Spins are tricky. After reading several aerodynamics texts and hundreds of pages of NASA spin-tunnel research reports, I find it striking how much remains unknown about what happens in a spin.
Here’s a basic yet important fact: if you don’t stall the airplane, it won’t spin. Therefore, let’s begin by reviewing stalls.
As discussed in section 5.3, the stall occurs at the critical angle of attack, which is defined to be the point where a further increase in angle of attack does not produce a further increase in coefficient of lift.
Nothing magical happens at the critical angle of attack. Lift does not go to zero; indeed the coefficient of lift is at its maximum there. Vertical damping goes smoothly through zero as the airplane goes through the critical angle of attack, and roll damping goes through zero shortly thereafter. An airplane flying 0.1 degree beyond the critical angle of attack will behave itself only very slightly worse than it would 0.1 degree below.
If we go far beyond the critical angle of attack (the “deeply stalled” regime) the coefficient of lift is greatly reduced, and the coefficient of drag is greatly increased. The airplane will descend rapidly, perhaps at thousands of feet per minute. Remember, though: the wing is still supporting the weight of the airplane. If it were not, then there would be an unbalanced vertical force, and by Newton’s law the airplane would be not only descending but accelerating downward. If the wings were really producing zero force (for instance, if you snapped the wings off the airplane) the fuselage would accelerate downward until it reached a vertical velocity (several hundred knots) such that weight was balanced by fuselage drag.
We can arbitrarily divide the wing into sections. Each section contributes something to the total lift. It is highly desirable (as discussed in section 5.4.3) to have the coefficient of lift for sections near the wing-root reach its maximum early, and start decreasing, while the coefficient of lift for sections near the tips continues increasing1 (as a function of angle of attack).
Therefore it makes perfect sense to say that the sections near the roots are stalled while the sections near the tips are not stalled. If only a small region near the root is stalled, the wing as a whole will still have an increasing coefficient of lift — and will therefore not be stalled.
We see that the wing will continue to produce lots of lift well beyond the point where part of it is stalling. This is the extreme slow-flight regime — you can fly around all day with half of each wing stalled (although it takes a bit of skill and might overheat the engine).
There is a very simple rule in aerodynamics that says the velocity of the fluid right next to the wing (or any other surface) is zero. This is called the no-slip boundary condition. Next to the surface there is a thin layer, called the boundary layer, in which the velocity increases from zero to its full value.
The wing works best when there is attached flow, which means that air flowing near the wing follows the contour of the wing. The opposite of attached flow is separated flow.
For attached flow, as we move through the boundary layer from the wing surface out to the full-speed flow, there is practically no pressure change. Sometimes it helps to think about attached flow in the following way: Imagine removing the boundary layer and replacing it with a layer of hard putty that redefines the shape of the wing. Then imagine “lubricating” the new wing so that the air slides freely past it; the no-slip condition no longer applies. Bernoulli’s principle can be used to calculate the pressure on the surface of the putty (whereas it could not be applied inside the boundary layer). Forces are transmitted from the air, through the putty, into the wing and the rest of the airplane. The putty-covered wing may not be the most desirable shape, but it won’t necessarily be terrible.
For separated flow, the putty model does not work. Suppose I want to pick up a piece of lint from the floor using a high-powered vacuum cleaner. If I keep the hose 3 feet away from the floor, it will never work; I could have absolute zero pressure at the mouth of the hose, but the low pressure region would be “separated” from the floor and the lint. If I move the hose closer to the floor, eventually it will develop low pressure near the floor. This is part of the problem with separated flow: there is low pressure somewhere, but not where you need it. Separation can have multiple evil effects:
In the simplest case, there is laminar flow, in which every small parcel of air has a definite velocity, and the velocity varies smoothly from place to place. The other possibility is called turbulent flow, in which:
The closer we look, the more fluctuations we see.
|Attached turbulent flow produces a lot of mixing. Some bits of air move up, down, left, right, faster, and slower relative to the average rearward flow.||For separated laminar flow, there will be some reverse flow (noseward, opposing the overall rearward flow) but the pattern in space will be much smoother than it would be for turbulent flow, and it will not fluctuate in time.|
You can tell whether a situation is likely to be turbulent if you know the Reynolds number. You don’t need to know the details, but roughly speaking small objects moving slowly through viscous fluids (like honey) have low Reynolds numbers, while large objects moving quickly through thin fluids (like air) have high Reynolds numbers. Any system with a Reynolds number less than about 10 is expected to have laminar flow everywhere. If you drop your FAA “Pilot Proficiency Award” wings into a jar of honey, they will settle to the bottom very slowly. The flow will be laminar everywhere, since the Reynolds is slightly less than 1. There will be no separation, no turbulence, and no form drag — just lots of skin-friction drag.
Systems with Reynolds numbers greater than 10 or so are expected to create at least some turbulence. Airplanes operate at Reynolds numbers in the millions. The wing will have a laminar boundary layer near the leading edge, but as the air moves back over the wing, at some point the boundary layer will become turbulent. This is called the transition to turbulence or simply the boundary layer transition. Also at some point (before or after the transition to turbulence) the airflow will become separated. The designers try to keep the region of separation rather small and near the trailing edge. In order to make a wing develop a lot of lift without stalling, it helps to minimize the amount of separation.
One scheme2 for controlling separation involves the use of vortex generators. Those are the little blades you see on the top of some wings, sticking up into the airstream at funny angles. Each blade works like the moldboard of a plow, reaching out into the high-velocity airstream and turning the layers over — plowing energy into the inner layers.
Re-energizing the boundary layer allows the wing to fly at higher angles of attack (and therefore higher coefficients of lift) without stalling. This improves your ability to operate out of short and/or obstructed fields.
The vorticity created by these little vortex generators should not be confused with the bound vortex, the big vortex associated with the circulation that supports the weight of the airplane. As discussed in section 3.14, to create lift there must be vortex lines running along the span, associated with air circulating around the wing. Vortex generators can’t provide that; their vortex lines run chordwise, not spanwise.3
Boundary-layer turbulence (whether created by vortex generators or otherwise) also helps prevent separation, once again by stirring additional energy into the inner sublayers of the boundary layer.
On a golf ball, 99% of the drag is form drag, and only 1% is skin-friction drag. The dimples in the golf ball provoke turbulence, adding energy to the boundary layer. This allows the flow to stay attached longer, maintaining the high-pressure region behind the ball, thereby decreasing the amount of form drag. The turbulence of course increases the amount of skin-friction drag, but it is worth it.4
Bernoulli’s principle does not apply inside the boundary layer, separated or otherwise. As discussed in section 3.6, Bernoulli’s formula is a force-balance equation, and does not account for frictional forces.
Do vortex generators play the same role as dimples on a golf ball? Not exactly. Unlike a golf ball, a wing is supposed to produce lift. Also unlike a golf ball, a wing is highly streamlined; consequently, its form drag is not predominant over skin-friction drag. Vortex generators are typically used to improve lift at high angles of attack (by fending off loss of lift due to separation). They might improve performance at high speeds, i.e. low angle of attack, by decreasing form drag at the expense of skin-friction drag – but probably not by much.
If you want ultra-low drag, and don’t care about short-field performance, you want a wing with as much laminar flow as possible. Designing a “laminar flow wing” is exquisitely difficult, especially in the real world where the laminar flow could be disturbed by rain, ice, mud, and splattered bugs on the leading edge.
There is always some separation on every airfoil section. The separation grows as the angle of attack increases. If there is too much separation, it cuts into the wing’s ability to produce lift. If there were no separation, the wing could continue producing lift up to a very high angle of attack (thereby achieving a fantastically high coefficient of lift).
Having lots of separation is the dominant cause (but not the definition) of stalling.5 Remember: the stall occurs at the critical angle of attack, i.e. the point where max coefficient of lift is attained.
A full discussion of turbulence and/or separated flow is beyond the scope of this book; indeed, trying to really understand and control these phenomena is a topic of current research. There is nothing simple about it. However, there are a few useful things we can say.
For more information, see e.g. reference 11.
The name Coanda effect is properly applied to any situation where a thin, high-speed jet of fluid meets a solid surface and follows the surface around a curve. Depending on the situation, one or more of several different physical processes might be involved in making the jet follow the surface.
As a pilot, you absolutely do not need to know about the Coanda effect or what causes it. Indeed, many professional aerodynamicists get along just fine without really understanding such things. The main purpose of this section is to dispel the notion that a normal wing produces lift “because” of some type of Coanda effect.
Using the Coanda effect to explain the operation of a normal wing makes about as much sense as using bowling to explain walking. To be sure, bowling and walking use some of the same muscle groups, and both at some level depend on Newton’s laws, but if you don’t already know how to walk you won’t learn much by considering the additional complexity of the bowling situation. Key elements of the bowling scenario are not present during ordinary walking.
You can demonstrate one type of Coanda effect for yourself using a piece of paper. Limp paper, such as tissue paper, works better than stiff paper. Drape the paper over your fingers, and then blow horizontally, as shown in the following figures.6
If the jet passes just above the paper, as shown in figure 18.1, nothing very interesting happens. The jet just keeps on going. The paper is undisturbed.
On the other hand, if the jet actually hits the paper as shown at point C in figure 18.2, the downstream part of the paper will rise up. This is because the air follows the curved surface; as it does so, it creates enough low pressure to lift the weight of the paper.
You are encouraged to try these experiments for yourself. Hint: It helps to blow through a piece of flexible tubing. For starters, the tubing serves as a better nozzle. Also it allows you to aim the airstream better. Last but not least, it allows you to view the experiment from a better angle.
You can easily observe that a jet that is strong enough to lift the paper in the geometry of figure 18.2 will not lift the paper in the geometry of figure 18.1.
The air in your lungs, at point A, is at a pressure somewhat above atmospheric. At point B, after emerging from the nozzle, the air in the jet is at atmospheric pressure (to a good approximation, more than good enough for present purposes).
As discussed in section 3.5, the fact that the fluid follows a curved path proves that there is a force on it. This force must be due to a pressure difference. In this case, the pressure on the lower edge of the jet (where it follows the curve of the tissue paper near point D) is less than atmospheric, while the pressure on the upper edge of the jet (near point E) remains more-or-less atmospheric. This pressure difference pulls down on the jet, making it curve. By the same token it also pulls up on the paper, creating lift.
People who only half-understand Bernoulli’s principle will be surprised to hear that the jet leaves the nozzle at high speed at atmospheric pressure. It’s true, though. In particular, the crude statement that “high velocity means low pressure” is an oversimplification that cannot be used in this situation. The correct version of Bernoulli’s principle says that the stagnation pressure of a particular parcel of air remains more-or-less constant. If you want to compare two different parcels of air, you’d better make sure they started out with the same stagnation pressure. Compared to ambient air, the air in the jet leaves the nozzle with a higher stagnation pressure and a higher total energy. Your lung-muscles are the source of the extra energy.
When this high-velocity, atmospheric-pressure air smacks into the paper at point C, it actually creates above-atmospheric pressure there. Indeed, we can use the streamline-curvature argument again: if the air turns a sharp corner, there must be a very large pressure difference.
In order to make this sharp turn, the air needs something to push against. A good bit of the required momentum comes from the air that splatters backward, as suggested by the squiggles in the figure, just below and upstream of the point of contact. This process is extremely messy. It is much more complicated than anything that happens near a wing in normal flight. To visualize this splatter, blow a jet of air onto a dusty surface.7 Even if you blow at a very low angle, some of the dust particles blow away in the direction opposite to the main flow.
Since we saw in section 18.3 that de-energizing the boundary layer is bad, you might think adding energy to the boundary layer should be good... and indeed it is. One way of doing so uses vortex generators, as discussed in section 18.3. Figure 18.3 shows an even more direct approach.
Once again, the Coanda effect cannot explain how the wing works; you have to understand how the wing works before you consider the added complexity of the blower.
In this case we expect one spectacular added complexity, namely curvature-enhanced turbulent mixing. This phenomenon will not be discussed in this book, except to say that it does not occur near a normal wing, while it is likely to be quite significant in the situation shown in figure 18.3.
Curving flows with lots of shear can be put to a number of other fascinating uses, but a discussion is beyond the scope of this book. See reference 23.
Another example uses a jet of water following a curved surface. You can easily perform the following experiment: let a thin stream of water come out of the kitchen faucet. Then touch the left side of the stream with the convex back side of a spoon. The stream will not be pushed to the right, but instead will follow the curve of the spoon and be pulled to the left. The stream can be deflected by quite a large amount. In accordance with Newton’s third law of motion, the spoon will be pulled to the right.
I don’t understand everything I know about this situation, but it is safe to say the following:
To convince yourself of these facts, it helps to have a higher velocity and/or a larger diameter than you can conveniently get from a kitchen faucet. A garden hose will give you a bigger diameter, and if you add a nozzle you can get a higher velocity. You can easily observe:
It appears that surface tension plays two very important roles:
In both respects this is quite unlike the air-in-air jet, where the air/wing surface tension has no effect and there is no such thing as air/air surface tension.
To convince yourself of this: Take a thin sheet of plastic. Get it wet on both sides, and drape it over a cylinder. You will not be able to lift it off the cylinder using a tangential water jet. The surface tension holding the wet plastic to the cylinder is just as strong as the tension between the plastic and the jet. In contrast, when the same piece of plastic has air on both sides, you can easily lift it off the cylinder using an air jet.
You may have heard stories saying that the Coanda effect explains how a wing works. Alas, these are just fairy tales. They are worse than useless.
In contrast, (a) the typical fairy tales imply that the entire flow pattern of a normal wing can be explained by mentioning the magic words “Coanda effect”, yet (b) they cannot explain how thick a chunk of air is deflected by the wing. One inch? Six inches? A chord-length? A span-length? Some amount proportional to the viscosity of the air? It would be very hard to calculate how much ... nonsensical things are often rather hard to calculate.
Don’t let anybody tell you that squirting a spoon or blowing on tissue paper is a good model of how a wing works.
If you want to “get the feel” of lift production, the obvious methods are the best. These include holding a model airfoil downstream of a household fan, or sticking it out of a car window. (You can think of this as the first step toward a home-made wind tunnel.) Among other things, you will quickly discover that precise control of angle of attack is important.
Case 1: In normal flight, rolling motions are very heavily damped, as discussed in section 5.4. Even though the static stability of the bank angle is small or even negative, you cannot get a large roll rate without a large roll-inducing torque; when you take away the torque the roll rate goes away.
Case 2: Near the critical angle of attack, the roll damping goes away. Suppose you start the aircraft rolling to the right. The roll rate will just continue all by itself. The right wing will be stalled (beyond max lift angle of attack) and the left wing will be unstalled (below max lift angle of attack).
Case 3: At a sufficiently high initial angle of attack (somewhat greater than the critical angle of attack), the roll will not just continue but accelerate, all by itself. This is an example of the departure12 that constitutes the beginning of a snap roll or spin. The resulting undamped rolling motion is called autorotation.
At a high enough angle of attack, the ailerons lose effectiveness, and at some point they start working in reverse.13 Figure 18.4 shows how this reversal occurs. Suppose you deflect the ailerons to the left. This raises the angle of attack at the right wingtip and lowers it at the left wingtip. Normally, this would increase the lift on the right wing (and lower it on the left), creating a rolling moment toward the left. Near the critical angle of attack, though (as seen in the left panel of the figure), raising or lowering the angle of attack has about the same effect on the coefficient of lift, so no rolling moment is produced (for now, at least).
