesses how accurately a twopoint kite model approximates this swinging motion with two approaches: approximated as a transition through steadyrotation states and solved dynamically. The kite model comprises the rigidly linked point masses of the control unit and wing and extends a discretised tether model. The motion of the wing point mass is constrained to a figureofeight manoeuvre from the flight data of an existing prototype. The associated swinging motion of the kite is inferred from the attitude of the rigid link element. The computed attitude is compared against the measurements of two sensors mounted to the wing, which record varying pitch angles during the turns. The pitch and roll angles computed with the two approaches are similar during the straight sections of the figureofeight manoeuvre and match the measured angles within three degrees. Contrastingly, the two approaches exhibit systematic differences during the turns. Since a twopoint kite model resolves the roll, the lift force may tilt along with the kite to drive turns. Hence, intricate centripetal force modelling is avoided, as seen in a singlepoint kite model. Furthermore, the twopoint kite model complements the aerodynamic model as it allows computing the angle of attack of the wing by resolving the pitch. These characteristics improve the generalization of the kite model with little additional computational effort.
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Mark Schelbergen and Roland Schmehl
Status: final response (author comments only)

RC1: 'Comment on wes2023121', Anonymous Referee #1, 26 Sep 2023
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes2023121/wes2023121RC1supplement.pdf

RC2: 'Comment on wes2023121', Anonymous Referee #2, 10 Oct 2023
In the manuscript “Swinging Motion of a Kite with Suspended Control Unit Flying Turning Manoeuvres”, the authors present an interesting and insightful analysis of the physical mechanism inducing the turns in kites with suspended control units. The manuscript is wellstructured and clearly organized.
In my opinion, the main outcome of this work is the physical understanding of the mechanisms inducing the turns. However, this message is not given in the abstract and could be better clarified in some parts of the text. I suggest giving more importance to this result.
I have attached a pdf with my comments and I summarize here the main technical comments that should be addressed.
 The aerodynamic drag is generated only by the component of airflow perpendicular to the segment. This means that a component of the velocity parallel to the tether element would not generate any aerodynamic force. This should be corrected in eq. 5.
 The assumptions and mathematical derivations in Section 3.2 should be clarified. Is there a rigorous physical derivation for omega_turn? It would be nice if the straight omega and the turn omega could be derived as particular cases of a generic omega.
 The models with one single tether element for the tether from the groundstation to KCU and one element from the KCU to the kite employ a lumped drag model (eq. 7) and not the classic finite element method (eq. 5). I believe that calling this case “single tether element” is misleading, as the lumped drag model can be derived from continuous models of the tether (with infinite tether elements) under prescribed assumptions. I would name this case differently. Summarizing:
 multiple tether element > eq. 5 is used for the drag evaluation;
 single tether element > eq. 5 is used for the drag evaluation;
 lumped tether drag (or different naming) > eq. 8 is used for the drag evaluation.

RC3: 'Comment on wes2023121', Anonymous Referee #3, 18 Oct 2023
My overall assessment:
======================The authors of this paper are trying to better understand how the mass of the control unit effects the dynamics of the a soft wing airborne device during turns. The study is based on some noisy data from experimental tests. The authors used some optimization to smooth out this experimental data to give estimates of the path, velocity and acceleration. The authors create 2 models to better understand these dynamics. The first model is a quasistatic model that ignores dynamic effects, while the second is a dynamic model that accounts for these transient effects. To allow the authors to ignore aerodynamic forces, they run both models on fixed paths based on the kinematic data extracted and smoothed from the test data. The study shows that during turns, the inertia of the control unit will induce a roll rotation on the wing, which inturn provides the centripetal force needed to turn the control unit. The authors also make several comparisons between the two models and other measured data to help validate these models. The authors also state that these 2 mass models may be more appropriate for control design. It's my opinion that this is an interesting study and worthy piece of work for publication.
