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It's a well known fact bridges can break due to self-amplified oscillations creating excessive loads on their structure, by resonance (galop). It happens from time to time. The Tacoma-Narrows bridge catastrophic failure is popular, but there are modern and less known stories about wind/rain creating a problem which needed to be solved after the bridge opening.

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US Tacoma-Narrows bridge collapse in 1940, source (video)

A wing and a bridge roadway have similarities, and they are both exposed to a transverse wind.

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Several aircraft in flight with flutter, source (video)

How are wind/rain/resonance-created oscillations (flutter) managed in airplane design? How are these effects tested in flight?

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  • $\begingroup$ Related, maybe a dupe? $\endgroup$ – Pondlife Oct 27 '17 at 21:19
  • $\begingroup$ @Pondlife, related for sure :-) but not a dupe as this was calling for a generic information. I'm expecting something about Dutch roll, flexing design, and flight-test safe testing method. $\endgroup$ – mins Oct 27 '17 at 21:25
  • $\begingroup$ youtube.com/watch?v=qpJBvQXQC2M $\endgroup$ – abelenky Oct 27 '17 at 21:32
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    $\begingroup$ Possible duplicate of What is the purpose of flutter testing? $\endgroup$ – Koyovis Oct 28 '17 at 22:45
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    $\begingroup$ @Koyovis: Correct! $\endgroup$ – mins Oct 29 '17 at 8:59
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Flutter happens when the eigenfrequencies of two oscillations move close together so their motions can reinforce themselves mutually. When that happens, then the amplitude will increase with each oscillation, up to a point where the amplitude is big enough to break things. That is how bridges are destroyed: Ever more energy is accumulated in the structure, a tiny bit with every oscillation, until the total overwhelms the strength of the weakest part.

If the two eigenfrequencies are not close enough together, both motions will still exist but will normally be damped so they die down quickly after being excited, e.g. by a gust. A typical example is the wing bending motion: When the aircraft flies into an updraft, the wingtips flex up, elastic energy is accumulated and set free once the extra lift from the updraft dies down. The wingtips move down and will very briefly oscillate around their long-term vertical position.

Now add a free-flying aileron (mechanical control system with stick free). This also can oscillate around its long-term deflection angle. As long as the eigenfrequencies of both motions are sufficiently apart, they will not interact. This should be ensured throughout the normal flight envelope. However, flying faster will increase the aileron eigenfrequency, and in this case we should focus on the first antimetric bending motion of the wing. At one point the aileron frequency will come close to the wing bending eigenfrequency, and only then this particular flutter mode will happen.

The glider in the second picture of your question is the SB-9, a longer-span version of the SB-8 (which itself is flutter-free). The added span moved the wing eigenfrequencies down, so they met with the aileron frequency at a lower speed. Now flutter could be observed when flying at the right speed, but it could be stopped simply by gripping the stick.

Therefore, the possible protections against flutter are:

  • Limit the flight envelope. Prohibit flight speeds at which flutter is possible.
  • Increase damping. This can be as simple as adding some friction. The rudder cables in gliders are run in PE tubes which add some friction, eliminating rudder flutter.
  • Increase eigenfrequencies by increasing stiffness. In the SB-13 flying wing glider high modulus carbon fiber was used in the spar to shift the wing's eigenfrequency sufficiently up to avoid a coupling of the wing bending mode with the short period mode of the airplane
  • Increase eigenfrequencies by mass reduction: When a wing is made lighter especially towards the tips, e.g. by clipping the wing tips, its eigenfrequency will move up, shifting flutter speeds up. Conversely, by adding wingspan to the sound SB-8 design, the eigenfrequency of the SB-9 wing went down.
  • Change eigenmodes: By running the aileron pushrods near the wing shell, wing bending can effect an aileron deflection which helps to dampen the wing's bending mode.
  • Cross-coupling of eigenmodes: By reducing the wing spar sweep of the SB-13 by 3° relative to that of the whole wing, the bending motion causes wing torsion which reduces incidence when the wingtips are bent up and vice versa. This is similar to the pushrod trick and is an application of aeroelastic tailoring.

