Airplane flights are a daily occurrence and almost everyone has flown at least once in their life, but few ever consider how it is done. Lift is what makes flight possible and although many of us were once taught that the Bernoulli principle explains flight, Newton’s law explains it better and is easier to understand. The wing diverts airflow down, with most of the airflow pulled down and over the wing.
Lift is defined in textbooks and training manuals three ways, the first is most often used by aeronautical engineers and is called mathematical aerodynamics. This description uses computer simulations or complex math to calculate the circulation or rotation of the air around the wing. While helpful information, it isn’t truly useful in understanding flight.
Another description is what may be called the most popular, which is the Bernoulli principle. While it is easy to understand and is what has been most often taught, it relies on the principle or assumption of equal transit times. It assumes that air travels faster over the top of the wing and focuses on the shape of the wing, while ignoring important phenomena such as ground effect, inverted flight, power, and the dependence of lift on the angle of attack of the wing.
The third explanation is more of a physical description of lift. It is based on the three laws of Newton and the phenomena called the Coanda Effect. It is unique and useful to the understanding of flight. It considers how the stall speed increases with altitude or how power increases with load. It also allows for rough estimates of lift, allowing the pilot to use his intuitive understanding on how to fly the airplane.
Lift – The Popular Description
Physics and aerodynamics students learn that an airplane flies due to the Bernoulli principle. This principle states that as air speeds up, pressure is lowered. The problem is that this is not always true; the fact is that the altimeter still will read the correct altitude even though air is flowing fast over the static port. This usually unchallenged way of thinking states that the wing has lift because the air rushes faster over it, thus creating an area of low pressure, but some wonder why it would go faster only over the top of the wing.
To explain why, people turn back to the geometric argument that says the distance the air travels is directly related to its speed. The thinking is that when the air separates at the leading edge, the part that splits over the top must meet again with what is coming from below creating the equal transit time mentioned above.
When looking at the second, most popular description, one wonders if the numbers are right. For example, imagine the high winged Cessna 172. This plane’s wings must lift 2300 lbs. at its maximum flying weight. The top of the wings air path is only 1.5% greater than it is under the wing. The popular description of lift indicates that at 65 mph, the wing would develop only 2% of the lift needed. The figures actually show that the airplane must be traveling at 400 mph for the specifications of this particular wing. This would make the difference in path length, according to the popular description, 50% in order to account for lift in slow flight, with the thickness of the wing being about the same as the chord length.
One must ask how anyone knows for sure that the separated air meets at the trailing edge at the same time. Airflow going over a wing when done in simulated conditions using smoke, shows that the air moving over the wing gets to the trailing edge much faster than that coming from below. In fact, this simulation showed that the air traveled faster than what is predicted by the equal transit times principle. The air that traveled below the wing also was shown to slow down from the free stream velocity of the air. This proves that only a wing with zero lift fits into the equal transit times principle. Using the same popular description would also imply that inverted flight is impossible. Since the top and bottom surfaces are shaped the same, it would deny that acrobatic planes could fly. It also ignores how a wing adjusts during dives and steep turns for load changes.
Knowing all of this, why do people still rely on the popular description? Most likely it is because the Bernoulli principle is easy to explain and understand. While there is nothing wrong with the principle or its definition of over the wing air speeds, it is not a complete explanation. It is missing a vital piece. While with the knowledge of air speed it explains pressures around the wing, it does not determine the speed. As will be explained, air accelerates over the wing because pressure is lower, not the other way around. Along with this shortcoming is that lift requires power (work per time). The key to understanding the phenomena of lift is that of understanding power.
Lift and the Laws of Newton
To understand how a wing generates lift one must first look to Newton’s first and third laws. The first law says, “A body at rest will remain at rest, or a body in motion will continue in straight-line motion unless subjected to an external applied force.” Air is not at rest if it has to bend or is accelerated into motion, there is a force at work on it.