We see that at this angle of attack, anything that creates a rolling moment will cause the aircraft to roll like crazy, and indeed to keep accelerating in the roll-wise direction. There will be no natural roll damping, and you will be unable to oppose the roll with the ailerons.
There are two main ways of provoking a spin at this point:
The word “spin” can be used in several different ways, which we will discuss below. The spin family tree includes:
Figure 18.5 shows an airplane in a steady spin. You can see that the direction of flight has two components: a vertical component (down, parallel to the spin axis) and a horizontal component (forward and around).
Figure 18.6 is a close-up of a wing in a steep spin. We have welded a pointer to each wingtip, indicating the direction from which the relative wind would come if the wing were producing zero lift; we call this the Zero-Lift Direction (ZLD). (For a symmetric airfoil, the ZLD would be aligned with the chord line of the wing.) Remember that the angle between the direction of flight and the ZLD pointer is the angle of attack.
In this situation, both wingtips have the same vertical speed, but they have significantly different horizontal speeds — because of the rotation. Consequently they have different directions of flight, as shown in the figure. This in turn means that the two wingtips have significantly different angles of attack, as shown in figure 18.7. The two wings are producing equal amounts of lift, even though one is in the stalled regime and one in the unstalled regime.
Figure 18.8 shows another spin mode. This time the rotation rate is higher than previously. The spin axis is very close to the right wingtip. The outside wing is still unstalled, while the inside wing is very, very deeply stalled, as shown in figure 18.9.
Figure 18.10 shows yet another possible spin mode. In this case, the outside wing is stalled, while the inside wing is, of course, much more deeply stalled. Whether this spin mode, or the one shown in figure 18.9 (or both or neither) is stable depends on dozens of details (aircraft shape, weight distribution, et cetera).
There is a common misconception that in a spin, one wing is stalled and the other wing is always unstalled. This is true sometimes but not always, especially not for flat spins.
It would be better to define “spin” as follows:
A samara is a winged seed. Maples are a particularly well known and interesting example.
Maple samaras have only one wing, with the seed all the way at one end. Its mode of flight is analogous to an airplane in a flat spin. In an airplane, the inside wing is deeply stalled, while in the samara the inside wing is missing entirely.
In a non-spinning airplane, if one wing were producing more lift than the other, that wing would rise. So the question is, why is a flat spin stable? Why doesn’t the outside wing continue to roll to ever-higher bank angles? The secret is centrifugal force.14 Suppose you hold a broomstick by one end while you spin around and around; the broomstick will be centrifuged outward and toward the horizontal.
In an airplane spinning about a vertical axis, the high (outside) wing will be centrifuged outward and downward (toward the horizontal), while the low (inside) wing will be centrifuged outward and upward (again toward the horizontal). In a steady flat spin, these centrifugal forces cancel the rolling moment that results from one wing producing a lot more lift than the other. This is the only example I can imagine where an airplane is in a steady regime of flight but one wing is producing more lift than the other.
As discussed in reference 20, an aircraft with a lot of mass in the wings will have a stronger centrifugal force than one with all the mass near the centerline of the fuselage. In particular, an aircraft with one pilot and lots of fuel in the wing tanks could have completely different spin characteristics than the same aircraft with two pilots and less fuel aboard.
In the 1970s, NASA conduced a series of experiments on the spin behavior of general-aviation aircraft; see reference 22 and reference 21 and other papers cited therein. They noted that there was “considerable confusion” surrounding the definition of steep versus flat spin modes, and offered the classification scheme shown in table 18.1.
spin mode Steep Mod’ly Steep Mod’ly Flat Flat angle of attack 20 to 30 30 to 45 45 to 65 65 to 90 nose attitude extreme nose-down less nose-down rate of descent very rapid less rapid rate of roll extreme moderate rate of yaw moderate extreme wingtip-to-wingtip difference in angle of attack modest large nose-to-tail difference in slip large largeTable 18.1: Spin Mode Classification
The angle of attack that appears in this table is measured in the aircraft’s plane of symmetry; the actual angle of attack at other positions along the span will depend on position.
