Aeronautical Calculations: What’s with All Those Coefficients Anyway?

Aeronautical Calculations: What’s with All Those Coefficients Anyway? 

         When aircraft designers decide on the design specifications for a new aircraft, they develop a model that is tested in a wind tunnel. The data collected from wind tunnel tests are used to develop a comparison to how the aircraft will fly at full scale. They make these and other comparisons by using proven aeronautical equations using dimensionless coefficients. 

In the previous sections you saw that thrust, lift, weight, and drag are forces and are usually expressed in pounds or newtons. You also saw that pitch, yaw and roll are moments and are expressed in inch-pounds, foot-pounds or newton-meters. So when we talk about our test data we may say, "The wing generated 12 pounds of lift," or "The engine generated 3000 pounds of thrust." That will work fine as long as we are willing to talk only about one specific wing, or one specific engine. What do we do when we want to compare a wing that was tested at one scale and set of conditions, and apply it to another scale and a different set of conditions? Suppose we tested a scale model of a jet transport Model X in the wind tunnel, and now we want to know if the full-scale airplane based on this model will be able to fly from San Francisco to London. The following scenario will show how dimensionless coefficients can help address this problem.

The wind tunnel tests run on the model gave us the following data:

wind tunnel tests run on the model gave us the following data." border=1 cellspacing=0 cellpadding=0>

Model X Data	Test 1	Test 2	Test 3	Test 4	Test 5	Test 6	Test 7	Test 8
Angle of Attack (deg)	0.0	0.5	1.0	1.5	2.0	3.0	5.0	10.0
Lift (pounds)	11.9	238.0	476.4	714.1	952.5	1785.9	2381.4	4048.3
Drag (pounds)	2.5	23.8	42.9	59.6	78.4	118.8	238.1	476.4

The model tested is 5% of full-scale, and the wind tunnel was operated at sea level pressure and a velocity of 300 knots. It is anticipated that the real airplane will fly at 35,000 feet at a velocity of 550 knots. The actual airplane is anticipated to weigh about 550,000 pounds (without fuel) and have a wing area of about 4,800 square feet. The aircraft designers believe that the airplane will have about 200,000 pounds of fuel available for the cruise portion of the flight. The weight of the aircraft (550,000 pounds) plus the weight of the fuel (200,000 pounds) equals a total weight of 750,000 pounds. Engineers anticipate using 2 engines that together, burn about 25,000 lbs of fuel each hour while creating 50,000 pounds of thrust. Does the wind tunnel data show that the airplane would make the 5,300-nautical mile trip?

This is exactly the kind of problem that aerospace engineers evaluate every day. How can we take data from a wind tunnel test and apply it to the real vehicle, especially if that vehicle has yet to be built? Fortunately, we have a hundred years of aeronautical experimentation to back us up. We will use the non-dimensional coefficients that were implemented over those one hundred years to solve the problem.

Over the years the engineers have determined that much of the data can be non-dimensionalized into coefficient form. This means that coefficients will not have units of pounds or foot-pounds like the original data; they will have no units attached. So what this means is that a quantity that was measured in pounds will be divided by something else that has units of pounds, and since pounds divided by pounds results in '1' the units effectively disappear. For example:
3 pound / 1 pound = 3

Treat 'pound' as you would any other number. Now the '3' is a non-dimensional or 'dimensionless' coefficient. Now we just need to find something that has units of 'pounds' to divide by. However, we can't just divide by any old 'pounds' since we are really looking for a way to account for scale, pressure, and velocity effects so we can use our wind tunnel data to predict how the actual airplane will perform.

Instead of proving to ourselves the statement below, this time we will take advantage of the hundred years of aeronautical data that came before us and accept the following statement as fact:

The dynamic pressure "q" and wing area "S" put together will give us the necessary quantity that will "non-dimensionalize" the force measurements, and permit them to be scaled (Think: "Cancel out the units."). The unit part is easy to verify. See the calculations below.

q = pound / foot2
S = foot2
so q * S = pound

There are literally hundreds of reports and research papers that put the scaling effect under scrutiny, so let us just say, that for the most part, and especially for what we are trying to show, non-dimensionalizing forces by dynamic pressure and wing area give the appropriate coefficients. (There are instances and conditions where this may not be true, but those are beyond the scope of this web site.) Similarly, moments are non-dimensionalized by dynamic pressure, wing area, and mean aerodynamic chord. "C" which is usually expressed in feet.

