Advanced Question Speeding up Moon > Earth return flight

[davidweb]

Background:
I'm off work for a couple weeks recovering from a minor surgery and decided to build a really neat UCGO lunar base next to the tram-line at Brighton Beach. Started off using XR2 but figured I'd get bored doing 50+ round trips to build my base so now am doing the XR5 with just one of Woo482's palets full of 24 UCGO station stuff and a couple more filled with fuel in case I run low on my way back.

Challenges:
I'm fairly proficient with Orbiter and have Earth > Moon flights down to a science. I tend to extend the apoapsis out enough so that I can get to the moon in 2.5 - 3 days. BUT... when returning to earth I am having a brain fart in terms of how to shorten the "free return" to shorter than 4.5-5 days. If I do my prograde burn in lunar orbit with delta v of around 800-820 i "tighten" up the free-fall, but it doesn't seem to shorten my return.

Question:
What is the best, fuel efficient way of getting back from moon to the earth in approx 2.5-3 days? I'm using Transx but open to using another MFD if it would help.

Thanks!

 

[asbjos]

The absolutely easiest way to perform any Earth<-->Moon trip, is by using the Lunar Transfer MFD.

But you say you are using TransX. How much experience/knowledge do you have? Because it is possible to plan an Apollo-style TEI-burn fairly easily with it.

 

[davidweb]

I have a lot of experience with basic tasks, but I wouldn't call my Transx knowledge advanced. I will check out the Lunar Transfer MFD!

 

[dgatsoulis]

I'm assuming that you are using TransX in this way for the ~5 day Earth return:

Stage 1: Maj Body Moon → Escape
Stage 2: Maj Body Earth → View: Eject Plan → Target: None
and then you apply negative Prograde (~820 - 850 depending on where the Moon is in its orbit).

Apply also negative Outward. For a ~3 day trip you'll need almost as much as the negative prograde, if not more.

A better way to do it is to take off from the Moon the usual way (TransX plan as above without negative Outward) and when you get ~1000 sec before the burn setup a maneuver. Match the prograde ΔV and the Date with the burn already shown on stage 1 and then go to stage 2 and reset the prograde Vel.

Then (on stage 2) turn the "autoplan: off" and the "advanced: on".
Select "Plan type" :"Through point" and "Plan: Encounter". (edit: hit VW) Now you will be able to see the result of the maneuver with more detail. On stage 1 you will need to apply more ΔV and change the date (Hyper setting) untill you get the flight time and Periapsis altitude you desire.

 

[blixel]

Apply also negative Outward. For a ~3 day trip you'll need almost as much as the negative prograde, if not more.

I've wondered myself how to shorten the Moon to Earth transfer time with just TransX. I knew from reading the DeepSpaceManual.pdf TransX manual that negative outward could be used as a way to "speed things up", and positive outward could "slow things down" a bit:

The final variable “Outward velocity” is useful if you for some reason want to leave earlier or later in the launch window than the absolute optimum day.

...but it wouldn't have occurred to me to add in that much negative outward to get the desired result. I would have assumed I was doing something wrong if I added more than 50-100 m/s (negative outward) and didn't see my arrival time come down significantly.

Anyway, no real point here. Just one of those, "I learned something new today" remarks. Thanks Dimitris.

 

[dgatsoulis]

There is a mistake that I used to make when I was adding ΔV in one of the directions other than prograde. (Pl.Change and/or Outward). And i think (or I like to think) it's a common one that many people make. I facepalm myself now, but a few years ago, I didn't know any better.

I used to think that the total ΔV was the sum of those 3 (regardless if they were + or -). That is wrong, at least in the arithmetical sense. When you apply additional velocity in one of the other directions, you are adding vectors, not numbers; and these ones are perpendicular to each other. Here is a pic to explain a liitle bit better:

The Total ΔV is the square root of the sum of the squares of the velocities applied in each direction.
ΔVtot = sqrt(VPro²+Vpl.ch²+Vout²)

So if you have -850 prograde and you add -800 outward the total ΔV is sqrt((-850²)+(-800²)) = 1167.26 m/s , just 317.26 m/s more than the ΔV for the negative prograde burn.

 

[Cras]

Fwiw, when I use LTMFD to do a direct return in the XR-2, it takes me like 2.5 days to get back. I dont recall a trip ever taking me more than 3.

 

[blixel]

The Total ΔV is the square root of the sum of the squares of the velocities applied in each direction.
ΔVtot = sqrt(VPro²+Vpl.ch²+Vout²)

This idea is something I picked up on fairly quickly through observation, but I never knew the formula behind it. So this is good information, thanks.

But I realized if I added 100 m/s prograde and 100 m/s + plane change, the total dV would not have to be 200 because I wouldn't burn 1 direction, and then do a separate burn in the other direction. Rather, TransX has you burn at an angle between the two directions.

A basic analogy would be if I wanted to walk 1 mile to the east and 1 mile to the north, I could simply walk diagonally to save myself some of the walking distance. I don't even have to work out any math to realize that it will save me time and effort to walk in a straight line rather than going over and up.

But knowing the math is cool! So in my example of 100 m/s VPro + 100 m/s Vpl.ch, I come up with 141.42 by using that formula.

I tested the result in TransX: