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enter image description hereImage source

Flight controls in airliners have long cable lengths in between the cockpit controls and the control surfaces. For instance in the picture above: the pilot operates the yoke, which deflects a steel cable running through the front fuselage and the wings, which then opens a servo valve for the hydraulic actuator moving the aileron.

  • The cables are made of steel, the aircraft from aluminium.
  • Thermal expansion of aluminium is twice that of steel.
  • The aircraft can be standing in the sunshine at 40°C, and half an hour later be at cruise altitude at -50°C.
  • The difference in thermal contraction would cause a couple of centimetres slack in the cables at cruise, with the pilot then experiencing a control deadband: turn the yoke some degrees and nothing happens. Or the cables would be appropriately tightened for the cruise situation, causing tight cables and high control friction at take-off: try to turn the yoke by pushing hard.

But the forces and (lack of) deadband are identical at take-off and cruise. How is this possible?


Edit

Yes there is a Cable Slack Takeup drawn in the picture, but the working of it is a little bit more complicated than it seems, I've added an answer below.

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    $\begingroup$ Wouldn't tension increase at colder temperatures? $\endgroup$ – acpilot Nov 29 '17 at 2:58
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    $\begingroup$ @acpilot aluminium shrinks more than steel does... $\endgroup$ – Koyovis Nov 29 '17 at 4:10
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    $\begingroup$ I wonder how many early aircraft crashed and burned before engineers figured this out and came up with the cable slack take-up spring solution. Great question. $\endgroup$ – Devil07 Nov 29 '17 at 4:29
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    $\begingroup$ I would say your answer is in the image you posted. "cable slack take up" $\endgroup$ – DJ319 Nov 29 '17 at 11:22
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    $\begingroup$ Do you have any data justifying that the slack is at all significant? My garage door opener works perfectly both at +35C and at -40C. $\endgroup$ – Martin Argerami Nov 29 '17 at 18:17
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If you look closely at your drawing you will see the cables are not really simple pull cables but really act like steel belts. That is, there is a pulley at each end and when you actuate the control the cable is rotated around the system in a loop.

The end pulleys and or idler pulleys are spring loaded to maintain a predefined tension on the cables and should take up any slack in the system caused by operation, temperature, or aging of the cable.

enter image description here

If the top left pulley above is the yoke in the cockpit, and you turn it, the top cable rotates around the loop, like a belt, and turns the actuator bottom right. Note that also means when you turn the yoke, it does not pull significantly on the springs, the cable just rotates.

Interestingly, the Concorde had to handle both contraction and expansion. When cruising at supersonic speeds the aircraft stretched up to about ten inches.

ADDITION:

For non looped cables, and occasionally for looped cables where the cable needs to traverse between objects that move relative to one another, cable housings are also used.

enter image description here

You are probably familiar with these on bicycles. The trick to them is the ends of the housing are attached, or anchored, to the frame somewhere. The housing is flexible so can be arranged in a loop or s-shape that can be extended or compressed as the fixed end points move relative to one another.

The control cable on the other hand always has a fixed length within the housing despite the change in the end positions.

The issue with these though is friction is high compared to pulleys, the inside of the housing can become contaminated with dirt and debris, and it is impossible to inspect the cable within the housing.

As with the looped system, a spring is still required, usually at the business end, to pull back on the cable. In the single cable case, actuating the cable from the control end also involves pulling on the spring.

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  • $\begingroup$ ..the cables are not really cables but really steel belts. Not sure what you mean by that? $\endgroup$ – Koyovis Nov 29 '17 at 4:43
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    $\begingroup$ @Koyovis it acts like a belt, they are cables, but they are looped like a belt.Looking at the image in my answer, if the top left is the yoke in the cockpit, and you turn it, the top cable pulls and rotates the pulley bottom right, the bottom half of the loop, obviously, goes the other way at the same time. $\endgroup$ – Trevor_G Nov 29 '17 at 4:47
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    $\begingroup$ @Koyovis that means when you turn the yoke, it does not pull on the spring, the cable just rotates around the loop. $\endgroup$ – Trevor_G Nov 29 '17 at 4:51
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    $\begingroup$ The Concorde is not the only aircraft handling contraction/expansion... The SR-71 Blackbird was actually leaking fuel while on the ground, since the tanks only sealed at high temperatures resulting from the extremely high speeds. $\endgroup$ – Lolgast Nov 29 '17 at 10:29
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    $\begingroup$ @Koyovis Since cable systems must be either sloppy or have high load they are always designed with high load to avoid being sloppy. Now, how do you reduce friction at high loads? Bearings. $\endgroup$ – slebetman Nov 29 '17 at 19:20
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They probably do, but there are springs that take up the slake. In fact the diagram you posted shows it. Its called the "cable slack take-up."

See the little spring in the bottom center.

enter image description here

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    $\begingroup$ So then we're not only stretching the cable but also deflecting slack-spring? $\endgroup$ – Koyovis Nov 29 '17 at 4:13
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    $\begingroup$ The tension is on the pulley, so the wheel of the pulley continues to turn just the same even if there is slightly different tension on the pulley by the spring, thus preserving the deadband at different temperatures/cable lengths. $\endgroup$ – Devil07 Nov 29 '17 at 4:40
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Cables can only transfer tension loaded forces, that is why we need two cables in order to be able to deflect into two directions: the control cables going from the cockpit to the control surfaces can be seen as a loop, as Trevor correctly identifies.