Let’s take another look at the table:

The wind tunnel tests run on the model gave us the following data with the appropriate coefficients added. 

wind tunnel tests run on the model gave us the following data with the appropriate coefficients added." border=1 cellspacing=0 cellpadding=0 >

The wind tunnel tests run on the model gave us the following data with the appropriate coefficients added.

Model X Data	Test 1	Test 2	Test 3	Test 4	Test 5	Test 6	Test 7	Test 8
Angle of Attack (deg)	0.0	0.5	1.0	1.5	2.0	3.0	5.0	10.0
Lift (pounds)	11.9	238.0	476.4	714.1	952.5	1785.9	2381.4	4048.3
Drag (pounds)	2.5	23.8	42.9	59.6	78.4	118.8	238.1	476.4
Dynamic Pressure 'q' in pounds/ft^2 at 300 knots and0 ft alt.	301	301	301	301	301	301	301	301
Wing Area ft^2	12	12	12	12	12	12	12	12
Coefficient of Lift CL	.0033	.0659	.1319	.1977	.2637	.4944	.6593	1.1208
Coefficient of Drag CD	.0007	.0066	.0119	.0165	.0217	.0329	.06593	.1319

We have added some more data, and have expressed the lift and drag in coefficient form. We will now use those coefficients to compute and create some predicted values for lift and drag on the actual airplane.

We will now use those coefficients to compute and create some predicted values for lift and drag on the actual airplane.

We will now use those coefficients to compute and create some predicted values for lift and drag on the actual airplane.

Aircraft X Data	Test 1	Test 2	Test 3	Test 4	Test 5	Test 6	Test 7	Test 8
Angle of Attack (deg)	0.0	0.5	1.0	1.5	2.0	3.0	5.0	10.0
Coefficient of Lift CL	.0033	.0659	.1319	.1977	.2637	.4944	.6593	1.1208
Coefficient of Drag CD	.0007	.0066	.0119	.0165	.0217	.0329	.06593	.1319
Dynamic Pressure 'q' in pound/ft^2 at 550 knots and 35K ft alt.	316	316	316	316	316	316	316	316
Wing Area ft^2	4800	4800	4800	4800	4800	4800	4800	4800
Lift (pounds)	5,000	100,000	200,000	300,000	400,000	750,000	1,000,000	1,700,000
Drag (pounds)	1,000	10,000	18,000	25,000	33,000	50,000	100,000	200,000

We can see within the column marked "Test 6" that the airplane needs to maintain an angle of attack of at least 3 degrees to hold its own weight in the air. We can also see that it generates 50,000 pounds of drag at that condition which matches those engines our designers pick out. We are now very close to determining whether our airplane can fly from San Francisco to London.

We need one more equation: the Breguet Range. This equation is used to calculate the range of an aircraft given a specific flight plan or profile. A typical flight profile includes taxi and takeoff, steep initial climb, climb, cruise, descent, approach and landing. The changing weight of the aircraft as it burns fuel is also taken into consideration. Furthermore, reserves are also calculated as part of a contingency plan for when an approach is missed, which would require additional maneuvers and flight time.

To find the range is much more complex than simply dividing the total fuel by the average hourly fuel consumption and then multiplying by the velocity. That's why we need the Breguet Range equation to predict how far an airplane will fly accounting for flight performance and the change in weight of the airplane as it burns or uses its fuel.

The Breguet Range equation is given below.

Range = (V/C) * (L/D) * ln(Wi/Wf)

V= Velocity in knots

C= Specific fuel consumption in pounds fuel per pounds thrust per hour

L= Lift in pounds

D= Drag in pounds

ln= Natural logarithm, or loge

Wi= Weight of aircraft at start of cruise in pounds

Wf= Weight of aircraft at end of cruise in pounds

The Breguet Range equation will give the flying range of our actual aircraft in nautical miles. For our aircraft we hope the range will be greater than 5,300 nautical miles for our hypothetical trip.

