Stress in a cable pulled from 1 end or bothe 2

[lemonbreath]

Hello all
Apologies if this is in the wrong section.
The below tv show about an air crash investigation makes a statement about forces on a cable that did not ring true to me. I wanted to check my understanding of forces.

Simplified as I understood it the following seemed to be suggested: Cable A with a joint midway is fixed to a static point. Cable B with joint midway is pulled from both ends. Cable B is more likeley to break. In both cases one end can apply a max force that can not be exceeded (this would be the pilot end).

A link to the video is below. I would appreciate any guidance on this matter.

Thanks

The comment I refer to is made at 41 min 27 Sec

http://youtu.be/pRUNaH0HguM

 

[MacGruber22]

I think the case of Cable B may involve a bit of upping the ante with a bit of tug of war, so to speak. If there is a very slight difference in forces at each end of Cable B, there will be some displacement in that direction. Easy enough. If the mechanism (or person) on the opposite end of the cable can feel the displacement start to happen, it may elect to increase the force on the cable to counteract the displacement. If the response is excessive, then the other side may respond in kind. After enough back and forth, the tension in the cable (or joint) may have built up to a degree not anticipated. I think the difference that makes Cable B not exact like tug of war, is that there is likely a fixed point beyond each end of the cable that allows for a lever arm to build up a lot of additional force to keep upping the ante.

Hopefully, an aerospace/mechanical person can provide a better comment.

"It is imperative Cunth doesn't get his hands on those codes."

 

[BAretired]

GUTS = Guaranteed Ultimate Tensile Strength

It makes no difference whether a cable is pulled from one end or both. It will fail at its ultimate tensile strength.

BA

 

[MacGruber22]

It makes no difference whether a cable is pulled from one end or both. It will fail at its ultimate tensile strength

Absolutely.

But I *think* the extra degree of freedom in Cable B allows for other things to possibly take place (not say that this is how it actually happened in the crash). If the change in force is independent at each end of Cable B, then in order to keep equilibrium of the cable position each source of force would need need to increase to offset the displacement forced form the other side. In this struggle to keep position equilibrium, I could see the two independent forces collectively increasing in small iterations until rupture.

I still don't like the explanation in the video.

"It is imperative Cunth doesn't get his hands on those codes."

 

[DavidHansen]

I agree that the explanation doesn't seem totally sufficient. There are several things that can go wrong in each scenario, but you would think more measures would be taken to keep both ends of cable B from breaking with different tensions. Interesting thread- I hope an expert comments!

 

[3DDave]

Makes no difference. The free-body diagram for both cases is identical. The explanation in the program that there is a difference is incorrect.

There can't be a difference in tensions unless there is another item that balances the forces, something that Newton suggested as a law. If there is nothing else to balance the force the entire control cable should accelerate and keep on accelerating as long as the external forces are out of balance. Being attached to the plane, the cable can't do that, so there is no imbalance.

What was missing from the program was how much leverage the throttle lever had on the cable. It also failed to explore how strong the lever was and how much force the engine could apply. Perhaps the first officer used his leg, or wedged his arm against his seatback to put his ulna and radius** into pure compression, eliminating the need for using his muscles.

The biggest failure was by Fokker, which realized that the reverser could deploy accidentally and designed a system to offset it, but then told the customer that it could never happen, and not to bother the pilots with the possibility.

The second biggest failure is that there is no indicator of the position of the thrust reversers. It could have been as simple as using an additional red bulb behind the autothrottle warning light.

**One source I just found indicates around 3kN/700lbs as an estimate of radius bone axial strength. If the first officer thought he was going to die if that throttle moved, a potentially broken arm would be a fair trade. If there was even a 2:1 ratio between the lever and cable pulley radius, that would put more that 1400 pounds available to resist cable pull.

 

[BAretired]

The First Officer held the throttle forward to restore full power to the engine according to the video. The cable failed at the connector between Cable A and Cable B. It is not clear what failed. Perhaps one of the cables unraveled at the connector, but failure occurred at about 900#.

