All-Attitude and Spin Training

Upset Recovery and Spin Training Sources

Government Publications

Commercial and Private Publications

Test Pilot School and Flight Research Publications

Test pilot school literature is listed on a separate page of our bibliography. Chapters 9 and 10 of the USAF TPS “Flying Qualities Textbook”, Vol. 2, Part 2 (1986) have an excellent treatment of roll coupling (Chapter 9), including the Ixz effect, and spins (Chapter 10) of great relevance to the pilot. The rigid body equations of motion underlying any proper spin treatment are derived in Chapter 4 of USAF TPS “Flying Qualities Textbook”, Vol. 2, Part 1 (1986).

For spin research papers and videos, conducted on models in spin tunnels and with real airplanes, see the Flight Research Section of our bibliography.

Reading Advice for the Above Spin Literature

This section refers to spin training exclusively, not general upset recovery training. Read Chapter 10 in Bill Crawford’s Flightlab for an excellent and reasonably concise treatment of the physics of spins at a perfect level for the general pilot, with the minimum level of mathematics and physics needed to understand the basics of spins. This is a must read for any CFI. Crawford’s treatment should be your starting point. You can then continue on into several different complementary directions:

  • USAF TPS Textbook, “Flying Qualities”, Vol. 2, Part 2 (1986), Chapters 9 and 10: For the hardcore reader, a fairly thorough mathematical treatment of roll coupling (including the Ixz entry in the moment of inertia tensor) and spins (though not at spin research level) and of spin flight test procedures. The derivation of the equations of motion can be found in Vol. 1 Part 1. For finer points about spins, like the relationship between bank angle, sideslip angle, and helix angle of the flight path, you will have to consult additional references though.
  • Gene Begg’s “Spins in the Pitts Special”: Good treatment of the practical aspects of inverted spins and of the hands-off Parke-Mueller-Beggs Emergency Spin Recovery Technique.
  • Rich Stowell’s “The Light Airplane Pilot’s Guide to Stall/Spin Awareness”: A general aviation classic which offers a detailed treatment of the history of spin research and airplane certification, narrates some test pilot experiences during NASA spin tests of light GA aircraft, compares several spin recovery techniques, and discusses spin modes of different airplane makes and models. It offers many insights that the above mentioned three works do not. However, do not read this work for the physics of spins or to understand spins – not only will you end up disappointed, but also outright confused. Stowell writes down only one equation: the most complicated one he could possibly find including all control surface terms – and then gives up completely on discussing it in favor of a string of partially contradictory handwavy arguments. Rotational physics is never sufficiently explained in this work.

After having read all four of these works, spin research literature may be your next stop, as well as watching spin research videos (of spin tunnel tests as well as of real aircraft), which illustrate many of the concepts you have read about.

Stall/Spin Training and Accident Studies

  • Rich Stowell, “An Evaluation of Stall/Spin Accidents in Canada” (1999): In Canada spin training is mandatory for the Private Pilot Certificate (however only during training, it is not demonstrated on the practical test to the examiner). This document studies if stall/spin accidents in Canada are fewer than in other countries without such a training requirement (such as the United States), and concludes that actual in-flight spin training is not useful in most cases, because most such accidents happen at such low altitudes that recovery is impossible once the spin develops. (However, it would be a misinterpretation of this document to infer from this that in-flight spin training is useless for safety.)
  • Brent W. Jett, “The Feasibility of Turnback from a Low Altitude Engine Failure During the Takeoff Climb-out Phase” (1982), AIAA Paper 82-0406, presented at the 20th Aerospace Sciences Meeting, 11-14 January 1982, Orlando, FL.
    Not a stall/spin study per se, but investigates in a simulator if pilots can be trained in the turnaround maneuver after engine failure after takeoff reliably without getting into a stall/spin accident (and finds that this is indeed the case).