In a similar way, the forward location of the engines on an airliner wing creates an inertial torsion moment when the wing flexes. This increases damping, so this example could had equally appeared in the first point.

To ensure a design is free of flutter, a range of tests is performed prior to first flight and during flight testing. From this answer:

Since maybe fifty years every new design must go through a static vibration test to check which elastic eigenfrequencies exist. Analytical methods are used to predict the (speed dependent) aerodynamic frequencies and the structure must be modified to remove any possibility of resonance. Next, the airframe is tested in flight at ever increasing speeds and with exciters at the tips of all surfaces (those can be like the vibration motor in your smartphone, only bigger, or, in the simplest of cases, the pilot moves the control surfaces). At increasing speeds, the exciters are run through a frequency sweep (typically from 5 to 60 Hz) and the resulting amplitude is measured by strain gages or accelerometers.

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Flutter is an aero-elastic problem, a complicated sort of spring-mass-damper issue. Complicated because spring, mass, damping and the applied force are linearly distributed over the wing span.

Basically, the problem is as follows:

  • The wing root is fixed to the aircraft fuselage, the wing tip is not fixed and can twist.
  • The air streaming over the wing creates lift, but also creates a twisting moment. A longish body in a fluid stream wants to position itself perpendicular to the stream, that is why we need empennages.
  • So the wing would like to position itself perpendicular to free stream - the tip is twisted by the stream, and stopped by the torsion stiffness of the wing box.
  • The torsion stiffness and the damping need to be sufficiently high to stop the construction from overshooting, and then being pulled back and overshooting, etc. Which is the failure mechanism in the video of the Tacoma Narrows bridge.

So the torsion stiffness of the cross section of the wing needs to be considered. It is mainly composed of cross section area and -shape, upper and lower wing skin thickness, and spacing of the ribs. These are the factors that need to be tuned to provide adequate torsion stiffness, but the shape and area are mainly determined by the aerodynamicists, not the structural engineers.

enter image description hereImage source

The wing is primarily dimensioned to counteract upward bending. In aircraft pre-design, some methods have been developed to estimate wing structural mass from the geometry. The original method developed by Torenbeek (Appendix C) underestimated actual structural weight, due to absence of torsional stiffness considerations in the estimation method.

The correction factor for the required structural wing weight to counteract flutter is given as:

$$ k_{st} = 1 + C \cdot \frac{{(b \cdot cos\Lambda_{LE}})^3}{W_{des}} \cdot (\frac{V_D / 100}{{(t/c)}_r})^2 \cdot cos\Lambda_{1/2}$$

For the Fokker 50 this results in a correction factor of about 4% of basic wing weight, which would be the extra weight required for preventing flutter. Notice that this is a problem where wing sweep actually helps: the sweep wants to twist the wing tip back to neutral. It also helps if the engines are mounted on pods underneath the wing, in front of the aeroelastic axis. In that case no extra structural weight is required for torsional stiffness increase

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This is flutter. The ways to counteract the flutter, as found here (section Flutter Fixes), are:

  • Move the center of gravity of the wing closer to the center of twist.
  • Raise the frequency of the flutter by making the wing stiffer and lighter (better energy dissipation).
  • Tune shape and other characteristics with the help of computer simulations or wind tunnel.
  • Set the maximal allowed airspeed below the speed at that the flutter occurs.
  • During test flight, check if there is no flutter in the flight envelope.
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The discipline that deals with flutter and other air-structure interactions is called "aeroelasticity".

Aeroelasticity analyses the dynamic modes of the structure taking into account the coupled effects of the air (that causes pressure change) and the effects of the deformed structure geometry on the flow.

Flutter is a nightmare for flight and is not simple to analyze accurately. Therefore designers keep flight regime away from predicted flutter speeds or conditions to mitigate the risk of losing the aircraft or redesigning the structure.

"Flutter survey" is the general name of the flight tests where engineers intentionally excite the relevant modes using flight test instruments, shakers, actuators; or using flight control system itself. These tests are candidates for getting out of control. Therefore there are automatic test-stop criteria and also override features in case the test crew determine any particular problem.

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