What open-loop control inputs can guarantee non-divergent descents in fixed-wing aircraft?

Question

(Inspired by What's the best way to get through clouds when not instrument rated? which has at its heart a good question, but isn't getting good answers because everyone is jumping on the "don't be an idiot" bandwagon. That's generally good advice, but not salient to the question.)

Non-instrument flight into IMC happens. Sometimes because people are manifestly idiots, other times because of momentary inattentiveness, sometimes because instruments fail, and yet other times because of surprising meteorological conditions[*][**]. Knowing that no amount of planning and execution can ever guarantee we will have one of either function instruments or a visible horizon, it would be a useful arrow in our quiver to know what kind of open-loop control inputs could guarantee a stable descent.

• I've oftentimes half-joked that the safest way to get through a layer of IMC in a Citabria is to enter an immediate spin. Even a flat spin is quickly recoverable in the 7ECA, so the real concern is avoiding a graveyard spiral. Obviously, the spin remedy is not universal.
• Some gliders will enter into a gentle bank when hands and feet are taken off the controls and the airbrake are extended. Some will continue to bank and enter into a graveyard spiral (the AC-5M is an example of this).
• A slip was thrown out as an idea, and I can see a lot of merit to full deflection cross-controlled rudder and aileron while maintaining an airspeed which is north of stall and south of Vne.

Questions:

• What are the sets of known open-loop control inputs which can result in non-divergent descent?
  • The best answer to this question is a catalog of inputs which have been shown to work on specific airplanes, not a specific control which can work on all airplanes.
  • To help frame this question, let's allow that a recoverable spin is considered to be a non-divergent descent. The maneuver does not diverge without active inputs, and can be entered into without reference to the horizon.
• What is the best way to determine which, if any, of the above are applicable to a specific airplane?
  • Are there general guidelines, and do these guidelines vary based on fuel and baggage loadout (e.g. tip tanks full vs empty, c.g. forward vs aft)? Does turbulence change the optimal deflections, or just make them less effective?

Note, this is a question about pure aerodynamics. Answers pointing toward operations, preflights, calling ATC, referring to instruments to try to keep wings level, etc.. will be downvoted. Those are are useful and accurate answers for a different question, but not this one.

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[*] Raise your hand if you knew that highly humid air minutes after sunset is a ripe condition for clear-air icing? I sure didn't until I found my windshield coated in 1mm of ice within 60 seconds of passing through a humid area. There was-- and continued to be out my side windows-- horizon-to-horizon visibility. It was most strange and would have been a lot scarier if I hadn't been randomly lined up on a 3mi final on the airport I was flying past.

[**] The FAA considers cloudless, nighttime, moonless flight over the ocean to (potentially) be IMC. C.f. https://www.ifr-magazine.com/technique/actual-conditions/

Answer 1

One possible solution may be to monitor airspeed/rate of descent. Lacking all other sensory input, this (aside from the parachute (for the the pilot or the aircraft)), may be one way to keep control in IMC.

Aircraft that are staticly stable will drop their nose and pick up speed until their vertical lift requirement is made. Interestingly, a banked plane does the same, resulting in a higher airspeed than one that is wings level:

banked trimmed airspeed$^2$/wings level trimmed airspeed$^2$ = 1/cosine bank angle

Unfortunately, cosine functions at low degree values are very close to 1, so that leaves rate of descent.

minimum rate of descent for a given trim is at wings level.

But which way to turn?

Perhaps one way is to enter a 1 G emergency descent spiral. Here one has plenty of airspeed and low enough AoA to avoid stalling.

Airspeed control is with ... the ailerons --> more into, less away from the turn.

Trimmed for 90 knots wings level flight:

20 degree bank = 93 knots
30 degree bank = 97 knots
45 degree bank = 107 knots

5 degree angle of descent trimmed for 90 knots:

20 degree bank = 5.3 degrees
30 degree bank = 5.7 degrees
45 degree bank = 7.1 degrees

Rate of descent trimmed for 90 knots:

0 degrees bank = 7.8 knots or 794 fpm or 13.2 fps
20 degrees bank = 8.6 knots or 869 fpm or 14.5 fps
30 degrees bank = 9.6 knots or 976 fpm or 16.3 fps
45 degrees bank = 13.2 knots or 1339 fpm or 22.3 fps

Answer 2

Given that you’re now in this situation (and what you SHOULD HAVE DONE was A PROPER PREFLIGHT PLANNING SESSION to avoid being here in the first place), you’re going to be limited by the equipment aboard the airplane.

Stuck above clouds in an aircraft certificated for VFR operations only and/or not instrument rated is an emergency situation, so take a moment to trim the airplane up and wind your wristwatch. Step two is going to be here to get all the help that you possibly can. You should immediately make contact with ATC, declare an emergency, and explain the situation. Determine how much fuel you have a board and how far you can make it from your current position before a fuel emergency happens. Work with ATC and flight services to find out whether there are breaks in the cloud layer nearby that you may be able to descend through in visual conditions. If a descent through IMC is inevitable, see if you can find areas of flat land below that do not have obstacles or hilly, terrain, and have cloud bottoms high enough above the ground to facilitate a visual recovery once you break out if needed.

If you were flying an airplane which is certificated for IFR operations and were instrument rated, this would be the best situation to be in here. In that case, you would simply request an IFR clearance to either your destination airport or an alternative airfield, if the destination is not possible.

Flying an IFR certificated aircraft without an instrument rating at least gives you the required equipment aboard the aircraft to have the best chance of this. In this situation, and also in accordance with ATC instructions, I would do the following steps:

• Pick a medium speed, cruise power setting. For example, 2100 RPM, 24” MAP/2400 RPM, or similar. Check your manufacture, approved, airplane flight, manual for the aircraft to fly and select from what they recommend.
• Trim the aircraft as needed to neutralize control pressures.
• Hands off the yoke or stick.
• Keep the turn coordinator centered using rudder pressure alone - center needle. DO NOT CENTER THE BALL.
• Configure the aircraft for approach. Lower the landing gear, if so, equipped. Flaps to be set an approach setting.
• maintain directional control with your feet. Center needle.
• Trim the aircraft is needed to maintain altitude. Center needle.
• To begin your descent, to begin your descent, reduce the throttle setting slightly. The aircraft should maintain approximately the same airspeed throughout the descent - center needle.
• At all times throughout the descent, maintain a constant attitude and heading, keeping the term coordinator needle centered using rudder pressure only.
• Once you break out of the clouds and are back in Visual conditions, you may resume normal operation of the airplane. Do not attempt to re-enter IMC.

Aircraft that are not certificated for IFR flight operations are going to present more difficult challenges for the pilot. How difficult it is is largely dependent upon what equipment is aboard this airplane. Antique aircraft was very limited. Cockpit instrumentation may make it almost insurmountable to descend through IMC and still maintain control over the aircraft. If the aircraft happens to be equipped with a turn in bank indicator, a turn coordinator, or a AHARS driven EFIS, the procedure above can be followed for maintaining control during the descent.

Spins through cloud layers, and IMC have been done in the past. In the 1920s it was standard procedure for US air mail pilots in case they ended up in such a situation. Survivability using that method depends on several things:

• The spin worthiness of the aircraft.
• Altitude lost during recovery
• Altitude in which the pilot breaks out. This technique is not workable and low IMC or in fog.
• Pilot skill.
• This technique is only applicable during daylight conditions.

Again, the stuff isn’t magic. And it should never be considered normal flying practice; this is meant for use only in dire emergencies were no other alternatives exist for the pilot.