prompter: What is a winglet?
assistant: The term "winglet" was previously used to describe an additional lifting surface on an aircraft. It's, essentially, the bendy part on the end of the wing.

According to Wikipedia wingtip devices are intended to improve the efficiency of fixed-wing aircraft by reducing drag.
The upward and outward angles, as well as the size and shape are critical for correct performance and are unique in each application.

Anything else you want to know about winglets?
prompter: Yes please.  What does NASA say about winglets?  For example what does the mathematical equation Cd = Cdo + Cdi quantify?  Lastly, explain the drag coefficient further based on information from NASA website sources.  Thank you.
assistant: NASA has provided extensive information on the factors that affect drag on an aircraft, including the drag coefficient, which quantifies the amount of drag generated by an object. The drag equation states that drag (D) is equal to a drag coefficient (Cd) times the density of the air (r) times half of the square of the velocity (V) times the wing area (A). The drag coefficient is composed of two parts: a basic drag coefficient, which includes the effects of skin friction and shape, and an additional drag coefficient related to the lift of the aircraft, known as induced drag. The induced drag coefficient (Cdi) is equal to the square of the lift coefficient (Cl) divided by the quantity: pi (3.14159) times the aspect ratio (AR) times an efficiency factor (e). The aspect ratio is the ratio of the square of the span to the wing area. Long thin wings have low induced drag, while wings with an elliptical planform also have lower induced drag than rectangular wings, as expressed in the efficiency factor in the induced drag equation. The value of the efficiency factor is 1.0 for an elliptical wing and some smaller number for any other planform, with a value of about .7 for a rectangular wing. 

The Wright brothers, who designed and built the first powered aircraft, learned about induced drag the hard way. Following their first glider flights in 1900, they knew that they had to increase the size of their wings to allow flight in reasonable winds. For the 1901 aircraft, they increased the chord of the wing but kept the span nearly the same, producing a wing with an aspect ratio of 3.0 and high induced drag. The brothers had made mathematical predictions of the performance of their aircraft, but the 1901 aircraft did not meet their range predictions because of lower than expected lift and higher than expected drag. During the winter, with the aid of their wind tunnel, they began to understand the role of induced drag on their aircraft's poor performance. They then designed the 1902 aircraft wing to have a longer span and shorter chord than the 1901 aircraft, changing the aspect ratio to 6.0 with nearly the same wing area. By doubling the aspect ratio, the brothers cut the induced drag in half. The 1902 aircraft was able to meet their performance goals, and they were able to attain glides of over 650 feet.

NASA has also provided information on winglets, which are vertical extensions of wingtips that improve an aircraft's fuel efficiency and cruising range. Winglets reduce the aerodynamic drag associated with vortices that develop at the wingtips as the airplane moves through the air. By reducing wingtip drag, fuel consumption goes down and range is extended. Winglets are designed as small airfoils and are used on aircraft of all types and sizes, from single-seat hang gliders and ultralights to global jumbo jets. Some aircraft are designed and manufactured with sleek upturned winglets that blend smoothly into the outer wing sections, while add-on winglets are also custom made for many types of aircraft. The concept of winglets originated with a British aerodynamicist in the late 1800s, but the idea remained on the drawing board until rekindled in the early 1970s by Dr. Richard Whitcomb when the price of aviation fuel started spiraling upward. NASA extensively studied winglets in an effort to reduce the induced drag on airliners, and they are now one of the most successful examples of a NASA aeronautical innovation being utilized around the world on all types of aircraft.


Sources:

* https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/winglets/

* https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/induced-drag-coefficient/

* https://www.nasa.gov/centers/dryden/about/Organizations/Technology/Facts/TF-2004-15-DFRC.html

* https://wright.grc.nasa.gov/airplane/drageq.html

* https://www.grc.nasa.gov/WWW/K-12////airplane/winglets.html