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Where Mathematics Meets the Sky:

Academic Flight

Flight Test Engineering and Flight Training with a Test Pilot Approach

Recovery from a Cross-Controlled Stall – FAA Flight Instructor Practical Test Standards for Airplane, Area of Operations XI, Task D

A Unique Learning Environment

Rotary wing example: AFCS written in Python hovering a Robinson R22 helicopter in X-Plane, implementing translational rate command position hold (TRC/PH) , yaw rate command heading hold (RCHH), and altitude hold.

Flight Test Engineering

Practically oriented flight test engineering courses with lots of programming in Python (or alternatively MATLAB) and simulator-based flight testing. Highlights include:

  • Development of an automatic flight control system (AFCS) between inceptor and flight simulator
  • Vehicle state estimation (Kalman filters, sensor fusion)
  • PID control and nonlinear dynamic inversion
  • Flight test planning, flight test data analysis, and reporting

Covers both fixed wing and rotary wing, as the modern flight test engineer and test pilot is ideally versed in both. Can be attended as a flight test engineer and test pilot course work load sharing pair.

Primary Flight Training
for Flight Test Engineers

Are you a flight test engineer who is thinking of learning to fly an airplane and obtaining a pilot certificate, in order to improve your understanding of flight? You have come to the right place. Our primary flight training course is specifically designed for you:

  • Connect your flight training to your flight test engineering education, and bridge the disconnect between the flight training industry and the aerospace industry.
  • We will form this connection for you, rather than you having to connect the dots yourself.
  • Progress faster and save money on your pilot’s license.
  • Use what you have learned as a pilot to become more effective at your job as a flight test engineer.

Our test pilot school educated flight instructor staff will present the flight training materials in the language you are accustomed to from flight test engineering.

Learn more…
Lift and Drag Equation Flowchart
Efficient, precise aerospace engineering communication can convey many concepts relevant to piloting an aircraft all on one slide. Click on the button on the left for more info and an explanation.
Spin entries can produce upsets rather quickly. As a flight instructor, do not fly your students in circles. Student pilots need to be shaken, not stirred—it enables them to form a stronger bond with the aircraft.

Advanced Flight Training
for Airplane and Glider Pilots

Academic Flight provides advanced flight training to experienced airplane and glider pilots and those who strive to become. We use flight test techniques as cockpit teaching tools to promote airmanship development and superior understanding of flight dynamics. Our flight training courses include:

  • Multi engine training (based on USAF Test Pilot School textbooks)
  • All-attitude and emergency maneuver training (incl. turnback maneuver)
  • Tailwheel training
  • Glider training
  • Advanced CFI training (incl. creation of animated teaching materials)
  • Seaplane training (in owner’s own aircraft only)
Learn more…

Aircraft Certification and Regulations

The aircraft certification process and its underlying regulations are not only of great importance to the flight test engineer and test pilot, but also to the operational pilot, as their understanding has a profound impact on flight safety. The pilot needs to comprehend what specifically the aircraft has been designed to do and how it is intended to be used. Conveying this information to operational pilots has become even more important, since the details of the Part 23 aircraft certification regulations disappeared behind the ASTM paywall and are not freely accessible anymore.

At Academic Flight we are regulation aficionados and have — in addition to a discussion of regulations relevant for flight testing and certification — also compiled one of the most popular online selections of FAA legal interpretations of interest to the general aviation pilot and flight instructor regarding aircraft operations, flight instruction, and flight time logging.

Amphibious adventure — we serve our clients in a variety of environments.
Python Contour Plot
Illustrative contour plot, showcasing Python’s capability to create beautiful data visualizations
Animation of an IFR holding pattern created with Python
scikit-learn classifier comparison example by Gaël Varoquaux, Andreas Müller
scikit-learn classifier comparison example by Gaël Varoquaux and Andreas Müller
Bode plot with control.matlab submodule
Control theory: Bode plot showing the frequency response of a system
PID Controller in 1D
Illustration of Proportional-Integral-Derivative Control (PID Controller)

Python enables you to create stunning visual data presentations and animations with just a few lines of code and does not require any prior programming knowledge to produce amazing results quickly.

Data Science and Computer Programming for Pilots and Flight Test Engineers

Learn how to read data into a computer, process it, and create appealing plots conveying a strong message. Our programming courses in Python and C++ give an introduction to a variety of topics relevant for test pilots and flight test engineers, but also for operational pilots and flight instructors, including:

  • Data analysis and presentation
  • Visualizations and graphics (incl. animations)
  • Scientific computing
  • Control systems
  • Image processing and computer vision
  • Machine learning and artificial intelligence
  • Embedded systems programming (in C++)

Developing good Python skills (or alternatively MATLAB) is essential for success in our flight test engineering courses.

Mathematics in Aerospace Engineering

Mathematics in aerospace engineering is omnipresent; it is insightful and enjoyable to explore mathematics formally.

Learn how to define the number 2—in ways a mathematician does—, and understand vectors in the language of abstract algebra.

Discover that moments in reality are bivectors, not vectors with the right-hand rule to be applied. Realize that quaternions form an even subalgebra of the geometric algebra, and learn how to visualize spatial rotations with unit quaternions as an alternative to Euler angles.

Remind yourself that the vector field of an incompressible, irrotational, inviscid 2D flow happens to satisfy the Cauchy-Riemann equations for holomorphic functions in complex analysis, which enables the use of the residue theorem to prove the Kutta-Joukowski theorem (relating lift to circulation around the airfoil of a wing) elegantly.

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Quaternions and Geometric Algebra
Academic Flight lecture slide showing the relationship between quaternions and geometric algebra (Clifford algebra). A visualization of spatial rotation using unit quaternion conjugation and an interpretation of moments as bivectors is also provided.

Direct Links to Selected Courses

Quick links to specific selected courses not already linked directly above.

Flight Training

Academic Flight LLC provides aerospace education and flight training. In our flight training, we use flight test methods as cockpit teaching tools – in conjunction with the test pilot’s and flight test engineer’s knowledge of flight dynamics – for advanced airmanship development. This approach can be applied in thorough courses leading to FAA ratings and certificates, or reach beyond into the realm of aerobatics and upset prevention and recovery training (UPRT). We teach online as well as in an in person format. Please contact us for details and see our more comprehensive mission statement.

Online Ground Schools

Multi Engine Training

All-Attitude and Emergency Maneuver Training

Additional Ratings and Endorsements

Ready for aerobatic flight with a student.