Sloppiness

Own work, could be better

Cables also stretch, and for applying remote loads that is a disadvantage. The cable stretch is in series to all the dynamic and static behaviour of the flight controls: mounting a sloppy cable results in vague and inconsistent stick behaviour, and a feel as if the pilot is stirring in a pot of soup. The feel spring stiffness is diluted by the cable stiffness, and can never be higher. Cables must have high stiffness, so let's tension them up, let's give them a high pre-load.

However, putting a high pre-tension on the cables causes high structural forces. The cables run over pulleys, which are mounted on a bearing fastened to a structural member. One bearing. So the pulley loads the bearing with a torsional load and the cable tries to skew it, not a good situation for a cable run. It might run off the pulley and get stuck, resulting in an aircraft that cannot be controlled and a crash. Unfortunately everything in an aircraft must be light and bendy and we cannot beef up the bearing housing.


Two-sidedness

So we cannot put a very high pre-load on the cable. But a certain amount of pre-tension is beneficial:

  • Cables only pull, and the cable not pulling may not be slack, otherwise it could run off as well.
  • Pre-tensioned cables can provide push loads, by reducing the pre-tension it was subjected to.

enter image description here


Variability

An aircraft is a structure subjected to a variability of loads:

  • Wing tips bend upwards during flight, bend upwards more when fuel runs out, and slam down at landing.
  • As mentioned in the OP, the structure expands and contracts as a function of temperature. Thermal expansion is 23.1 µm/(m·K). A 747 is 70 m long, temperature differences of 90 °C can be reached, so the resulting stretch is 15 cm. Steel cables stretch half that amount, and the total cable run is differs 7 cm from the temperature alone.
  • During flight, the elevators & tail plane put up/down loads on the fuselage as well, bending it up/downwards. Ailerons bend the wings more or less.
  • During turbulence, the wings flap up and down.
  • After spending 12 hours at -60 °C at cruise altitude, the fuel in the wing is very cold and only the lower wing skin is exposed to it. The upper wing skin is exposed to the sun, and upon approach gets warmed up more and more: upper skin stretches because of the heat, and the wing tip comes down by a surprising distance.

So all in all, the flight control cables must accommodate a difference in length that in a large aircraft is in order of magnitude of 10-20 cm. The control cable has a diameter of 3-5 mm. Steel elastic modulus is 200 GPa, a stretch of -0.2/70 m/m causes a tension of 500 MPa, twice that of structural steel, and a force of 4,000N (800 lb). Way too much. Yes you can increase the cable thickness with associated heaviness, but best to reduce the pre-load to the level where the non-pulling cable still has some tension.


The solution

We want some pre-tension in the cable loop, but not too much. We want it to not vary with varying length and bending, it must be always constant. And we want high differential stiffness: nice and easy springiness when not deflected, very high stiffness when deflected. What to do?

enter image description hereImage source

The solution is indeed in applying a spring, but not one that is attached to the aircraft structure:

  • The "wheel" is not a multi-rotation unit, but two cable quadrants that deflect about 40 degrees each total.
  • Springs pull them towards each other when no load is applied, when the pilot does not apply a force to the stick.
  • A blocking mechanism prevents the two halves from moving relative to each other when the pilot does apply a force. A more detailed description is found in the image source above.

So while the flight controls are trimmed, the cable is tensioned nicely and accommodates varying circumstances. When forces are applied, this mechanism is partially blocked, only lightly when light forces are applied.

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    $\begingroup$ 'Cables must have high stiffness, so let's tension them up, let's give them a high pre-load." Preload makes sure that the stiffness of the cable is present regardless of input force (as long as the pre-load is higher than the input force), it does not add additional stiffness. Also, could you give sources for your information and diagram? I'm really curious how and why this blocking mechanism is present. $\endgroup$ – Sanchises Nov 30 '17 at 8:18
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    $\begingroup$ @Sanchises Total effective stiffness is higher when preloaded because the non-pulling cable contributes to the force transfer, effectively doubling the cross sectional area. The source of information is a uni lecture from long ago, sadly I don't have the books anymore. Have added the image source. $\endgroup$ – Koyovis Nov 30 '17 at 8:24
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    $\begingroup$ I was confused for a second because you used the phrasing 'high preload', suggesting that a higher preload causes a higher stiffness (I would suggest 'high enough preload'). Thanks for the image source, but if I interpret it correctly, there is no brake, but a simple kinematic mechanism (a link and a spring) that prevents relative rotation between the quadrants. I suppose the brake mechanism you refer to is similar to the patent you linked, which completely decouples the control surface in case of a cable breaking. $\endgroup$ – Sanchises Nov 30 '17 at 9:15
  • $\begingroup$ @Sanchises the image is used as an illustration. $\endgroup$ – Koyovis Nov 30 '17 at 9:50
  • $\begingroup$ But I still don't know what a drum brake would accomplish. Are you sure you're not referring to e.g. the trim tab drum brake like described here? $\endgroup$ – Sanchises Nov 30 '17 at 11:14
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They do. See http://www.billzilla.org/aviationpage3.html, in particular:

After a few hours in the cold atmosphere cruising along, the throttle cables that run from the bottom of the throttle all the way out to the engines all shrink slightly different amounts, and so to get the same RPM's you often have the throttles sitting at odd angles to each other. This is what they looked like on descent from 37,000' one day.

enter image description here

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    $\begingroup$ What was the maintenance status of this aircraft? $\endgroup$ – Koyovis Dec 2 '17 at 2:30

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