


Thank you Johnny. No way of knowing whose experience will save me from one of those really hair pulling mistakes







Mitch Covell
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A search of the thread will produce answers to many of your questions. I look forward to seeing your design of a large slow flying canard. Captain Canardly Johnny Quote:
1. Nose high three point landings. 2. Low aspect ratio wings for quick rolls. 3. Elevons front and rear for positive longitudinal control. 4. Extended rudder for better yaw control 5. Symmetrical airfoils for outside maneuvers. 6. Canard wing to finalize delta shape and control front of model. The ability to spin was an afterthought of completion. Charles 






Seems like the job is getting done!
more later, am still absorbing infos'/ datas snow forecast, should be great for CAD Works! later, Johnny 
Latest blog entry: Underway: Shifting colors for 2018





poor lil' renolds numbers being bludgeoned
I got a bit distracted during my data search, came up with this sequence of events:
pic1) Stokes Law Pic 2) Stokes Radius 3)boundary layer http://www.symscape.com/. 4)flow seperation Not necessarily guaranteed to be the actual sequence of searched data, as I was actually looking for Conical lofting, and came across this fellow! the daddy of the Spline! Pic 5) Shoenburg Johnny 
Latest blog entry: Underway: Shifting colors for 2018





Try:
http://technology.calumet.purdue.edu...97/ilin97.html The father of this technique was A. Roy Liming, who was in charge of the lofting of the shapes for the P51 Mustang. He later wrote a book about the method, "Practical Analytic Geometry with Applications to Aircraft". The method uses conic sections (circles, ellipses, parabolas, hyperbolas) to define the shape of the object. The key thing about this is that conics are secondorder curves. In other words, the highest exponent of "X" in their equations is two, i.e.: X^2 (in other words, "X squared"). So, exactly why is that important? For those of you who had basic Calculus, and were not so traumatized by the experience that you immediately purged all memory of it from your mind, you might recall that the two basic operations in Calculus are differentiation (finding the derivative) and integration (finding the integral). Finding the integral of a curve's mathematical equation gives you the area under the curve. If you have a funnyshaped wing planform, but you have an equation mathematically describing the shape, then integrating that equation will give you a formula for the area of that shape. If you find the derivative of the mathematical equation for a curve, that new equation gives you a formula for the slope of that curve at whatever point along that curve you plug in the "X" value for that point. When you take the derivative of an equation, the resulting formula has an order that's one less than the equation it came from. The derivative of a secondorder equation (such as a conic section) is a firstorder equation (the equation for a straight line). The derivative of a firstorder equation is a zeroorder equation, which is a constant. The slope of a straight line (the firstorder equation) is constant (a zeroorder equation) along its entire length, from minus infinity to plus infinity. If the slope was not constant along its entire length, then the line would not be straight! Now, why should we care? If we have an equation for the shape of something, and therefore the path that an air molecule takes when flowing along it, or the path your eye sees when studying that shape, and that shape is lumpy, it does not look pleasing to the eye. If it has wiggles, it will not "look" all smooth and pretty to an air molecule, there will be velocity and pressure fluctuations in the flow. From a kinematics standpoint, the first derivative of the basic shape gives you the velocities along that shape. The second derivative (the derivative of the derivative) gives you the accelerations, and those also tell you what's going on with the pressures along that surface. If the shape you have is a secondorder curve (such as a conic section), then the second derivative is a zeroorder equation, which is a constant. Therefore, a conic section is a shape with constant acceleration. That means it is physically incapable of having any wiggles in it. It is mathematically smooth. The only way to get an inflection point or other sort of wiggle is if you join two or more conics together to deliberately create that wiggle. It's like a manual transmission in a car, it will never shift on its own, only if you specifically tell it to. This means it will be naturally pleasing to the eye, and naturally smooth to the airflow. The NURBs and splines commonly used by a lot of "modern" CAD programs are higher order curves, at least third order and in some cases higher than that. Those are capable of having wiggles, including ones that are so small you don't consciously see them, but still significant enough to be subconsciously distracting, and enough to cause pressure fluctuations that could trigger flow separations. You can't be sure you have them under control. A shape constructed from conics will only do exactly what you tell it to. Conics are trustworthy. 

Last edited by Don Stackhouse; Nov 12, 2010 at 09:05 AM.




