3
$\begingroup$

I'm writing a simulation of a flying wing and I need clarification on some of its behavior.

Specifically, the simulation suggests to me that a flying wing (or any tailless aircraft) with two single elevons along the whole of the two trailing edges is not controllable. If the elevons are deflected to pitch up, for example, it generates negative lift over both wings and the torque (assuming CoG is ahead of CoL) pitches the aircraft up. But this rapidly increases AoA and therefore lift and positive torque, pitching the aircraft back down until it stabilizes at Cl = 0 (steady state AoA depending on elevon deflection) because Cl = 0 is the steady state where no torque exists. However, it also generates no lift and the aircraft naturally crashes.

This result makes sense to me mathematically, but I struggle to observe this in real aircraft.

In a conventional aircraft the elevator is much farther back than the main wing and can balance the torque at a positive sum of the lift vectors. On a tailless delta aircraft with split elevons, the set of elevons towards the wing root have a CoL different from the elevons near the tips, which would allow small effective Cl according to the logic above. But this seems barely controllable to me and only reliable at high speed to compensate for the abysmal Cl.

Am I making a mistake? Is this really how it works?

$\endgroup$
6
  • $\begingroup$ Surely pitching upward moves the CoL towards the leading edge, does it not? $\endgroup$
    – Frog
    Apr 28 at 10:06
  • $\begingroup$ Flying wings are normally swept, including the trailing edge, and the elevons are at the tips only. But I am not sure how it works for tailless delta either. $\endgroup$
    – Jan Hudec
    Apr 28 at 11:47
  • $\begingroup$ @Frog But not ahead of the CoG, right? So the sign of the torque will not flip. $\endgroup$
    – fnd
    Apr 28 at 11:47
  • $\begingroup$ "CoL"-- it is unclear what you mean by this. Do you mean the Center of Lift of the wing itself, excluding the effect of the deflected elevons? Or the Center of Lift of the whole aircraft? Are you using the Center of Pressure concept where the entire effect of the lift vector is expressed by assuming it acts at the Center of Pressure? (In contrast to the more modern concept of an Aerodynamic Center that remains stationary, plus a pitching moment coefficient? $\endgroup$ Apr 28 at 13:42
  • $\begingroup$ I was using it in the Center of Pressure sense. Since the elevons are across the whole wing and this is discussing pitch, the wings are symmetric and elevon deflection just moves the aircraft CoL around. $\endgroup$
    – fnd
    Apr 28 at 13:58
5
$\begingroup$

Specifically, the simulation suggests to me that a flying wing (or any tailless aircraft) with two single elevons along the whole of the two trailing edges is not controllable.

This is certainly not true. Many radio-controlled model airplanes and gliders with an all-wing, chevron-shaped configuration and no tail have this exact configuration of the elevons, which are the sole control surfaces.

enter image description here

For example, in the photo above, the elevons are red.

Google "Zagi flying wing" for many more examples.

If the elevons are deflected to pitch up, for example, it generates negative lift over both wings and the torque (assuming CoG is ahead of CoL) pitches the aircraft up.

This is not true either. When flying a wing like this, an aft stick input generates a nose-up pitch torque that increases the angle-of-attack of the wing. In the long run, the wing's lift coefficient is increased, not decreased. There is no visible evidence of even a temporary tendency for the aircraft to "settle" (accelerate downwards) when the elevons are first deflected upwards, before the wing has had time to rotate to a higher angle-of-attack, though in theory this tendency must exist to some slight degree due to a temporary decrease in the wing's lift coefficient (but not to the extent that it actually becomes negative). This "settling" tendency might be more significant if the aircraft's pitch rotational inertia were greater.

