Fortunately (or perhaps unfortunately, given the number of crashes that had to occur for us to figure it out), the use of throttle manipulation to control an airliner with disabled primary flight controls (usually due to a total hydraulic failure) is fairly well established (at least in theory): symmetrical throttle advance to pitch up, symmetrical throttle chop to pitch down, advance left throttle(s) and chop right throttle(s) to yaw and roll right, advance right throttle(s) and chop left throttle(s) to yaw and roll left.1 Pitch control is fairly straightforward (a throttle increase causes an increase in airspeed, which causes the aircraft to pitch up,2 while a throttle chop causes a decrease in airspeed, which, assuming that you are not excessively close to stalling,3 causes the aircraft to pitch down). The remaining two attitude components, yaw and roll, cannot be controlled separately from each other in the air (because the rudder, which is used to deliberately uncoordinate a turn, is a primary flight control surface, and, thus, is inoperative during this discussion), but this is not a great hindrance, as they generally do not need to be controlled separately in the air unless you’re doing aerobatics (or unless... well, see below). The aircraft will generally tend to maintain straight flight, unless you happen to also have a failure of a non-centerline engine while your primary flight controls are out fishing (in which case you are both very, very unlucky and very, very screwed).4 Advancing the throttle(s) on one side and chopping the throttle(s) on the other side will yaw the aircraft towards the spooled-down engine(s), which will (as all aircraft producing net positive aerodynamic lift have positive yaw-roll coupling)5 roll the aircraft towards the spooled-down engines; reequalising the throttles will stop the yaw, but (as most large commercial airliners have rearward-swept wings, and, thus, positive slip-roll coupling)6 the aircraft will continue to roll towards the recently-spooled-down engine(s) (even as its natural weathervane stability causes it to yaw slightly back away from said engine(s)) until the aircraft is in a coordinated turn.
In contrast, an aircraft with forward-swept wings will have negative slip-roll coupling, meaning that, although it will still, initially, roll in the desired direction, as soon as the aircraft’s yaw rate decreases below a certain threshold value, it will immediately start to roll in the opposite direction, and will continue to do so as long as the aircraft has a significant sideslip angle. Unfortunately, this natural rolling tendency takes the aircraft further and further away from a coordinated turn, continuously increasing the aircraft’s sideslip angle and worsening the problem. As roll and yaw cannot be independently controlled using the engines alone,7 this presents somewhat of a problem for throttle steering on aircraft with forward-swept wings.
I can think of two potential ways in which throttle steering of a forward-swept-winged aircraft could be successfully accomplished:
Method 1: Yaw in the wrong direction to roll in the right direction
- Briefly advance the throttle(s) on the outside of the intended turn as far forward as possible, and chop the throttle(s) on the inside of the intended turn to the minimum approach setting. (Not all the way to flight idle - the engine(s) take much too long to spool up from there!)8
- As the aircraft is rolling in the desired direction, equalise the throttles, and then advance the throttle(s) on the inside of the intended turn, but only slightly more than those on the outside of the turn (in order to keep the aircraft’s yaw rate below the threshold value where the opposite rolling moments from the aircraft’s yaw-roll coupling and slip-roll coupling are equal).
- Once the aircraft is yawed slightly to the outside of the turn, retard the inside throttle(s) just enough to null the aircraft’s yaw rate and hold it yawed slightly to the outside of the turn. (The inside throttle(s) should still be very slightly further forward than the outside throttle(s), in order to cancel out the yawing moment produced by the aircraft’s weathervane stability.) The aircraft’s negative slip-roll coupling will continue to roll it slowly in the desired direction as the aircraft is held in a slight sideslip.
- As the aircraft’s roll angle approaches the desired value, equalise the throttles and let the aircraft’s weathervane stability yaw it back into a coordinated turn. (Some increase in roll rate, courtesy of yaw-roll coupling, will occur as the aircraft weathervanes back in the desired direction.)
Method 2: Yaw fast and hard, but don’t stay yawed
- Slam the throttle(s) on the outside of the intended turn forward, and chop the throttle(s) on the inside of the intended turn.
