CHAPTER 10
Aerodynamics for the Hacker
A bit of theory helps with hacking the skies. This chapter covers the major parts of why airplanes fly and how they are controlled.
Lift
Lots of explanations of how wings generate lift are like a six-year-old’s conception of where babies come from—wildly inaccurate but somehow plausible. Below is another wrong explanation, but it gets the ball rolling until you enroll in a proper fluid dynamics class. So here it goes …
Conditions for Lift: Positive Aerodynamic Angle of Attack and Airflow
Take a piece of cardboard and spin it around or put your hand out a car window and notice that upward force happens when the front of your cardboard or hand is higher than the rear with respect to the airstream flow. Compare that to when your cardboard or hand is aligned with the airstream and generates no upward force—this is a neutral aerodynamic angle of attack. When you have a positive aerodynamic angle of attack, there is an upward force or lift. This ought to be obvious by experience.
Lift, Part 1
Now think about how you are generating the upward force. There is an obvious simple component, which is shown in Figure 10-1, that has air molecules bouncing off the bottom of the cardboard—it is increasing the pressure on the bottom of the wing. You can just think of Mr. Air Molecule as bouncing off the cardboard downwards, which by Newton’s Third Law will impart an equal upward motion to the cardboard. For the sake of completeness, you should realize that the cardboard is also pushing Mr. Air Molecule forward a bit, which translates into a backwards force on the cardboard. This is drag. Drag resists the forward progress of the cardboard.
FIGURE 10-1 The two basic components of lift.
Lift, Part 2
With all those air molecules ricocheting off the bottom, what happens to the air molecules that just make it over the top of the cardboard? Well, Ms. Air Molecule no longer has Mr. Air Molecule next to her because they were separated by the cardboard. In fact, there is nothing there (a vacuum) unless Ms. Air Molecule moves. That vacuum will draw her in and the other molecules around her down, which will (1) accelerate them and (2) retain less pressure because the same number of molecules will be spread out over a larger volume. My 10-year-old niece Annika observed that Ms. Air Molecule was accelerating like she was on a roller coaster with vacuum replacing gravity. This reduction in pressure is the second component of lift and is called Bernoulli’s principle. That’s it, folks. There are lots of other factors that can come into play like curved airfoils but it is all doing the same basic thing. Send hate mail to [email protected].
Stall
Stall is what happens when the wing loses the Bernoulli component of lift, which then leads to the airplane no longer having sufficient lift to support it and it falls. The classic version of a stall occurs when the angle of attack is increased so much that the nice vacuum bubble detaches from the top of the wing. There are lots of ways that the bubble can be detached. Well-designed airplanes react to stall by dropping the nose automatically to aid in reducing the angle of attack and increasing airspeed.
Pitch, Roll, and Yaw
Airplanes can move in three dimensions, and they come with names. Figure 10-2 shows the definitions of pitch (nose up/tail down or opposite), roll (left wing up/right wing down or opposite), and yaw (nose swinging to the left/tail to the right or opposite).
Center of Gravity (CG)
The CG is simply the single point where the aircraft can be suspended in any orientation and it will remain there. Another way to think about it is as the point where the weight of the airplane balances in pitch, roll, and yaw as shown in Figure 10-2. It is more generally known as the center of mass or barycenter, but talking that way will just confuse folks at the field. On plans, it is marked with a crossed circle. When you see the CG mark on plans, it means that the airplane needs to balance on that point to fly well, which dictates how components and additional weights are distributed on the aircraft. Rarely is there an issue with CG in dimensions other than fore/aft, but see the Carrot plane, where left/right CG is important, in Figure 10-3.
FIGURE 10-2 Pitch, roll, and yaw explained.
FIGURE 10-3 Asymmetric shapes will require determination of left/right CG as well as standard fore/aft CG. Top/bottom CG can be an issue as well, but it is unlikely with flat-plate designs.
Why we care about the notion of CG is stability. Generally speaking, lift is pretty easy to generate. Where things get tricky is in controlling that lift so that the aircraft is stable and can maneuver.
Yaw Stability
A weather vane’s only degree of freedom is yaw. The pivot point functions just like the CG, but it is determined by a bearing. The weather vane in Figure 10-4 is not going to work very well because there is equal area in front of the bearing and aft of the bearing.
FIGURE 10-4 Weather vane stability demonstration.
The wind is going to spin it around. If this is not clear, go ahead and grab a coat hanger, some cardboard, and a fan and experiment for yourself. How can this be fixed? Two options present themselves immediately:
1. Increase the surface area on one side of the bearing.
2. Move the bearing more to one side.
Figure 10-5 shows each approach. But note that they are essentially doing the same thing, increasing surface area on one side of the bearing and decreasing it on the other. Figure 10-6 shows a side view of the Flack with the bearing at the CG. With those huge stabilizers, you can see that this design is going to point into the wind without any problem.
