Review Reports - Estimation of Propellant Mass Requirements for Thruster-Driven Momentum Exchange Tether Deployer Vehicles

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Comments for authors

The paper provides a generalized analytical framework for estimating propellant requirements for Momentum Exchange Tethers (METs). The topic aligns well with the practical needs of collaborative multi-payload deployment in the current commercial space industry and demonstrates clear engineering application value.

Here are some suggestions:

1.The paper justifies neglecting environmental disturbances based on a "deployment time of 1-2 hours." However, what is the specific magnitude of impact from various environmental disturbances? Could the persuasiveness be enhanced by comparing their order of magnitude against the deployment parameters?

2.The paper only presents formulas without analysis using actual mission parameters. This makes it impossible to compare theoretical calculations with practical errors and fails to intuitively demonstrate the method's practicality.

3.The citation rate for literature published after 2020 is less than fifty percent. It is recommended to supplement the references with recent research.

4.It is recommended to strengthen the relevance between some cited literature and the paper's content. For example, references [9][10][11] mention that Mission X employed Technology Y – what is the specific connection between this and the research content of this paper?

5.It is recommended to emphasize the paper's contributions more strongly in the Introduction and Conclusion sections, highlighting the innovative points of the work.

Author Response

Comment: The paper justifies neglecting environmental disturbances based on a "deployment time of 1-2 hours." However, what is the specific magnitude of impact from various environmental disturbances? Could the persuasiveness be enhanced by comparing their order of magnitude against the deployment parameters?

Response: Added order of magnitude information based on information from references 18 and 19.

Comment: The paper only presents formulas without analysis using actual mission parameters. This makes it impossible to compare theoretical calculations with practical errors and fails to intuitively demonstrate the method's practicality.

Response: A similar comment/response is included with material from Reviewer 3’s feedback. Separate work in progress (being published within the next few months) dives into this topic. In full there are a wide range of parameters that must be defined such as deployer/payload mass and inertial properties, tether hardware design, and orbit maneuver requirements. In the last paragraph of section 6, there is mention of a forthcoming publication for the 76^th International Astronautical Congress that builds from the concepts introduced in this paper and applies them to a conceptual Falcon 9 upper stage deploying different payload sizes via tether, and evaluates propellant mass required as a function of desired deployment velocity for each payload size. An additional publication (publishing organization still to be determined) will come later expanding on this by incorporating mass contributions due to tether hardware as well.

Comment: The citation rate for literature published after 2020 is less than fifty percent. It is recommended to supplement the references with recent research.

Response: The authors have not found accessible/relevant literature published more recently than the sources currently listed while preparing the first draft. Do you have recommendations on additional sources?

Comment: It is recommended to strengthen the relevance between some cited literature and the paper's content. For example, references [9][10][11] mention that Mission X employed Technology Y – what is the specific connection between this and the research content of this paper?

Response: Additional connection/relevance for citations has been added through the text where applicable. If there are specific citations/areas that need more attention, please let us know.

It is recommended to emphasize the paper's contributions more strongly in the Introduction and Conclusion sections, highlighting the innovative points of the work.

Response: Additional material has been added to Sections 1 and 6.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents a general methodology for estimating propellant mass requirements in thruster driven Momentum Exchange Tether (MET) systems. The focus is not on introducing a new hardware concept but on providing a structured framework for preliminary design calculations, and in this sense the paper has potential value. Simplified analytical models such as the one proposed can play an important role in early stage mission design, where fast estimation tools are needed before more detailed simulations are required. The organization of the methodology into spin-up, spin-down, and orbit correction manoeuvres is clear.

Nevertheless, the contribution as it currently stands, in my humble opinion, falls short of what is expected for a scientific journal like Aerospace. The principal issue is not the use of simplifications itself, but rather the absence of “something more” that could demonstrate the usefulness of the framework. For instance, the paper develops the equations for the method but does not show how they perform in practice. A case study with representative values of payload mass, tether length, deployer size, and thruster performance would make the methodology more concrete, allowing the reader to assess whether the mass savings are substantial or negligible, and whether this approach could be competitive against more conventional deployment methods, also showing in the process the utility of the proposed methodology. Without this, this study remains at the level of an academic exercise rather than a scientific contribution.

