This section is about lift.
The location of it.
The effects of it.
The pursuit of it.
The Zen of it.
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First things first. Air is a fluid. If you do not believe this to be true......well......sorry, but it is. And air, as most fluids, generally behaves according to Sir Isaac Newton's laws of motion. In specific, fluids behave per the laws of fluid dynamics. The bulk of these laws and postulates are good only for giving aerodynamics students migraine headaches and putting readers to sleep. But some of the simpler ones have applications that touch the realm of the experimental aircraft builder/designer. Most notable of these is the concept of Control Volume. That is to say, if you take a big enough ball of air and call it a Volume, then anything that happens inside of that ball of air will not affect the air outside of the ball. For example, one of the greatest hurricanes in recent history ( ANDREW ) was a fluid dynamic system of some 1000 miles in diameter and 6 miles thick. If you were inside that control volume, you felt something, if you were outside of that volume you didn't even know it existed. From a little distance away ..... say Alaska....... that raging swirl of air in the Caribbean was just a " LOW " pressure system on the map. It had little or no effect on your local weather. If you got really far away..... say the Moon..... it would have just been a dot on the globe surrounded by many other pressure dots. In fact, from outside of the control volume, any atmospheric system on earth is just a point source of activity.
Yea.......Interesting.......but what does any of this have to do with airplanes ???
Second things Second. Well, if you look at any aerodynamic or fluid system from far enough outside of the control volume, the stuff that is going on inside of the control volume is seen as happening at a point. The principal of heavier than air flight is based upon high pressures trying to get to the low pressure areas. There is some stuff about forces imparted from the air to objects as they impede its path, but for now, we will just stick to pressures and keep it over simple. Birds, bees and Boeings all make lift. They are aerodynamic systems. And as aerodynamic systems go they do fairly well at obeying the laws of motion and aerodynamics. From a few chord lengths in front of or behind the wings of any of these systems, they can be represented as pretty much single point lifting systems. Bird's wings have thousands of individual feathers, but the combined effect of all that plumage is lift at a specific location. So........ all you have to do is get far enough away from the action and it gets simplified. How far is far enough??? Well, in theory you have to be infinitely far away. In reality if you are studying airplane wings you only need be a few chord lengths away for the entire aerodynamic systems to be considered point sources. This seems too simple. All we have to do is be a step or two back and we have greatly simplified the investigations of flying systems.
Yea.......Interesting.......but what does any of this have to do with airplanes ???
Third things Third. Aircraft ( in general ) have numerous aerodynamic surfaces and all sorts of silly things sticking out into the wind. From a few chords away from the individual lifting surfaces, these surfaces can be seen as point lifting sources. If you look about the entire aircraft, you can sum up all point sources of lift and see that they are acting through one point. The number or complexity of separate components of lift are not really important for those looking to analyze the "system" as a whole. That single point is called the Center of Lift. Sometimes seen as Xcol, it is usually at the top of the designers "must know this stuff" list. No matter that you are looking at a bee with four tiny wings, or a Boeing with four great wings......all the individual parts of lift add up and act through a single point.
Lost Count ....... Lift is the force that is pointed up. Lift is good. The absence of lift is bad. Lets take a collective moment in respect of such a profound thought. Ok, moment over. It is the opinion of the Mad Rocket Scientist Team that aircraft are magically suspended from a single point called the Center of Lift. This point is a point. That is to say it is not a line, or a shpere or a fuzzy zone in space. It is the summation of all the bitty bits of lift, both upwards and downward scattered about the entire aircraft. The Center of Lift may be located inside of the actual confines of the fuselage ( like in a low wing Piper ) or it may be located outside the actual confines of the fuselage (as in a high wing Cessna). This Center of Lift is the pivot point in the struggle of forces that try to pull an aircraft out of our beloved sky. This is not new stuff. Aircraft designers have known about the Center of Lift for 100 + years.
As is fair to any great concept, this discussion has been an recurring topic of discussion with the DragonFly community. As with all great ponderances, the facts are simple : If you got lift, you go up....... without it, you go down. The implications of these truths is what gets us simple pilots into so much trouble.
A Study in Case Studies
To start off.......... Lets look at a few cases in which aircraft of different designs take to the air and attempt to stay there.