However, the presentation of this work can be greatly improved. Overall there are a lot of important details that are not well explained, vague or presented in ways that add to the confusion. I was very confused on many parts of the manuscript and it was difficult for me to judge the different results. I have made several comments below that outline all the different points where I think the presentation can be improved. Overall, the results show agreement between the models and the experimental data. However, there are also plots that show poor agrement. Furthermore, it's unclear how different assumptions, test conditions/configuration, modelling error, data postprocessing error could have contributed to the agreements or errors in these models and the results. The author doesn't really give a satisfactory explaination of these points. So this is second point where I think the manuscript could be further improved.
Given the difficulty of working with noisy experimental data, and the added complexity of these two models, it's clear that this was likely a difficult study to carry out. So despite these problems in the presentation, I have a positive opinion on the overall quality of the scientific work. So I recommend that this work is published once the presentation is improved.
Further comments:
=================The title could be improved
First, you need a conjunction between Unit and Flying
Idea 1: Swinging Motion of a Kite with Suspended Control Unit while Flying Turning Manoeuvres
Next, I am not sure you are talking about 'swinging motion', but more the interaction of this control unit and the wing in these turns so the next idea is as follows. 'Swinging' brings up thoughts of pendulum motion, but what you have here is different than that.
Idea 2: The dynamic interactions of a kite wing and control unit during turning manoeuvresLine 3: how accurately => the accuracy
Line 5: Inserted a 'be' " The motion of the wing point mass is constrained to be a figureofeight manoeuvre from the flight data of an existing prototype"In my opinion the abstract is much more detailed and technical than it should be. This effects the readability in my opinion. I needed to read it multiple time to understand what it was saying. I think this paper could benefit from having the abstract written to explain the study and the results with higher level language. This would make it much more attractive for people browsing the literature.
In the introduction, the author is explaining the configuration of the kite, how the wing deforms, a range of models according to their kinematic description. It could be helpful to have a diagram showing these different descriptions to help make sense of it.
Line 62: The wording of the hypothesis is vague and I am confused by the hypothesis. First you posit that the roll (I presume this is rotation, not a spelling mistake like role) is induced by the inertial of this KCU. It's the second part of the sentence that is vague and confusing, it's a rather vague statement to say "... has a crucial role in the turns". So first, is it the roll or the inertia that has this crucial role? What is this crucial role? The turning force? the radius of the turn? generating the aerodynamic force? The time delay between actuation and effect? Is this link between the KCU inertia and it's effect on roll in question? (in other words, is this also a research question?)
In my opinion this paper has multiple contributions that aren't always stated so clearly in the abstract and the introduction. First it uses experimental data and two different models to explores the dynamic interaction between this control unit, the wing and the tether. Second it introduces two different models for modelling this behaviour. The paper does suggest in multiple locations that such a model could be an improvement in control design over 1 mass models. So the second contribution is these two models and some effort in trying to validate these models. So I would try to be more clear in stating these contributions.
Line 95, the position of these pixhawk sensors could be labeled in figure 2, 3 or 5 just so that it is clear
Figure 4: This work depends heavily on the kinematic information of specific points of the wing and control pod. It would be good if the author made a more clear statement about what point on the kite figure 4 describes. I guess that it is the control pod?
Figure 5, the socalled wind reference frame is described in the caption of figure 5, the same frame is used in figure 6. In figure 5, it could be useful to state that y is in the direction of the wind. Furthermore, in figure 6, just restate that the coordinate system is the same as the one described in figure 5.
I think figure A1 needs to be moved to section 2. Since the study depends heavily on the kinematic data, it's important that this data is shown in section 2. I can understand that it's better to keep most details in the reconstruction in the appendix, but again, due to the importance of this, I would state in section 2, that the this data was solved with an optimization.
Section 2: As stated earlier, this work depends heavily on the kinematic information of specific points. So I would like a more clear description of where the sensors were located, what sensors were used to generate what kinematic data. Since not all sensors were colocated, how did you assume that measurements from one location were related to another location? Did you assume the kite and bridle were rigid?
Line 199 "We allow for rotations other than greatcircle rotations", maybe a mistake, but I assume 'we allow for no other rotations ..."
