Blog Elements : Flight Training Central

I have heard from a couple of different pilot examiner friends that there are a number of basic aerodynamic concepts that are often misunderstood by pilot applicants. At the private pilot level, this is disappointing, but may be understandable. What is not understandable or acceptable is seeing a number of their commercial and CFI applicants having little more than a cursory understanding of some of these key concepts. Commercial pilots are seeking to eventually be paid, not only for their flying ability, but also for their knowledge. CFIs are supposed to be the purveyors of knowledge to all of those pilots that come after them. If they don’t have the knowledge to share, the vicious cycle continues.

Baffled by Bernoulli

A CFI applicant was asked to teach lift during their practical exam. They responded with something about Bernoulli’s Principle creating low pressure on top of the wing. When asked to explain this, the examiner was met with a blank stare. They couldn’t get to or beyond even the basics of the principal.

Daniel Bernoulli was a Swiss mathematician who lived in the 1700s. When he created his principle of differential pressure, he had no thoughts about its future application to the development of airfoils and lift production. Heavier-than-air flight was more than a century away. He died the year before the Montgolfier Brothers sent their first passengers aloft in a lighter-than-air aircraft. Bernoulli’s Principle was put forth in his 1738 book on the properties of fluid flow called Hydrodynamica.

Bernoulli’s Principle states that as the velocity of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases.

This principle can be demonstrated using a device known as a venturi tube. A venturi tube has larger inlet and outlet diameters but has a smaller diameter within the tube that creates a constriction. As a fluid is forced through the tube, the fluid must move faster through the constriction to keep up with the flow of the fluid in the rest of the tube. Due to the conservation of energy, this extra speed doesn’t come out of nowhere. Another factor is changing with the increased speed and that factor is a decrease in pressure. These changes can be demonstrated with the proper measuring equipment on the venturi tube.

The venturi tube is the start of the explanation, but it doesn’t really show the use of Bernoulli’s Principle in the production of lift without some modifications. First, let’s cut the top off the tube and trim it to the beginning and end of the constriction. With some imagination this looks a bit like the top of an airfoil. Next, instead of forcing the fluid through the tube, let’s force our tube, or at least its bottom half, through the fluid. In the case of our airfoil, we’ll assume that the fluid is air and that the air is relatively still.

As we force the airfoil through the still air, it is separated by the airfoil. Looking at the curvature or camber of a typical general aviation wing, the top has more curvature and thus surface area than the bottom of the wing. Add a bit of angle-of-attack, which moves the separation (stagnation) point vertically down on the leading edge of the wing, and the upper surface area becomes larger. Looking at it from the tip of the wing, the air above the wing has a greater distance to travel to be reunited with the air below at the trailing edge of the wing. This causes the acceleration witnessed in the venturi tube and lowers the pressure on top of the wing.

This lower pressure on the top of the wing is a part of the lift production.

Another aspect of the airflow around the wing that must be considered is happening below the wing. At a point close to the leading edge, the airflow is virtually stopped (the previously mentioned stagnation point) and then gradually increases speed. At some point near the trailing edge, it again reaches a velocity equal to that on the upper surface. Applying Bernoulli’s Principle, where the airflow was slowed beneath the airfoil, a positive upward pressure was created. Just like the faster flow, but with the opposite pressure change; as the fluid speed decreases, the pressure must increase. Since the pressure differential between the upper and lower surface of the airfoil increases, total lift increases.

Notorious Newton

Another pilot applicant was asked about Sir Isaac Newton’s contributions to aerodynamic theories and how they would apply during the flight. The applicant could come up with a couple of Newton’s laws but struggled with the application.

Sir Isaac Newton was an English polymath. He was not only a mathematician, but also a physicist and an astronomer. He also dabbled in theology and alchemy. He wrote his book, Mathematical Principles of Natural Philosophy, approximately 50 years before Bernoulli’s Hydrodynamica. In his book, Newton formulated the law of universal gravitation and also described the three basic laws of motion.

