### Author Topic: LM max tilt angle for safe lunar liftoff?  (Read 30959 times)

#### joema

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #20 on: 07/01/2013 09:49 pm »
...If your X+185.9 (source?) is correct it puts CG 113" above landing leg pads. If the 31' distance from opposite landing leg pads is simplified to a square, shortest support length from center to edge is 131.5". Atan(113/131.5) = 41 degrees so theoretical tip over angle is 49 degrees..

Thanks. At the bottom of this page, the Apollo 14 LM mass properties shows the X-axis cg was 185.9 inches at powered descent initiation, and 213.6 inches at lunar landing: http://www.hq.nasa.gov/alsj/a14/a14mr-a.htm

This makes sense because the descent stage is much lighter after landing, but the ascent stage is the same mass. The overall vehicle cg will then be higher, making tip over easier.

This would put the LM touchdown cg 27.7 inches higher than at PDI, or 140.7 in. above the foot pads.

By the above calculation the tip over angle would be:

90 - Atan (140.7 / 131.5) = 43.1 degrees (I think).

However 43.1 degrees is still a pretty steep angle. From the prior-listed "Boundary of Acceptable Angles" graph, ascent staging would be possible far beyond this (the point where it tips over).

During landing if a footpad inner edge got caught on a crater rim and the vehicle hung from one leg at a 70 degree angle from vertical, it apparently could still stage and take off.

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #21 on: 07/02/2013 12:33 am »
Silly practical matter here... could the crew have stayed at their stations at any of these extreme angles? Would their restraints have held them?

#### ClaytonBirchenough

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #22 on: 07/02/2013 12:53 am »
Silly practical matter here... could the crew have stayed at their stations at any of these extreme angles? Would their restraints have held them?

Haha made me laugh but a valid point. Seems like lunar gravity wouldn't be pulling them terribly... seems it would be way too difficult to operate in that kind of environment though.
Clayton Birchenough

#### joema

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #23 on: 07/02/2013 01:38 am »
Silly practical matter here... could the crew have stayed at their stations at any of these extreme angles? Would their restraints have held them?

On Apollo 10, the LM crew restraints held Cernan and Stafford when the LM was gyrating out of control above the lunar surface. In Cernan's autobiography The Last Man On The Moon, he said: "we made about eight cartwheels above the Moon...After analyzing the data, experts later surmised that had we continued spinning for only two more seconds, Tom and I would have crashed."

It would seem those same restraints could hold the LM crew in a fixed tilt in lunar gravity.
« Last Edit: 07/02/2013 01:39 am by joema »

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #24 on: 07/02/2013 01:50 am »
It's all academic, but I don't think that can be assumed.

#### joema

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #25 on: 07/02/2013 02:29 am »
It's all academic, but I don't think that can be assumed.

If you examine the attached documents, each LM crewmember was restrained with (a) boots velcro'd to the floor, and (b) A constant force reel assembly applying 15 pounds per side, split between fore and aft directions.

Not well shown in those diagrams, their forearms formed another point of contact on hydraulically-damped arm rests.

In the Apollo 10 LM control problem pitch and yaw rates were about 25 degrees per second, and they stayed restrained. However I don't know what the g force was.

Info from: Apollo Experience Report -- Crew Provisions and Equipment Subsystem.

#### ClaytonBirchenough

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #26 on: 07/02/2013 03:24 am »
Very interesting joema. Where are you finding these pictures!?
Clayton Birchenough

#### joema

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #27 on: 07/02/2013 03:27 am »
Very interesting joema. Where are you finding these pictures!?

Apollo Experience Report -- Crew Provisions and Equipment Subsystem:

http://www.hq.nasa.gov/alsj/tnD6737%20-%20CrewProvisnsEquip.pdf

#### ClaytonBirchenough

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #28 on: 07/02/2013 03:36 am »
Apollo Experience Report -- Crew Provisions and Equipment Subsystem:
http://www.hq.nasa.gov/alsj/tnD6737%20-%20CrewProvisnsEquip.pdf

Ahhhh... Another long night it's going to be;).