The third law of Newton says that, “For every action there is an equal and opposite reaction.” So, an object sitting atop another object creates a force by its very weight, thus the object below equally and oppositely uses the same force on the object to hold it up. For a wing to generate lift, it must create an action against the air. The air then reacts to that action.
Imagine airflow or streamlines over a wing, the air flows straight into the wing and then must bend around it before returning on its straight path after leaving the wing. Without a net action on the air, there can be no lift. In actuality, the air flows over the wing and is bent down just as Newton’s law states. Lift requires the generation of lots of air being diverted downward. There must be an opposite reaction to the action of the wing coming into contact with the air.
There is a change in momentum (the product of mass and velocity or ma) from the lift of the wing. Newton’s second law in common form is, “F=ma, or force equal mass times acceleration.” In this form, the law shows that to accelerate an object of certain mass, there must be equal force. Newton’s alternative form to the second law could be written: Wing lift is vertical velocity of the air, times the proportional to the amount of air diverted. It’s that simple. The more lift needed the more air (mass) can be diverted. This can also be achieved by increasing the vertical velocity or downwash behind the wing. This downwash is visible to the pilot and appears as air coming off the wing at about the same speed of travel and the angle of attack. To those on the ground (if even possible) it would appear to be coming off the wing in a slow almost vertical direction. The greater the wing angle, the greater the vertical velocity of the air, which ultimately gives the wing lift.
So, as the observer on the ground sees air going almost straight down behind the plane, imagine a tight column of air behind a propeller, under the blades of a helicopter, or even a household fan. All rotate and if the air coming off the blades is at an angle, the air becomes cone shaped instead of in a tight column. Lift is then developed by the wing, which transfers momentum to the air. This theoretically would allow the plane to be weighed in flight.
Looking at the example of the Cessna 172 again, figure that the weight is 2300 lbs. and it travels at 140 mph. Assuming an effective angle of attack at 5 degrees, we can figure a vertical velocity for the air of around 11.5 mph at the wing. Also, assuming that the average vertical velocity of the diverted air is half the value from Newton’s second law, then the amount of air diverted is around 5 tons. This would create lift in the Cessna 172, if traveling at cruising speed, and diverting about 5 times its own weight in air per second.
This makes the notion of lift being only a surface effect unlikely; too much air is needed for the popular explanation to work. For it to be true, the Cessna 172 would have to accelerate all of the air needed within 18 feet above the wing in order to divert the 5 ton/sec required. The density of air at sea level is about 2 lbs. per cubic yard, when one considers that for a plane to punch a hole through fog there must be a tremendous flow down from the wing, one may ask how the air diverted? Air from above the wing is being pulled down, this causes the pressure to change, and brings the air lower. It is this acceleration from above traveling in a downward motion that gives lift.
Upwash at the leading edge of the wing is a complication. Not only is air diverted down at the rear of the wing as the plane travels, but it is pulled up at the leading edge. This can cause negative lift, which means more air must be diverted to compensate. More on this subject will follow.
To a pilot, the wing seems stable while the wind travels over it, but what is happening to the air under the wing? Remember that air starts at rest until the wing moves through it. On the leading edge, air moves up, called upwash. The trailing edge is where air is diverted down, called downwash. Under the wing, air is slightly accelerated forward and over the top, it is accelerated towards the trailing edge.
What makes the air follow this pattern? Air is considered an incompressible fluid for low speed flight, which means there is a resistance to the formation of voids and its volume can’t change. Through the reduction of pressure, air is accelerated over the top of the wing. Air is then drawn from in front of the wing and goes off behind the wing in a back and downward flow. That area must then be filled, so the air shifts to compensate, which means that this air is not the driving force of lift. Although the lift can be calculated if one were to determine the circulation around a wing.
It can be said that the top of the wing does much more to move the air than the bottom, making the top surface more critical. This is why airplanes can carry such things as drop tanks under the wings, but not on top of the wings and why wing struts are located under the wings, while upper struts are rare. Any thing that obstructs the top of the wing interferes with lift.