Spin Training Videos

Rigid Body Dynamics and Inertial Coupling

In order to understand inertial coupling in spins properly, it is instructive to study the torque-free rotating motion of rigid bodies, i.e. their spinning motion without any external moments (torques) acting. (In a spin, aerodynamic moments modify the motion further.) Without external moments, the angular momentum is conserved in the inertial (world) frame (but not in the body frame), and the angular momentum vector is therefore constant. The angular velocity vector, on the other hand, generally moves in both the inertial and the body frames, unless the body is spinning around one of its three principal axes – the coordinate system where the moment of inertia matrix is diagonal.

Most of the references below are from Wikipedia, which has a nice set of articles with some illustrations and links to further explanations and videos.

Basic Rotational Physics Prerequisites

  • Angular Velocity:
    https://en.wikipedia.org/wiki/Angular_velocity
  • Moment of Inertia (inertia matrix or tensor):
    https://en.wikipedia.org/wiki/Moment_of_inertia
  • Angular Momentum:
    https://en.wikipedia.org/wiki/Angular_momentum
  • Torque:
    https://en.wikipedia.org/wiki/Torque
    Torque is often called “moment” in aerospace engineering (and the word “torque” is reserved for the moment produced by an engine); it is “rotational force”, so to speak. It is not to be confused with “moment of inertia” (inertia matrix), which is rotational mass.

Rotating Motion of Rigid Bodies

  • Euler’s Equation of Rigid Body Dynamics:
    https://en.wikipedia.org/wiki/Euler%27s_equations_(rigid_body_dynamics)
    These three coupled differential equations based on the conservation of angular momentum in the inertial frame determine the three-dimensional rotating motion of a rigid body. The entire motion follows from these equations, given a set of initial conditions.
  • Precession (in particular torque-free in this context):
    https://en.wikipedia.org/wiki/Precession
    The angular velocity and angular momentum vectors are typically not parallel, causing the angular velocity vector to move with time. (What really causes the angular velocity vector to move is that it must undo the change with time of the inertia matrix in the inertial frame, because their product must be constant, since it is the angular momentum vector.)
  • Poinsot’s Construction (describes motion of angular velocity vector in the inertial (world) frame):
    https://en.wikipedia.org/wiki/Poinsot%27s_ellipsoid
    Tip of angular velocity vector travels on line described by the inertial ellipsoid of rotational energy conservation rolling on the invariable plane without slipping, in the inertial frame, describing a herpolhode:
    https://en.wikipedia.org/wiki/Herpolhode
    The invariable plane comes from the component of the angular velocity vector in the direction of the conserved angular momentum vector being constant. (The article also explains the polhode construction in the body frame, which describes the .)
  • Polhode Construction (describes the motion of the angular momentum vector in the body frame):
    https://en.wikipedia.org/wiki/Polhode
    In the body frame, the constant rotational-energy-conservation inertial ellipsoid intersects the angular-momentum-conservation sphere, forming a set of closed loops or sometimes intersecting lines. The tip of angular momentum vector travels in the body frame on the lines of the intersection between the ellipsoid and sphere. In the inertial (world) frame the tip of the angular momentum vector does not travel, as the vector is constant due to angular momentum conservation in the absence of any external torques/moments
  • Intermediate Axis Theorem (Tennis Racquet Theorem):
    https://en.wikipedia.org/wiki/Tennis_racket_theorem
    Instability of rotation around second principal axis. Also shows visual illustration of Polehode construction of angular-momentum-conservation sphere intersecting the inertial ellipsoid of rotational energy conservation, and a video of the Dzhanibekov effect (which is another name for this theorem).
  • Veritasium, “The Bizarre Behavior of Rotating Bodies, Explained,” (intermediate axis theorem illustration and explanation):
    https://www.youtube.com/watch?v=1VPfZ_XzisU

    Shows Dzhanibekov effect video, illustrating the instability of rotation around the second (intermediate) principal axis. Also contains illustrations of the first principal axis (smallest moment of inertia) being stable if the body is solid, but being unstable if the body is liquid and dissipates energy due to internal flows, forcing the body to assume rotation around its third principal axis (largest moment of inertia), which has the least amount of rotational energy for a given angular momentum.