How could we make a fair comparison between space rockets regarding their payload mass in low Earth orbit and Earth escaping?

Question

I was searching for comparisons between space rockets regarding their payload mass in low Earth orbit and Earth escaping. First one to see capability of the space booster (the first stages) and second one to see results and efficiency of upper stages.

Comparisons could be found in wikipedia, but these aren't a fair comparison since low orbit heights and inclinations for these rockets are different. If we compare something should be used the same standard. Many USA rockets are launched in 28.7° (or 28.5° or 28°) inclination, and their low orbit values are for 185 km or 200 km. Russian rockets are launched from Baikonour in 51.6° and values for low orbit are mostly from 200km or 220km. ESA rockets are launched from Kourou site at 5° inclination. Soyuz rocket is launched from both these sites ( Baikonour 51.6°, Kourou 5°). We could understand how much influences inclination for this Soyuz from here. But with Soyuz case we are lucky since it is launched in different inclinations. Question is what about all other rockets. Values would be different for low Earth orbits in 185 km - 200 km - 220 km, and in different inclinations. Maybe their influence would not be to much but still the comparison is not real and fair.

For low Earth orbit we need the same orbit and inclination. For Earth escape were orbit's heigh doesn't matter still the inclination should be the same. Is there any program or website that could compare rockets with the same standard and in the same conditions?

Until now i found this site silverbirdastronautics were we could change inclination and orbit's height, but this is not a reliable site because payload values are differnt from official results for those rockets and it hasn't a high level of accuracy.

Could we make a fair comparison of space rockets regarding their low Earth orbit and Earth escape payloads?

Answer 1

Launch vehicles are complex machines and each one behave in a complete different way, i.e. each rocket have its own variation of the gravity turn maneuver having different aerodynamic and gravity loss profiles. To account all effects and precisely determine the mass to "LEO", as said in the comments, the only way is to integrate the trajectory.

Another important aspect is to note that metrics like "payload to LEO", "payload to LTO", "payload to GTO", etc. are, per se, inaccurate measurements, since, as you pointed out, none of these orbits are strictly defined. These data are usually considered only in the zeroth iteration of the mission design, when one is selecting something like a rocket-class requirement and only a rough estimate of the rocket's payload capability is needed.

To make a truly precise characterization and comparison one would need to standardize the final orbit, launch site, weather conditions, and simulate with a full model, or measure it in the case of an experimental study.

Considering that this characterization would be extremely complex, and that the rough "payload to LEO" estimate is enough for a preliminary design, this detailed study in general makes no sense. In a second phase, the team would jump from this approximate number to a detailed simulation to ensure that the system can accomplish the mission and what is its real capability.

Answer 2

I don't know if I'm right, but it could be interesting to compare the final energy of the payload rather than its mass. It would give you (I think) a better metric and a more fair one.
The formula could be this :

$$E_{total} = \frac{1}{2}mv² + mgz$$

With m the mass of the payload, z the altitude of its orbit and v its speed. We could also use the fact that orbital velocity is directed by : $$ {\sqrt {\frac {GM}{R}}} \leq v \leq{\sqrt {\frac {2GM}{R}}}$$

With M the mass of the Earth and R the distence between the center of the Earth and the satelite.

Answer 3

I think Lui Txai Calvoso Habl has the right answer, that is, your question is beyond the scope of this forum to answer well. Your best bet for accuracy without spending a lot of money is to look at the mission planner guides for each launch vehicle, usually available at the vendor websites.

If instead you want to "get a feel" for things without the concern of being too precise then read on.

I had a quick look at the silverbird site you mentioned in the question. As it seems to be something of a "black box" its hard to see what assumptions it is making though, in addition to the point raised by Lui Txai Calvoso Habl for the type of trajectory and gravity turn, it is also plausible that the silverbird site is using time average estimates for thrust and specific impulse. In the grand scheme of things I don't think that's too bad at all if it helps one get a rough understanding of each launcher.

As an alternative you might like to explore the Space Launch Vehicles site. Of particular interest are the tables such as these for Soyuz where the author has collected together parameters and turned them into a Total Impulse, in mega Newton Seconds, MNs, for each stage. I think this is quite a good way of understanding more about the hardware. Of course it still doesn't help you with the problems of gravity turns, dogleg manoeuvres, time spent in the atmosphere and the time average values of thrust and Isp, but you can do your own sums and see how far out you are from the tabulated figures.

Lastly, if you really want to be able to hypothesise the performance of a given vehicle launched from a different launch latitude then you could simply rank the launch vehicles by total impulse to get an idea of which would be best. Once again, its not going to solve the detailed sums but it might help understand the big picture.

Lastly, this previous question addresses the idea of comparing launch vehicles in a rough-and-ready way and is quite illuminating.