The dutch roll flight mode shows up in a yaw only behavior driven in frequency by the yaw stiffness Nβ and in damping by yaw damping Nr. A pilot would identify the behavior as a snake dominated dutch roll behavior. With zero effective dihedral, we could also reasonably expect only little to modest yaw-roll coupling through the rate terms, which would be primarily driven by the vertical offsets of surfaces. For the engineers, this simplified 2DOF model of dutch roll has a frequency and damping term approximated as: (derivation)
Interestingly enough, the dutch roll behavior seems to appear even if the aircraft has zero effective dihedral AND zero effective yaw stiffness, provided the product of yaw damping and sideforce derivatives are positive. Both Nr and Yβ are almost always expected to be negative.
Coupled Roll-Yaw Analysis
The dutch roll flight modes show up in higher fidelity dynamics models. The lateral 4DOF model below contains the spiral, roll, and dutch roll modes with sideslip, roll rate, yaw rate, and roll angle perturbation states:
The USS Alabama Battleship Memorial Park in Mobile, AL displays an interesting collection of WW2 ships and aircraft not normally seen. The collection includes several rare museum items. The park is well worth the visit. https://www.ussalabama.com/
The Battleship Memorial Park visit is contained in 3 parts:
In 2019 and 2020, I had the opportunity through my job to fly in the mountains of Colorado on a DHC-6 Twin Otter. Here are some images of the flight campaign. See https://rsc.ua.edu for more information.
As the advisor of the TuskaUAV group, I was asked to give a 30 minute chat to the student group on the topic of aerodynamics and propulsion with a special emphasis on small unmanned aerial vehicles. The four-up double sided handout is available below. The formal talk concluded with a Q/A session both during and after the meeting. Thanks for the opportunity!
Stanley Farlow’s textbook Partial Differential Equations for Scientists and Engineers is a reasonable introductory book for undergraduate and graduate students in the sciences and engineering. This book covers classical solution techniques, basic numerical methods, and -finally- the use of special techniques for solving non-trivial problems. This book is NOT acceptable for graduate students in mathematics, as can be seen directly in the title. Theory is briefly discussed, but the heart of the book is solving problems.
I taught a graduate course (GES 554, see here) for engineers with the book. ISBN-13:978-0486676203
Reasonable coverage of classical methods
Very low cost ($12).
Discusses the physics of why terms appear in PDEs
Basic at best.
No formal mathematical proofs.
Only 1 section (Burger’s equ) discussing non-linear PDEs
Solutions in the back are often not correct
Topic order (especially for classification) is scattered.
Today, I created a CATIA CAD model of the Gulfstream GV / G550 aircraft. There are a few discrepancies in the details, especially with the windows and doors; however, the basic aircraft geometry is lofted from drawings.
Sharp aerospace engineers may question several of the fundamental design parameters and wonder about the airfoil selection (yes, supercritical, but GIII airfoils), surface quality (certainly not production quality), and purpose. It’s definitely not trivial to reverse engineer a CAD model from scratch, but it is doable for low to medium fidelity requirements. The CAD model is available here: https://grabcad.com/library/gulfstream-gv-g550-low-fidelity-2