People who design for powered flight tend to be very concerned with stability and control of the system. Imagine that ! ! ! The farther you get away from the design of a lawn dart, the more complex the problem becomes. There are many kinds of winged flying things out there to confuse and befuddle the designers, but for this discussion we will dump them all into two groups. The huge group of "Things with Wings and Tails" and the tiny group of "Tandem Wing Things ". These are stupid, made up classifications to be sure....... but we are just winging this discussion anyway ;--)
In the beginning, there was the " one wing " type aircraft. This shape is best represented by the "delta dart" or "hang glider". From a flying kind of perspective, this is as simple as it gets. Powered or not, this flying machine is easy to analyze. The forces of lift and fall are easily laid out on its physical shape. The big, cloth triangle thing makes all the lift and the earth makes all the fall. The " UP " force made by all that fabric and aluminum tubing is concentrated in one spot, the Center of Lift. This magic spot is located " on " or " very near " the pilot's own center of gravity. In straight and level flight (glide) the forces of lift are balanced by the forces of gravity ( the pilot's weight and the gliders weight). To affect stability and control, the Center of Gravity of the pilot is shifted around a bit. This shifting affects the Center of Gravity of the entire craft. In fact, it moves it quite a bit. For straight and level flight, the pilot brings the combined Center of Gravity directly under the Center of Lift. In this flight condition, no moments are made to pull the nose up or push it down. If the pilot wishes to go nose up or down, a shift in the center of gravity relative to the center of lift must occur. If the pilot wishes to go nose down, the center of gravity of the system must be brought forward of the Center of Lift. If the pilot wishes to go nose up, the center of gravity must be brought to be behind the center of lift. Changes in center of gravity create a moment ( weight times the distance from the center of lift ) and the nose of the glider is rotated in reaction to the moment's action. If the movement is to the aft, the nose will stay up until the pilot shifts his weight forward of the Center of Lift. Right up to moment of stall, the nose will stay up. At stall, the lift collapses and (hopefully) the glider's forward inertia pulls it out of the screwed up air that it caused, and get the nose down. If not, the pilot better make some adjustments to the Center of Gravity to make this happen. Until the pilot moves, the wing may stay completely stalled. This interesting condition is usually terminated by the ever solid earth. Note : The Center of Lift of this delta dart shaped aircraft is a fixed point. Once it is established by design and testing, it can be marked on the frame and taken as fact that it will not change. All pitch control is a matter of Center of Gravity shifting with respect to Center of Lift. This is about as simple as it gets.
As complexity increased and powered flight evolved, lawn darts with multiple wings came to be. The Cessna 172 is a great example of a more complex aircraft. Of course we all know that Cessna's have two wings. They have a main wing up front and and little wing located way back there on the end of the tail. Yes, tails are wings also. They pull down (most of the time) but they make lift and drag and we kind of need them if we are going to get anywhere in this discussion. For the most part, we call the tail wing a horizontal stabilizer and understand that it has a moving part called an elevator dedicated to pitch control. Naming conventions aside, all the vertical lift of the flight system eventually comes from the big wing up front. That "thing" back there is a control device, not a lifting component. You may think that the Cessna's tail is a lifting wing and that its lift is added to the system as a whole, but it is not. To explore this a bit more, we will enlist the aid of a fearless, virtual test pilot. We will give him a new, virtual, C172 and a top notch digital parachute.
All wings pretty much fly the same. From an aerodynamic standpoint, all wings have a Center of Lift located very near the 1/4 chord position. ( Refresher : a chord is the distance from the leading edge to the trailing edge and the span is from one wing tip to the other.) The location of the Center of Lift does not change no matter what you do to the wing's lifting surfaces. Deployment of flaps, slats, spoilers, and drag brakes only act to change the amount of lift the wing makes, not its point of application. This is true for all subsonic, chambered wings like the ones on everything you are ever likely to fly. Birds and (most) Boeings obey this simple rule. Note : Bees kinda obey the rules too, but discussions about them have to include turbulent and non adiabatic flow theory........ so we will just leave our little honey making friends "bee" for the moment and concentrate on the simple stuff.
