Geometry and Aerospace

[Jemiba]

Just imagine, you got the task to measure the thickness of a rod. You've got a suitable measuring instrument,
maybe a sliding caliper, but you cannot see the shape of the cross section of that rod. Your measurements give
always the same thickness, no matter of the angle you have turned the rod.
What conclusion you could draw with regards to the shape of the cross section ?

If you said something like "The cross section is circular", then ...welcome to the club !

I would have said the same before reading an article in "Spektrum der Wissenschaft", August 2013 issue.
Honestly I hadn't heard about the Reuleaux triangle before, probably I just was ill that day at school..
The way it can be constructed geometrically is show below (from the mentioned mag).

The connection to aerospace mentioned there is tragic indeed: What I didn't know, seems to have
been unknown to those, too, who were responsible for checking the SRB of the Space Shuttle. To check
for deformations, the thickness of the segments was measured. Same thickness on a number of measurements
meant the reuse of that segment.
On the 28th of January 1986 a seal in the SRB of the Challenger Space Shuttle, that had lost a lot of its flexibility
due to low temperatures didn't remain attached properly to a deformed segment, with the too well known consequences.

That a failure of a seal was the reason for the Challenger disaster can be read everywhere, but this more in-depth
explanation was new to me.

 

[Arjen]

From Wiki:

 

[Jemiba]

Yes, this animation reminds on the Wankel engine, which uses the Reuleaux
triangle, too.

 

[Arjen]

The drawing also reminded me of a Wankel engine, but its rotor usually has slightly flatter curves to leave more room for the combustion chamber.
http://www.der-wankelmotor.de/Techniklexikon/techniklexikon.html

 

[Byeman]

The connection to aerospace mentioned there is tragic indeed: What I didn't know, seems to have
been unknown to those, too, who were responsible for checking the SRB of the Space Shuttle. To check
for deformations, the thickness of the segments was measured. Same thickness on a number of measurements
meant the reuse of that segment.
On the 28th of January 1986 a seal in the SRB of the Challenger Space Shuttle, that had lost a lot of its flexibility
due to low temperatures didn't remain attached properly to a deformed segment, with the too well known consequences.

Huh?

How is the triangle related to the thickness of a cylindrical SRM segment.

 

[Arjen]

I suppose fitting a non-cylindrical section O-ring in a non-cylindrical section groove could cause gaps between components.
<edit> did a little close reading

 

[Jemiba]

Arjen is right, the idea behind the method of checking, that the SRB segments were not distorted,
was unsuitable. Equal thickness i all directions isn't necessarily an indication for a circular cross section,
as it can also be a "Releaux triangle". In the case of the SRB this led to bad matching of the section
and its seal.

 

[Byeman]

I suppose fitting a non-cylindrical section O-ring in a non-cylindrical section groove could cause gaps between components.
<edit> did a little close reading

I don't see any gaps with the triangle in the groove.

 

[Byeman]

Arjen is right, the idea behind the method of checking, that the SRB segments

You mean O-ring cross section. SRB segments are large metal casings which hold the solid propellant.

 

[Byeman]

Same thickness on a number of measurements meant the reuse of that segment.

It had nothing to do with reuse. The o-rings were used only once.

 

[Orionblamblam]

I don't see any gaps with the triangle in the groove.

Yes, but the sharp point makes for a terrible a seal.

 

[Arjen]

I suppose fitting a non-cylindrical section O-ring in a non-cylindrical section groove could cause gaps between components.
<edit> did a little close reading

I don't see any gaps with the triangle in the groove.

As OBB already pointed out, any gasket / O-ring that connects with a pointed surface makes for a terrible seal. You won't need to ask if such a seal will fail, you'll need to ask when it will fail.

