Kline–Fogleman airfoil

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Aircraft wing showing the KFm2 Step
Aircraft wing showing the KFm3 Step

The Kline–Fogleman airfoil or KF airfoil is a simple airfoil design with single or multiple steps along the length of the wing. It was originally devised around 50 years ago for paper airplanes.

In the 21st century the KF airfoil has found renewed interest among hobbyist builders of radio-controlled aircraft, due to its simplicity of construction.[1] But it has not been adopted for full-size aircraft capable of carrying a pilot, passengers or other substantial payloads.


The KF airfoil was designed by Richard Kline and Floyd Fogleman.

Aircraft wing showing the KFm4 Step

In the early 1960s, Richard Kline wanted to make a paper airplane that could handle strong winds, climb high, level off by itself and then enter a long downwards glide. After many experiments he was able to achieve this goal.

He presented the paper airplane to Floyd Fogleman who saw it fly and resist stalling. The two men then filed for a patent on the stepped airfoil.

Further development resulted in two patents and a family of airfoils known as the KF airfoil and KFm airfoils (for Kline–Fogleman modified). The two patents, US Patent # 3,706,430 and US Patent # 4,046,338, refer to the introduction of a step either on the bottom (KFm1) or on the top of an airfoil (KFm2), or both on top and bottom (KFm4). It can also be used with two steps on the top (KFm3), or two steps on the top and one on the bottom (KFm7).

The purpose of the step, it is claimed, is to allow some of the displaced air to fall into a pocket behind the step and become part of the airfoil shape as a trapped vortex or vortex attachment. This purportedly prevents separation and maintains airflow over the surface of the airfoil.


Time published an article,The Paper-Plane Caper[2] about the paper airplane and its Kline–Fogleman airfoil in the Science section of its issue of April 2, 1973.

Then, CBS 60 Minutes did a 15-minute segment on the KF airfoil in 1973, and repeated the show again in 1976.

In 1985, Kline wrote a book entitled "The Ultimate Paper Airplane".[3] To publicize the book, he went down to Kill Devil Hills, NC in 1985, to the site where the Wright Brothers first flew where their first manned powered flight went 122 feet. A crew from Good Morning America came along to film the event. The longest flight by Kline with his paper airplane traveled 401 feet, four inches.

Independent scientific testing[edit]

KFm2 airfoil showing purported laminar flow vortex

In 1974, a NASA-funded study prompted by Klein and Fogelman's claims and the resulting national coverage found the airfoil to have worse lift-to-drag ratio than a flat plate airfoil in wind tunnel tests.[4]

In the 1990s, with 20 years of technical progress opening up new possibilities and with the original patents expired, researchers returned to the topic of stepped wings. For example, a 1998 study by Fathi Finaish and Stephen Witherspoon at the University of Missouri tested numerous step configurations in a wind tunnel.[5]

While many made wing performance worse, they got promising results with backward-facing steps on the lower surface of the wing – in some cases giving considerable enhancement in lift without much of a drag penalty. However, they concluded that a single configuration could not be best solution at every angle of attack and flight speed. Indeed, "vastly different configurations may be needed during a single maneuver." The idea works, Finaish and Witherspoon concluded, but only with active automated re-configuration of the shape of the step(s) during flight. Further testing has shown that this airfoil is effective in low Reynolds number flow.

A 2008 study by Fabrizio De Gregorio and Giuseppe Fraioli at CIRA and the University of Rome in Italy tried this out.[6] The model aerofoils used in their wind tunnel tests were equipped with numerous small holes through which air could be blown or sucked in an active way.

They concluded that the trapped vortex formed by a cavity or step could not be held in place without such active control. Just relying passively on wing shape wasn't enough – the vortex would detach possibly giving you worse characteristics than the original unstepped airfoil. But when active controls were used to keep the vortex stably in place they found the results "really encouraging".

Such scientific experimental work seems to have put paid to the idea that the original KF airfoil will find a simple practical application in the world of full-size aircraft. But the basic idea of the stepped wing has mutated, and is now bound up with a new body of research into actively controlling the airflow over a wing's surface with new mechanisms unthinkable 50 years ago.

Research led by Ranganadhan Voona in 2012 at Missouri University of Science and Technology was to investigate the lift and drag characteristics of a stepped airfoil with backward facing steps; apply active flow control technique to enhance the aerodynamic performance of stepped airfoils and examine the possibility of using such airfoils on Unmanned Aerial Vehicles (UAV’s).[7] A step was introduced at mid-chord, with a depth of 50% of the airfoil thickness at mid-chord position extending till the trailing edge of a NACA 4415 airfoil.