So, in general, we have a big wing up front making a bunch of "up", a little wing (in back) making some "down". Lets remember that the only reason the tail is back there at all is to balance the nose down rotational force that the main wing generates as it makes lift. The Center of Lift of the system is somewhere. Lets see if we can't pin that spot down some. Lets say for a moment that the big wing did not need any counter force. For this the tail would not have to make any "down". The forward wing would be alone and the Center of Lift of the system would be at the 1/4 chord point of the big wing. Now lets say the little wing is called to make a little "down". The center of lift of the system now moves a bit "forward" of the 1/4 chord point. As the amount of tail down force grows, the location of the center of lift of the system moves farther and farther forward. Well..... go figure. The total amount of tail surface back there is known. The maximum amount of elevator deflection is a given. Some junior engineer could calculate all the unknowns and a clever design team could mark out the "range" of the Center of Lift. Actually, with the main wing located above the pilot's head, the center of lift is not even located inside of the confines of the fuselage. For level cruise it is located in space a few inches over the pilots head and centered on the fuselage's mid-line and a few inches ahead of the 1/4 chord position of main wing. Lets call on that junior engineer to mark its position on the fuselage floor just to make things a little easier for our test pilot.
For all this talk of wings and things, our virtual C172 aircraft still has to weigh something. Virtual pounds are considered just as heavy as real pounds and every aircraft sitting on the ramp has to have a Static Center of Gravity. Stuff in what you will ( including our reluctant test pilot ) and the total weight of the plane has to come to rest somewhere between the main wheels and the nose wheel. Unless that stuff moves around in flight (and we will not let that happen) we will call this weight static. Summing all the weight and giving it a location, we define a point called the Static Center of Gravity ( Xcg for short). Since gross can change a little every time you fly, this spot changes as you load the aircraft. With all this talk about centers of gravity and such, our digital test pilot is feeling very cautious and has made very sure he loaded up the test aircraft in accordance with Clyde Cessna's best guess on Forward / Aft loading range. We once again call the lowest ranking engineer and have him mark the exact location of the Static Center of Gravity onto the fuselage floor. Senior engineering will take out a big life insurance policy on the test pilot.
There is another really important basic fact of aircraft design : All aircraft designers put the Static Center of Gravity in the very most forward range of the expected Center of Lift. Hummmm...... what did they just say ??? All aircraft designers want their creations to fall forwards given any opportunity. That means the plane will always be trying to fall on its face as it is flying!!! That can not be right??? These flying machines go straight and level most of the time. Don't they??? The answers to this and many more perplexing questions to follow.......but for now, believe that all sane aircraft designers put the Static Center of Gravity way up in the very front of the Center of Lift range. (Note : the X-29 designers were not sane, were not normal, and built one very strange flying machine that we will not mention in this paper). As our test pilot looks at the marks on the floor of the aircraft. He can see the 1/4 chord mark for the main wing. There are marks a few inches forward of this that designate the forward most range of the Center of Lift and a mark a little behind the 1/4 chord mark that is the aft most location of the Center of Lift. He sees the Static Center of Gravity marked a few inches forward of the 1/4 chord mark and well into the forward portion of the Center of Lift range. The design team is all safely back in their offices as fearless test pilot is having serious second thoughts about all of this.
Oh yea........ almost forgot to mention that the Static Center of Gravity times its distance from the Center of Lift makes another nose down moment. In our virtual 172's, these nose down moments add up to a big nose down moment. Hummmm. So how is this thing ever going to get off the ground ??? Well, there is that nasty old tail " wing " located way back there in the aft. It is just hanging around making drag and looking prehistoric. Our designers decide to make it work for its supper. As the tail pulls down and the Center of Lift moves forward, eventually it overtakes the Center of Gravity and all them nose down moments are canceled. As we accelerate down the runway and pull the elevator into the airstream, the tail down moments overpower all the nose down moments and the aircraft rotates into the sky.
Things get very interesting at stall speed. Just before stall, the main wing is making a ton of lift and demanding a lot of work from the tail. The wing is working and the tail is working....... and for the most part, all is well. At stall, the wing stops making lift. The center of lift rockets backwards to the 1/4 chord position of the tail and our old friend gravity takes over. The Xcg (that did not move) is now many feet ahead of the new Center of Lift. The weight of the aircraft times this distance creates a massive nose down moment, and the aircraft falls onto its face. Actually, the aircraft begins to fall from the sky.......nose first. The only thing that caused our wing to stop flying was loss of airspeed. As the nose falls, and the airspeed comes up, the main wing begins to fly again. The Center of Lift of the system rockets forward again and the whole mess starts over. Our fearless test pilot is torn between cursing and praising the designers of this crazy flying machine.