Specific fuel consumption was alluded to earlier, even though it was not specifically named. It was mentioned in the line: "using 2 engines that together, burn about 25,000 pounds of fuel each hour while creating 50,000 pounds of thrust." That comes out to a specific fuel consumption of 0.5.

C = Fuelflow/Thrust
C = (25000 pounds/hour)/(50000 pounds) = 0.5/hour 

Notice that "C" isn't quite a non-dimensional coefficient, since it has units of "per hour." We can also see that L/D could be replaced with CL/CD since we could divide both the numerator and denominator by q * S and not change the equation since (q*S)/(q*S) is like multiplying by 1.0. We can now solve the Breguet range equation. See the solution below.

The aircraft will not make the 5,300 nm trip. Using the Breguet equation range with the data collected from the wind tunnel tests on the model, it appears we need to either land in Scotland or make some changes to our airplane. From the Breguet equation we know that we can increase range by increasing the values of V, L or Wf, and by reducing the values of C, D, and Wi. Changing these values will affect other design aspects of the aircraft that have problems and complications associated with them in real life. Since Wi and Wf are manipulated by the ln function, the impact of changing these parameters is less dramatic. This is referred to as modifying the "fuel fraction." This will involve reducing the structural weight so a larger percentage of the total weight is fuel. This can be very tricky and expensive since it has the potential to affect just about everything on the aircraft. For example, we really cannot increase the lift on our actual aircraft since we want to maintain a steady altitude. To increase the lift in this case it would mean a change in the structural weightof the airplane. We could increase the speed, but that might also increase the drag if we go too fast.

Our best choices for improvement really come with specific fuel consumption and drag. If we can refine our design a bit more, we may get a reduction in drag. If we can get some help from the engine manufacturer, they might be able to reduce the amount of fuel needed to generate the same amount of thrust. We only need 3.4% improvement in either one or in a combination of both to meet our goal. Of course, that may not sound like a lot, but it is enough to financially make or break an aircraft company.

Tools of Aeronautics

Tools of Aeronautics

The Four Tools

       Researchers in the field of Aeronautics primarily use four "Tools" to test their hypotheses: Computational Fluid Dynamics, Wind Tunnel Testing, Flight Simulation and Flight Test. Each of these four "Tools" consists of unique and specialized equipment and experts trained in the development, management and operation of the Tools. These Tools were developed only within the last 100 years and have evolved in parallel with technology in other areas. On one hand their evolution was dependent on the development of technology and on the other hand, their evolution pushed the technology faster and to greater heights. Each Tool has its own niche in the design cycle of a new airplane or in the modification of an existing one. Data from one Tool can feed into the tests performed using another Tool. Oftentimes, research will be completed using one Tool and proceed on to another, only to return to the previous Tool because of a new question generated during tests using the second Tool. Selecting which Tool to use is based on the question being asked. A Tool that can provide excellent data on, say, the aerodynamics of a wing may not be able to give any information about how that wing affects the controllability of the entire airplane.

Wind Tunnels
        Wind Tunnels were the first Tool to be developed and have been used since the time of the Wright brothers. The name "Wind Tunnel" isvery appropriate. A wind tunnel is basically a long tube or tunnel through which air is blown at controlled speeds. A scale model of an airplane, or part of an airplane is mounted in the tunnel and measurements are taken of the forces and pressures that the model experiences when the air is blown. The basic idea of a wind tunnel is to move wind past a stationary airplane, instead of flying the airplane through the air. This is safer, cheaper, and provides a more controlled environment in which to test. It has been proven that data gathered in this way is able to accurately predict forces and pressures generated during real flight.