At one point, about 38 minutes into the video, the investigator says "The cable was designed for an amazing 632#. I don't see how the pilot could pull that apart". But we do not know what mechanical advantage the throttle stick had over the cable tension.

It is incorrect to talk about the "combined force" of the First Officer and the Reverser. They are not additive. The total force was applied by the Reverser. The throttle was simply being held in position when the plane went down.



BA

 

[IDS]

I haven't watched the whole video, but I don't think the statement at 41'27" says anything wrong.

For the cable to break you need an action and an equal and opposite reaction that exceed the tensile strength of the cable or the connection. That force is a result of the combination of what is happening at the engine end, and what is happening at the pilot end, so it is reasonable to describe it as a combined force.

This does not imply that if the engine end was fixed the pilot could not apply enough force to break the cable. Obviously with sufficient motivation he could have applied exactly the same force, but the point is that the only reason he applied this large force is because of the initial force applied at the other end.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Ron]

Can you say "Free body diagram"?

 

[IDS]

Can you say "Free body diagram"?

If that was directed at me, why would you want me to say that?

If you are suggesting that anything I wrote is inconsistent with the concept of a free body diagram, you are wrong.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[dhengr]

Lemonbreath:
I think your two scenarios are wrong, leading you to ask the wrong question in the wrong way. You have to learn to read/listen/watch, three times, sometimes, to really understand what’s being said. If it doesn’t ring true listen again, and see if you are missing something btwn. the lines (i.e. read btwn. the lines).

They said that the cable had a failure/design strength of about 600lbs. (632#) and that it broke at about 900lbs., at a quick disconnect joint in the cable. These results were from a lab test after that accident. In fact, the cable did not break, the quick disconnect came apart. They also implied that it was hard to imagine that a pilot could possibly apply 600lbs. to the cable, so there was a significant FoS in that respect. He is pushing on the top (handle) of the throttle lever, which then has a pivot pin at the bottom of the lever and assuming the cable is connected an inch or two above the pivot pin. Maybe the pilot can apply 40-60lbs. to the top of the lever, and that arc of travel is maybe 8 or 10". The statics of the problem (free body diagrams, etc. etc.) are that the cable connection would move through a couple inch arc, but with a potential tension force of (6, 8, 10 multiplier, times)(40-60lb. pilot force, on the handle), maybe approaching the 600lb. ult. cable cap’y. Once the pilot has the throttle lever fully extended, with his straight arm behind it (holding it extended), he can probably hold more than the 40-60-lbs. I suggested above. Furthermore, at that point the throttle lever is probably starting to be in an over centered position, giving it some added mechanical holding and force advantage.

Then they said that the second pulling force was applied by the plane’s own mech. system (safety system), in particular connected to (interacting with) the thrust reverser on the copilots side, which was acting up. The trust reverser kept deploying, which caused the safety system to automatically pull the throttle lever back under these conditions, this was all unbeknownst to the pilots at the moment; and the copilot would push the throttle forward again. All he knew at that instant was that they needed power to gain altitude. Full thrust, with the trust reverser deployed on the copilot’s side, would cause the plane to roll and dive to the right (copilot’s side).

You said.... “ Cable A with a joint midway is fixed to a static point. Cable B with joint midway is pulled from both ends. Cable B is more likeley to break. In both cases one end can apply a max force that can not be exceeded (this would be the pilot end).
--“fixed to a static point”, not true at all.
--“Cable B is more likeley to break”, they didn’t say that.
--“In both cases one end can apply a max force that can not be exceeded”, they didn’t say that either.
--Your use of the phrase ‘fixed joint, static point’ is pretty misleading. In fact, you have not characterized the test you watched at all well. The test had nothing to do with pulling from both ends causing the cable force/stress to be higher. They were pulling from both ends during the first phase of the test, to 600lbs., too.