Massive nose down moments built into the design all the time!!!!! Are these designers mad ??? No, not mad, just over cautious of your safety. In general the designers always want the nose to pitch down so the aircraft will always try to pitch away from stall. During normal flight, pilot controlled changes in the Center of Lift is achieved by use of the elevator. By pulling on the elevator controls, the pilot changes the tail down moment ( the force of the tail pulling down times its distance from the center of lift ) and thus the location of the Center of Lift. Dial in more tail down moment, and the Xcol forward of the Xcg ( nose goes up). Dial in less tail down moment and the Xcol goes behind the Xcg (nose goes down). Just the right amount of tail down moment and the Xcol is brought directly under the Xcg ( nose stays level). It is this balance of forces, acting through the Center of Lift that allows the aircraft to " teeter-totter " in the air from that singe point in space called the Center of Lift. This is completely normal and expected of a well balanced and aerodynamically engineered flying machine.
Depressing Note : If the Static Center of Gravity were ever to get behind the aft most range of the Center of Lift, the nose down tendency at stall would not occur. This would be bad on so many levels. This is so bad a thought that we warn every pilot about "Aft Loading" so often they never forget. They never overload the aircraft without doing a complete weight and balance. They never push the Xcg aft by mistake. This would be very bad. So we do not let it happen. We design "fail safe" airplanes.
Tandem Wings :
Now, set aside all that silly stuff we just decided was true about how airplanes fly .......... NOT ! ! ! Tandem wing aircraft fly and are controlled the same exact way as their brethren........only they do not have to pay the drag penalty of tail feathers.
Tandem means two. Wings means........well......wings. So we are going to be talking about two wings that make lift. Remember that lift is good, so all lifting wings are by definition "GOOD". Our tandem wing "do inhale" and we are proud of it.
First up, lets take a look at the old fashion Bi-wing aircraft : This seems a familiar starting point for talking about tandem wing systems. In a Bi-wing, the two wings up front act, for the most part, as one wing. They make all the lift of the system. The aircraft has a tail and all the trappings of the last case study. So we will brand this type of tandem a "Things with Wings and Tails" and just acknowledge that it has an identity crises. Note: The only reason there were Bi-wings in the olden days, was that they did not know how to make enough lift with a single wing to get the job done. Strength to weight ratios forced designers to use two, three or even four wings. It's many wings acted as a single wing making all the lift and the tail did all the control work. We are just being nice and letting them think they are part of the tandem family.
Next up, lets look at a truly confused puppy. The 3 surface design (not to be confused with the Red Barron style tri-wing) has two lifting wings that are separated and a tail. Like the old Bi-wing plane above, neither of these two main wings would have an elevator. The elevator (back at the tail) would be doing all the work of pitching the aircraft. Ignoring the tail for a moment, the center of lift of the two wing system would be located somewhere between the forward wing and the aft wing. The exact location of this mystical point seems to be in some dispute, however, if you believe in formulas, then this < equation > is as good as any. It will give you a Center of Lift to whatever precision your calculator can achieve. The tail in this design just moves the center of lift around a bit (as described above) and makes a lot of drag in the process. This test case aircraft is starting to look a lot like the Eagle aircraft. For all its tandem wing looks, it is just a variation on a theme, and a silly looking one at that.
Now lets look at some true tandem wing aircraft. Hummmm, the Wright Flyer comes to mind. In general, a tandem wing design will have two lifting wings and no nasty tails. It will make 100 % lift with its wings and use gravity to balance the forces of flight. It will be optimized for cruise and nearly impossible to stall. It will be a joy to analyze and a breeze to manufacture. Yea, right. Well at least it don't have no stinking tail to mess up the performance.
First up, lets look at the case where the aircraft's wings will be the same size, shape, and airfoil. There will be no elevator on either wing and they will be separated by a few feet of fuselage. Essentially we have an aircraft that makes all positive lift. In this case study, the center of lift of the two wing system is located somewhere between the 1/4 chord position of the forward wing and the 1/4 chord position of the aft wing. The exact location of this point can be found by setting both wing parameters to the same values and using this equation again. Or, for short, you can say the forward wing makes 50% of the system lift and the aft wing makes 50%. That would put the center of lift exactly between the quarter chord positions. If the front wing made 60% of the lift and the aft 40%, then you would do the math and mark the location on the fuselage for that set of parameters. It would, of course, have moved the Xcol towards the front (60%) wing and away from the aft (30%) wing. For any case, the math is simple enough and could do it. The Xcol of any tandem wing system could be computed with the formula and marked on the fuselage. In this test case study, neither wing has an elevator to change the amount of lift it makes with respect to the other wing. The location of the Xcol does not not change. Once established by the designer, the ratio of lift ( forward vs. aft ) would remain a reassuring constant. You could load the aircraft up with all the stuff it can carry and never worry about getting out of loading limits. The only restriction on this simple design would be not loading the Static Center of Gravity behind the Center of Lift. Yup, its all good. The only problem with this imaginary tandem wing setup is that the pilot has no way to control the pitch of the aircraft. There is no tail, no elevator, no shifting of Center of Lift, no moving of Center of Gravity....... Hummmmm. In the old-time Bi-wing aircraft, we had tails with elevators to do the control work. We paid for this control with loss of performance. but at least it worked. From an aerodynamic standpoint, a simple tandem wing aircraft is extremely efficient, but it will not fly.