Newton’s First Law: “Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it.”

This means that nothing starts or stops moving until some outside force causes it to do so. An aircraft at rest on the ramp remains at rest unless a force strong enough to overcome its inertia is applied. Once it is moving, its inertia keeps it moving, subject to the various other forces acting on it. These forces may add to its motion, slow it down, or change its direction.

Newton’s Second Law: “Force is equal to the change in momentum per change in time. For a constant mass, force equals mass times acceleration.”

When a body is acted upon by a constant force, its resulting acceleration is inversely proportional to the mass of the body and is directly proportional to the applied force. This takes into account the factors involved in overcoming Newton’s First Law. It covers both changes in direction and speed, including starting up from rest (positive acceleration) and coming to a stop (negative acceleration or deceleration).

Newton’s Third Law: “For every action, there is an equal and opposite reaction.”

In an airplane, the propeller moves and pushes back the air; consequently, the air pushes the propeller (and thus the airplane) in the opposite direction—forward. In a jet airplane, the engine pushes a blast of hot gases backward; the force of equal and opposite reaction pushes against the engine and forces the airplane forward.

Looking at our wing again, the air being hit by the bottom of the wing while it moves through the air with a positive angle of attack, gets deflected downward. This creates an equal and opposite reaction to deflect the wing upward creating additional high pressure below the wing.

Newton’s Third Law of Motion is contributing to the total lift on the wing.

Flummoxed by the Flows

Beyond the direct lift created by the high- and low-pressure differentials on the wing, the changes to the air flows imparted by the airfoils create positive and negative lifting effects.

The air flowing across the top surface of the wing imparts a downward direction or downwash to the air. This downwash meets the flow from the bottom of the wing at the trailing edge. Applying Newton’s third law, the reaction of this downward and backward flow results in an upward and forward force on the wing.

At the tips of the wings, the higher-pressure air below the wing tries to spill around the tip to the lower-pressure air above the wing. This spillage is the source of the wing-tip vortices that instructors warn about. Besides being a source of concern when produced by other aircraft, the vortices have a negative impact on the production of lift at the tips of the wings. The vortices produce a downwash, but instead of the downwash pushing down on the air behind the wing, the downwash pushes down on the wingtips themselves. This downwash creates a reduction of lift at the wingtips. Winglets are designed to reduce the spillage from the bottom of the wing to the top of the wing. Reduced spillage produces less downwash on the wingtips. Less downwash directly on the wingtips allows the wingtips to produce more lift, increasing the efficiency of the wing.

Detrimental Drag

Drag is the force that resists movement of an aircraft through the air. There are two basic types: parasite drag and induced drag.

Parasite drag is comprised of all the forces that work to slow an aircraft’s movement. As the term parasite implies, it is the drag that is not associated with the production of lift. This includes the displacement of the air by the aircraft, turbulence generated in the airstream, or a hindrance of air moving over the surface of the aircraft and airfoil. There are three types of parasite drag: form drag, interference drag, and skin friction.

Form drag is the portion of parasite drag generated by the aircraft due to its shape and airflow around it. Interference drag comes from the intersection of airstreams that creates eddy currents, turbulence, or restricts smooth airflow. Skin friction drag is the aerodynamic resistance due to the contact of moving air with the surface of an aircraft.

The second basic type of drag is induced drag. In level flight, the aerodynamic properties of a wing or rotor produce a required lift, but this can be obtained only at the expense of a certain penalty. The name given to this penalty is induced drag. Induced drag is inherent whenever an airfoil is producing lift and, in fact, this type of drag is inseparable from the production of lift. Induced drag is always present when lift is produced.

Recall the downwash into the wingtips produced by the wingtip vortices. Downwash points the relative wind downward, so the more downwash you have, the more your relative wind points downward. That’s important for one very good reason: lift is always perpendicular to the relative wind. When there is less downwash, the lift vector is more vertical, opposing gravity. When there is more downwash, the lift vector points back more, causing induced drag. On top of that, it takes energy for the wings to create downwash and vortices, and that energy creates drag.