Your question should have been, something like.... can the polit with the throttle lever fully extended, hold more than the 900lbs. it took to break the quick disconnect? And, the answer to that is yes, apparently. Can the safety system apply that much force (900#) to the throttle cable to draw it back to idle position; apparently, yes. We would have to know much more about these interconnected systems to make a more meaningful judgement about all the details. But, I don’t find my above explanation too hard to imagine, it fits what I think I heard.

 

[rapt]

It all depends if the cable force is controlled by pressure or by extension.

If by pressure, the 2 cases are exactly the same, except that the rate of increase will be higher for the case of applying the force from both ends. Even if one end leads then pressure will show the actual pressure in the cable and it will show the same pressure at both ends.

If it is controlled by extension at the ends, then it is additive for the case of application at 2 ends!

 

[lemonbreath]

Hello all

Thanks for the replies. I wanted to confirm my understanding of structural principals. I may have created some confusion by including the video and not setting the question up very well. At the time of asking I was not sure what the question was.

I had understood the programme stated that the forces combined to exceed the "GUTS". It was mentioned in the film that there was know way the officer could apply the force necessary to exceed this.

At 38.39 the programme states that the "investigators put an identical cable to the test...they pull from both ends, not only where it connects to the reverser but also to the lever" this seemed to suggest that the test was an enhanced test that would test for worst case scenario.

As I understand it (and this is what I am seeking to confirm) is that the test would be equally efficient from the point of view of examining the cables ability to withstand the applied forces, if one end had been fixed and not "pulling".
I am now fairly certain that is the case.

Thank you.

 

[Ron]

IDS.....not intended for you or anyone else. Just a reiteration of 3DDave's approach.

 

[KootK]

I think that the question can be answered more definitively if the arguments are tweaked a little. Try this:

Case A: Tension is adjusted at one end of the cable in a slow and controlled manner. Must the cable be pulled from only one end in order to be loaded in a slow and controlled manner? Of course not. However, it's more likely to be the case with the tension adjusted at one end and is almost certainly what we're talking about here where testing is being compared to in service behavior.

Case B: Tug-o-war to the death with tension adjusted rapidly, actively, and unpredictably at each end. Again, the only parameter that matters is the rate of loading but, in practical terms, the two degree of freedom tug-o-war is clearly more likely to result in rapid loading.

Case A is statics problem and case B is not. For identical cable systems, the extent to which this is true will depend on the relative rates of loading. For case B, a dynamic impact factor would apply. As such, while the cable would break at an identical GUTS tension, that tension would be associated with a lower applied load for case B.

My money says that the statement in the video originated from someone who knew what they were talking about but got bastardized along the way.









I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[rb1957]

I think it comes down to the mechanical advantage of the throttle quadrant, which isn't discussed. Cntl systems are funny things to stress ... you want low pilot effort for normal manoeuvres (so Aero predict the elevator load for the manoeuvre, and Stress run that load through the mechanical system to figure out the load applied by the pilot) and you want to understand max pilot effort like in response to an engine failure.

In the scenario, I think what they're trying to say is that the pilot is pulling the cable at one end and the reverser is pulling at the other end. These two forces do not add together, but react one another ... the pilot must be pulling at his end the same as the reverser is pulling at it's end. I guess the point is that the reverser can be applying a 900 lb load at it's end, then if the pilot's end did not react that then the throttle would move.

another day in paradise, or is paradise one day closer ?

 

[MacGruber22]

KootK - I think you did a better job than I did trying to communicate Case B. I think I was having an easier time imagining it than communicating it.

"It is imperative Cunth doesn't get his hands on those codes."

 

[KootK]

Hey, engineering is a team sport, right? You plant the seed, I put the bow on.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[rb1957]

if engineering's a team sport ... where are the cheer-leaders ?

another day in paradise, or is paradise one day closer ?

 

[MacGruber22]

KootK - unfortunately it often doesn't feel like a team sport, but that is another topic for the Pub. As usual, your attitude is greatly appreciated.

rb1957 - that is a good point. There needs to be computer-operated Eng-Tips accounts that randomly tell us how awesome and appreciated we are.

"It is imperative Cunth doesn't get his hands on those codes."