Moving on past this little control issue, we envision a wing up front with an elevator and a wing in back with ailerons. Hummmm ........ that sound like a canard. By the way, "canard" means "duck" in French and is usually associated to planes that look like they are flying backwards ( like ducks look ). Of course, the first shape that comes to mind is the Rutan EZ. In that design we have two wings making lift and no "bad old" horizontal tail pulling things down. The forward wing controls pitch by "elevating" the nose....... the way it should be done. The original Wright Flyer was also a tandem wing design and (strangely enough) had about the same lifting surface proportions as does the EZ. But we live in the DragonFly world and we want to make our point using our beautiful design. Actually, in the DragonFly world, we have a shape that is more baseline for the tandem class. We have an equal span tandem wings. We are not a special case in the canard world.....they are extreme cases of our tandem world. Regardless of what they look like, all tandem wing aircraft fly by the same set of rules. So, just think two........two is tandem......two is good. Now lets get down to the business of setting up a test case for this wonderful class of flying machine. We once again enlist the aid of our fearless virtual test pilot.
For our equal span tandem test case, we will establish that the forward wing will have a variable chamber device that allows for a change of the total quantity of lift independent of the aircraft's AOA. Further, we will require all change of lift mechanism to be under pilot control. The aft wing will not have this capability. Ummmmm........ yea......whatever he just said.......... In simpler language, we call this forward wing a canard and it has an elevator. The pilot has a control stick and can command the elevator to make more or less lift as needed to pitch control the airplane. The aft wing is fixed and has no way to change its amount of lift independent of the aircraft's AOA. With all this design nonsense in mind, our case study equal span tandem wing aircraft looks a lot like a DragonFly .
All
this talk about wings has not changed how the tandem aircraft sits on the ground
one little bit. waiting on the ramp stuffed full of pilot, passenger, maps and gas,
our equal span tandem wing test case aircraft
still has to be balanced over its landing gear. It has to have a Static
Center
of Gravity that falls somewhere b
etween the front and rear tires.
There is also the need for some
brave designer to have established an operational envelope for the Aft most
Center of Gravity. This was done (we pray) by some one who really knows
about this type of aircraft's performance characteristics. Looking at our test case, we see that
there is indeed a mark on the floor of the fuselage labeled "DO NOT ALLOW
THE STATIC CENTER OF GRAVITY TO GO AFT OF THIS MARK". Wow. That sounds serious. A lot of attention
for so small a mark on the floor. There must be something to this aft
Xcg limit business. Why is this??? You can load a Cessna 172 up
"way" past its gross weight and even a little past its aft Xcg limits and it flies fine. It may be a bit sluggish on stall recovery, but it always
recovers. So what is the big deal with this strange little tandem
wing aircraft's aft Xcg limit that warrants such big scary wording.??
Well lets take a look at the tandem's control concept for starters. Maybe, this warning is because the control system is sensitive to aft Cg loading. We enlist our test pilot (who is very wary by this point) to make a few test flights. Lets say we load our test case tandem airplane to its max gross weight and are very careful to keep it in the designers envelope concerning Aft most Static Center of Gravity. We sort of know in the back of our minds that we must keep the Static Center of Gravity in the front of the Center of Lift range....... cause we want to ensure a nose down stall recovery tendency...... but where is the Center of Lift of this tandem design??? We look on the floor and see a red line that goes from just behind the Aft Xcg mark to a few inches in front of it. That is absurd. The just barely goes behind the Aft most Xcg. What would happen if the pilot were not careful and loaded the plane wrong??? Or what if the aft wing were to stall a bit??? Our test pilot wants out of his contract. We better take a much closer look at this insane design before we commit to any long term illness clauses.