- Once the aircraft is rolled considerably beyond the desired angle, slam the throttle(s) on the inside of the intended turn forward, and chop the throttle(s) on the outside of the intended turn, in order to null out the aircraft’s sideslip angle before the aircraft’s slip-roll coupling rolls it too far in the wrong direction. (The aircraft will still roll considerably in the wrong direction, courtesy of both the aforementioned slip-roll coupling and the yaw-roll coupling as the aircraft yaws back towards the outside of the turn, which is why we deliberately overshot the desired roll angle by a considerable amount. The saving grace here is the aircraft’s angular momentum, which keeps it initially rolling in the right direction even as the two couplings work to roll it in the wrong direction; were the aircraft’s entire mass concentrated in a single point at its centre of mass, the adverse yaw-roll coupling from nulling out the sideslip would exactly cancel out the proverse yaw-roll coupling from initially yawing into the turn, resulting - when you factor in the negative slip-roll coupling as well - in the aircraft ending up rolled in the wrong direction.
- As the aircraft’s roll angle reaches the desired value, equalise the throttles.
Would either of these methods work, and are there any other possible throttle-steering methods for an aircraft with forward-swept wings? Or are forward-swept-winged aircraft uncontrollable in the lateral-directional axes using throttles alone?
1: Aircraft with neutral or negative static stability (such as a B-2 or an F-117) are impossible to control using throttles alone, as the engines cannot spool up or down rapidly enough to provide the constant control forces needed to keep the aircraft from tumbling like a leaf, which is (at least part of) why all aircraft with neutral or negative static stability are military combat aircraft with a rapid assisted egress mechanism for each occupant.
2: Aircraft with engines mounted high on the tail (such as a DC-9 or a Learjet) have the complication that a throttle increase causes an initial pitch-down moment (due to torque from their engine placement) before the aircraft pitches back up due to increased airspeed, and vice versa, but almost all large aircraft, and even most newer medium-to-small ones as well, have underwing engines, which produce a helpful initial pitching moment in the desired direction even before the airspeed has time to increase much.
3: If the aircraft’s speed is low enough for a throttle chop to stall the aircraft, then a) you’re screwed, and b) the aircraft will probably pitch down anyways, but 1) will do so much more violently than if you hadn’t stalled the thing, 2) will roll off to a very large bank angle in the process, possibly even becoming inverted (like I said, you’re screwed), and c) depending on the particular stall characteristics of the aircraft in question, and the trim setting the horizontal stabiliser was at when primary controls were lost, may actually pitch up instead, possibly all the way into a regime that is usually unrecoverable even with fully-functional primary flight controls, never mind without them (did I mention you’re screwed?).
4: A possible exception might be on an aircraft with two or more engines on each side, such as a 747 or A340 (2 engines on each wing) or an An-225 (3 engines on each wing), or an aircraft with one or more centreline engines in addition to the non-centreline engines, such as a DC-10 or L-1011 (one engine on each wing, plus one in the tail), where an asymmetric engine failure with primary flight controls disabled could be compensated for by shutting down the corresponding engine on the other side, but this would greatly degrade thrust capability (especially if the aircraft is near maximum weight), potentially resulting in an immediate or near-immediate off-airport forced landing.
5: The tendency for an aircraft that is yawing in one direction to roll into the yaw, because the outside wing is travelling faster (and, thus, producing more lift) than the inside wing.
6: The tendency for an aircraft with rearward-swept wings and a non-zero sideslip angle to roll towards the direction that the aircraft’s nose is pointing, because of various disputed effects which I will not go into here.
7: Unless you’re in a multiengine aircraft with thrust-vectoring capability, in which case the engines are themselves primary flight controls, and flying with disabled control surfaces should be little more difficult than normal flight.
8: The purpose of this step is to establish a nonzero roll angle in the right direction, so that the aircraft doesn’t end up rolled in the wrong direction - and, thus, turning in the wrong direction - during the subsequent steps.