Round 1

Reviewer 1 Report

General

The author mathematically models the working principles of a pumping foil, which is a surfboard elevated above water surface and connected to a tandem of hydrofoils by a strut. To achieve this, characteristics of flow past hydrofoils moving below free surface and propulsion properties of an oscillating hydrofoil are examined. Then, a simplified linear differential equation is written down that couples lifting and propulsive properties of the system. The solution of this equation, as presented for a range of exemplary numerical values, yields results which are apparently commensurate with actual cases (should be indicated).

Overall, the work is scientifically sound and the language is good. However, there are some problems concerning presentation. All these are stated below in the specific points in detail. After amending these minor points the manuscript should be ready for publication without a second review.

 

Specific Points

1.     Title: “A Simple Quantitative Mathematical Model of Pumped Hydrofoils” appears to be a more informative title. However, this is just a suggestion; the final decision lies with the author. (The model appears to be "quantitative" to this reviewer rather than "qualitative".)

2.     Typographic error: Page 9 (Line 317): “… density og water, …” Please check the entire manuscript for such typos.

3.     It may be better to shorten some parts of the equations. For instance, it is not necessary to write eqn. (19). Instead, just state that “Substitute eta_nh(tau)=…  into eqn. (13) -here do not rewrite eqn. (13) again as eqn. (20), it is unnecessary- to obtain D=… and its modulus |D|=… (no need to give them as eqns. (22) and (23)) just state them within the text.

As exemplified here, substantial reductions can be done in the number of equations. This would make it possible for the reader easier to follow the procedure without being distracted by too many equations.

4.     Eqns. (24) and (25): Do not use “double” minus signs; namely, in the first line and in the following line there are two minus signs. Just use one minus sign and place it to the second line. Besides, is it really necessary to give explicitly eqn. (25)? Probably not, just state that after differentiating eqn. (25) with respect to time and letting tau=0 we obtain eta*(0)=…

5.     Line 586: Within the same line there are two equations with numbers (37) and (40).

6.     Presentation of numerical calculations for Section 7 may be improved especially by referring to actually observed values of speeds and periods.

7.     Conclusions: Please add some comments concerning the numerical applications given in Section 7.

 

Conclusion

According to this reviewer, the manuscript is scientifically sound and its language is quite good. It is however necessary to improve the overall presentation especially concerning the equations and numerical results. Hence, it would be better if the author presents the equations in a more economical way by removing some (repeated eqns. and unnecessarily given intermediate steps) and stating some eqns. within the text (not as a numbered eqn.). Also, the numerical results (Section 7) should be presented in a better way as indicated above. After these minor arrangements the manuscript should be ready for publication.

Author Response

Please, see the attachment for Reviewer 1

Author Response File: Author Response.docx

Reviewer 2 Report

The paper presents a Qualitative Mathematical Model of Foil Pumping. The paper is interested in converting the complexity of the model to just some simple equation that can be able to solve the problem and used for design purposes. Also, it is interesting to mention the future work to clearly present the limitation of this model. I have a few comments as follows:

1. Abstract can be rewritten according to the sequence of the paper showing the main important results.

2. English needs improvement.

3. Please write the sentences in passive form.

4. The introduction needs to be rewritten, showing general information about the subject, what has been done in this field and then the novelty of this work related to the published work.

5. The novelty of the work is not clear enough. Please elaborate.

6. Did the author validate the model using real data? If yes, please mention it.

7. You can write the inputs in sec 7 in a table to be clear as an example.

8. Refs to be checked.

9. Please write the axis title out of the figure; for instance, the axis title of the y-axis is to be located left to the y-axis and the axis title of the x-axis is to be located under the x-axis; to be clear to the reader; also, include the units if available.

 

Author Response

Please, see the attachment

Note that the title has been changed by the author to "A Simplified Mathematical Model of Pumped Hydrofoil"

Author Response File: Author Response.docx