We start the analysis by finding the Center of Lift of the two wing system. We know that it has to be be somewhere between the forward 1/4 chord position and the aft 1/4 chord position. That must be it. We just use that silly formula to find it and mark it on the fuselage so we will not have to do the math a second time.......Right??? Wrong !!! The formula is only good if you put in the ratio of lift of one wing with respect to the other. At any speed, as you deploy the elevator, the amount of lift of the forward wing will change radically. The aft wing only changes its amount of lift as the AOA of the aircraft changes. So the ratio of forward to aft lift will change every time you move the elevator. That means that you to do the math for every possible elevator setting and AOA that the aircraft will ever see and mark the entire range of " Centers of Lift " on the fuselage floor. Each setting of elevator and AOA will generate a unique Center of Lift of the system. That is why there is a range of Centers of Lift and not a single point marked on the floor. It is starting to look like we are never going to get this strange flying machine off the ground. Hummm...... maybe that is the key.......what will it take to get this thing off the ground.......... or to be more specific, to stall it into the air ???
For the case of stalling an equal span tandem aircraft off the ground and into the air, we just need to know what each of the wings are doing at their maximum output. When both wings are working as hard as they can at the slowest speed they can work at, we are at stall. We find that information and put it into the equation and it will tell us where the Center of Lift is for stall. Now we are getting somewhere!!! Somebody go get that test pilot guy......we got a job for him.
The location of the Center of Lift at stall speed is about the most important bit of information we can have in a tandem wing aircraft. With the elevator full down, the canard will be at max lift output. We will be zooming down the runway at near 0 degrees AOA (nose down) and the canard will be making all the "Upward" lift it can make. Eventually lift from the canard will pull the nose up and the new AOA will allow the aft wing to make all the "Upward" lift it can make. Now bolt wings are singing for their supper. At some point, as we increase the forward speed (and if this thing was ever destined to fly) it will depart the ground. FREEZE FRAME. We have just stalled the aircraft off the ground. Ignoring ground effect for the moment, we have achieved stable flight that identical to stall at any place in the sky. At this point, we note the airspeed and the AOA of the aircraft. We do a little reverse engineering with the wing areas and aerodynamic data on the airfoils and compute the amount of lift each wing is making. We put that ratio into the formula and out pops our Center of Lift for stall speed position. We mark it on the fuselage and call it AFT MOST CENTER OF LIFT FOR STABLE STALL. We all get a cold (virtual) beer and spend the rest of the day patting each other on the back for a job well done. All we have to do to keep this thing in the air is go faster than this minimum speed and not allow the Static Center of Gravity to go behind the point we just marked on the floor of the airplane. We are designing gods and nothing can pull us from the sky now. Being the cautious designers we are, we mark the AFT MOST STATIC CENTER OF GRAVITY a few micro inches in front of the AFT MOST CENTER OF LIFT FOR STABLE STALL. Life is good for the design team.
But there is that nagging little question in the back of everybody's mind........what is really going on here. And what is really going on out there and what will happen if I load the aircraft aft of the AFT MOST CENTER OF LIFT FOR STABLE STALL line.
Well for that answer, we need to look at what forces are at work on the test case aircraft as it slips through the air. We know that each wing will be making a nose down rotation moment just because they are wings. These moments are both in the same direction so they are added together. There is a moment generated by the Center of Gravity times its distance from the Center of Lift. But were is that blasted Center of Lift. It keeps moving around. At some point it would make a positive moment and at some point it would make a negative moment. That is all there is. So we better nail this "free spirit" moment down or we are never going to figure out what is going on here.
For all steady state, non accelerated (straight and level) flight, the Center of Lift is determined by the ratio of forward to aft lift. We can use this formula for any "single" data point because all the aerodynamic properties of a single point can be determined and plugged in. These points keep changing because of the need for pitch control. So lets pull on the elevator control and see what happens. Well, as before, the Static Center of Gravity does not move. The ratio of forward to aft lift changes a lot. As we pull the elevator down into the wind, the Center of Lift of the system races forwards. Hummm........ could it be that pitch control of a tandem wing is achieved by moving the Center of Lift with respect to the Static Center of Gravity. If the Center of Lift moves ahead of the Static Center of Gravity then the moment made by the weight of the aircraft will act to rotate the nose up. That must be it!!! We make the nose go up by making more lift up front, and canceling the nose down rotational moment by a massive nose up (gravity induced) rotational moment. If you want to pitch a tandem wing aircraft nose up, you move its Center of Lift forward of its Static Center of Gravity. If you want to pitch a tandem wing aircraft nose down, you move its Center of Lift behind its Center of Gravity. Once again we are "teeter-toddering" about a point that is fixed on the aircraft. Except, this time it is the Static Center of Gravity and not the Center of Lift. This is how tandem wing aircraft stay in the air. It is completely normal and expected of a well balanced and aerodynamically engineered tandem wing flying machine.
