The answer is really not intuitive. You will gain more kinetic energy using propulsion when velocity is highest (the "Oberth Effect" - https://en.wikipedia.org/wiki/Oberth_effect ) and the side effect of that is you will want as much of your velocity change as possible to occur when velocity is highest, at perifocus. Heliocentric velocity is highest in an Earth-Mars transfer as the spacecraft is departing Earth. Another reason is it makes the math a lot easier if velocity changes can be treated as singular impulses. Since computers have become so prevalent, this is less of a concern these days and constant thrust is not as much of a problem in terms of control and determining where you want to go. I've mentioned it here before but there's a good book on the topic called "Spacecraft Trajectory Optimization". In terms of 2n vs n g of acceleration which is derived from the chemical energy of rocket fuel reacting and driving propellant, I won't do a good job of explaining but the wiki article on the Oberth Effect will explain fairly well. Realistically in the apollo CSM sense, we are limited by the exhaust velocity of the propellant. To get 2x acceleration we don't have the option of doubling the propellant exhaust velocity (though it would be nice if we did) so the only option is to double the mass flow, which requires doubling the amount of engines, which is additional mass to propel. If the question is how to accelerate for a longer period of time, for that we are limited by the efficiencies of the chemical reactions that drive the propellant. It just plain takes a lot of fuel and propellant mass to extract energy. Hall effect and other ion drives are commonly in use now and much more efficient for their high exhaust velocity, but thrust is very low.

It becomes even a more difficult problem using thrust over a long period of time as mass flow rate may be constant, but thrust will vary slightly and acceleration will increase over time as the mass of the spacecraft decreases due to the expenditure of propellant. In The Martian, by Andy Weir, the Hermes was simulated (by Andy Weir) to use constant acceleration rather than constant thrust, which was viewed as somewhat unrealistic when NASA looked at the flight plan with normal mission analysis tools( https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20150019662.pdf ). (as an aside, Andy Weir additionally simulated the whole system using a one day timestep in two dimensions and did not account for gravity other than that of the Sun. Even so, The Martian is probably the closest to hard science fiction that will ever make it to a movie screen).

I found out a lot about the Apollo program that I didn't know. Apollo could make use of a "skip reentry" - reenter, exit the atmosphere, then reenter again as a means of distributing the velocity change over a longer period of time to make it easier for the astronauts. The Apollos never did a full skip reentry where the spacecraft completely left the atmosphere after initial entry, but did "dip" reentry where they would enter, decend to some point, then reascend only to decend again. It seems that skip reentry for soviet spacecraft was a planned for contingency. I did redo the TEI timing and ended up with a multi-skip reentry in which acceleration was ~4.5 g max or so - distributed over a longer period of time.



On Mon, Jul 20, 2020 at 10:22 PM <xxxxxx@gmail.com> wrote:
Query: Why apply all at once?

I can see an argument that says 'Then you go further every time unit after that'... so it is time efficient.

But is it also dictated by the nature of the propulsion (rockets?) or for some other reason?

My earth-centric view would have me thinking that pushing from N Gs to Nx2 Gs would do more than double the energy required, but that may only be true in atmosphere or other places that have drag. Maybe in space, the N -> 2N rate of acceleration doesn't actually end up being less efficient and thus no reason NOT to do it that way....

It seems like 2010 had some of it right (burn, then a long time napping) or that and some others that use spin habs for the coasting stages. Ship designs using these sorts of criteria (rockets or other reaction mass propulsion, thrust-then-coast-then-decel modes)  will look very different than Type A Free Traders, Aluminum Falcons, and even Firefly.


On Mon, Jul 20, 2020 at 1:15 PM Vareck Bostrom <xxxxxx@gmail.com> wrote:
To comment a little on that, this is the type of thing that is unfortunate about sci-fi games. We're really far away from the kind of propulsion performance that Traveller or The Expanse has and the scifi is so pervasive that there's no real concept of what spaceflight might really look like now. With few exceptions, nearly all delta-v in spaceflight outside of gravity boost is applied as instant as possible and the majority of the flight is coasting. Well planned flights might not have a single burn outside of the initial trans mars injection until orbit insertion at mars. For example a 160 day mission to mars launching at the august 3 2020 window would require a 3.91 km/sec delta-V earth departure burn and a 1.1 km/sec mars insertion burn. Aside from those few minutes of thrust, the entire 160 day journey would be "coasting". For missions outside of Mars or Venus, gravity assists are relied on a lot and there might be thrusts at close approach time for those gravity assists as mechanical advantage at that point greatly increases the value of the thrust.

On Sun, Jul 19, 2020 at 10:03 PM <xxxxxx@gmail.com> wrote:

So this article https://www.bbc.com/future/article/20150809-how-fast-could-humans-travel-safely-through-space got me thinking....

The Apollo 11 capsule was doing around 40K km/h at top speed coming back. The distance to the moon was 377,349km at that time.

Now, I've seen some discussion of the S shaped curve to enter a retrograde orbit around the moon as well, but it was lacking in some of the information I wanted (I did find out about 600 m/s was the velocity you need to enter said orbit).

So if they left the moon starting with 600 m/s and accelerated half way back, flipped, and decelerated, and they were doing 40K km/h at flip over, if I get my math right, they would have reached 40 K km/hr  minus 600 m/s in half the distance of 377K km.

Close to 250 minutes at the flip.

Now, I don't think they did constant acceleration nor constant deceleration nor did they need to get intercept velocity to zero (the atmo helps here on the return).

Punching in:
V(0) = 600 m/s (orbital velocity of the moon)
V(final at th flip) = 40,000,000 m/s
Time = 250 mins

Acceleration then looks to be 42 m/s^2.

That looks like 4 gees for nearly 5 hours accel then flip and decel at the same, so that's about 10 hours of 4 gees... that seems pretty hard on the astronauts.

Am I off in space with my numbers? The G load would be worse if you accelerated like mad for some minutes and then cut off for the rest of the trip to the mid-point.

I'm trying to figure out what sorts of acceleration you could reasonably sustain during system travel without grav plates if the journey took more than a short window (say 10 minutes or so)...

Would system ships in these settings then boost at a maximum of about 1.25 gees for a long haul? Or would they burst at 2-3Gs or more for up to 15 or 30 minutes, then come down, then have another heavy accel again if needed every (insert period of hours)?

Thoughts?

(I'm also thinking about, for say a trip to mars with a conventional rocket, how much would be coasting and what sort of Gs would be applied to get you moving? I'm assuming you couldn't burn all the way due to fuel weight...)

(Also curious if some form of maglev launch from the moon (lower escape velocity) might get you some of your initial velocity for a trip out to mars ...)

(Also curious - having trouble figuring out (via research) how fast one could 'fly' with a good push off inside a station in zero-G - I'm not sure what sort of velocity a straight jump from a surface using strong leg muscles could produce...)

Tom B






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