I have a lot of things to say about the description of the dynamic model in section 3.3:
 It's difficult to fully understand equation 12, first a diagram of the kinematic setup could be helpful.
 I get that you are only looking at 2 point masses. Then you can say, row 1 is the equations of motion for the wing and row two for the tether connection point (maybe I am wrong, but there is some confusion with the subscripts).
 Furthermore, your explaination of the different subscripts are difficult to understand because you have kcu, and s which are not explained. It would be better to have less subscripts and to make them consistent.
 The bottom two rows, where you enforce your constraints, you should show your 'r' terms as transpose to indicate that it's a dotproduct with the acceleration.
 Second, these constraint equations are the derivative of equations 14, and 16 ... basically you are constraining the acceleration to be consistent with the enforced length. Enforcing the acceleration (instead of the position) is the index reduction.
 A consequence of using index reduction schemes is that small inaccuracies in the integration could lead to a situation where the velocities and positions are no longer consistent with the constraints. I am guessing that your solver has methods to correct for this? I don't know if it is possible, but I would be curious if your simulations had significant drift. If your dynamics give position and velocity, this can easily be checked with equations 1316, you could make a statement of how well the position and velocity constraints were respected.
 Also, to help gauge the quality of the dynamic solution, I would like to know more about the integration scheme. Presumably, those software packages that you use give the theory. Is it an implicit vs. explicit? constant time step vs. variable time step? RungeKutta? Generalized Alpha? What order? Is there numerical dissipation?
 Another problem I have is the fact that equation 12 doesn't actually describe the problem that you are solving... line 232, you explain that you use prescribed accelerations from one of the point masses. I think it's ok as a way of tryin to back out further dynamic information from the acceleration measurements ... but I think it would be better to have a diagram, showing that setup exactly (i.e. with a boundary condition triangle) and show the equivalent equation 12 for that setup. When you prescribe acceleration for one of the masses, then you in effect seperate the problem into two independent calculations: 1) A kinematic calculation, based on acceleration to get the wing position and velocity 2) a dynamic calculation for the second point mass.
 Equation 12 shows dependency on the position and the velocity. However, it's not clear to me what values were used for this calculation. Given the acceleration solution from 12, one could integrate to get the velocity and position. If this is the case, further description of the integration scheme would be needed. Another alternative is the kinematic data that you describe in section 2 and appendix A. Was this used in place of integrated quantities? If this is the case, then my earlier point about constraint drift might not be applicable. This detail is also important to me because it's not clear to me whether position and velocity is an input or an output of this dynamic model.
 What is important is differentiating between what is prescribed and what is solved in the dynamic model and this is very unclear by this description.
 In the results section, it appears that you use the dynamic model with 30 sections, not 1, I think it would be more appropriate to show equations and describe this model with N segments.
 Overall, I think the description of the dynamic model is a bit muddled and it is difficult to assess how results from this model could be used to understand and compared with the other modelIn both models, it's not clear whether tether force or tether elasticity is acounted for. Does tether force factor in any of the models? Does tether stretching factor into any of the models? If so, I am guessing you used standard linear relations? For the sake of reproducibility, what stiffness constants? In the quasistatic model, it would impact the sag solution. In the dynamic model, the net effect of tension and curvature is a lateral force. Equation 12 does not appear to show tension effects ... these effects could be important in the modelling, but there are no statements on these points. I also have similar concerns with the bridle, is there any deformation? in reality or in the model?
Figure 9, consider using different dash pattern (long vs. short), to make the differentiation between the dynamic and the 1 element model more clear. Please describe in more precise terms the directions, the terms 'Upapparent wind' and 'Cross Apparent wind' is vague. You already have this wind reference frame ... when I see 'apparent wind', I guess that is a new reference frame, aligned with the wind relative to some body. What body? Does this reference frame vary along the tether? Or is it the apparent wind at one location, then the deflections are measured against that ... it's really unclear to how to interpret this geometry.