The models mounted in the tunnel can either be a scaled version of the real airplane, or a scaled version of part of the airplane. Note that the scaling must be extremely accurate or the prediction of forces and pressures will be in error. Measurements are made by sensors which are embedded in the model and mounted throughout the tunnel. Examples of sensors are strain gauges, balances and pressure sensors. Examples of sensors mounted within the tunnel are floor balances (much like bathroom scales), barometers, thermometers, anemometers, pressure sensors and microphones. Data from all of these sensors are fed into computers. Researchers and engineers then display the data in numerical form (lists of numbers) or graphical form (graphs and plots). Some tunnels have the capability to inject oil, smoke or water into the airflow so that photographs may be taken. Other visualization techniques using lasers, paint that changes color in response to changes in pressure, and other high technology tools are currently being used.

	Wind tunnels come in all shapes and sizes, from small hypersonic tunnels (3000+ miles per hour) to very large low-speed (115 miles per hour) tunnels which can test full-sized models. Many wind tunnels exist throughout the world. The largest wind tunnel can be found at NASA Ames Research Center in California. The test section - where the model is mounted - is 80 feet high by 120 feet wide. A full-size model of a Boeing 737 airplane can be mounted in this test section. Wind tunnel testing is critical during the design of a new airplane or when making modifications to an existing airplane. A common usage of wind tunnel testing is to gather data to help build a mathematical representation of an airplane that can reside in a computer - called a mathematical model. This type of information is invaluable to researchers and enables them to more fully utilize the other Tools. Cars, trucks, parachutes and rotorcraft are also tested in wind tunnels.</p>
	Computational Fluid Dynamics      Wind tunnel tests can be very expensive. Wind tunnels themselves use massive amounts of electricity to generate the airflow. The maintenance of machinery, equipment and tunnels the size of multiple football fields is also very expensive. Airplane models with their rigorous requirements for precision and durability take much time and money to build. In the early 1960s the idea was conceived to run wind tunnel tests in a computer. In those days, computers were large, slow and cumbersome compared to the computers of today. However, given a mathematical model of an airplane, they were able to accurately predict forces and pressures in support of research in fluid dynamics. The real beauty of this technique, however, was the ability of the computer to display graphical pictures and representations of the data which allowed researchers to almost instantaneously perceive and analyze what was happening to a particular model. This visualization was only available in crude forms in the wind tunnel. The field of fluid dynamics was thus able to perform research computationally, inspiring the moniker Computational Fluid Dynamics or CFD.
	In the early days, however, computers had not evolved enough to handle the huge amounts of data and computations needed to accurately model modern airplanes. In an excellent example of research needs pushing the evolution of another technology, aeronautical researchers cried out for faster computers that could handle huge amounts of data. With the advent of the supercomputers, their dreams were realized. Supercomputers can easily perform over one billion calculations per second. It would take a person solving one equation every second, 24 hours a day, over 32 years (or a whole career) to solve what a supercomputer can in one second. As fast as today's computers are, however, many aeronautical models are so complex that hours are needed for these analyses. However, the results are well worth the wait! Modern computer graphics that can present data in three-dimensions give a researcher information about the aerodynamics of an entire airplane on one computer screen. While the graphics are visually striking and artistically beautiful, their most valuable contribution to aeronautical engineering is their ability to present an incredibly large amount of very complex information in a manner that enables researchers to quickly and accurately draw conclusions from their data. The capabilities of CFD will continue to expand and grow as computer and visualization technology continue to evolve.

Flight Simulation

The previous two Tools have not included one very important aspect of flight - the pilot. Flight Simulation incorporates the ability of a human to subjectively observe and analyze his or her experiences. As in CFD, a mathematical model of the research airplane is programmed into a computer. Instead of providing graphical images of the model, a flight simulation computer controls a cockpit mock-up designed to look like the interior of an airplane, a motion system to simulate the movements of an airplane, visual computers to create out-the-window scenes for the pilot, sound systems, and instruments all working together to provide the pilot with an extremely realistic flying environment. Again, the evolution of computers has greatly influenced the ability of flight simulators to accurately simulate real flight. There are twoprimary uses of flight simulators: training and research. Training simulators now enable pilots to learn to fly new airplanes on the ground. They are able to perfect their skills prior to taking off in the real airplane. Flight simulators are particularly adept at training pilots to handle emergency situations. Engine-out, loss of hydraulics, blown tires, and a host of other life-threatening situations can be accurately simulated and effective pilot responses learned, all without the possibility of loss of life or airplane.