The Coanda Effect
How then does the wing divert air down? Air is a moving fluid as was stated above. When a fluid comes into contact with a curved surface, it will naturally follow it, just as water around a rock in a river would. The tendency of fluids to follow a curve is known as the Coanda effect. The first law of Newton showed that the fluid would not bend unless there was force acting on it. Then using the third law of Newton, we know that there is an equal and opposite force made by the rock. Viscosity is why the fluid follows the curved surface; the resistance to flow makes it want to stick or be sticky, and to attach to the surface. The velocity between the surface and the nearest air molecules is zero and just above the surface, the fluid has some small velocity.
The farther from the surface, the faster moving the fluid is, until the external velocity is reached. Shear forces bend the fluid because of the change in velocity near the surface. The layer, which is less then one inch thick and appears stuck to the surface is called the boundary layer. The tighter the air bends around the wing, the greater its force. Most of the lift is on the forward section of the wing. The first ¼ of the chord length equals half of the total lift on the wing.
Lift as a Function of Angle of Attack
It makes no difference which type of wing is on a plane, all modern planes force the air down or rather pull the air down from above. All have an angle of attack with respect to the oncoming air, which is what is important in determining lift. The angle of attack’s role can be understood if it is known that the angle of the wing to the air that gives zero lift is zero degrees. If the angle is then shifted up or down than the lift will be proportional to that angle. It is similar for all wings regardless of design. Pilots adjust the angle of attack to adjust for speed and load. Shape is only an aid in understanding lift, but it is the angle of attack that is most important.
At about 15-degrees the lift begins to decrease. The forces needed to bend the air at such a steep angle cause the air to start separating from the wing, it is more than the viscosity of the air can support. This is called a stall.
Air Scoop Wings
Once again, imagine a wing. Don’t use the image of a flat thin blade that somehow cuts through the air and develops lift, but instead visualize a scoop that diverts air from a straight path to the angle of attack. Make the area of the scoop proportional to the wing. With the lift of the wing being proportional to the amount of air diverted, the lift would also be proportional to the area of the wing.
As mentioned, the amount of air diverted down is proportional to the lift of a wing times the vertical velocity of the air. The scoop diverts more air as the plane’s speed increases. The vertical velocity of the diverted air must be decreased proportionally since the load on the wing does not increase. This makes the angle of attack reduce so as to maintain a constant lift. As the airplane goes higher, the air is less dense, so at a given speed the scoop diverts less air, meaning the angle of attack would have to be increased to compensate.
Power is a Requirement for Lift
Lift requires power, this power can be provided by the airplane’s engine or possibly gravity when flying a sailplane. As a plane flies over, the air gains a downward velocity, which means it is in motion even after the plane leaves. This is energy; power is energy.
The energy created by the wing to the air is proportional to how much air is diverted down times the vertical velocity squared by the diverted air. Remember that the lift of the wing is proportional to the amount of air diverted times the vertical velocity of the air, so the power needed to lift the plane is proportional to the weight times the vertical velocity of the air. Double the speed and that doubles the amount of air diverted down.
Lift takes power and if one wants to go faster, then one needs more power. The airplane imparts energy to an air molecule, which is proportional to the speed. The amount or number of molecules that strike per time is proportional to the speed, so the faster the speed the more impacts. Thus to overcome parasitic drag from wheels, struts and other features, the power needed increases with the speed. Parasitic power dominates the power requirement at cruising speeds. A bigger engine will give one a faster rate of climb, but won’t really improve the cruise speed; even doubling the engine size will only increase the cruise speed by about 25%.
Efficient Wings
To define drag one simply divides power by speed. A slow flyer such as a glider is designed to minimize induced power, which is strongest at low speeds. Propeller planes are faster and use parasite power, while jets are completely reliant on parasitic drag.
The parasitic drag of a Boeing 747 wing is about the same as a ½ inch cable that is just as long. If the wing area were increased, the scoop size would also increase so it could divert more air. To achieve the same lift, the angle of attack would have to be reduced, as would the induced power, as it is proportional. This makes the wings lifting efficiency increase with the expansion in area. The bigger the wing, the bigger the increase in parasitic drag and the less induced power needed to produce the same lift.