Computational studies were conducted with the use of passive flow control constituting the activation of step and active flow control with the use of air injecting jets placed in the step cavity of the NACA 4415 airfoil with a goal of enhancing the aerodynamic performance. The jet angle and jet momentum coefficient were varied independently to identify the best setting for optimizing the aerodynamic performance of the stepped airfoil. Studies of a scaled wing model with the same airfoil were conducted within a wind tunnel for a range of Reynolds numbers to validate some of the numerical results that were obtained or the cases of base and stepped airfoils. The results that were produced showed that as much as 37% increase in Cl and as much as 12% increase in L/D ratios over conventional airfoil values could be obtained by using stepped airfoils.[8]

The case study conducted as a part of this research focuses on the UAV RQ-2 Pioneer employed in a stepped airfoil configuration by comparing its aerodynamic characteristics with the conventional NACA 4415 airfoil originally used on this aircraft. The main objective of the case study was to identify and outline a step schedule for the flight envelope of the UAV Pioneer using a stepped airfoil configuration at the same time applying active flow control to obtain enhanced aerodynamic performance over conventional NACA 4415 airfoil originally used and hence improve the flight performance characteristics like Range and Endurance of the aircraft.[9]

Applications of the KF airfoil today[edit]

Shows the known variations of the KFm family of airfoils.

Poor lift-to-drag ratio performance in wind tunnel testing has meant that to date the KF airfoil has not been used on any full size aircraft. But the KF airfoil and derivative 'stepped' airfoils have in recent years gained a following in the world of foam constructed radio controlled model aircraft. The low Reynolds numbers allow for the stepped airfoils to produce a significant amount of lift for the drag inured, making them increasingly popular among RC hobbyist.

The simple KF airfoil shape lends itself well to construction in sheets of various plastic foams, typically expanded polystyrene (EPS) or expanded polypropylene (EPP). The resulting stepped wing can have improved performance and flying characteristics compared to the even simpler 'flat plate' wing used in some radio-controlled models. The Airfoils illustrated in this article are examples of those used in radio control foam models.


  • U.S. Patent 3,706,430 AIRFOIL FOR AIRCRAFT, filed March 17, 1970, issued December 1972
  • U.S. Patent 4,046,338 Airfoil for aircraft having improved lift generating device, filed October 14, 1975, issued September 6, 1977

See also[edit]


  1. ^ Example of discussion at RC Groups forum
  2. ^ Monday, Apr. 02, 1973 (1973-04-02). "Science: The Paper-Plane Caper". TIME. Retrieved 2012-05-13. 
  3. ^ "The Ultimate Paper Airplane: With Step-by Step Instructions for Seven Different Models (9780671555511): Richard Kline, Floyd Fogleman: Books". Amazon.com. Retrieved 2012-05-13. 
  4. ^ Lumsdaine, Edward (1974-12-15). "Investigation of the Kline-Fogleman Airfoil Section for Rotor Blade Applications" (PDF). 
  5. ^ Aerodynamic Performance Of An Airfoil With Step-Induced Vortex For Lift Augmentation, Journal of Aerospace Engineering, January 1998
  6. ^ "Flow Control On A High Thickness Airfoil By A Trapped Vortex Cavity, 14th Int Symp on Applications of Laser Techniques to Fluid Mechanics, Lisbon July 2008" (PDF). Archived from the original (PDF) on 2012-03-20. Retrieved 2012-05-13. 
  7. ^ Ranganadhan, Voona (2012). "Voona, Ranganadhan. "Enhancing the Aerodynamic Performance of Stepped Airfoils." Master's Thesis, Mechanical Engineering, Missouri University of Science and Technology, 2012." (PDF). Archived from the original (PDF) on 17 May 2014. Retrieved 16 May 2014. 
  8. ^ Ranganadhan, Voona (2012). "Voona, Ranganadhan. "Enhancing the Aerodynamic Performance of Stepped Airfoils." Master's Thesis, Mechanical Engineering, Missouri University of Science and Technology, 2012." (PDF). Archived from the original (PDF) on 17 May 2014. Retrieved 16 May 2014. 
  9. ^ Voona, Ranganadhan (2012). Enhancing the aerodynamic performance of stepped airfoils Numerical and Experimental Study (1. Aufl. ed.). Saarbrücken: LAP LAMBERT Academic Publishing. pp. 45–54. ISBN 978-3-659-26600-3. 

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