Research flight simulators are used extensively to examine the handling qualities of an airplane. As drivers of cars we are intimately familiar with, and often critical of, how our vehicles handle. The same holds true with pilots and airplanes. Modern high performance airplanes (such as the X-29) are very difficult to "handle." Complex computer-based control systems are used to help the pilot fly. In some cases the airplane could not be flown without the aid of a control system. These control systems must be extensively tested and fine-tuned before they are incorporated into a real airplane. Much of this testing takes place in flight simulators. Research simulators are flown by test pilots. Test pilots are trained how to provide accurate and technically sound subjective evaluations of an aircraft's handling qualities. On some occasions, test pilots will fly a set of maneuvers in a simulator in the morning and fly the same set of maneuvers in the real airplane in the afternoon.

The Vertical Motion Simulator (VMS) at NASA Ames Research Center in California is the largest motion-base simulator in the world. It is known as a six-degree-of-freedom simulator. This means that the cockpit can move in the three translational directions (forward/back, up/down, side to side) and generate the three rotational movements (roll, pitch and yaw). The simulator cockpit can travel vertically over 60 feet and can experience accelerations close to 32 feet per second per second (or "1 g"). The VMS is one of the most technically advanced flight simulators in the world. Because simulators are so cost effective and can so accurately mimic the motion and environment of flight, they have become critical in the development of new airplanes and modifications to existing ones.

Flight TestAfter all the above three Tools have been used and used again, the true test of any airplane is real flight. This is where the Tool of Flight Test becomes critically important.

A new airplane, or a newly modified airplane, is not built and immediately pressed into service. It must undergo rigorous flight testing. All the predictions made using the other three Tools are only that - predictions. Flight Test is when those predictions are finally proved or disproved.

Flight Tests require much advance planning and preparation. Instruments are placed in the airplane to record forces, pressures, control surface movements, pilot movement of controls, and radio communications. Every possible bit of information about the flight is recorded.

On the ground, tracking stations are set up. Microphones and cameras are readied. Barometers, thermometers and anemometers are installed to record the environment during the flight.

A precise and exhaustive list of all maneuvers that researchers want the pilot to fly are compiled in a test plan. Every action of the pilot is prescribed in this test plan - from takeoff to landing.

A test pilot receives hours of training, not only on how to fly and how to handle emergency situations, but how to accurately report what he or she is seeing, feeling and hearing throughout the flight. Test pilots wear a flight suit that has snaps and straps that allow them to strap the test plan to one leg and a notepad on the other. Everything the pilot says is recorded and analyzed. A test pilot must be able to follow the flight plan precisely. And, if something goes wrong the test pilot must be able to quickly determine the cause of the problem and its severity. It is a point of honor for all test pilots to land their airplane. One of the most difficult but also the most challenging decision a test pilot must make is whether or not, when a problem arises, the airplane is still flyable. Unfortunately, history has seen test pilots who have "stuck it out" thinking they could successfully land the airplane, when in fact they couldn't. Being a test pilot is an incredibly demanding and dangerous occupation! The advent of flight simulators and CFD has helped reduce the risks of flight test by making sure the design is more mature before testing.

Based on the results of a flight test, an airplane may be tested further using one of the other three Tools, more flight tests may be recommended or it could be determined that the research questions have been adequately answered.

The Use of Coordinate Axes in Aeronautics

The Use of Coordinate Axes in Aeronautics

           For purposes of basic understanding all references to motion and direction will be made using an imaginary three-dimensional coordinate system. This coordinate system will help to describe the motions of an aircraft in three-dimensional space. The center of the coordinate system is found at the centroid of the aircraft - roughly between the wings in the middle of the fuselage. A centroid is an imaginary point around which all rotation takes place. The three axes intersect at the centroid at 90o degree angles to each other. Thelongitudinal axis runs the length of the aircraft from the nose through the tail. The lateral axis runs across the wings from tip to tip. Thevertical axis runs from the top (ceiling) of the airplane to the bottom (floor). These axes extend indefinitely from the center of the aircraft (see figure). Movement along or around one axis does not necessarily involve any movement on or around the other two.

