Fuel optimized lunar landing

Topper

Donator
Hello,

I have this question since some years so I will ask now:

How does the flightpath looks, from a (let's say ~circular) lunar orbit to landing with v almost 0 at the end, for a ~100% fuel optimized lunar landing? (Le't ignore terrain etc. in the first step)

And what's the "optimal" procedure in this sense?

My "feeling" is as follows:

1. Burn horizontal into the direction you are flying (Almost retrograte but with a pitch of 0) The result is, that the horizontal speed will be reduced and the ship wil begin to fall faster and faster into the direction of the ground (So vertical speed will increase more and more)

2. This will result in a curve from a straight line (parallel to the horizon) into a curve to another straight line (With a specific angle to the horizon). If this reqired "line" is reached, the engine has to be rotated so that horizontal ans vertical speed will be reduced proportionaly to it's values (The ship will follow the straight line, so the angle of the decent path is constant for a while). In an optimum case, an orbit has been selected before step one, that the length of this line is zero

3. The engine has to be rotated into a "specific" angle (which has to be calculated and is depending on the engines acceleration and the acceleration by gravity of the celestial body). The angle has to be selected that the following values are zero at the same time over the desired landing point: Horizontal speed, Vertical speed and altitude (plus some meters for final touchdown).

4. The engine has to be rotade exactly downwards for touchdown.

Is my feeling right?

Was that the way for the lunar moduels in the apollo program used in their "automatic procedure" or did they have to repsect other aspects (like a good view to the landing site ect.)?

Is there any documentation etc. how to calculate this things? (I havn't found anything I can understand)

Thanks!

Topper

Oh I just googled "apollo pitch over p66" and in pictures I found this interesting link:
https://dodlithr.blogspot.com/2014/08/lm-descent-to-moon-part-1-theory-and.html
I will study it now... Not sure if it's "fuel optimized"...

Last edited:

Linguofreak

Well-known member
I'm not sure of the degree to which an optimal procedure can even be specified without knowing more about the vehicle. If we're neglecting terrain, I'm pretty sure that the following procedure would work for spacecraft with wheeled landing gear in pre-terrain versions of Orbiter, and I may even have tried it in the past (though it's been a while if I did, and I don't recall the results):

1) Extend gear
2) Burn to lower PeA to a few meters above the surface.
3) At periapsis, burn to lower PeA to just below the surface.
4) Orient spacecraft to face among the velocity vector, with the landing gear facing down.
5) On touchdown, apply brakes. You will eventually come to a stop with no further fuel use after your periapsis burn.

This is, of course, patently absurd, but it demonstrates how dependent the answer to this question can be upon spacecraft characteristics.

Topper

Donator
- One engine spaceship
- Engine can be regulated in thrust

- RCS and/or gimbal for rotation

- No wheels (horizontal speed has to be 0 at touch down)
- One ignition (No DOI, from a circular orbit some km over the ground) (Becuase else you are right, we can choose an periapsis one meter over the ground, burn retrograde while holding altitude)...

Marijn

Member
Did you have a play with HoverMFD? I think it will help you understand and try out various techniques. It supports tailsitter style vessels as well, so it should be able to assist a main-engine down landing.

Assuming the plane is already ligned up with the base, my idea is that you have to optimize two things in order to burn as less fuel as possible:

-Brake retrograde as late and as hard as possible. The later and harder you burn without overshooting the base, the less time is needed for the final landing. If you brake to early, you'll spend some extra time countering gravity while flying horizontally. Of course, to avoid an overshoot, you need to account for some safety margin. Using HoverMFD, I tend to set the braking timer set to 95%. That means if you tend to overshoot, you can push it a little bit more to brake even harder.

-Burn as low as possible, so that you reach a vertical position just at touchdowntime. The earlier you reach a vertical position, the longer you'll fall towards the surface and the more fuel is needed to reduce this extra vertical speed at touchdown. Again, you'll need some margin, also because landing pads are often surrounded by buildings which you do not want to fly horizontally into.

