Comment 1. Equation 14 is our model for the aerodynamic force acting on the helix (and not in the rotor). Only the aerodynamic drag is considered, as such a force component may dominate the lift. The spinning helix is made of rigid bars and tethers and its function is not to generate any lift but to transmit the torque from the rotor to the ground station. The lift generated by the rotor is indeed important, but the rotor is not part of our model, which is focussed on the helix.

Comment 2. The numerical simulations predicted a resonance, but at a different frequency to the one observed in the experiments. We fully agree that the un-modelled hysteresis can contribute to this discrepancy. Following the advice of the Reviewer, we added a few sentences about this important point.

Comment 3. We really thank the Reviewer for providing this revision. Most of his/her suggestions were incorporated to the manuscript.

We are glad to know that the Reviewer found that our work provides interesting insights and has novel contributions. We thank him/her for providing the minor comments that we address in the lines below.

Comment 1. In our opinion, the results of Fig. 5 are a consequence of the structure of the helix, which is made of bars under compression connected by tethers and knots. As the torsional torque M_t increases, in steps to give a torsional angle of 10º, the tension T_e also increases and exhibiting hysteresis. Clearly, the behaviour of the structure depends on the history. We think that it is because the exact position of the knots and the contact points between bars are not fixed but certain sliding occur and also friction plays a role. The exact positions of such a contacts points depend on the internal tension imposed for zero torsion (for this reason the curve for T_e0 = 233N is so different) and also on the history. Due to the presence of knots and the sliding of the bars, each time the helix passes from being relaxed to be tensioned it acquire a slightly different configuration that translate into different mechanical properties.  

Comment 2. We are not sure to fully understand the question. In the experiments, frequency f₁ was imposed by the eccentric arm and it was measured and controlled.

In our model of the helix, frequency f₁ appears as a boundary condition in Eq. (76). In our numerical analysis such a frequency was varied to mimic the conditions of the experiment.

Comment 3. The model of the helix used in the bifurcation analysis of Fig. 8 is the model explained in Sec. 2 together with the boundary condition of Eq. (76). In the bifurcation analysis, we fixed a value of the frequency f₁ and integrated the equations of motion numerically by using the initial condition explained in Sec. 5.1. The integration was long enough to let the system converge to a solution, which is periodic. We then computed the maximum value of the tension for a given oscillations.

Comments 4. We revised all the equations carefully and we did not find any error. However, we agree that some key aspects can be highlighted to help the reader to understand the notation. We added several sentences in the revised manuscript to help its readability and clarity. We thank the Reviewer for this comment.

Comment 5. We made a search to the word “dynamic” and corrected it.

Comment 6. Yes, the typo was corrected in Line 71.

Comment 7. The Reviewer is right. We corrected it in Lines 266-267.

Comment 8. Vectors i_E, j_E  and K_E  are the unit vectors of frame S_E. We added a sentence in Sec 2.1 and another in Sec. 5.1 to remind their meaning to the readers.

Comment 9. We cannot add a text to the y axis because Fig. 6 presents two different quantities, which are explained in the legend.

Comment 10. We agree that such idea improves the readability of the manuscript. Part of the material of Sec. 3 was moved to a new Appendix.   

Comment 11. We revised the manuscript a fix some typos.