Moving on Three Axes

Once in flight, an airplane can have six motions along and around the three axes. Mathematically speaking, all possible movements that an airplane can make can be defined in terms of these six directions. This is the basis of the mathematical modeling of airplanes and flight. Three of the movements are linear: front and back along the longitudinal axis; side to side along the lateral axis; up and down along the vertical axis. The other three movements are rotational: movement around the longitudinal axis, called roll; movement around the lateral axis, called pitch; movement around the vertical axis, called yaw. We use stabilizers to keep the airplane flying primarily longitudinally. This is why mathematical modeling or even a simple description of airplane movement can become very complex.

Stability

Stability is the ability of an airplane to return, of its own accord, to its original attitude in flight after it has been disturbed by some outside force, like wind gusts. Stability also refers to an airplane's response to the pilot's use of the controls.

The empennage plays an important role in the stability of an airplane, much like the tail feathers of an arrow are critical to the stability of the arrow. If an arrow is shot without its tail feathers, it will wobble. The tail feathers keep the arrow stable and help it to stay on course. The empennage works the same way. The vertical fin helps to maintain stability in the direction of yaw. The horizontal stabilizer helps to maintain stability in the directions of pitch and roll. The empennage structures do produce drag, however. Researchers have developed ways to fly tail-less airplanes, but the airplanes must use computer-based control systems to maintain their stability. While the empennage structures of different airplanes can be very dissimilar, most modern airplanes still do have some form of fin and horizontal stabilizer.

The usable center of gravity range of this airplane is greater when it is gliding in stable horizontal flight with the engine off (TOP) than it is when the engine is on and the landing gear is down (BOTTOM).

An important component of stability for an airplane is the center of gravity (cg). The cg is an imaginary point about which the weight of an airplane balances. If you put a ruler across your finger and place it so it balances, your finger is at the cg of the ruler. The cg in an airplane does not stay in the same place at all times. A load of heavy cargo may shift the cg as will the drainage of fuel from the tanks during flight. Pilots have to recognize shifts in the cg and respond accordingly.

Sudden shifts in the cg can be catastrophic. If an airplane experiences turbulenceduring flight and a large cargo load shifts, the pilot may have trouble reacting quickly enough to the shift to maintain stability of the airplane.

Controlling MotionAn airplane has three control surfaces: ailerons, elevators and a rudder. Within the cockpit, two controls operate the control surfaces. The control stick controls theailerons and elevators. The rudder pedals control the rudders.

The table below explains flow from pilot controls to control surface to motion.

control in cockpit	control surface	motion
control stick (right and left) ailerons roll	control stick (front and back) elevators pitch	rudder pedals rudder yaw

The ailerons are flap-like structures on the trailing edge of the wings -one on each side. When the pilot moves the control stick to the right, the right aileron will tilt up and the left aileron will tilt down. This will cause the airplane to roll to the right. When the pilot moves the control stick to the left, the left aileron tilts up, the right aileron tilts down and the airplane rolls to the left. This happens because as the aileron tilts downward (effectively increasing camber) more lift is created and the wing rises. As it tilts upward, less lift will be created and the wing will descend. If the wing on one side of the airplane rises and the other descends, the airplane will roll towards the side of the decrease in lift.

The elevators are also flap-like structures that are mounted on each side of the horizontal stabilizer. When the pilot pushes the control stick forward, the elevators tilt downward. This causes the tail of the airplane to rise and the fuselage to tilt down - this is called pitching down. When the pilot pulls the control stick back, the elevators tilt upward, the tail goes down and the fuselage pitches nose-up. When the elevator tilts downward more lift is created (like the ailerons) and the tail rises. When the elevator tilts upward, less lift is created and the tail descends.