Figure 10 is also a little confusing due to lack of details in previous sections. In the turns, there are large discrepencies between all models for pitch. Since it's not clear what points of the wing each of these measurements correspond to, I am confused as to whether these discrepancies are due to measurements at different locations on a deforming structure, or errors in the models.
Line 286, this statement is vague in light of my confusion over how position and velocity factor into the equations.
Line 288, The author makes a statement about discrepancies in the tether reelout speed. reelout acceleration is an input, so I must assume that the dynamic model integrates this quantity. Yet, the dynamic model described in section 3 does not say whether it calculates the tether lenght and velocity and how these quantities are integrated. So it's difficult for me to interpret these statements.
Line 289. The term tether slack is not well defined. A slack of 0.3 sounds more like an elastic deformation (i.e. a change in length), where as I think of slack as more of a lateral displacement of the cable.
Figure 11 and the argumentation on line 291: So the argumentation explains that the tether force depends on 'slack' I am guessing that this slack variable effects the average over time tether forces? As such, since this 'slack' is tuned, then the overall agreement in figure 11 is due to your choice for slack ... so it begs the question how you chose slack? if you chose slack by other data, then figure 11 agreement is a sort of validation, otherwise, it's not. Now the spikes that occur in the turns ... I am not completely sure about this point because I had difficulties interpreting appendix A, but the procedure that was used to generate the flight path appears to have a smoothing effect on the flight path... So it's totally expected that a smooth flight path would produce a more smooth dynamic response, hence the failure to capture these spikes in the tether force. It's also unclear how ignoring turbulence or other unsteady aerodynamic forces could impact these results
It would be interesting to include results from a quasistatic model that ignores this extra point mass for the KCU and treats the whole wing bridle as a single point mass under rigid body motion. Such a comparison would show what you gain in terms of additional information by adding this 1 extra piece of complexity. This research question is implied in the introduction so it would be good to show that as well.
Line 390: Stating that the dynamic model solves the actual motion is a bit strong. In previous parts, you say that the dynamic model isn't more accurate. I guess what you are trying to say is that is simulates the transient effects.
So this paper is interesting in showing the dynamic effect of the control unit, so this is good.
This paper also introduces two models to help investigate these dynamics. In the introduciton, the author implies that these models could be used to better simulate these important dynamics. The author does present a lot of validation data for these two models. However, this reviewer feels that there are several sources of errors that are not adequately discussed in this paper. The author had to condition the experimental data, it's not clear how this conditioning effected the analysis. In the description of the study, many important assumptions and/or modelling details are not specified, so it's unclear how these could have contributed to the errors. Later the author implies that some things were turned (i.e. slack), yet it's not clear what that means and how it enters the model, so it's confusing on how to interpret comparisons as validation or not. Also on pitch, due to lack of details on the locations of sensors and the assumptions of how the wing bridle deformation, it also difficult to understand the differences in pitch in turns. I think the the author needs to state clearly the dynamics/kinematics the model predicted well and the parts where the models did achieve agreement. Then give some ideas on how that could be improved. To better improve the models and better improve the understanding of the dynamics, the author should suggest future work that is needed. I also think the author should discuss a little the role of unsteady aerodynamics on the discrepancies that they see in the tether forces.
The beginning of Appendix A, figure A1, all quantities are labelled symbolically, but there is no description on what these symbols mean. Also what sensor data was used for this, you have 2 GPS and 2 altimeters? or something else? Again past comments about the lack of details about the test setup makes this confusing.
I think that it's strange that A2 is described as an optimal control problem. This appears to be a type of least R^2 statistical curve fitting problem ... I can understand how the appearance is similar to an optimal control problem, but in my opinion it's a bit misleading to call it a control problem. There is nothing being controlled, you are trying to fit synthetic data to multiple points of measured data.
No major complaints on Appendix B. If anything, you could try to be more concise.
Citation: https://doi.org/10.5194/wes2023121RC3
Mark Schelbergen and Roland Schmehl
Mark Schelbergen and Roland Schmehl
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