Another important limitation is that the analysis considers the MET as already present in orbit, without accounting for the cost of placing such a system in orbit in the first place (could simply be measured in terms of the needed propellant mass). In the simplified context of the paper, where the comparisons are made strictly in terms of propellant mass, this omission is significant. The proposed methodology could be extended in a very natural way to address this point by estimating how many deployments a thruster-driven MET would need to carry out before paying for itself in terms of net propellant savings compared with traditional payload-based (or deployer-based) propulsion. Such an extension would strengthen the case for the methodology, as it would transform it from a set of algebraic expressions into a practical tool for mission trade studies.

In terms of novelty, the manuscript also raises my concerns. The equations presented are essentially direct applications of the classical rocket equation, adapted to rotational manoeuvres. This is perfectly acceptable in an educational or preliminary design context, but for a scientific journal of high impact index, more is expected. Similar levels of analysis can already be found in textbooks such as Sutton and Biblarz’s Rocket Propulsion Elements or in established reviews of tether technology (for instance, Cartmell & McKenzie, 2008, or Ziegler & Cartmell, 2001). By comparison, the present work does not convincingly show what NEW knowledge it contributes to the field.

To end with the formal aspect, the style of referencing could also be improved. Many references are introduced in groups without clear explanation of what each one adds to the discussion, and the manuscript relies heavily on self-citation. This makes the state-of-the-art review appear somewhat partial, and a stronger engagement with the broader tether literature would help situate the methodology in its proper scientific context.

A technical issue arises in Equations (17–20), where the deployer mass at earlier states is written as the mass at a later state MINUS the propellant consumed. Since the intention is to back-propagate from the final state (after the correction manoeuvre) toward the initial state (before spin-up), the correct operation is the addition.

Finally, an important methodological concern is the choice to base the propellant estimation for spin-up and spin-down manoeuvres on conservation of kinetic energy rather than on conservation of momentum. A more rigorous way to see the problem is through the mechanical energy balance of a variable mass system. For a rocket of instantaneous mass m, velocity V, mass flow rate mg, and exhaust velocity Vs, one can derive directly from the momentum equation the relation:

d(1/2*m*V^2)/dt + 1/2*mg*(V-Vs)^2 = 1/2*mg*Vs^2

This expression makes clear that the increase in the vehicle’s kinetic energy is not, in general, equal to the kinetic energy of the exhaust stream. Only in the trivial case where V=Vs they coincide.

To conclude, while I see the value of simplified analytical methodologies for preliminary spacecraft design, this particular manuscript remains incomplete in its present form.

Author Response

Comment: Nevertheless, the contribution as it currently stands, in my humble opinion, falls short of what is expected for a scientific journal like Aerospace. The principal issue is not the use of simplifications itself, but rather the absence of “something more” that could demonstrate the usefulness of the framework. For instance, the paper develops the equations for the method but does not show how they perform in practice. A case study with representative values of payload mass, tether length, deployer size, and thruster performance would make the methodology more concrete, allowing the reader to assess whether the mass savings are substantial or negligible, and whether this approach could be competitive against more conventional deployment methods, also showing in the process the utility of the proposed methodology. Without this, this study remains at the level of an academic exercise rather than a scientific contribution.

Response: A similar comment/response is included with material from Reviewer 3’s feedback. Separate work in progress (being published within the next few months) dives into this topic. In full there are a wide range of parameters that must be defined such as deployer/payload mass and inertial properties, tether hardware design, and orbit maneuver requirements. In the second paragraph of section 6, there is mention of a forthcoming publication for the 76^th International Astronautical Congress that builds from the concepts introduced in this paper and applies them to a conceptual Falcon 9 upper stage deploying different payload sizes via tether, and evaluates propellant mass required as a function of desired deployment velocity for each payload size. An additional publication (publishing organization still to be determined) will come later expanding on this by incorporating mass contributions due to tether hardware as well.

Comment: Another important limitation is that the analysis considers the MET as already present in orbit, without accounting for the cost of placing such a system in orbit in the first place (could simply be measured in terms of the needed propellant mass). In the simplified context of the paper, where the comparisons are made strictly in terms of propellant mass, this omission is significant. The proposed methodology could be extended in a very natural way to address this point by estimating how many deployments a thruster-driven MET would need to carry out before paying for itself in terms of net propellant savings compared with traditional payload-based (or deployer-based) propulsion. Such an extension would strengthen the case for the methodology, as it would transform it from a set of algebraic expressions into a practical tool for mission trade studies.

