Red
Very Strong User
Hey All,
Wayne asked for some info on the PRANDTL wings and suggested I start a new thread, so here it is.
Ludwig Prandtl was a German fluid dynamicist who was the first to create a tool (equation) to predict the performance of a wing in 1919. Dubbed Lifting Line Theory, he correctly predicted down wash and wing tip vortices (he called them Vortex ribbons) among other things. Lifting Line Theory states in part that the most efficient way for a wing to produce lift is with an elliptical lift distribution. This means that the wing should create the most lift at its center, tapering off in the shape of a 1/4 ellipse to nothing at the tip. This is the standard theory taught to all aero students around the world to this day. This creates a discontinuity at the tip however where the high and low pressures mix creating wing tip vortices. This is why you see modern airliners and high performance sailplanes with a winglet (a NASA invention BTW) to extract some of the wasted energy left in the wake. The elliptical lift distribution concept remains the most efficient if you don't hold structural weight constant.
Later in about 1933, Prandtl once again posited another theory. If you held structural weight and root bending moment as constants, is there an alternate left distribution that yields lower induced drag? Turns out that there is. It is often referred to as a non-elliptical lift distribution but is more commonly know as bell shaped lift distribution or BSLD for shot. He published his theory in a German soaring magazine. It was never officially translated into English, and largely forgotten by most in the aerodynamics world. Some of the advantages are approximately 11% reduction in induced drag (for 22% greater span) , same root bending strain and perhaps most advantages to us flying wing guys, it generates proverse yaw instead of adverse yaw. This is because of the unique downwash behind the wing. With elliptical (ESLD) you strive for even downwash behind the wing. With BSLD, this downwash becomes up wash at a point about 70% semi span. So when an aileron (elevon) is depressed for a roll control, it deflects downward into up wash, reducing drag and producing proverse yaw. Normally a downside aileron is in downwash, increasing drag and adverse yaw. This also means that you retain roll control during and after a stall event, and greatly reduces spin tendencies via the unloaded tips. Most airplanes have vertical tails (thanks to the Wright Brothers btw) to control adverse yaw. Ever seen a bird with a vertical tail? We are certain this is how birds produce lift as well. There has been over 22 years of research on BSLD by Al Bowers (and many others) Chief Scientist (Ret.) at NASA Armstrong Flight Research Center. This has resulted in two technical papers (linked below) as well as reams of supporting unpublished data.
The above is a very simple paraphrasing of a very complex idea. Please read the papers for a complete explanation including the supporting math and data.
I'm happy to answer as many questions as I can. I have built and flown all but 1 of the research vehicles. The very first one was built when I arrived at NASA, I did however get to repair it and enjoy many successful flights including the first ever data collected to support proverse yaw. These include (2) 12.5' span, (2) 25' span, 35+ others varying from 34" down to 13" span Mars exploratory prototypes. There has also been a full scale man carrying glider version built and flown.
On Wings of Minimum Induced Drag: Spanload Implications for Aircraft and Birds
Experimental Validation of the Prandtl 1933 Bell Spanload
More info:
www.nasa.gov
Flight footage of the full scale early towed flights
Cheers
Red
Wayne asked for some info on the PRANDTL wings and suggested I start a new thread, so here it is.
Ludwig Prandtl was a German fluid dynamicist who was the first to create a tool (equation) to predict the performance of a wing in 1919. Dubbed Lifting Line Theory, he correctly predicted down wash and wing tip vortices (he called them Vortex ribbons) among other things. Lifting Line Theory states in part that the most efficient way for a wing to produce lift is with an elliptical lift distribution. This means that the wing should create the most lift at its center, tapering off in the shape of a 1/4 ellipse to nothing at the tip. This is the standard theory taught to all aero students around the world to this day. This creates a discontinuity at the tip however where the high and low pressures mix creating wing tip vortices. This is why you see modern airliners and high performance sailplanes with a winglet (a NASA invention BTW) to extract some of the wasted energy left in the wake. The elliptical lift distribution concept remains the most efficient if you don't hold structural weight constant.
Later in about 1933, Prandtl once again posited another theory. If you held structural weight and root bending moment as constants, is there an alternate left distribution that yields lower induced drag? Turns out that there is. It is often referred to as a non-elliptical lift distribution but is more commonly know as bell shaped lift distribution or BSLD for shot. He published his theory in a German soaring magazine. It was never officially translated into English, and largely forgotten by most in the aerodynamics world. Some of the advantages are approximately 11% reduction in induced drag (for 22% greater span) , same root bending strain and perhaps most advantages to us flying wing guys, it generates proverse yaw instead of adverse yaw. This is because of the unique downwash behind the wing. With elliptical (ESLD) you strive for even downwash behind the wing. With BSLD, this downwash becomes up wash at a point about 70% semi span. So when an aileron (elevon) is depressed for a roll control, it deflects downward into up wash, reducing drag and producing proverse yaw. Normally a downside aileron is in downwash, increasing drag and adverse yaw. This also means that you retain roll control during and after a stall event, and greatly reduces spin tendencies via the unloaded tips. Most airplanes have vertical tails (thanks to the Wright Brothers btw) to control adverse yaw. Ever seen a bird with a vertical tail? We are certain this is how birds produce lift as well. There has been over 22 years of research on BSLD by Al Bowers (and many others) Chief Scientist (Ret.) at NASA Armstrong Flight Research Center. This has resulted in two technical papers (linked below) as well as reams of supporting unpublished data.
The above is a very simple paraphrasing of a very complex idea. Please read the papers for a complete explanation including the supporting math and data.
I'm happy to answer as many questions as I can. I have built and flown all but 1 of the research vehicles. The very first one was built when I arrived at NASA, I did however get to repair it and enjoy many successful flights including the first ever data collected to support proverse yaw. These include (2) 12.5' span, (2) 25' span, 35+ others varying from 34" down to 13" span Mars exploratory prototypes. There has also been a full scale man carrying glider version built and flown.
On Wings of Minimum Induced Drag: Spanload Implications for Aircraft and Birds
Experimental Validation of the Prandtl 1933 Bell Spanload
More info:
PRANDTL Wing
NASA brings you images, videos and features from the unique perspective of America's space agency. Get updates on missions, watch NASA TV, read blogs, view the latest discoveries, and more.
Flight footage of the full scale early towed flights
Cheers
Red