The rudder is located on the fin. The two rudder pedals are located at the pilot's feet. When the pilot pushes on the right rudder pedal, the rudder tilts to the right and the airplane yaws "nose-right." When the pilot pushes on the left rudder pedal, the rudder tilts to the left and the airplane yaws "nose-left." Again this is due to lift. However, the direction of this lift force is different than the lift force that causes the airplane to rise. When the rudder tilts to the right, more lift is created on the right, which "lifts" or pushes the vertical stabilizer to the left.

This, in turn, causes the airplane to yaw nose-right. The opposite motion occurs when the rudder tilts to the left.

In trying to figure out all of this tilting right and left, remember that if the rudder is extended so that it obstructs the airflow, then the airflow is going to push hard on that rudder. An imbalance will be created between the side where the rudder is obstructing the airflow and the side where it isn't. This will cause the airplane to move away from the side where the rudder is extended. That is why when a pilot pushes the right rudder pedal, the rudder tilts to the right - the air will push harder on the right side of the tail causing the tail to swing left, which will cause the nose to swing right.

At the dawn of powered flight, the Wright brothers used the method of actively warping an aircraft's wings to turn their aircraft. Now NASA researchers are teaming up with the U.S. Air Force Research Laboratory and Boeing's Phantom Works to develop a new high-tech version of this method. The Active Aeroelastic Wing (AAW) concept has been tested at NASA's Dryden Flight Research Center using an F/A-18A Hornet. The aircraft's wings were modified to enhance flexibility and to take advantage of a new actuator and flight control computer system. 

The program investigated the potential of aerodynamically twisting flexible wings to improve roll maneuverability of high-performance aircraft at transonic andsupersonic speeds. Because this type of wing would require fewer moving parts for controlling flight, wings could be made thinner, lighter, and more aerodynamically efficient—translating to more economical operation and greater payload capability. Data obtained from these tests will aid in the design of a wide variety of future aircraft including high-performance fighters to high altitude, long endurance unmanned aerial vehicle (UAV) concepts, large transport aircraft, and high-speed, long-range aircraft.

Maneuverability
There is often a trade-off between stability and maneuverability. An airplane that is highly maneuverable and can do amazing things in the air is probably not very stable. Sometimes we refer to an automobile as having "tight" steering. That means that the car responds readily to movements of the steering wheel. There is no slack or lag. On the other hand, it also means that the automobile responds quickly and decisively, but does not over-respond. It does precisely what the driver tells it to do through the steering wheel - no more, no less. An airplane works the same way. "Tight" stability means the airplane responds precisely to the pilot's controls. The X-29 is a good example of this. The X-29, with its forward-sweep wing, is amazingly maneuverable. It can move like no other aircraft. However, the X-29 is also very unstable. A computer-based control system is required to help the pilot keep the airplane under control. The control system operates all the control surfaces based on a combination of what the pilot tells it to do and what its sensors say the airplane is doing. It makes minute and extremely rapid changes in the control surface positions to maintain the stability of the airplane. A human cannot perceive, absorb and react to this much information in the infinitesimally short time required and computer help is needed.

You're flying a large transport plane carrying hundreds of passengers and instantly you are unable to control the airplane - your control system has gone out. As a pilot or a passenger, you hope that this scenario never presents itself, but if it did, what if there was a way to safely land the airplane by using throttles only? With a system known as Propulsion Controlled Aircraft (PCA) not only is the concept a possibility, but it is a reality. By using a specially designed software system, a successful flight test program at NASA Dryden Flight Research Center was accomplished.

The PCA concept is simple -- for pitchcontrol, the program increases thrust to climb and reduces thrust to descend. To turn right, the autopilot increases the left engine thrust while decreasing the right engine thrust. Since thrust response is slow, and the control forces are relatively small, a pilot would require extensive practice and intense concentration to do this task manually. Using computer-controlled thrust greatly improves flight precision and reduces pilot workload.

Initial tests were done using a simulator. After refinements, the system was installed on an F-15 aircraft, and then progressed to successful tests on an MD-11, similar to commercial jets in which you may have flown. Aircraft manufacturers have decided that a PCA system will be valuable for use in the design of future airplanes. When they incorporate this for future design, it will eliminate the need for a less capable hydraulics-dependent backup flight control system.