Response: This concept proposes implementing the MET hardware into the existing deployment/separation hardware already present on the dispenser/deployer hardware. In-progress work (being prepared for a separate future publication) incorporating additional mass contributions due to added hardware using conventional materials/design suitable for deployments on the scale of rideshare payloads has shown that propellant mass tends to be the dominant contributor of overall deployment-specific mass required (roughly 80% or more for most cases in current models being analyzed). Mention of this future publication has been added to the second paragraph of Section 6, and clarification of hardware intending to be added to existing systems has been added to the second paragraph of Section 2.2.

Comment: In terms of novelty, the manuscript also raises my concerns. The equations presented are essentially direct applications of the classical rocket equation, adapted to rotational manoeuvres. This is perfectly acceptable in an educational or preliminary design context, but for a scientific journal of high impact index, more is expected. Similar levels of analysis can already be found in textbooks such as Sutton and Biblarz’s Rocket Propulsion Elements or in established reviews of tether technology (for instance, Cartmell & McKenzie, 2008, or Ziegler & Cartmell, 2001). By comparison, the present work does not convincingly show what NEW knowledge it contributes to the field.

Response: This manuscript intends to present a method of determining propellant mass requirements for driving a MET system with thrusters, blending elements of classical rocket propulsion with MET technology in a manner which, from the authors’ search through previous literature, does not appear to have been done before outside of our prior work. If there are sources you know of that have done this before, we would appreciate your recommendations so we can review them. Some additional material has been added to the introduction and conclusion sections to help clarify what new contributions are made.

Comment: To end with the formal aspect, the style of referencing could also be improved. Many references are introduced in groups without clear explanation of what each one adds to the discussion, and the manuscript relies heavily on self-citation. This makes the state-of-the-art review appear somewhat partial, and a stronger engagement with the broader tether literature would help situate the methodology in its proper scientific context.

Response: Similar to a response for a comment from Reviewer 1’s material, the authors have not found much accessible/relevant literature published recently than the sources currently listed while preparing the first draft. If there are additional sources you know of that should be referenced, we can review them. With some of the citations made in the manuscript, additional material has been added to better connect the referenced material to the surrounding text.

Comment: A technical issue arises in Equations (17–20), where the deployer mass at earlier states is written as the mass at a later state MINUS the propellant consumed. Since the intention is to back-propagate from the final state (after the correction manoeuvre) toward the initial state (before spin-up), the correct operation is the addition.

Response: This was a typo that has now been corrected to be additions rather than subtractions, thank you for catching that.

Comment: Finally, an important methodological concern is the choice to base the propellant estimation for spin-up and spin-down manoeuvres on conservation of kinetic energy rather than on conservation of momentum. A more rigorous way to see the problem is through the mechanical energy balance of a variable mass system. For a rocket of instantaneous mass m, velocity V, mass flow rate mg, and exhaust velocity Vs, one can derive directly from the momentum equation the relation:

d(1/2*m*V^2)/dt + 1/2*mg*(V-Vs)^2 = 1/2*mg*Vs^2

Response: The initial motivation for pursuing the energy-based approach was to avoid requiring thruster orientation, placement, geometry, quantity, and maneuver transient effects, and instead just the exhaust velocity or specific impulse of the thruster(s) being considered. This would allow a developer to quickly estimate a lower bound or minimum order of magnitude for propellant mass consumed during spin-up/spin-down early on in the mission/spacecraft design process. It could be possible to augment the current set of equations towards the momentum-based approach with the addition of new variables associated with thruster placement, but these would require additional design effort on the part of the developer while accounting for operational factors. A first pass at an updated set of equations with this could include something like the following:

Angular momentum change between states (angular momentum ΔL, moment of inertia I_sys, and change in rotation rate Δω): ΔL = I_sys*Δω

Linear impulse required by a thruster (linear impulse Δp, radial distance of thruster exhaust vector normal from center of rotation r_thruster, propellant mass consumed m_prop, and exhaust velocity V_e): Δp = ΔL / r_thruster = m_prop * V_e

Arrange to get m_prop: m_prop = Δp / V_e = ΔL / (V_e*r_thruster) = (I_sys*Δω) / (V_e*r_thruster)

