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In the specific context of the sudden failure of one engine, would twin-engine airplanes (with wing-mounted engines) be safer if designed with minimal dihedral, so that aerodynamic coupling between sideslip and roll torque was minimized? (In the case of swept-wing aircraft, or high-wing aircraft, that might actually require some anhedral (like the Tupolev Tu-104).

If not, why not?

If a specific example is needed, then take for instance the Beechcraft King Air, but the question is not intended to be limited to that. Swept-wing designs are also of interest.

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  • $\begingroup$ OT but I was typing an answer for the guy that posted the Piper Cub question before it was deleted. What he saw was a Cub with a left side door mod, which incorporates the throttle into the same spot it was without the door, using a mechanism to transfer its movement to the throttle linkage when the door is closed. Left side doors are done on Cubs, and Citabrias/Champs, for operating on floats so you can get out either side. It becomes a big deal when you can only approach a dock from one side due to winds or space constraints. I owned a Citabria on floats with the single right side door. $\endgroup$
    – John K
    Mar 2, 2023 at 20:09
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    $\begingroup$ @JohnK-- thanks, was wondering where that question went-- kind of a shame, that would have been a worthwhile answer- $\endgroup$ Mar 3, 2023 at 1:29
  • $\begingroup$ I've created a chat room intended for discussion of all aspects of the current question, including any answer-- I've copied one comment chain under another answer over there already-- chat.stackexchange.com/rooms/144335/… $\endgroup$ Mar 3, 2023 at 17:39

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When flying single engine in a twin, the normal technique is to apply ~5 deg of bank into the live engine. This actually cancels dihedral effect because the offsetting force of the rudder, being applied to keep from turning, prevents the plane from sideslipping toward the low wing, and without sideslip, dihedral effect can't work.

You are actually flying along straight through the air, that is, no sideslip, and if there is a yaw string on the windshield it will be straight, even though the wing of the live engine is low because the rudder application is "holding the plane up" on an inclined plane (the bank) you might say.

If you don't apply the bank into the live engine, the lateral rudder force being applied to keep the nose pointed straight results in the plane sideslipping toward the dead engine with wings level. Dihedral effect will create a rolling moment the opposite way, toward the live engine, and to hold the wings level you will actually be holding a small amount of aileron into the dead engine as you slew along. Bad news all around.

So the proper steady state coordinated flight condition for a straight wing twin is non-side slipping flight, which means dihedral effect is not even a factor, while slightly banked. This is why when you are correctly configured, the ball will be pointing at the ground, which because you are banked a bit, means it's offset in the tube by the amount of bank, say half a ball width.

So the result is you still design for the dihedral effect you want for desirable lateral stability in normal flight.

In fast swept wing airplanes (at least in the CRJ - guys here who fly heavies with wing mounted engines may have something to say) you didn't try to lower the wing into live engine; you just kept wings level and the brick (skid ball) centered. I was never able to find out exactly why banking into the live engine wasn't necessary, but I think that with the thrust reserve you have with a jet while single engine, it wasn't worth the effort to hold the bank because the moderate sideslip you get with tail mounted engines wasn't worth correcting for.