WARNING..... WARNING..... WARNING.......did you understand what we just said. Go back and re-read that last paragraph. We are tossing out the outrageous idea that tandem wing aircraft control their pitch by moving the Center of Lift. We are further proposing that for some portion of the flight envelope, the Center of Lift of the aircraft is forward of the Static Center of Gravity. That means for this portion of the operating envelope, the aircraft is no longer Pitch Nose Down Stable in stall. In this portion of the flight envelope you do not have the built in massive nose down rotation moment always trying to flip the plane into a nose down attitude. What happens if you were to stall the aircraft during one of these "strange and crazy" moments ? ? ? Well......it is not pretty. If the Center of Lift is still ahead of the Static Center of Gravity when you stall, you fall backwards onto your rear stinger and put your aircraft into an (inverted) flat spin called " DEEP STALL ". This is bad on so many levels. This is so very bad that there is likely no recovery. It is so bad that we never let it happen. It is so very completely bad that we design our tandems to never ever let it happen for any reason. It is so very very bad that we are going to look at a little closer to see what is going on with these strange, dangerous designs that can have Deep Stall.
First of all, it would be nearly impossible to deep stall a well designed tandem wing aircraft that was loaded correctly. Even from an accelerated stall maneuver, it would be nearly impossible. Not to say you could not try real hard and do it, but it will not generally happen. Lets say our fearless tandem wing test pilot is zooming along at 3000 AGL at 150 kts and straight and level. His craft is correctly loaded and not in danger of being aft overloaded. We tell him (from the safety of the virtual ground) to pull the aircraft into an accelerated stall. Our fearless test pilot pulls back on the control stick and commands the aircraft to go into a hard climb. We cringe as the test aircraft rockets up into the sky. The pilot has commanded the elevator to deflect and that has made a huge amount of lift in the canard. The Center of Lift rushes forward (from just below the Static Center of Gravity) and a huge tail down moment develops due to the weight of the aircraft times its distance from the new Center of Lift. As long as the canard does not stall, the aircraft will continue into an accelerated climb. Of course, during this maneuver, the airspeed plunges in response to all that drag you just made and in a few seconds, the aircraft runs out of kinetic energy (airspeed). The canard stalls. The Center of Lift leaps backward in response to drop in the amount of lift that is being made up front and the nose pitches down. The aircraft starts picking up forward speed and our virtual pilot can start breathing again. All is right with the tandem design world. The canard stalls first. That breaks the climb and the moments are restored to a nose down pitch condition. That is why some clever designer put a sharp stall airfoil up front and a gentle stall airfoil in back. Alas, we have discovered the designers fail safe system. This design does have a saving grace after all. Somewhere there is a design team having a group hug.
Is that all that really happened ? ? ? Well....... yea. There were lots of aerodynamic components going on, but that is all in that "control volume" thing we talked about way up front. Once you get a few spans away from the action, it all acts as a point source. The canard was at stall speed just before the nose fell and was working as hard as it could. The aft wing still had lots of potential to give, but the silly canard stalled and a gravity induced moment pulled the nose down. As the nose dropped (taking away a bunch of Angle of Attack) the aircraft began to gain airspeed again. Except for stall, where the elevator ain't got no more to give, a tandem wing design has lots of elevator travel in both directions to facilitate a pitch up or pitch down attitude. It is this change in lift ratio that allows the pilot to respond to any changes in the flight dynamics. So right up until the stall, our fearless test pilot could have lowered the nose just by releasing the stick. He elected to hold the nose up by applying max elevator control. But at stall, there ain't no more stick to apply. Our test pilot is hoping very hard that the canard will stall before the aft wing does. If we had loaded our test case aircraft to far aft, then the aft wing may have stalled before the forward wing gave up and we would have been watching Deep Stall. The aft wing stalls and the tail falls fast. This generates an inverted flat spin. Remember, the aft wing is going to stall when its airspeed can no longer support the weight that is is being asked to carry.
