Re: How do acrobatic planes fly?

Hi Nathaniel,

That's a really good question!

Airfoils, such as airplane wings, helicopter rotors, and even turbine blades in jet engines are all based on the same principles. They operate by producing a pressure difference between one side and the other. There are a number of factors that determine the pressure difference on a surface, but the basic equation looks something like this:

P = ½pv²

What this says is that the pressure is proportional to p (rho), which is the density of the surrounding air (or any fluid for that matter) and the the square of the velocity (speed) relative to the air. With this simple equation, we can roughly estimate the required wing area needed for a plane of a given weight and speed. For a plane to fly straight and level, the lifting force of the wings must equal the weight. The lifting force of a wing is:

F = PA (A is the area of the wing)

F = ½pv²A

Let's run some quick numbers. Let's say we want to design the wings for a single engine plane like the Cessna 172. We want to operate the plane with gross weight approximately 1500 lbs at 100 knots. The density of air at 0º C, sea level is 1.293 kg/m³. Working in MKS (metric) units, the minimum required wing area is roughly:

A = F/P

A = 0.2 m²

0.2 square meters is not much! It's much smaller than we would expect looking at real aircraft. In this simple analysis, we have ignored the realities of aerodynamics, which involve complex airflow. To develop practical airfoil sections, aerodynimicists test different airfoil sections in a wind tunnel and measure two important numbers: the lift coefficient (C_l) and the drag coefficient (C_d). Lift and drag coefficients multiply the pressure in the above equations. These numbers vary depending on airfoil shape and angle of attack. Angle of attack is the angle between the chordline of an airfoil and direction of the relative wind. In general, the lift coefficent increases with angle of attack, as does drag. There is a point at which drag overtakes lift, and little or no lift is produced. This is known as the stall angle, which is around 15 degrees. Pilots try to avoid the stall regime during normal flight, as it could develop into a hazardous condition. Helicopter rotors can also stall under certain conditions, which is extremely dangerous.

How does this relate to your question? As I mentioned, there are many different airfoil types that exhibit differing flight characteristics. Thick sections tend to produce more lift at low speeds, but yield greater drag. Curved airfoils will also produce more lift than uncurved types. There is a standard airfoil section, known as type NACA 0012 which has no curve to it at all. This airfoil is numbered 12 because it's thickness is 12% of it's length. The number 12 airfoil is good for a wide range of airspeeds, and is often used in helicopter rotor sections where airspeed varies widely. Many acrobatic aircraft also use this airfoil section because they fly upside down as much as right side up.

So if the number 12 airfoil is symmetric, how does it generate lift? It turns out that at zero angle of attack, symmetric airfoils do not develop lift (although they still produce drag). Like all other airfoils, symmetric airfoils produce positive lift with increasing angle of attack, until they stall. So an airplane with symmetric airfoil sections must fly with a slightly positive angle. When they fly upside down, they must still maintain a positive angle. In either case the right amount of lift is produce to keep the airplane airborne. Pilots don't really think about the angle of attack, they simply adjust the engine power and flight controls to maintain level flight. In the end, the wings will be angled just enough for proper flight.

Curved airfoil sections can produce lift at zero angle of attack. Most commercial aircraft, including jet airliners, use curved airfoils. The curve is not great, but it is enough to improve performance and meet the design gols set by the manufacturers. Low speed airfoils have less curve than high speed. This is very noticable during landing when flaps are engaged. At low speeds, greater lift is need to keep the plane flying, so the pilots increase the area and curvature of the wings using flaps.

Even with curved airfoils, it is possible to fly inverted, but most commercial aircraft are not designed to do so. Their fuel delivery systems and airframe structure don't meet the requirements for inverted flight. Even with these restrictions, acrobatic maneuvers have been demonstrated in commercial airliners. In the 60's, Tex Johnson, the chief test pilot for Boeing, perfomed two slow, 1G rolls in a Boeing 707 over an outdoor festival in Seattle, WA. Needless to say, the Boeing management was not pleased. Rolls and loops have also been demonstrated in helicopters as well. In all of these cases, the aircraft did not maintain sustained inverted flight due to design constraints. Acrobatic aircraft, on the other hand, can maintain inverted flight indefinately.

I hope this answers your question, if not, don't hesitate to email me at madhu@madhu.com