This is a detailed and comprehensive analysis of how the engine parameters of bypass, propulsive efficiency, and engine size end up affecting how contrails form. This is a significant and important advance over related prior work in this area and offers useful insights for how contrails will form when H₂ is used as the fuel.  Many of the results also apply to kerosene-fueled engines, but the authors are careful to highlight in which ways the conclusions may not hold for kerosene combustion.

The conclusions of the analysis are important in that, in many cases, some of the details of the complex exhaust mixing are not important and simplifying model assumptions can be made. This will be a boon for further analysis. The conclusion that overall propulsive efficiency can be understood by considering flight at a different ambient pressure is not intuitively obvious (at least to me) but is also a useful conclusion for model simplification. Again, many of these conclusions apply regardless of the kerosene/H₂ fuel difference, and the authors point out where the conclusions may not apply to kerosene combustion.

I have no major criticisms of the manuscript which is well-structured and clearly written throughout. I will list a few minor comments that the authors may decide if they would care to address.

(and several of these perhaps relate more to ChatGPT than the authors!)

1. I thought that the spelling “parameterizations” (on pages 1 and 2) was the more accepted/common spelling for that term, even though “parametrizations” seems to an acceptable alternative.
2. Line 431: “whether these neglects . . .” is an unusual grammatical construct. It is probably not confusing, but might read better as “whether neglecting these changes . . .”
3. Line 164, equation (9): Given the attention to detail and rigorous nature of the analysis, this approximation jumped out at me. While the air-to-fuel ratio is a large number even for kerosene combustion, presumably (for the conditions chosen for the H₂ combustion case) this is an even larger number here. Perhaps a word or two and/or a rough air-to-fuel number for this H₂ combustion case might be useful to justify this approximation (since it probably would not be much computational burden to carry the full expression forward). I am sure that the approximation does not impact any conclusions at all, but the approximation is just summarily included without any justification as things stand.
4. Line 541, “does not contain an explicit dependence on engine size” would be preferable?
5. Lines 612 on, and Lines 673 on: When oil is discussed, it seems to implicitly assume that the oil emissions are included in the core flow. That is true for some engines, but certainly not all. Since the authors are introducing the subject of oil and their extensive analysis differentiates exhaust emissions and entrained nuclei, I think a more nuanced discussion should be offered. While GE/CFM engines release oil breather flow into the core flow, many other engines release oil breather flow into the bypass or external to the nacelle. Especially for the nacelle release location, the oil would be entrained with ambient air and so would be more like ambient nuclei entrainment (although all at a very early location for oil, as opposed the continual downstream entrainment of ambient nuclei). The bypass oil breather case would be somewhere in between.

• Since this analysis also pays strict attention to particle size distributions, it is also worth noting that oil breather flow being released in the hot core exhaust vaporizes the oil that then recondenses in small nucleation mode particles. Conversely, release that is external to the nacelle results in oil particles with a few hundred nm sized oil droplets.
• The authors can decide how much additional detail they wish to say about oil, but the current language suggesting that oil should be considered an exhaust emission is misleading and incorrect for some engines.

This work describes a deep evaluation of some ways in which engine design might affect the long-term behavior of a contrail, focusing on the intermediate quantity of the number of ice crystals formed. The work is timely, important, and – since it primarily concerns hydrogen engines – of great immediate value to both the contrail science and aeronautical engineering communities.

The central question posed – whether engine design can affect contrail impacts – is both interesting and important. The methods used are appropriate, and the conclusions are well supported by the data produced. This work constitutes a useful methodological advance while also bringing a greater level of technical depth to bear on the question of how contrails from LH2-fuelled aircraft might behave.

I have no methodological concerns, and relatively few comments on the manuscript; those are listed below.

My biggest question relates to the assumed properties of the ambient aerosols. Is it accurate to say that the ambient aerosol concentration is more strictly the concentration of ambient aerosols which it can be assumed would be effective nuclei for contrail ice? Given the amount of recent research dedicated to the question of efficacy of soot in this regard, it would be useful if the authors could comment on what they are assuming about the ambient particles and how the assumed ambient aerosol number would relate to typical measurements taken in the upper troposphere.

I believe the statement on line 631 is an accidental double negative: “Lewellen (2020) showed that neglecting the plume heterogeneity is not critical”. Should “neglecting” here instead be (e.g.) “accounting for”?

There are some minor grammatical errors throughout (e.g. “whether these neglects”, line 431; “low sensitivity on” (rather than to), line 633; “will show to dominate”, line 674). I would recommend that the authors perform an additional sweep to remove these.

The abstract currently provides little actionable information, and I found myself unable to gather much insight from it. Given that the authors have compiled a compelling set of findings in the conclusions, I would recommend at least summarizing some of these in the abstract.

My last comment is a plea rather than a concern, but I would nonetheless be very happy to see addressed. As has become unfortunately common in the contrail literature, the authors refer to the “overall propulsion efficiency” (see e.g. Equation 2). This is confusing terminology, as standard textbooks on engine design (see e.g. Hill and Peterson, or Cumpsty) define both an overall engine efficiency (ratio of thrust power output to heat input – what is intended here) and an engine propulsion efficiency (ratio of thrust power output to the rate of production of propellant kinetic energy – decidedly not what is intended here). The distinction is important, because the propulsive efficiency is (by definition) always greater than or equal to the overall efficiency and, if used by accident by a reader of this manuscript, would change the meaning of the equations. Given that I have had to correct many confused manuscripts, students, and colleagues that have accidentally applied the wrong definition as a consequence of the term "overall propulsion efficiency" being used in prior contrail literature, I would be very grateful if the authors would avoid propagating this issue. This can be fixed by explicitly stating that they are using the “engine overall efficiency” and avoiding use of the term “propulsion efficiency” except when they actually mean the propulsion (or propulsive) efficiency.