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  • $\begingroup$ The combination of offset thrust forward, and lateral thrust applied by the rudder to prevent a yaw into the dead engine, results in a resultant thrust vector that is, say, 10 deg into the dead engine with wings level. Banking into the live engine tilts the lift vector, introducing an offsetting lateral thrust vector. If the thrust was symmetrical, the tilt initiates sideslip, which the fin coverts into a turn. The thrust being asymmetrical, with a lateral thrust being applied by the rudder, the sideslip tendency offsets the rudder's lateral force, and you fly straight even though banked. $\endgroup$
    – John K
    Mar 3, 2023 at 15:18
  • $\begingroup$ The instinct during multi-engine training is, engine quits, you apply rudder to stop the yaw, and bank 5 deg into the rudder application. It becomes automatic. You glance as the ball, and it should be sitting offset in the vial appropriate to the 5 deg bank angle, indicating no lateral acceleration is happening. 5 deg is a ballpark number that gets you close enough; the precise value for a given airplane may be 4, or 6, or whatever. If the plane has a windshield yaw string, you just straighten it. Doing this correctly can mean the difference between climbing and descending in a piston twin. $\endgroup$
    – John K
    Mar 3, 2023 at 15:26
  • $\begingroup$ That makes sense-- $\endgroup$ Mar 3, 2023 at 15:27
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    $\begingroup$ I appreciate the reply to the lengthy comments-- I think there are some subtle points here about what we are really accomplishing by slightly banking the aircraft toward the good engine-- copying all comments to chat room chat.stackexchange.com/rooms/144335/…, feel free to post any more thoughts-- thanks $\endgroup$ Mar 3, 2023 at 16:52
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For a GA twin with one failed engine, the difficulty one always hears about is yaw authority: can the fin and rudder at least prevent the airplane from circling?

Yes, if sideslip is needed to maintain course, less dihedral means less roll. But aileron authority isn't reduced with one engine out, so correcting for roll should be easy. Certainly less of a safety concern (even within the realm of pilot workload) than managing the airplane's reduced performance and finding where to land.

(John K mentions examples where quite a bit of aileron is needed.)

Over all the durations of all the flights made by the whole fleet of a type, overall safety is likely optimized by choosing the dihedral that's best for the most common flight regime: both engines running.

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Here it is important to differentiate between wing "dihedral", which is there for roll stability, and "dihedral effect", which (including wing dihedral and all side area above the CG$^1$) affects roll tendency in a slip.

removing wing dihedral is probably the worst way to reduce dihedral effects

Now, let's see what a 5 degree bank angle does with a twin engine aircraft losing one engine.

banking the plane causes it to slip to the side it is banking.

This has a beneficial effect of creating side pressure on the tail: a yaw torque into the live engine. This enables rudder input to be reduced.

what about heading?

We actually need to create a forward slip to maintain heading. Very safe, stable configuration, but, as John K pointed out, not the best for long distance due to higher drag. Perhaps better (depending on model) to use rudder to compensate for live engine yaw and hold fuselage straight for fuel economy, at the expense of reduced available rudder travel into the live engine (for turning)$^3$.

Would reducing wing dihedral make it "safer"?

From the standpoint of rolling tendency in a slip vs available roll control, a better approach much be to increase roll control authority with larger ailerons and/or spoilers, and to seek, in design, to minimize excess dihedral effect$^4$.

It was heartening to learn the Tu-104 also suffered Dutch Roll, even with wing anhedral$^2$.

$^1$ items that create greater (lateral) yawing and rolling force, such as T-tails, large and tall vertical stabilizers, and fillets must be carefully considered.

$^2$ see the more "traditional" Tupolev Tu-114

$^3$ maintaining adequate airspeed is critical

$^4$ see B-52 Stratofortress

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  • $\begingroup$ @quietflyer generally, if it banks that way its gonna move that way. But thanks for creating chat. I will check it out. $\endgroup$ Mar 3, 2023 at 17:10
  • $\begingroup$ Banking HAS to create a slipping tendency, because banking tilts the lift vector. The slipping is the lateral movement in reaction. If airplanes didn't have vertical fins, they would turn by sliding sideways, like a helicopter moving sideways in hover when the rotor disc is tilted. The "turn" only happens because the fin keeps the body weathervaned into the stream as it moves laterally, resulting in an arc. $\endgroup$
    – John K
    Mar 3, 2023 at 18:08
  • $\begingroup$ I've copied all comments above over to the chat room chat.stackexchange.com/rooms/144335/…, and deleted my own. Among other things they address whether or not banking really creates a significant slipping tendency in general, versus in the specific case where the pilot is using the rudder as needed to hold heading constant. -- further discussion there is welcome-- Robert DiGiovanni has also posted some new content there. $\endgroup$ Mar 4, 2023 at 16:18

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