Seriously never saw that before, great find and thank you!
Clayton Birchenough

#### joema

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #29 on: 07/02/2013 03:43 am »
Apollo Experience Report -- Crew Provisions and Equipment Subsystem:
http://www.hq.nasa.gov/alsj/tnD6737%20-%20CrewProvisnsEquip.pdf

Ahhhh... Another long night it's going to be;).

Many others here: http://www.hq.nasa.gov/alsj/ApolExpRpts.html

#### ClaytonBirchenough

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #30 on: 07/02/2013 03:56 am »
Clayton Birchenough

#### joema

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #31 on: 07/02/2013 04:01 am »
Many others here: http://www.hq.nasa.gov/alsj/ApolExpRpts.html

Thank you, thank you, thank you!

A minor correction: the 2nd LM crew restraint graphic was from page CPE-9 of this 267-page Grumman document "Apollo Spacecraft News Reference" (109 megabyte PDF). The entire document or sections thereof are downloadable from here: http://www.hq.nasa.gov/alsj/LMNewsRef-Boothman.html

#### R7

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #32 on: 07/02/2013 11:38 am »
However 43.1 degrees is still a pretty steep angle. From the prior-listed "Boundary of Acceptable Angles" graph, ascent staging would be possible far beyond this (the point where it tips over).

The graph also confirms your calculation, see where "neutral stability line" crosses when attitude rate hits zero

One physical limit is the angle where ascent engine thrust generates enough vertical force to at least hover. From your link Apollo 14 weighted 10779.8lbs at lift-off, with 3500lbf ascent engine the max angle is ~59 degrees. Beyond that and the ascent stage falls towards the surface.

The powered ascent happened in three phases: 1) engine fires for two seconds while maintaining constant attitude. 2) orient vehicle up and continue firing until predefined radial velocity (40fps) is achieved 3) begin pitch-over to follow ascent trajectory. (source)

Here's a silly question: if the LM would have landed close to dangerous tilt could the astronauts have tried to level it by digging regolith from under foot pads, did they pack shovels?

#### joema

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #33 on: 07/02/2013 12:59 pm »
One physical limit is the angle where ascent engine thrust generates enough vertical force to at least hover. From your link Apollo 14 weighted 10779.8lbs at lift-off, with 3500lbf ascent engine the max angle is ~59 degrees. Beyond that and the ascent stage falls towards the surface.

Thanks, this is unavoidable physics so *apparently* the graph did not account for this -- it shows the "emergency manual control" line intersecting y-axis at 70 degrees tilt angle.

However, the total available thrust was actually greater than 3500 lbs; each RCS thruster produced 100 lb, so that would be 3900 lb total liftoff thrust. Also they wouldn't take back any moon rocks in a contingency, so that reduces vehicle weight about 100 lb (for Apollo 14) or 244 lbs (Apollo 17).

Taking those into account the thrust/weight-limited liftoff angle is about 62 degrees:

(10779.8-100 lbs)/6 = 1780 lbs ascent stage mass on moon
Vert thrust @ 62 degree liftoff angle = 3900 * sin (90-62)
Vert thrust component = 1830 lbs

However if ignition overpressure, or any other effect momentarily increased takeoff thrust, it would need less than one second (at 35 deg/sec^2) for RCS to pitch the ascent stage and increase the vertical thrust component.

Here's a silly question: if the LM would have landed close to dangerous tilt could the astronauts have tried to level it by digging regolith from under foot pads, did they pack shovels?

Thanks, I had often wondered about this, esp. given the alleged 12-15 degree tilt limit. However -- our calculations indicate the ascent stage can liftoff at a greater angle than the LM is neutrally stable. IOW > 43 degrees and the LM would fall over after landing, but the ascent stage can lift off up to about 62 degrees.

#### ClaytonBirchenough

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #34 on: 07/02/2013 05:03 pm »
Here's a silly question: if the LM would have landed close to dangerous tilt could the astronauts have tried to level it by digging regolith from under foot pads, did they pack shovels?

Haha the idea of astronauts doing that on national television gave me a laugh;D.