The NASA tests demonstrated that general aviation aircraft not approved for intentional spins commonly had unrecoverable flat spin modes.
In all cases NASA studied, the flat spin had a faster rate of rotation (and a slower rate of descent) than the steep spin. Meanwhile, reference 7 reports experiments in which the flatter pitch attitudes were associated with the slower rates of rotation. This is not a contradiction, because the latter dealt with an unsteady spin (with frequent changes in pitch attitude), rather than a fully stabilized flat spin. A sudden change to a flatter pitch attitude will cause a temporary reduction in spin rate, for the following reason.
In any system where angular momentum is not changing, the system will spin faster when the mass is more concentrated near the axis of rotation (i.e. lesser moment of inertia). The general concept is discussed in section 19.9. By the same token, if the mass of a spinning object is redistributed farther from the axis, the rotation will slow down.
When the spinning airplane pitches up into a flatter attitude, whatever mass is in the nose and tail will move farther from the axis of rotation. Angular momentum doesn’t change in the short run, so the rotation will slow down in the short run.
In the longer run — in a steady flat spin — the aerodynamics of the spin will pump more angular momentum into the system, and the rotation rate will increase quite a lot. The rotation rate of the established flat spin is typically twice that of the steep spin.
Recovering from an established flat spin requires forcing the nose down. This brings the mass in the nose and tail closer to the axis of rotation. Once again using the principle of conservation of angular momentum, you can see that the rotation rate will increase (at least in the short run) as you do so — which can be disconcerting.
If you find yourself in an unusual turning, descending situation, the first thing to do is decide whether you are in a spiral dive or in a spin. In a spiral dive, the airspeed will be high and increasing; in a spin the airspeed will be low. You should be able to hear the difference. Also, the rate of rotation in a spiral is much less; the high speed means the airplane has lots of momentum and can’t turn on a dime. In a spin, the aircraft will be turning a couple hundred degrees per second.
To get out of a spin,15 follow the spin-recovery procedures given in the Pilot’s Operating Handbook for your airplane. The literature is full of home-brew spin recovery procedures that probably work most of the time in most airplanes, but if you want a procedure that works for sure, follow the handbook for your airplane.
For typical airplanes, the spin recovery procedure contains the following items:
Now let’s discuss each of these items in a little more detail.
Retarding the throttle is a moderately good idea for a couple of reasons. For one thing (especially if you have a fixed-pitch prop) it keeps the engine from overspeeding during the later stages of the spin recovery. More importantly, gyroscopic precession of the rotating engine and propeller can hold the nose up, flattening the spin and interfering with the recovery (depending on the direction of spin).
By way of counter-argument: In some situations, propwash might increase the effectiveness of the horizontal tail and therefore assist in the spin recovery. However, you should not depend on this, since the propwash might be blown far away from its normal path, blown away by the abnormal relative wind. For highly-developed spins, including flat spins, this becomes even less dependable. Also, depending on the direction of spin, gyroscopic precession might assist in spin recovery — but you shouldn’t depend on this, either.
Neutralizing the ailerons is usually a good idea for the simple reason that it is hard to think of anything better to do with them. Deflecting the ailerons effectively increases the angle of attack of one wingtip and decreases the angle of attack of the other wingtip. In a spin, the part of the wing where the ailerons are may (or may not) be in the stalled regime — so deflecting the ailerons to the left may (or may not) produce a paradoxical rolling moment to the right.
Retracting the flaps is a moderately good idea because you might exceed the “max flaps-extended speed” if you mishandle the later stages of the spin recovery and you don’t want to damage the flaps.
