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I've noticed on many military and commercial jets, the trailing edge control surfaces (ailerons and flaps) are separate from each other.

Why is this? Can't both serve the same function? It would save weight and complexity if one combined control surface ran the length of the trailing edge, instead of being split in half.

A particular example I found is the F-102 Delta Dagger. There's no conventional tail to experience disrupted airflow, so why have separate ailerons and flaps?

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A similar idea that I know exists is the V-tail, such as in the F-117, which has "ruddervators"---combined elevators/rudders. It can still control yaw and pitch at the same time by somehow averaging the deflections. Presumably, combining and averaging ailerons and flaps should be even simpler, since they're both deflecting on the same axis.

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Same reason you have split ailerons on most big airliners. The inboard surfaces deflect at higher speeds and the outboard ones are locked, reducing the twisting (torque) forces on the wings. It also allows for finer control (in fly-by-wire cases) as well. Like a lever, a small deflection of the outboard surface results is higher rate pitch/roll (in this delta wing elevon example) compared to same deflection of the inboard surface.

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There is no "usually" here. For every aircraft with split control surfaces you come up with, I believe it would be possible to come up with an aircraft that either has one combined control surface (eg F-16 has flaperons), an aircraft that has some kind of a combination (eg F-18, which has an inboard flap and an outboard flaperon as can be seen here - warning headphones users -

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or even an aircraft that doesn't even use ailerons (eg F-14, that only uses elevons and spoilers on the top of the wing for roll authority).

What you may consider to be less complex structurally might end up being more complex as much as the Fly-By-Wire software logic is concerned.

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    $\begingroup$ What you may consider to be less complex structurally might end up being more complex as much as the Fly-By-Wire software logic is concerned. Well okay but I'm pretty sure saving weight and moving parts at the exchange of a more complex software is acceptable these days with the kind of computers we have. For the record, I wasn't thinking of anything with an all-moving tail. I wasn't thinking of elevons. I was thinking of flaperons or any long control surface on the wing itself, because presumably the wing is big enough to hold a large combined control surface. $\endgroup$ – DrZ214 Jun 8 '16 at 1:02
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It would save weight and complexity if one combined control surface ran the length of the trailing edge, instead of being split in half.

If the trailing edge real estate is there, it makes sense to split control surfaces along their functionality. The issue is maximum deflection: at full flaps, a flaperon cannot command any additional aileron down input. Combining two or more surfaces poses issues such as identified in this answer.

Having said that, combining control surface functionality and applying computer controlled functionality means that the flight controls can be reconfigured, in case of battle damage for instance. That would increase weight and complexity, and also redundancy and survivability.

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