---------- Post added at 10:43 PM ---------- Previous post was at 10:17 PM ----------

Edit: This actually requires two burns. I'll do the first one (from the parking orbit) using BaseSyncMFD 0.5 orbits from the base and burn so that the PeA right over the base is low, somewhere between 200 and 500 meters. Then I use HoverMFD to brake at the right time.

Urwumpe

Not funny anymore
Donator
Well, you should lower the PeA to about 4-5 km above the landing site (if you can), since otherwise, you would likely waste a lot of fuel to lunar gravity. The shorter the burn, the better. The Apollo trajectory was also the compromise between having enough control over the thrust during landing and using the maximum possible thrust most of the time during powered descent (And then came factors like visibility, landing site corrections, etc)

Next, its better to burn horizontal as long as possible - you can extend this time by keeping the vertical velocity as low as you can, so you only need a small amount of vertical thrust to control it.

So, you should gradually slide your trajectory between four kinds of strategies:

1. reducing horizontal velocity.
2. When the vertical velocity reaches a vessel-dependent threshold, start controlling it by pitching.
3. When you are slow enough, start aiming for the landing site. With the DG, I simply turn horizontal and play with retro thrust and hover thrust to keep the velocity symbol a tiny bit above the target, for entering a nearly linear descent, reducing both horizontal and vertical velocity.
4. When you arrive above your target, stop horizontal velocity and just try to land soft. You should only need small corrections in horizontal direction from now on.

What would make this much easier would be a HUD mode that projects a virtual landing site 50m above the landing site.

Topper

Donator
Did you have a play with HoverMFD? I think it will help you understand and try out various techniques. It supports tailsitter style vessels as well, so it should be able to assist a main-engine down landing.

Yes I tried out that MFD. But it's not fullfit my requirements or I don't know how... See later why...

Assuming the plane is already ligned up with the base, my idea is that you have to optimize two things in order to burn as less fuel as possible:

-Brake retrograde as late and as hard as possible. The later and harder you burn without overshooting the base, the less time is needed for the final landing. If you brake to early, you'll spend some extra time countering gravity while flying horizontally. Of course, to avoid an overshoot, you need to account for some safety margin.
Yes i absoloutly agree.

- Use the heaviest engine you have (If you have more then one). Because as more power the engine has, so faster your brake phase is. That means, that you don't have to spent so much time and in precentage power from your engines from the total power, to work against gravity.

- Use only one engine at same time (E.g., Not hover and retro at same time). Thats a gemetrical issue because it's always cheaper to have only one vector (a²=b²+c²)

I don't know how this is possible with hover MFD or is there a way to:
- Avoid to use two engines at same time
- Use main engine for braking and control decent by pitch?

Marijn

Member
I don't know how this is possible with hover MFD or is there a way to:
- Avoid to use two engines at same time
- Use main engine for braking and control decent by pitch?
Check the manual. I think it does. I haven't found a simple tailsitter for Orbiter 2016 to test it with. Tailsitter mode seems to require that the main engine is pointing towards the bottom, not the rear. The manual says all axes will get rearranged.

Ripley

Tutorial translator
Donator
Hi Topper,
are you cooking some new juicy goodie for us?

I mean, after
[ame="https://www.orbithangar.com/searchid.php?ID=3503"]BaseLandAutopilot (fourth BETA)[/ame]

and
[ame="https://www.orbithangar.com/searchid.php?ID=6398"]Surface Speed MFD V2.11[/ame]

Looking forward to it!

Topper

Donator
Ripley yes I'm developing BaseLand further...
I did some test, here are some values for my needed dv:

DV used for stock DG:
1. Brake using main engine, touchdown by hover engine: 1.735 m/s
2. Hover engine only landing: 1.791 m/s
3. Brake using retro engine, touchdown by hover engine: 1.998 m/s

All of these programs are supported by the new version of Baseland, so you can always select the best program for your requested use case.