One of the added challenges is that the value of r_thruster must be defined differently for each maneuver, since for spin-up this means that it includes geometric positioning around the deployer craft’s center as well as the tether segment length L_dep from the deployer to the overall system’s center of mass/rotation, then for spin-down r_thruster is based on geometric positioning around the deployer only since the tethered payload is then detached. If it is suitable to include a statement along the lines of requiring the developer to define r_thruster as two versions such as r_thruster_spin-up and r_thruster_spin-down based on deployer vehicle design, where r_thruster_spin-up ≈ L_dep + r_thruster_spin-down, and r_thruster_spin-down is the radial position of a thruster about the deployer’s center of mass, then the equations in the manuscript can be updated in the next draft.

In summary, a proposed momentum-based update could include:

1. Adding an equation for angular momentum change
2. Adding an equation for linear impulse required by a thruster to impart required angular momentum change
3. Adding an equation for propellant mass required by a thruster based on rearrangement of the prior two equations
4. Adding an explanation on defining r_thruster used in the prior added equations for spin-up and spin-down maneuvers based on placement on the deployer vehicle and tether geometry

With that in mind, what would be your thoughts on potential solutions?

1. Keep the original energy-based approach but add an explanation of it being used for general lower-bound estimation in early mission conceptualization (already partially added to address part of Reviewer 3 feedback)
2. Incorporate the momentum-based equations described in this response with explanation for r_thruster needing to be defined by the developer, then update subsequent equations accordingly
3. Other recommended approaches?

Reviewer 3 Report

Comments and Suggestions for Authors

The authors focused on the propellant mass requirements of a MET system for orbital transfer. The conceptual design and some related equations were presented. This paper can be accepted for publication provided that the following issues are properly addressed:

In the design, where will the thrusters be mounted on and how to give the force to spin? Please describe the way for spin-up and spin-down in detail.
The parameters in the equations should be defined, such as ve, Isp in Eqs. (4-6).
The authors gives Eqs. (3-6) to clarify the relationships between the propellant mass and rotational kinetic energy. However, Eq. (4) was not used in this process. What is the function of Eq. (4) ?
Did the authors consider the effect of mass loss due to the consumption of propellant on the mass moment of inertia of the system?
Although the theoretical equations were developed, no simulation results can intuitively show the accuracy and correctness of the proposed theory. The authors can add some simulation examples.

Author Response

Comment: In the design, where will the thrusters be mounted on and how to give the force to spin? Please describe the way for spin-up and spin-down in detail.

Response: Section 4.2 discusses estimating propellant mass purely from rotational kinetic energy requirements, independent of thruster location. Additional information has been added to the start of section 4.2 to clarify this and that different thruster locations might increase propellant mass required. This might be updated further pending feedback on Reviewer 2’s material.

Comment: The parameters in the equations should be defined, such as ve, Isp in Eqs. (4-6).

Response: Definitions have been added for Eqs. 4-6 at the end of the first paragraph in Section 4.2

Comment: The authors gives Eqs. (3-6) to clarify the relationships between the propellant mass and rotational kinetic energy. However, Eq. (4) was not used in this process. What is the function of Eq. (4) ?

Response: Eq 4 is given for convenience/context for the reader, and the kinetic energy expression associated with that equation is given in Eq 5. That kinetic energy expression is then used throughout most other equations in the manuscript. Modified the variables used in Eq 4 to make the connection more apparent.

Comment: Did the authors consider the effect of mass loss due to the consumption of propellant on the mass moment of inertia of the system?

Response: Yes, moment of inertia of the system and deployer through the different states in the sequence is denoted with I_sys,1–I_sys,4 and I_dep,1–I_dep,4 where applicable, where subscripts 1-4 correspond with states 1-4. Paragraph 3 of Section 4.2 describes each of these states, and later equations involving propellant consumption use moment of inertia states based on the state of the system just before a maneuver.

Comment: Although the theoretical equations were developed, no simulation results can intuitively show the accuracy and correctness of the proposed theory. The authors can add some simulation examples.

