Prandtl Lifting Line theory remains an excellent tools for preliminary design and gaining intuition about the aerodynamics of unswept wings.
Implementing a PLL solver is relatively simple; I made this version in a few hours with Fortran. The solver generates SVG files displaying the wing geometry, gamma and lift distributions as well as the integrated lift and drag coefficients for arbitrary wing geometries (as approximated by linear sections). The program and input files are available at: https://charles-oneill.com/code/prandtl/prl2.zip
A flat elliptical wing demonstrates the flat sectional lift coefficient distribution resulting from an elliptical lift distribution.
The beauty of the Prandtl lifting line theory is the ability to modify the wing geometry and airfoil sections. For example, given a 20% flap deflected 20 degrees on inner wing sections, the sectional lift distribution reflects the flap deflection. Of particular interest is that the shed vorticity is proportional to the slope of the green lift distribution.
The PLL theory is also instructive for understanding control surface behaviors. In the following image, the 20% ailerons are deflected approximately +-10 degrees (Thin airfoil theory is used to determine the equivalent zero lift line.). Of particular concern is that aileron deflections at high AOA can push the local angle of attack into a stalled state.
Back in 2006 as part of an independent study course, I used an inviscid CFD solver to estimate the aerodynamic performance of actual low aspect ratio wing configurations. The report (lowargeometryco2006.pdf) was written in a handbook style inspired by the classic Hoerner Lift and Drag books. The configurations were: monoplane, biplane, joined-tip biplane “box”, disc, monoplane with endplates, and a shroud cowl. Biplane gap, stagger, and decalage were considered. Performance criteria such as lift slope, induced drag, lift to drag ratio (L/D) were compared for multiple configurations and aspect ratios.The final portion of the report provides a visual display of the pressures and flow fields near the configurations.
Wake rollup of an AR=1 wing:
Wake aft of a biplane:
Pressure field interference with respect to biplane gap.
A brief description of IEEE 754 floating point numbers
Spacecraft Attitude (Guest Lecture)
Propulsion (Guest Lecture)
The notes contain numerous hand drawn images of systems and references to many books.
Detailed Aircraft Systems of Particular Aircraft were analyzed through flight manuals, NTSB accident reports, AIAA case-studies, and expert guest lectures.
Cessna 170 & 310
VTOL: VJ101 and VAK191B
WW2 Dam Busters (system development case study)
DHC-7 (aka. EO-5C / RC-7B)
A behind-the-scenes guided tour of the Southern Museum of Flight in Birmingham by two (2) PhDs in History and Engineering.
The course also included a set of lectures titled “Failure Fridays” which investigated aircraft incidents and accidents by tracking the failure points and symptoms with a special emphasis on systems. These included:
Cessna 182 Fuel Contamination
A320 Fly By Wire
Boeing 737 Rudder Actuator
Advisory Circulars (AC)
The largest non-nuclear explosion known to man. (Not aerospace, but still an impressive and covertly intentional systems failure!)
This course was particularly interesting; as the instructor, I learned a great deal about many topics. I had to work hard to stay ahead of the students. The students gave one of the best ratings that I have ever received. One student said:
The course was very interesting and likely one of the most valuable classes I have had in college. Rather than sticking strictly to theory as most of the Aerospace curriculum does, this class covers details about the what, why, and how for a wide range of
systems that will be particularly useful in any aerospace career.
Another student said:
This course provided me with an otherwise unobtainable insight into the real world of engineering systems, something not talked
about in other courses. This class is great for the industry engineer.
Not every comment was so positive. One student mentioned that this course required several prerequisites and that “newly transferred” students would find the course “difficult”.
More information and the full course notes are available by contacting Charles O’Neill.
This summer, my lab in conjunction with Dr. Branam developed an aircraft for testing a prototype flight control system. The aircraft flies beautifully for a rudder-elevator control system. Low power and a large efficient wing allows for exceptional performance at the design weight. As a design decision, the rudder-dihedral roll control is sufficient for the mission purposes.
The aircraft specifications are:
Wing span: 8 ft
Powerplant: OS 3815-1000 with 5000 mAh 3S LiPo
Differential spoilers (marginal for roll control)
Thanks to the following engineers and designers:
Josh Richards (chief design engineer, air-to-air video pilot)
Counterfeit Futaba servos exist. My students and I managed to purchase a few for a recent aircraft project. These were purchased off of Amazon. We now call these “Faketaba” servos.
Question: How many ways can you tell that the following servo is a counterfeit Futaba S3003 servo?
The servo performance is significantly worse than a genuine servo. In fact, I (Charles O’Neill) initially discovered that these servos were not genuine after performing a systems check of installed servos. The return to zero had a hysteresis of about several millimeters at the servo horn, which gave a surface deflection static hysteresis “zero” of about +-10 degrees. This was completely unacceptable for our application. These were immediately removed and replaced.
The Futaba logo and font is not correct. As a typography enthusiast, I spotted the slight imperfections in the name sticker.
Gear noise is sigificantly higher for these fake servos. The gear geometry and tooth count are different from actual Futaba servos.
In addition to the gear noise, the output shaft tolerance created an issue with the bearing surfaces. Also, the spline shaft poorly fit the servo horns. The servo horns themselves were significantly thicker than genuine horns.
After installation, I went back and found the box that the servos were shipped in. This is obviously not a genuine Futaba box.
I opened one servo to investigate the counterfeit quality. The grommet was not sealed correctly, a mistake that the Japanese Futaba company would never allow. The motor is only press fit into the servo case; this is a sneaky possible failure point. The servo case is geometrically different from an actual case.
The mounting holes are opened at the end. Actual Futaba S3003 servos are closed.
One additional point of discussion, the cost for these counterfeits was similar to actual genuine servos. My students learned a difficult lesson in trust.