# Dynamic Stability

## An airplanes dynamic stability can have a major impact on whether it makes a good instrument platform. Heres how you can measure yours.

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by Greg Lewis

In this third in a series of articles exploring what makes an aircraft good to fly on instruments in weather, well address aircraft dynamics. Our first two articles discussed static stability (pitch stability, July 2004; lateral-directional stability in September 2004).

Static stability is about what initially happens if an aircraft is disturbed from some steady starting point. The example used was the ball in a cup, as shown below. If the black ball starts at the bottom of the cup and is then moved up the side and released, the ball will start moving downhill back towards its starting point. Thats a definition of static stability: An object displaced from equilibrium initially tends to return towards equilibrium.

By contrast, dynamic stability is about the longer term behavior of a system if left alone after being released from a disturbance. Mathematically, there are two broad categories of dynamic response: oscillatory and non-oscillatory. If the response does not oscillate then the system will either return towards equilibrium and stop or diverge steadily away from the initial condition. This would happen if the system was statically unstable, as could be demonstrated by placing a ball on top of an inverted cup.

Oscillatory responses can be thought of as the behavior of a weight suspended from a spring, as pictured in the diagram below. If the damping is low, then the weight will oscillate freely for a long time. If there is a lot of damping or friction in the system, then the springs oscillation could die out quickly. And if something adds energy with each oscillation then the system could diverge.

Aircraft have five different dynamic motions, three of which can be oscillatory. In this article well focus on these three oscillatory modes, the ones that can have a significant impact on the way a pilot perceives the flying qualities of the aircraft, especially when trying to accomplish a high-gain task, such as flying precisely in bad weather. As in our previous two articles, well describe ways for the non-test pilot to qualitatively assess their own aircrafts stability characteristics, this time with respect to dynamic stability.

Short Period
The most important oscillatory mode is called the short period mode. It is a dynamic mode in the pitch axis with a frequency on the order of one cycle each second.

It is important that this mode be highly damped for a good-flying aircraft. Imagine the problems you would have each time you made a pitch change (e.g., rotating for takeoff, lowering the nose to intercept the glideslope on an ILS final, flaring for landing, etc.) if the aircrafts nose oscillated up and down multiple times like a weight on a loose spring!

The FAAs certification regulations recognize the importance of this characteristic, so all FAA-certified aircraft are required to have a highly damped short period mode. The term highly damped is not rigorously defined by the FAA, but two observable overshoots after a disturbance is generally considered the most that should be seen if the mode is to be considered acceptable. In fact, its pretty rare for an FAA-certified aircraft to exhibit any noticeable overshoots at all.

In previous articles we stressed the importance of the center of gravity (CG) on static stability in pitch, with an aft CG being the least stable and the aft limit being the critical case for testing. The CG position will also affect the dynamic stability in pitch.

You can think of the CG position being the factor that determines how strong the spring is in the weight, as illustrated in the sidebar on the opposite page. If the CG is forward, the spring is strong; if it is aft, the spring is weaker. However, strong or weak springs dont have an overwhelming effect on how many overshoots youll see. Instead, the damping of an oscillating system is determined by more factors than just how strong the spring is. Which means that the FAA will want to see that the short period mode is highly damped at all CGs for certification. When doing in-flight testing of your aircraft, any CG within the published envelope is adequate for a qualitative assessment.

Long Period
A less important dynamic mode in the pitch axis is a longer period, slower oscillation, called the phugoid mode by aircraft designers. Interestingly, the word phugoid is Latin for to flee. The aerodynamicist who named the mode didnt know his Latin well. He thought it mean to fly, but the term is now entrenched and were stuck with fleeing.

Whereas the short period mode is a quick oscillation in angle of attack at nearly a constant airspeed, the long period mode is slow oscillation in airspeed at a nearly constant angle of attack. Because of its long duration, the phugoid mode is easily controlled by the pilot. But a lightly damped phugoid will require more pilot inputs and thus can make the aircraft less pleasant to fly in high workload situations-like approaches in bad weather.

The period of the phugoid is directly proportional to the true airspeed. At a true airspeed of approximately 150 kts, a typical period might be 30 seconds for a single oscillation. A high-speed aircraft like a fighter or transonic transport might have a phugoid period that takes 90 seconds or even two minutes for one oscillation. At the other extreme, a paper airplane exhibits a phugoid oscillation in pitch with a cycle taking on the order of three or four seconds. The symptom is speed change and the worst case would be quicker changes; these happen at lower speeds, so the most important phugoid assessment would be in the approach configuration, trimmed for normal approach speeds.

Most aircraft have very lightly damped phugoid modes. Poorly damped phugoids are acceptable for FAA certification because they dont typically pose a threat to flight safety. In fact, FAA criteria basically state that the mode must not lead to a dangerous condition, which leaves open a lot of room for interpretation. But if the mode is not divergent, then certainly it is not dangerous. And even if it were slightly divergent, the amount of time that a pilot would have to ignore his or her airplane before it led to a dangerous condition would be exceedingly long. Even so, it will make the pilots job easier if the mode is convergent.

You can tell if your aircraft is convergent pretty quickly by noticing the peaks and valleys of the airspeed variations during the free response. If the oscillating minimum speeds are getting higher and the maximum speeds are getting lower, then the mode is convergent. A graph of speed versus time will probably look something the following for a lightly convergent phugoid:

Dutch Roll
The last oscillatory mode to discuss when considering dynamic stability is called the Dutch Roll mode. This is a combined lateral and directional oscillation reminiscent of the motion an ice skaters shoulders make while skating: rolling and yawing at the same time. Almost all general aviation aircraft have lightly damped Dutch Roll characteristics making precise instrument flying more difficult than it needs to be.

The Dutch Roll mode can be excited by either rudder or aileron inputs. And a little turbulence will excite it as well. A single cycle will typically take three to four seconds, and the number of overshoots can commonly be eight or more. All this means that it can seemingly take forever for a Dutch Roll oscillation to dissipate. Meanwhile, the aircrafts heading is bobbing back and forth and the passengers in the back are swaying around. In extreme cases, they may be feeling a little ill. In larger aircraft yaw dampers are installed to damp out this mode, improve ride quality for paying passengers and making it easier for the pilot to fly precise approaches.

The FAAs certification requirements for Dutch Roll characteristics are minimal. Essentially, the mode must be convergent, but the tendency to converge is allowed to be small. As a result, even if you see 14 overshoots when you test your aircraft, it easily meets FAA criteria for this mode! The reason is that a lightly damped Dutch Roll mode is not a dangerous thing. It may make your mother-in-law sick in the back seat, but it wont kill her.Pilot workload may go up a bit, but it wont prevent you from making that instrument approach in low weather.

Faster oscillations are also better than slow ones. In a good airplane, the quicker the free response oscillation dies out, the better it is, both for the passengers and also for the pilot trying to maintain precise control of the airplane in the weather. It might not be better for your mother-in-law, however.

Conclusion
Most FAA-certified airplanes will have fairly similar dynamic stability characteristics. The short period mode will certainly be heavily damped, otherwise the airplane would be dangerous to fly. It is likely, however, that both the phugoid and Dutch Roll modes will be lightly damped. An evaluation of these modes may show a preference towards one airframe over another for instrument conditions. And perhaps even more significant for your passengers would be to find an airframe with good Dutch Roll characteristics!

-Greg Lewis is deputy director and an instructor pilot at the National Test Pilot School, Mojave, Calif., (www.ntps.com).