Response: A similar comment/response is included with material from Reviewer 1’s feedback. Separate work in progress (being published within the next few months) dives into this topic. In full there are a wide range of parameters that must be defined such as deployer/payload mass and inertial properties, tether hardware design, and orbit maneuver requirements. In the last paragraph of section 6, there is mention of a forthcoming publication for the 76^th International Astronautical Congress that builds from the concepts introduced in this paper and applies them to a conceptual Falcon 9 upper stage deploying different payload sizes via tether, and evaluates propellant mass required as a function of desired deployment velocity for each payload size. An additional publication (publishing organization still to be determined) will come later expanding on this by incorporating mass contributions due to tether hardware as well.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for your responses to the comments. The quality of the manuscript has
improved.

Author Response

Comment: Thank you for your responses to the comments. The quality of the manuscript has improved.

Response: Thank you for your feedback in the review process!

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have certainly improved the manuscript, although many of the shortcomings identified in my first review still remain. These shortcomings are not of a formal nature, but rather conceptual: the proposed method is very basic, and not even a generic case study is presented to illustrate its results. The authors indicate in the aswer to reviewer letter that such material will be included in future publications, but in my view this omission significantly limits the present work. For this reason I initially recommended rejection. Nevertheless, I acknowledge that my judgment may be subjective, and since the manuscript has been returned to me for reevaluation, I assume that the editor and other reviewers consider the current level of contribution acceptable. If that is the case, I have no objection to the editor’s decision and will not stand in the way of publication.

Regarding the estimation of propellant consumption based on equating the kinetic energy gained by the system with the kinetic energy of the jet, I still believe this to be a highly optimistic assumption, for obvious physical reasons. Among the approaches discussed, I find Option B (as proposed by the authors themselves in their response letter) to be more realistic. That said, I understand the authors’ argument that their preferred formulation avoids the need to define the radius of application of the thrust forces. My suggestion is that, if they decide to retain Option A, they should explicitly acknowledge this simplification and explain how the calculation would be performed more rigorously using the momentum-based approach, as a more reliable alternative. At least, they should include a simple comparative example of a spin-up maneuver with generic parameters, showing the angular velocity obtained from both methods (the momentum approach and the jet energy equivalence approach) so that the reader can appreciate the difference between them.

Author Response

Comment: The authors have certainly improved the manuscript, although many of the shortcomings identified in my first review still remain. These shortcomings are not of a formal nature, but rather conceptual: the proposed method is very basic, and not even a generic case study is presented to illustrate its results. The authors indicate in the answer to reviewer letter that such material will be included in future publications, but in my view this omission significantly limits the present work. For this reason I initially recommended rejection. Nevertheless, I acknowledge that my judgment may be subjective, and since the manuscript has been returned to me for reevaluation, I assume that the editor and other reviewers consider the current level of contribution acceptable. If that is the case, I have no objection to the editor’s decision and will not stand in the way of publication.

Response: Thank you for your communication on the matter. At the moment, other reviewers’ feedback does not contain any additional unresolved changes/recommendations in this area. Forthcoming publications will dive deeper into example cases for particular vehicles/spacecraft.

Comment: Regarding the estimation of propellant consumption based on equating the kinetic energy gained by the system with the kinetic energy of the jet, I still believe this to be a highly optimistic assumption, for obvious physical reasons. Among the approaches discussed, I find Option B (as proposed by the authors themselves in their response letter) to be more realistic. That said, I understand the authors’ argument that their preferred formulation avoids the need to define the radius of application of the thrust forces. My suggestion is that, if they decide to retain Option A, they should explicitly acknowledge this simplification and explain how the calculation would be performed more rigorously using the momentum-based approach, as a more reliable alternative. At least, they should include a simple comparative example of a spin-up maneuver with generic parameters, showing the angular velocity obtained from both methods (the momentum approach and the jet energy equivalence approach) so that the reader can appreciate the difference between them.

Response: In the interest of keeping one method to avoid potential confusion to the reader, relevant equations and surrounding material have been updated to accommodate the Option B solution/momentum-based approach rather than the prior energy-based approach. The primary area changed is from lines 285-390 in the newest draft of the manuscript. The material in lines 285-293 originally introducing the energy-based method have been replaced/updated with the material in lines 293-314 to instead introduce the momentum-based method. Subsequent material was then updated to accommodate these changes, and additions were made around lines 338-343 and 354-367 to describe the situation regarding thruster placement. From line 367 onwards there are minor changes to accommodate prior equation updates (mainly expressions/variables and equation numbering).