The Relationship between Wing Loading and Power
When flying at a constant speed, the vertical velocity must be increased to compensate if the wing loading is increased. How? By increasing, the angle of attack, which would be doubled if the weight of the plane were doubled, making the induced power proportional to the load, times the vertical velocity of diverted air. Look to the rate of fuel consumption when trying to measure the total power. If the speed were constant than a change in fuel consumption would be due to a change in induced power. Just as in Newton’s theory, there is an effect of load on the induced power.
The downside, other than the need for more power, is the increase in the angle of attack with increased load. A wing will surely stall at some point when air can’t follow the upper surface. This is called critical angle. The angle of attack that causes stalling is constant and is not a function of wing loading. It increases the load in a turn, which is why pilots practice stalling. An airplane can stall at any speed because at any speed there is a stalling load.
Downwash Visual
Like a sheet, the downwash comes off the wing and is related to the distribution of load. As the load changes so does the downwash along the wing. Near the base more air is being scooped up than at the tip and since it is scooping so much air the effect of the downwash sheeting is to curl outward and around itself, called the wing tip vortex.
One can often see vertical extensions on the tips of wings; these are called winglets and are there to improve the efficiency of the wing. The winglet increases the effective length and area of the wing. On a normal wing, lift goes to zero at the tip due to the wrap around the end. The winglet blocks this flow and the lift can extend further out on the wing, which gives increased efficiency. While winglets are very useful, they can be detrimental to the flow; it is necessary that they be installed properly.
Increased Efficiency and the Ground
Ground effect is when there is increased efficiency to a wing because it is within a wingspan of the ground. Just like a goose that glides low to the water before landing, an airplane with low wings can get a drag reduction of up to 50% when in the process of landing. Pilots often use soft runways or grassy areas for ground effect.
Upwash also plays a part in ground effect landings. The upwash increases the load on the wing and to compensate the wing needs to fly at a greater angle of attack, creating a greater induced power. Just like Newton’s third law of an equal and opposite force. The circulation under the wing is inhibited as it nears the ground and there is a reduction in the upwash as well as in the additional load caused by the upwash. The wing becomes more efficient because the angle of attack is reduced by compensation and so is the induced power.
The weight of the plane is than equal to the added load of the plane times two, due to the upwash. With the majority of smaller planes having an aspect ratio of 7-8, they can expect to experience up to a 25% reduction in wing loading because of ground effect. When the Cessna 172 was mentioned before, it was estimated that it could fly at 110 knots and must divert about 5 ton/sec to provide lift, but since those calculations did not include the contribution of upwash, the number would be closer to 6 ton/sec of diverted air.
Review
After all of this, what should one conclude?
1 – The speed of the wind and the air density is proportional to the amount of air diverted by the wing.
2 – The speed of the wing and the angle of attack is proportional to the vertical velocity of the diverted air.
3 – The amount of air diverted times the vertical velocity of the air is proportional to the lift.
4 – The lift times the vertical velocity of the air is proportional to the power needed for lift.
Using the perspective of the physical explanation, we can see that when a planes speed is reduced, the physical view states that the angle of attack will be increased to compensate for the amount of reduced air diverted and lift power is increased. We can also see that when a planes load is increased, the amount of air diverted is equal, but the angle of attack needs to be increased for extra lift. Also increased is the power needed for lift. Both of these scenarios are not explained with the popular explanation. Even when a plane flies upside down, the physical view applies, nothing need be explained when adjustments are made to the angle of attack of the inverted wing for desired lift. The popular explanation cannot allow for this and implies that it is impossible.
One can see that the popular explanation just doesn’t cover the subject of lift in flight; it merely applies a simplistic answer without insight to the question of lift. To truly understand it, the physical description fills the gaps while being just as easy to understand.
U.S. Centennial of Flight Commission