For stable flight in a tandem wing aircraft, the Center of Lift is brought to be exactly over the Center of Gravity. Again, our test case is suspended from a single point in space. All the forces are balanced and our test pilot is once again very happy. Gravity is supplying the balancing forces for the system. The wings pull up....... the earth pulls down. When the wings stop pulling up, the earth wins. We now see all there is to see. The static Center of Gravity ( Xcg ) does not move and the Center of Lift does. So long as you do not load the aircraft aft of the CENTER OF LIFT FOR STABLE STALL line or do not grow a bigger canard, you are "Fail Safe". This is how tandem wing airplanes fly.
Center of gravity chart for the Eos Raptor aircraft
The current Dragonfly designs, like their predecessors, are forward favored, tandem wing aircraft. The origin of the design ( Rutan's Quickie ) used a 68% forward to 32% aft load distribution. This ratio provided a generous and stable operational envelope for the single passenger craft. With the advent of the two passenger versions, the static margin for positive stability became more of a concern. The center of lift must always be located behind the center of gravity to maintain a positive margin of control. As powerplants get heavier, canards grow and shrink at the designers whim, and the airfoils used to create lift change, the need increases for a math model capable of predicting the effects of all these variables on the center of lift.
Center of lift equation for the Eos Raptor aircraft
A little example of what happens if you change something in a tandem wing design :
A discussion on changing of the canard : I'm doing this from memory, so don't hold me to the exacts.
The Mark 1 had a 22 ft span on the front and aft wings. In the aft, 22 ft x 2.25 ft average chord was about 49.5 sq ft. This did not change for the Mark 2.
In the front, the Mark 1 had 22 ft of total span and about 20 ft of useable span for lift. Analysis shows that the original lift ratio was set at 68% to 32% (forward to aft). At a gross of 1050 pounds......the load on the canard was 715 lb. That weight is carried on 2.5 ft average chord x 19.5 ft span = 48.75 sq ft) of surface. That is 14.7 LB per sq ft. For now, lets call that 14.7 LB/sq ft a constant of the GU-25 type canard.
The weight and balance of the Mark 1 was then established based on the center of lift of the tandem system and its flight characteristics. The aft most CG was set at 60" something. For now, lets say 60".
Remember, the center of a tandem wing lift system is given by a formula (see discussion above) or approximated by the lift ratio. At just before stall speed and with the elevators at full deflection downward, the canard is working as hard as it can work. The Xcol has to be in front of the Xcg for you to have a pitch up condition. For this discussion, lets put the Xcol of this condition at 59". As long as you can reduce the lifting power of the canard by releasing the elevator, you can send the Xcol aft of Xcg and re-establish a nose down stall recovery attitude. This is good.
Now, the same airfoil that was used in the Mark 1 was used in the Mark 2 for the extended canard. So doing some math ( 22 ft x 2.5 = 55 sq ft of canard lifting surface). Using our canard constant for lift of.....14.7 LB/sq ft......we have our new extended canard generating 808.5 pounds of lift. The total weight of the aircraft is now 1150 pounds, so, the canard is lifting 808.5/1150 percent of that weight, or 70.3%. The center of lift, given by the ratio of forward to aft lift, moves a little forward. Actually it moves 70.3% -68% = 2.3% forward. How much should you care that your center of lift moved 2.3% forward? Well......lets see. Doing the math....2.3% of 59" is 1.36". The aircraft's Xcg envelope did not change. So, a well intentioned pilot could load his plane up to the aft most limit and think he is safe in his weight and balance. But as the Xcol moves forward, so moves the aft range of the envelope. The change in loading of the canard has moved the Xcol forward by 1.4" or in affect, our luckless pilot has loaded his aircraft 1.4" aft of the max aft Xcg line. Does the discussion on deep stall come to mind?
This is only an example. The real numbers are less scary, but no less important at showing the problem. You have to know what is happening before you can use anybody's equations to compute anything.
The more weight you balance over the canard, the more problem you are making. It aint magic. I is just basic aerodynamics.
The fix is a serious look at how the weight and balance is affected by changes the builders make.
Not to knock anybody else's efforts, but using the Mark 1's envelope on a Mark 2 or 3 is just plane wrong. It just aint that hard to get it right, so why do it wrong.
page information was last updated on 05/16/01.
