To save everyone digging around for earlier comments, this is what jr knowing wrote about this specific document. JR, I have pointed out where there are outstanding questions for you to answer in bold.
Hi Everyone,
Here is one of the MIT documents.
The document provided is a memo, not a paper.
Do you understand there is a difference between a paper and a memo, and concede that this document is not what you present it as? I will try to dig up the much more in depth paper.
It is months later, so where is this 'more in depth' paper?To be clear it states
"Due to the presence of jet plume deflectors on the LM descent
stage, the use of +X thrusting LM jets for pitch or roll attitude control
of the CSM-docked configuration will" "cause a
serious control instability"
This is what it actually states, and I have highlighted the bits you failed to quote:
Due to the presence of jet plume deflectors on the LM descent stage, the use of +X thrusting LM jets for pitch or roll control will, for some mass loadings, cause a serious control instability if any -X thrusting jets have failed off or been disabled.
Why did you snip those out of your quote?I have attached an image of the text from the memo as well.
As is made quite clear, this instability ony arises in certain cases, where a very specific combination of mass loading of a CSM-LM docked spacecraft and failed or disabled -X RCS jets occurs. This is
not an inherent instability of the craft caused by plume deflectors as jr mischaracterises it by his selective quoting.
Further it goes onto state that less than ideal conditions will lead to a positive feedback loop that will cause
"the vehicle will spin uncontrollably
in the counter clockwise direction."
What it actually says is that in very specific circumstances (not 'less than ideal', which makes it sound like the circumstances under which stability is achieved are the anomalous ones) a positive feedback loop will result under automatic control.
The memo includes a diagram (also attached) and a very simple mathematical equation to describe the circumstances where this instability will arise. The equation is:
M+X = (89lb)D1 - (59lb)D2M
+X is the net rotational moment (clockwise in relation to the diagram) around the centre of gravity caused by a jet plume from the RCS jet on the left side of the diagram that impinges on the plume deflector, assuming the one on the right is not working. Treating the spacecraft stack as vertical with respect to the LM (so the CSM is 'on top of' the LM) D
1 is the horizontal distance between the centre of gravity and the RCS nozzle (essentially half the width of the LM and to all intents and purposes a constant in this equation), and D
2 is the vertical height of the centre of gravity above the plane of plume impingement on the deflector. Because of the changing fuel and consumable loads of the two vehicles during the mission, D
2 is the variable.
It can be seen that if D
2 is long enough then the result for M
+X can be negative. In this case the spacecraft stack will actually rotate in the opposite direction than intended. Under automatic control of course the system would try to compensate by firing the jet more and hence increasing the rotation in the wrong direction.
JR, do you understand that the memo is referring to the stacked spacecratf only?
Do you understand that the instability only occurs if a -X jet is not working or has been disabled?
Do you understand that this instability only occurs under automatic control?Now we can do a little bit of mathematics ourselves. If:
M
+X = 89D
1 - 59D
2It follows that M
+X is negative (the condition under which the control instability occurs) only if 59D
2 > 89D
1. This can be re-written as D
2 > (89/59)D
1. 89/59 is near enough 90/60, or 1.5, so M
+X is only negative where D
2 > 1.5D
1.
JR, do you accept that or not, and if not why not?JR claims that this control instability must be worse for the LM in solo flight, but you can see from the mathematics that instability only occurs when the centre of gravity lies more than 1.5 times the horizontal radius of the LM RCS system above the plane of impingement of the jet plume on the deflector. This places it
above the docking hatch of the LM, so you can see that this instability can
only occur with the CSM docked.
There is also a graph (again attached) that shows the region of instability in terms of mass and centre of gravity and total spacecraft mass, and again you can see that the LM alone does not fall into this zone of instability. What's more, the zone outside the grey area is described as a zone of
increased stability in the case of diabled or failed -X jets.
Fially, the memo finishes with an instruction on how the crew can avoid the instability by using manual control and siabling other jets to avoid it in the first place.
JR, do you accept that this instruction is included in the memo?With all of this information in this one document, I expect JR to be able to show how it actually supports his contention of LM instability caused by the plume deflectors, or to concede it does neither.
JR, which of these will you do?And here is the ink to the memo itself:
https://www.ibiblio.org/apollo/Documents/LUM117_text.pdf