FIGURE 10-5 Two solutions to stabilizing the weather vane from Figure 10-4 that amount to the same solution—get increased surface area aft of the hinge point.
FIGURE 10-6 Flack mounted as a weather vane at the design CG.
Static Stability
The Flack relies entirely on what is called static stability for yaw, which is provided by the big stabilizers automatically, just as a weather vane gets automatic corrections from the greater surface area aft of the CG.
Pitch Stability
Pitch stability is more complicated than yaw stability because lift is being generated in addition to active control surfaces. But each complication will be introduced in turn. Consider the Flack in a straight-down dive as in Figure 10-7. At this moment, the wing is generating no lift, and the airplane is stable in yaw because of the greater stabilizer area behind the CG. Remember that the CG is the balance point of the airplane in all orientations.
FIGURE 10-7 The Flack in a dive showing both pitch and yaw stability.
Consider what is happening in pitch. We can just pretend that the surface area of the wing is a weather vane, as shown in Figure 10-7, and pretty obviously it would make an excellent weather vane with that shape. If we moved the bearing/CG back to the location in Figure 10-8, we would not get as good a weather vane because there is equal area before and aft of the bearing/CG. If this does not make sense, get out some cardboard and do the experiment. At this point, enough has been explained to make sense of why the CG is forward for both yaw and pitch stability. Our planes do not need to be roll stable because there are no serious destabilizing roll forces in level flight. At this point, no more learning is necessary to go out there and hack at some sky. But greater mastery can be had by reading on.
FIGURE 10-8 The Flack with an aft CG/bearing demonstrating that the plane will not be stable in pitch.
Adding in Lift
We have shown how the location of the CG affects the weather vane stability of the Flack. Essentially, we know how an arrow remains stable in flight or how the plane is stable flying in a vertical dive. Lift makes things very interesting. Lift is an upward force generated by a positive aerodynamic angle of attack that has both the air on top of the wing sucking it up and the air on the bottom pushing it up, as explained earlier. The point at which the lifting forces are balanced is called the center of pressure, and for symmetric airfoils, this is located approximately at the dividing line on the wing that has 25 percent of the area in front of it and 75 percent behind, as shown in Figure 10-9.
FIGURE 10-9 The 25 percent/75 percent dividing line shown on the Flack that indicates the center of pressure.
The CG is one of the factors that helps us make an airplane stable and controllable. A rule of thumb for aircraft design is that the CG of flying wings splits the surface area such that 20 to 25 percent of the wing area is ahead of the CG.
If the CG is ahead of the center of pressure, the plane will have a tendency to raise the nose on dives because the reduced angle of attack will decrease lift, which will lower the tail. On climbs, the effect is reversed because the wing will generate more lift, which will rotate the nose down. This autostabilizing component is how free-flight planes manage to keep flying in turbulent air. With the Flack, the 10½-inch CG placement is slightly autostabilizing in this way. You can tell by trimming the plane for level flight (see Chapter 5) at two-thirds throttle. The plane should be able to fly 100 feet without any control inputs (it helps if the wind is calm). Place the plane in a shallow dive, and release the controls. You should see the plane gently recover. This is an excellent way to test whether the CG is correct. A slightly forward CG is the preferred setup for beginners because it makes the airplane more docile. It will also handle turbulence and wind better.
If the CG is at the center of pressure, then the plane will have no tendency to recover from dives or climbing. This is generally how I fly my planes. When trimming a new airplane, I start with the CG too far forward and incrementally keep moving it back until the plane stops recovering from dives on its own. I do this because I value maneuverability over stability.
If the CG is aft of the center of pressure, then the plane can be a real handful to fly. When the nose pitches down, the lift decreases ahead of the CG, and the dive worsens. When the nose pitches up, the lift increases ahead of the CG, and the plane climbs more. Planes with a CG slightly aft of the center of pressure will feel very twitchy in pitch, and they require constant pitch correction. A really aft CG plane is pretty much impossible to fly without onboard gyroscopic intervention.
Reflex and Flying Wings
You may have noticed that none of the airplanes in this book have a traditional tail like a 737 or a Cessna. They are all flying wings, which are sometimes called tailless airplanes. Given that a Flack flies just fine without a tail, why does a Cessna need one? It’s not there to look cool.