They brought various tools with them, see link:

http://www.lpi.usra.edu/lunar/samples/apollo/tools/

I imagine they could, but if it was that dangerous and another landing site was not in the vicinity, an ATO could be used, right?
Clayton Birchenough

#### A_M_Swallow

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #35 on: 07/02/2013 06:37 pm »
To bring this up to date, today Project Morpheus tilt tested the ALHAT unit by putting blocks under their lander's legs.  If they go up to 62 degrees they may need bigger blocks.

#### joema

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #36 on: 07/02/2013 10:18 pm »
...the idea of astronauts doing that on national television gave me a laugh...I imagine they could, but if it was that dangerous and another landing site was not in the vicinity, an ATO could be used, right?

We now believe the LM could lift off from any stable attitude (up to 43 degrees from vertical) and could even lift off *while* tipping over -- up to the limits shown in this graph: http://forum.nasaspaceflight.com/index.php?topic=32246.msg1068329#msg1068329

Therefore any need for corrective digging seems unlikely.

However say they had to, for some reason -- would it be possible? The LM weight on the moon is about 2728 lbs, so it would be like trying to dig out a stuck car -- except in a space suit. If one footpad was elevated precariously on a rock, they might have been able to push it off or dig out the rock. But it would be very difficult and questionable. In space suits it was very hard to pull out a stuck drill, much less change the resting angle of a nearly 1 1/2 ton vehicle.

Re ATO, if they knew the landing would result in a bad situation they could abort prior to touchdown, using either the descent or ascent engines. However this was constrained by the "dead man curve" shown in this post: http://forum.nasaspaceflight.com/index.php?topic=32246.msg1069160#msg1069160

Once they were below a certain combination of decent rate and altitude, abort was not possible. Note the options were different for an abort using the descent stage vs ascent stage. See attached graph.
« Last Edit: 07/04/2013 02:56 pm by joema »

#### dbaker

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #37 on: 07/24/2013 03:41 pm »
I finally found some official info related to this. A paper titled "Apollo Lunar Module Landing Strategy" was presented at the Apollo Lunar Landing Mission Symposium, held at the NASA Manned Spacecraft Center on June 25, 26 and 27, 1966. Therefore all the other descriptions of a 12 degree tilt limit cannot be right. Apparently the LM ascent stage could successfully lift off from any conceivable orientation.

Only just seen this and as I was one of the sources quoted as being incorrect, forgive me pitching in late. I am impressed by all the theorising but I am afraid that there are other issues regarding the tilt boundary and abort corridor, most of which refers to a FITH abort with a running DPs.

I am posting (in haste as I am in travel) a page from one of our presentations on the ISLLS in early 1969 which was being promoted as a more capable version of the basic LM. As seen on the attached, the basic LM was considered to have the tilt boundary of about 12 deg, heavily challenged in this strand, while the ISLLS with modified landing gear (superimposed over the standard LM) was being demonstrated to have a higher angle of repose, allowing it to "land on slopes much steeper than is possible with LM." This was in response to a request to Grumman for landing in exceptionally rugged areas when the expectation was that we would build a sequence of extended LM missions.

Also please note, with ref to the 1966 study quoted, the tilt boundary was set at 40 deg, not the 70 deg and more that is assumed from paper calculations by other contributors. That is affirmed in the text of the report from whichthe earlier diagram comes. I have to say, when it was presented in 1966, a lot of folks at Grumman didn't believe it!

#### joema

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #38 on: 07/24/2013 08:05 pm »
...I was one of the sources quoted as being incorrect, forgive me pitching in late...

Dr. Baker thanks for responding. Your History of Manned Space Flight book is magnificent in both encyclopedic scope and extreme attention to accuracy.

We were just trying to figure out what the actual LM tilt limit was for lunar liftoff and reconciling the different historical documents on this.

The  1966 "Lunar Module Landing Strategy" has a graph (figure 59) showing a staged abort was possible up to 62 degrees if using the Digital Auto Pilot (DAP) and up to 70 degrees if the attitude rate was 0 and if "emergency direct" RCS was used (ie full hard over on the hand controller).

On page 206 the article text elaborated, saying a staged abort was possible at 60 degrees if the attitude rate was below 10 deg/sec. If it could abort from 60 deg. tilt immediately after lunar touchdown -- even while falling over at 10 deg/sec, it would seem an abort from greater than a static 12 degrees would have been possible.