Also, retracting the flaps may help with the spin recovery itself. Recall from section 5.4.3 that the flaps effectively increase the washout of the wings. Washout ensures that the airplane will stall before it runs out of roll damping. (This produces a nice straight-ahead stall.) In the spin, though, when you have lost all vertical damping and roll damping, the washout doesn’t help. The early stages of spin recovery are not like the early stages of stall entry.
Depressing the rudder to oppose the spin is obviously a good thing to do.
Finally, you want to move the yoke to select zero angle of attack. In typical trainers, this means shoving the yoke all the way forward, but in other aircraft, especially aerobatic aircraft, all the way forward might select a large negative angle of attack. Shoving the yoke all the way forward in such a plane would likely convert the spin to an inverted spin — hardly an improvement. This is just one example of why you want to know and follow the spin recovery procedure for your specific airplane.
Some of the items on the spin-recovery checklist require sequencing, while others do not. Note the contrast:
|The first three items on the list can be done more-or-less simultaneously. That is, while you are retarding the throttle with one hand, there is no harm in neutralizing the ailerons with the other hand.||In some airplanes, the checklist calls for depressing the rudder pedal all the way to the floor before pushing the yoke forward.|
The relative significance of the rudder compared to the flippers in breaking the spin depends radically on the design of the airplane, the loading of the airplane, and on the spin mode, as discussed in reference 20.
In normal non-spinning flight, you should apply smooth pressures to the controls. Spin recovery is the exception: it calls for brisk, mechanical motions of the controls, almost without regard to the pressures involved.
If you get into a spin in instrument conditions, you should rely primarily on the airspeed indicator and the rate-of-turn gyro. The inclinometer ball cannot be trusted; it is likely to be centrifuged away from the center of the airplane — giving an indication that depends on where the instrument is installed, telling you nothing about the direction of spin. The artificial horizon (attitude indicator) cannot be trusted since it may have tumbled due to gimbal lock. It is better to trust the rate-of-turn, which cannot possibly suffer from gimbal lock, since it has no gimbals. Remember, it is a rate gyro (not a free gyro), so it doesn’t need gimbals.
Recovery from a so-called incipient spin (one that has just gotten started) is easier than from a well-developed spin. Normal-category single-engine16 certification requirements say that an airplane must be able to recover from a one-turn spin (or a 3-second spin, whichever takes longer) in not more than one additional turn. If you let the spin go on for several turns, you might progress from a steep spin to a flat spin. Recovery could take a lot longer — if it is possible at all.
If you load the airplane beyond the aft limit of the weight and balance envelope, even the incipient spin may be unrecoverable; see section 6.1.3. Imperfect repairs to the wing, or slack in the control cables, could also impede spin recovery.
Finally, the spin is yet another reason why it is NOT SAFE to think of the yoke as simply the up/down control.17 In a spin you have a low airspeed and a high rate of descent. If you think of the yoke as the up/down control, you will be tempted to pull back on the yoke, which is exactly the wrong thing to do. On the other hand, if you think of the yoke as (primarily) the fast/slow control, you will realize that you need to push forward on the yoke, to solve the airspeed problem.
It is quite impressive how well a samara works. A maple seed descends very slowly, riding the wind much better than a parachute of similar size and weight ever could. Flat spins can be extremely stable; a wing by itself loves to spin. That’s why spins (and flat spins in particular) are so dangerous: it takes a lot of rudder force to persuade a wing to stop spinning.
Spins are extremely complex. Even designers and top-notch test pilots are routinely surprised by the behavior of spinning airplanes. Spin-test airplanes are equipped with cannon-powered spin-recovery parachutes on the airframe, and quick-release doors in view of the distinct possibility that the pilot will have to bail out. Tests are conducted at high altitude over absolutely unpopulated areas. Therefore please don’t experiment with spinning a plane except exactly as approved by the manufacturer — one unrecoverable spin mode can ruin your whole day.