Conceptually, this is no different than the idea that when we are flying a "conventionally" shaped aircraft, and we move the control stick aft, there must some temporary "settling" tendency (downward acceleration) due to the fact that we've increased the downforce (or in some cases, decreased the upforce) generated by the tail, so the net upward lift generated by the aircraft is now less than weight. Of course, this situation only persists until the aircraft rotates in the nose-up direction enough to increase the angle-of-attack of the wing sufficiently to bring everything back into balance, at a higher angle-of-attack and lower airspeed than were present initially. In actual practice, this "settling" tendency is almost always so negligible as to be undetectable.

It might help you understand what is going on if you were to consider reflexed airfoils. In such an airfoil, the trailing edge of the airfoil is permanently "bent" upwards, contributing a nose-up pitch torque, yet the airfoil still creates positive lift over a wide range of angles-of-attack.

For example:

enter image description here

(Source: https://www.diva-portal.org/smash/get/diva2:450812/FULLTEXT01.pdf )

It appears you are getting into trouble by relying on the idea that the Center of Lift is behind the Center of Gravity. In reality, the Center of Pressure is not fixed, and in steady-state flight, the Center of Pressure (of the whole aircraft including the contribution from the elevons) and the Center of Gravity must coincide. When we raise the elevons to create a nose-up pitch torque, this pitch torque can be conceptualized as a forward shift of the Center of Pressure. Then when the wing rotates to a higher angle-of-attack, the Center of Pressure moves back aft until it coincides with the CG again, and the aircraft ends up in steady-state flight at a higher angle-of-attack and higher lift coefficient and lower airspeed than it started with.

A more modern way to think about aerodynamic forces and torques is to view the aircraft as having an Aerodynamic Center that is fixed at the quarter-chord point of the airfoil, plus a pitching moment coefficient that varies according to the shape of the airfoil. With this convention, the lift vector can be viewed as acting at the Aerodynamic Center, but we also have to consider the effect of the pitching moment coefficent. Raising the elevons shifts the pitching moment coefficient in the nose-up direction, as well creating some decrease in the lift coefficient. A symmetrical airfoil has a pitching moment coefficent of zero, and conventionally shaped cambered airfoil with no reflex has a nose-down pitching moment coefficient.

$\endgroup$
7
  • $\begingroup$ Right, I was expecting to be wrong because the simulation did not seem realistic to me. But I don't see what precisely the mistake is. Why DOESN'T the aircraft go into a steady state wherever Cl = 0 is? $\endgroup$
    – fnd
    Apr 28 at 13:33
  • $\begingroup$ "This is not true either. When flying a wing like this, an aft stick input generates a nose-up pitch torque that increases the angle-of-attack of the wing. The wing's lift coefficient is increased" This cannot be. An upwards elevon deflection reduces lift on the wing from an airfoil PoV (ignoring AoA for now). Textbooks say that too and you can also see it in XFLR5. $\endgroup$
    – fnd
    Apr 28 at 13:42
  • $\begingroup$ @fnb -- content added-- may help? $\endgroup$ Apr 28 at 14:01
  • 1
    $\begingroup$ What might have been missing to begin with is that the center of gravity is displaced forward of the center of lift to produce stability -- so absent a swept/twisted wing (like some Lippisch designs, or a Klingberg Wing -- or split surfaces, with primarily elevator at the tips and mainly aileron near the roots -- either airfoil reflex or elevon deflection is necessary in steady state to produce longitudinal stability. Those special cases just divide up which part of the wing is doing what job, of course. $\endgroup$
    – Zeiss Ikon
    Apr 28 at 14:21
  • 5
    $\begingroup$ The elevon is creating a localized downward lifting force that subtracts from but doesn't eliminate the overall lift force. It's just doing the same job as a tail surface, just nestled right up against the wing. The moment arm is really short, but the balance of forces for trim is the same. $\endgroup$
    – John K
    Apr 28 at 14:27
2
$\begingroup$

I’m a bit rusty on my aerodynamic theory but having flown the Avro Vulcan B2 for several years I can assure the that a delta wing with elevons works very well! The only slightly unconventional handling trait was the ‘flap effect’ if you pushed the stick forward on finals and suddenly got a bit of extra lift!

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.