For a bunch of reasons not worth getting into, wings generate a forward-pitching moment when generating lift. Thus, in addition to lift, the wing wants to roll forward about the CG or tuck under. The horizontal stabilizer exists to provide a countering downward force to prevent the plane from tucking as shown in Figure 10-10. The figure shows the elevator raised a few degrees to make clear that downward force is being generated. Usually no deflection is seen because the downward force comes from the stabilizer’s angle of attack to the airstream, which is angled downwards a bit because of the lift being generated by the wing. The horizontal stabilizer also controls the pitch of the entire airplane by increasing or decreasing the amount of downward force.
FIGURE 10-10 How an elevator uses downward force to counteract the forward-pitching moment inherent in the generation of lift for stable aircraft.
One way to conceptualize why lift generates a rolling forward force is to assume that the area in front of the CG generates 25 percent of the lift and that the area aft of the CG generates 75 percent of the lift. Since the CG acts like the pivot point of the wing, there is more lift aft of the CG, which explains the rolling forward force. In reality, the amounts of lift being generated fore and aft of the CG vary on many factors, but the general idea is sound.
Flying wings, then, are an anomaly because they apparently don’t have any horizontal stabilizer to resist this pitching moment—how come they don’t pitch forward? Figure 10-11 shows that the elevons are responsible for resisting the pitching moment of the wing by having a little bit of up trim in them. This is called reflex. What has happened is that the flying wing does have a horizontal stabilizer; it just happens to be right where the wing ends.
FIGURE 10-11 How the elevons on a flying wing counteract the forward-pitching moment.
The downward-acting force also helps to keep the airplane stable in pitch. When the nose drops, the angle of attack for the elevator/elevon increases, as does airspeed, which increases the downward force and helps to bring up the nose. If the nose pitches up, then the elevator/elevon gets less of an angle of attack and less airspeed, which reduces the downward force and helps to move the nose up to level flight.
Before anyone’s panties get into a knot because their flying wing flies with no reflex, there are ways to require very little or no downward force by having the CG be right on the center of pressure or slightly aft of it, but all that is happening is that we are carefully counteracting the pitching moment with the mass of the plane. That balance will become unbalanced when the airspeed changes, and the plane will not be able to self-stabilize.
Reasoning about Lift
It is worth learning the basic shape of the lift formula if you are designing your own airplanes. It contains some crucial information for the kinds of design decisions you will need to make. A simplified formula for lift is
Lift = ½ × air density × velocity × velocity × how “lifty” the wing is X how big the wing is
The “liftyness” of the wing is called the lift coefficient and it can be looked up for all sorts of wing shapes and airfoils. For the standard Flack, lift will have to be 15 ounces in level flight, more for climb, and less for descent. What is the crucial information?
1. Velocity is squared, which means that to get twice the lift, you only need to go about 1.4 times as fast.
2. If I want to fly half as fast, the plane will have to either lose 75 percent of its weight, get four times as much surface area, or use an airfoil that generates four times the lift or some combination of the factors. Airspeed makes a huge difference in whether we get off the ground or not.
3. Slightly bigger, slightly heavier is not going to be that big a deal if we can just go a little faster.
How “lifty” the wing is depends on the angle of attack, the efficiency of the airfoil, and the overall shape of the wing. A flat plate is a pretty good airfoil that can generate gobs of lift at the cost of a lot of drag. It is beyond the scope of this book to explore more efficient airfoils, but they are out there if you are interested.
Drag
Drag is the aeronautical version of friction. It is the force resisting the forward motion of the aircraft. All the airplanes in this book generate a lot of drag because they are simple airfoils and designs optimized for maneuvering rather than efficiency. It is the reason that your Flack flies so badly with party streamers and a balloon tied to it—it’s the increased drag. You only need to know that too much drag will keep an airplane from flying well or flying at all, so be aware of it.
Glide Ratio
This term refers to the distance the airplane goes forward for the amount of altitude lost in a power-off glide. A sailplane can have a glide ratio of 40:1, meaning that for every foot dropped, the sailplane will go 40 feet forward. The Flack’s glide ratio has never been measured, but I would estimate it to be between 3:1 and 2:1. This means that the Flack comes down fast, which is a good thing if you are landing in a tight spot with lots of obstructions. It is a bad thing if you smoke the motor over a lake while carrying a camera, and the poor glide ratio causes you to land in the last foot of lake.
Conclusion
This chapter was meant to introduce the rough shape of what makes a plane fly. It is a big topic. Martin Simons’ Model Aircraft Aerodynamics is an good start for a more thorough treatment that has gotten respect from serious aerodynamics folks. NASA also has a good web site at www.grc.nasa.gov/www/k-12/airplane/. This chapter hopefully provided enough information to get you into trouble designing your own airplane. Chapter 11 gives you the gritty details of how we do it at the Brooklyn Aerodrome.