I think the 40 deg. tilt boundary mentioned on page 206 of the paper is the static stability limit whereby the LM would topple over due to c/g. It was not an abort limit.

The 1966 paper didn't provide the underlying technical reasoning on how these limits were calculated but previous calculations in this thread imply it was derived from ascent stage RCS control rates, c/g,  and APS thrust/weight ratio. Maybe later study showed there were issues with separation dynamics which imposed a much small acceptable tilt angle.

The graph wasn't meant as an operational guideline, it was just a technical presentation back in 1966. At that conference Tom Kelly (Grumman chief of LM design) questioned some of the statements made, but I don't know the specifics.

So we still don't know where the 12 degree tilt limit came from. This has some historical relevance since Apollo 15 came within one degree of hitting that limit.

#### dbaker

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##### Re: LM max tilt angle for safe lunar liftoff?
« Reply #39 on: 07/25/2013 09:59 am »
Joema, you do me an unjust compliment but thanks.

I think you hit it spot on. Coming at it from a variety of positions it is possible to predict boundaries according to the factors entered in: physical tip-angle (as you say); mechanical/stage-separation issues; rate of attitude correction with the AGS; etc, etc.

I know for certain that the Grumman folks had a ballpark of 12 deg and that is reflected in the diagram on the cryogenic LM (ISLLS) presentation given in 1969 which I posted earlier. The generally accepted redline was 12 deg but that seems to have had a life of its own. I can recall how that figure was arrived at as the sum of all the boundaries known through calculation and test. But there were so many unknowns. The very justification for the remodelled leg config on the ISLLS was that it could land on steeper slopes.

The engineering world of the 1960s was a completely different planet to that we live on today. Nobody really knew how to do a Moon lander. Grumman actually borrowed Hughes' Surveyor leg design math for the ISLLS - because that was how you would do it if you did it over. The ISLLS would have been cleared to land on slopes of up to 35 deg - but of course there was no ascent as it was a pre-positioned supply base. The fact that 12 deg was, at the time, considered to be the limit, is evidenced by the comparative drawing using the limits of the standard LM as a baseline.

Constraints had been placed upon Grumman from the program office about getting the basic LM folded up inside the limitations of the SLA for Saturn. The ISLLS LM following the J-series missions however was to have been launched by Titan IIID/Centaur for pre-positioning - which was originally part of "insurance" with the LOR mode, rejected in 1963 but reintroduced in 1969 as a way of extending surface stays rather than providing a rescue ship as it had been envisaged when first mooted six years earlier.

Until the LM flew, noone knew for sure precisely how it would behave and the variables were such that, if you took the worst case of this and the worst case of that, go for the least risk and asume a line that stayed the correct side of uncertainty.

On a slightly more philosophical note, all these factors were new. Nobody had run the vehicles through a complete duplication of a lunar landing, only a simulation based on best-known performance. When Apollo 11 flew there were a lot of unknowns and even in the spring of 1969 there were concerns at Grumman (especially from Tom Kelly) that the tip angle at liftoff could prejudice the ascent trajectory.

An interesting fact is that some stress/force analysis was done on the legs and it was discovered that as designed the first redlines would occur at an angle of around 15 deg - the geometry was not ideal (as was pointed out when they went from a five- to a four-legged config). Simple force comparisons will show that the 75 lb mass saved by having a four-leg config was not worth the march to the right on the support barrier graph that showed a potential fracture with the final design of just four legs.

In other words, assuming a reposed LM, apart from the angle of the thrust line, never forget the stability of the platform. A descent abort through a FITH has totally and completely different factors to a reposed LM on the surface at those angles.

Interesting, but not relevant to the original question (so forgive the march off-topic) but in egress/ingress simulations (where 5/6th Earth g was compensated), it was shown by suited test subjects that the lunar astronaut would be unable to get back up safely through the forward hatch off the porch against a ladder closer than 5 deg to vertical - so you wouldn't land anyway.

Sorry to drift off topic slightly but its the "global" factors that count.

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