As you rightly pointed out, it wasn't the O-rings that were being reused, it was the booster segments. Deformation in the segments was only allowed to a very limited degree for them to be allowed to be reused; to which extent the segments were deformed was apparently determined by checking their width from various viewpoints, and comparing the measured width with width-as-specified. As the Reuleaux-triangle shows, that way of measuring deformation was not enough to determine whether the segments were close enough to circular for reuse. As a further complication, consider the Reuleaux-polygons:

Try precision-mating a segment deformed to the left lower shape to a segment deformed to the right lower shape, or even a to circular segment, fresh out of the factory.

 

[Byeman]

As the Reuleaux-triangle shows, that way of measuring deformation was not enough to determine whether the segments were close enough to circular for reuse. As a further complication, consider the Reuleaux-polygons:

Try precision-mating a segment deformed to the left lower shape to a segment deformed to the right lower shape, or even a to circular segment, fresh out of the factory.

Again, it is not the segment circularity that was the issue, it is the o-ring cross section.

 

[Arjen]

The connection to aerospace mentioned there is tragic indeed: What I didn't know, seems to have
been unknown to those, too, who were responsible for checking the SRB of the Space Shuttle. To check
for deformations, the thickness of the segments was measured. Same thickness on a number of measurements
meant the reuse of that segment.
On the 28th of January 1986 a seal in the SRB of the Challenger Space Shuttle, that had lost a lot of its flexibility
due to low temperatures didn't remain attached properly to a deformed segment, with the too well known consequences.

That a failure of a seal was the reason for the Challenger disaster can be read everywhere, but this more in-depth
explanation was new to me.

Jens's first posting explicitly mentions deformed segments. Mating deformed segments gives badly fitting seals.

 

[Jemiba]

I can only pass here, what's written in that article: It were the segments, or probably just a single segment
that was deformed, so, unnoticed it wasn't circular anymore. The O-ring actually was,as it was new. Under higher
temperatures, the O-ring still had enough flexibility to fit the deformed segment reasonably well, but due to the
low temperatures on the day of the launch, it had become too stiff to fit anymore to the deformed cross section
of that segment.

 

[Orionblamblam]

due to the
low temperatures on the day of the launch, it had become too stiff to fit anymore to the deformed cross section
of that segment.

Not quite right (or at least, not quite complete). As the booster sat there on the pad, the o-ring fit just fine in the joint. Sealed just fine, even cold. But being cold, the o-ring was stiff and inflexible. When the motor fired up, the hoop stress caused by the internal pressure caused the *steel* to deform, ballooning outwards in diameter very slightly. Even if the segments were not precisely round or precisely matched up, the o-ring would normally be able to flex with the steel and provide a seal. But being cold, when the steel flexed, the o-ring didn't.

It normally wouldn't matter if the segments were slightly out of round. Clearly they couldn't be *much* out of round, or the segments would have never fit together. The internal pressure would cause any out of roundedness to go to round real fast (imagine a balloon made to be square... unless there is a whole lot of internal bracing, the slightest pressure will make that square balloon round).

 

[Byeman]

I can only pass here, what's written in that article: It were the segments, or probably just a single segment
that was deformed, so, unnoticed it wasn't circular anymore. The O-ring actually was,as it was new. Under higher
temperatures, the O-ring still had enough flexibility to fit the deformed segment reasonably well, but due to the
low temperatures on the day of the launch, it had become too stiff to fit anymore to the deformed cross section
of that segment.

No, it has nothing to do with the deformed segment. That was never an issue. It is a cold o-ring being able to seal during joint rotation due to combustion pressure.

Oops, just saw the above post. Yeah, what he said.

And again, it was the shape of the o-ring cross section that was concern and not the SRM segment. And they were more concerned with SRM segment ovality for assembly than the Reuleaux triangle. A round segment can not become a Reuleaux triangle anyways and stay within a certain diameter, because as one direction is pushed inward there will be an outward expansion elsewhere (the ovality issue). But then again, mating two segments tend to make them more circular. Which still leaves the o-ring cross section.

In summary, the issue is not with the SRB segment cross section but the o-ring.