The greater the size and strength of the vortices and consequent downwash component on the net airflow over the airfoil, the greater the induced drag effect becomes. This downwash over the top of the airfoil at the tip has the same effect as bending the lift vector rearward; therefore, the lift is slightly aft of perpendicular to the relative wind, creating a rearward lift component. This is induced drag.

Looking at parasite and induced drag on the same graph:

As airspeed slows, parasite drag decreases and induced drag increases.
As airspeed increases, parasite drag increases and induced drag decreases.
The point where the 2 drag curves cross is the minimum drag possible for the aircraft configuration.

Beyond the Basics

The information presented above should be considered as a basic understanding of some aerodynamic concepts. Aerodynamics is a much more in-depth subject than will be covered in FAA handbooks and a simple blog post. Many engineers spend a lifetime studying and improving on the subject.

Some additional “pilot level” study might include a review of a few formulas that are found in the Pilot’s Handbook of Aeronautical Knowledge related to lift and drag.

The coefficient of lift (C_L) is defined as “The ratio between lift pressure and dynamic pressure.”

Lift can be calculated using the lift formula.

It should be noted that since velocity is squared, if all other factors remain equal, doubling the velocity of the wing will quadruple the lift.

Inevitably, doubling the velocity and quadrupling the lift is only possible as a mathematical formula. An aircraft could not continue to travel in level flight at a constant altitude and maintain the same AOA if the velocity is increased. The lift would increase and the aircraft would climb as a result of the increased lift force or speed up. Therefore, to keep the aircraft straight and level (not accelerating upward) and in a state of equilibrium, as velocity is increased, lift must be kept constant. This is normally accomplished by reducing the AOA by lowering the nose. Conversely, as the aircraft is slowed, the decreasing velocity requires increasing the AOA to maintain lift sufficient to maintain flight. There is, of course, a limit to how far the AOA can be increased, if a stall is to be avoided.

Drag can be calculated using a similar formula with the difference being that a coefficient of drag is used.

Doubling velocity in this formula would quadruple the drag.

The lift-to-drag (L/D) ratio is determined by dividing the C_L by the C_D, which is the same as dividing the lift equation by the drag equation as all of the variables, aside from the coefficients, cancel out.

An element of both equations is dynamic pressure. Dynamic pressure is often expressed as “q” where:

The L/D ratio is the amount of lift generated by a wing or airfoil compared to its drag. A ratio of L/D indicates airfoil efficiency. Aircraft with higher L/D ratios are more efficient than those with lower L/D ratios. In unaccelerated flight with the lift and drag data steady, the proportions of the C_L and C_D can be calculated for specific AOA as shown in the graph below.

Notice that the coefficient of lift curve (red) reaches its maximum for this particular wing section at 20° AOA and then rapidly decreases. 20° AOA is therefore the critical angle of attack. The coefficient of drag curve (orange) increases very rapidly from 14° AOA and completely overcomes the lift curve at 21° AOA. The L/D ratio (green) reaches its maximum at 6° AOA, meaning that at this angle, the most lift is obtained for the least amount of drag.

Note that the maximum lift/drag ratio (L/D_MAX) occurs at one specific C_L and AOA. If the aircraft is operated in steady flight at L/D_MAX, the total drag is at a minimum. Any AOA lower or higher than that for L/D_MAX reduces the L/D and consequently increases the total drag for a given aircraft’s lift.

Conclusion

Having at least a basic understanding of aerodynamics is important for all pilots and it will be evaluated on the practical exam for a certificate or rating. The further along a pilot is in their certificates, the more advanced their understanding of aerodynamics should be. Pilots should take the time to study this information and be prepared for the practical exam along with being prepared for flight situations that will test the application of their understanding.

Fly and stay safe!