Wings are very cool things. Many pilots like wings; they fly wings and most know the working speeds of wings (if only by rote). The question is, though, exactly how does a wing work? Keep in mind that designing an airplane is an exercise in compromise. How well a wing will or will not work on a particular aircraft is dependent on many factors.
A good design begins with the end mission in mind for a new aircraft. The engineers have to ask the question, what do we want the plane to do? Then there are the follow on questions: How much weight should the plane be able to carry? How fast should it cruise? How slow should it be able to fly? How far do we expect it to go on one tank of gas? And there are more questions, too.
The first thing pilots should know is the math behind wing design. Truly to understand what a wing can do aerodynamically, you “have to know the numbers.” The first batch of numbers are those that describe the wing, which will inevitably determine how well the wing will work and what it will do. The dimensions include things like wingspan, wing area, and chord.
Wings come in many shapes and sizes. The shape and particularly the size of the wing determine what the wing is capable of doing. The bigger the wing, the better or more it can lift. Conversely, the smaller a wing, the faster it can fly. Of course, there is mathematics involved in defining the design of any wing.
First, there is wingspan, sometimes referred to simply as span. The abbreviation for wingspan is the lowercase letter ‘b.’ Another important measure of a wing is chord, or the distance from the leading edge of the wing to the trailing edge. The lowercase letter ‘c’ represents wing chord.
Knowing these two numbers will allow you to determine another important feature of the wing: Wing area. Mathematically, the capital letter ‘S’ equals wing area, which can be determined by multiplying span (b) by chord (c). So, the equation looks like S = b x c.
Take for instance, the Cessna 172. It is a great little airplane with a wingspan of 36 feet 1 inch with an average chord of 4 feet 9.8 inches. This gives the airplane a wing area (S) of 174 square feet. Remember the equation, S = b x c? Inputting the values of 36.08′ for b and 4.98 for the average chord (equation now looks like this: 36.08′ x 4.82′ = 173.99′ square).
As mentioned, the size of the wing plays an important part in how the wing will work. Aircraft with a great wingspan coupled with a broad chord will of course, have a very large wing. The larger the wing, the greater lifting power it has for heavier loads. Look at the airliners and the transport airplanes of the military, the C-17, the C-5, and the old C-141. The aircraft are very large with great wing area (S), allowing for great lifting capability.
It also reduced their working speeds. With great S, comes higher drag (D), which naturally makes the airplane fly slower. Another way to put this is that because of the drag created by bigger wing, the airplane just cannot fly as fast as … a fighter, which has a much smaller wing, lifts considerably less weight, and has a better power to weight ratio.
In addition to the wing, the power plant also plays an important role in the way an airplane is going to operate. One would naturally think that more horsepower, more speed. To a degree, this is true, but you also have to consider the issue of the wing and the weight of the aircraft.
Again, we go back to the basics of L=W and D=T in straight and level, unaccelerated flight. Keep in mind, the heavier the airplane, the more lift is necessary to keep the airplane flying. With more lift, comes more drag, which limits the airplane’s maximum speed.
The first way to counter the increase in drag is by increasing power. Another way to control the amount of drag is to reduce the weight of the plane. A third way to “speed up” is to decrease the total wing area. These three methods of flying faster will work, some better than others. Again, though, you must also keep the “compromises” in mind as you seek the best method of flying faster.
A photograph that comes to mind is of a couple of Reno race pilots sawing about three feet off each side of a P-51’s wing. Three feet off one side, three feet off the other, and suddenly b for this particular Mustang is six feet less. As a result, S for this Mustang is about 20 square feet less.
Once you alter the wingspan by chopping off part of the wing, realize you have just changed another part of the “wing numbers.” This is the number that describes the wing in terms of aspect ratio, or AR.
AR is the ratio of chord to span. In the example of the Cessna 172, if you apply the formula, AR = b/c, you find the AR for the 172 works out to 7.5:1 (AR = 36.1/4.82 = 7.48). This means the ratio of chord to span is 7.5 feet of wingspan for each foot of chord. For general aviation aircraft, AR is typically about 5.7 to 8.0; transport aircraft AR is higher while for fighter and attack aircraft AR is lower. If you look at a high performance sailplane, you will find AR is much higher. For example, the Schweizer 2-32 sailplane has a wingspan of 57 feet with an average chord of 3.15 feet. This gives the craft an AR of 18 (AR = 57/3.15 = 18. 05).
How does this help or hinder the flying characteristics of a particular aircraft? Take a look at airplanes and their missions. As mentioned, the Cessna 172 has an AR of 7.5:1 and the 2-32 sailplane is 18:1. What about a Pitts Special?
With a reported S of 120 square feet and a wingspan of just 20 feet, the AR works out to 6.2:1. Now think about how each of those aircraft maneuvers. Ask the questions about mission and flying characteristics. Which aircraft is the most economical? Which flies the slowest? The fastest? Of the three, which rolls the fastest?
©2016 J. Clark
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