Thanks Don!
Thanks for confirming I'm tracking like a young pup after his first bird! I had forgotten, during my search, that I had saved that (page) as PDF, for lunch time reading My search for proper conics is 2 fold (pics) What had driven me nutz earlier this year, was that there is "no" public data of the actual fuse layouts for the mustang, as I have a conversion from 3 views to 3D as a tutorial video planned. sleepin' time now! 
Latest blog entry: Underway: Shifting colors for 2018





Thanks Don and Johnny for the interesting material. The review of Calculus brought back memories. It is satisfying to see how it works with Conics to produce sections of our flying machines. It would be great to see the perfect canard design.
Charles 





Wow! Well done Don. You've managed to break 40 years of sublimation. I studied all that stuff once but I never saw it as having a practical application, apart from giving me a way to string out my student days a little longer. What a waste! I wish we could convince youngsters today about the relevance of applied maths. I've always approached it on a needtoknow basis. Maybe the solution is to show kids the problems that can't be solved without it. The problems are interesting, even if the maths are just a set of tools.
Now, here's my newest cunning plan. As always when I'm having fun, my favorite planes end up with the fuselage smashed to matchwood sooner or later. First I had a Delta Duck, then a ChuddleDuck. Now I've done it again and, as usually happens, the wings stubbornly survive. Next time I plan to mount the motor on the tail and build a Polaris Seaplane type of body, with a canard. There are quite a few variants on this theme, I know Laddie is one of the forces behind it, also TheKM with his Twinkle, and I've always admired them. My airfoil is symetrical, so I can turn the wing over to put the servo arms on top, out of harms way. This should give me the roughterrain plane I need and a seaplane in the bargain. Here are some of my thoughts: 1.The Polaris has the elevator panel right in the propwash, the Polar Duck won't. Should be fixed by the elevon  elevator combination. 2. Battery and motor at opposite extremes  not good for gyroscopic forces, nor for the long power cables. Videos of the Polaris flying show it to be very well behaved. 3. Get the CG right and set the thrust incidence to 2 degrees. What could go wrong? Suggestions gratefully received. cheers Nick 





Sorry to be chiming in late here, I needed to settle some other issues and deadlines, and I wanted to think a bit about how to respond.
Mitchell, I'd also like to apologize in advance for being blunt. I don't like playing the role of "wet blanket", but sometimes it's necessary. Frankly I see some serious red flags, and I would rather bring a monsoon down on your parade now (when you can more easily do something about it) than tell you a bunch of pretty lies that give you a warm fuzzy feeling, but set you up for an even bigger disappointment later, when you have a lot more invested, both financially and emotionally. That would be doing a disservice to both of us, as well as the other members of this discussion. Quote:
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[quote]• If the AC’s for both lifting surfaces are behind the CG, then the first lifting surface must stall first, and the second lifting surface must produce a small (relatively) negative lift. This describes the “conventional” configuration.[quote] Not quite. It is very possible, in fact in certain flight conditions commonplace with many conventional afttailed aircraft, for the tail to make positive lift, and for the plane to still have positive static pitch stability. What actually matters is not the lift of the wing and tail (or canard), but rather how much they each change in response to the attitude change, and whether the resulting change in their moments about the C/G wants to correct the disturbance, or make it worse. The "long way" to look at stability is through "stability derivatives". Recall in my last post on conic sections how the derivative of an equation gives you the formula for the slope of the original equation? If we construct the formula for all the different forces acting on the airplane about the pitch axis, or the yaw axis, or the roll axis, then take the derivative (the "stability derivative" about that control axis), we get the formula for the slope, or changing of the forces about that axis. That slope tells us how these forces change for a given disturbance about that axis. Whether that slope is positive or negative tells us if the plane will be statically unstable or stable about that axis, and the steepness of that slope tells us how strongly the plane responds to a disturbance. A plane with exactly neutral static stability will have a horizontal line for the sum of its forces, and therefore the slope of that line, and the value of its stability derivative about that axis, will be zero. Quote:
Let's look at that parameter "dCl/dalpha". It's a term from calculus (funny how that keeps popping up!). The slope of something is the ratio of how much one parameter changes for a given change in the other parameter. "dCl" is the difference in Cl, the lift coefficient. "d alpha" is the change in the angle of attack, or "alpha". I stick the dash in there between the "d" and the "alpha" just to separate the two, so folks don't get confused and start asking me what this funny new word "dalpha" means. It is not a negative sign. Ideally, what should be there is the lower case Greek letter alpha. So, dCl/dalpha is the slope of the lift coefficient vs. angle of attack curve, the change in Cl for a change in alpha. And, if we have an equation for that Cl vs alpha curve, taking the derivative of it gives us the formula for that slope. In the case of your C/G behind both AC's design, if, for a given change in alpha, the rear surface changes its lift proportionately more than the forward surface, you can still get a net selfcorrecting behavior from the plane. I only know of one series of aircraft that do this, but there might possibly be some others I don't know of from other designers. The ones I'm aware of are a series of flying wings I've been developing for over a decade that have the C/G at 52% of the Mean Aerodynamic Chord (the AC is at 25%), have conventional nonreflexed airfoils, essentially zero twist, positive lift all the way out to the tips, an elliptical lift distribution, and are naturally statically stable in pitch. No, I won't tell you the details of how I did it. However, it's not something you're likely to find in any of the aero textbooks. Quote:
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You express concern about "small changes in the position of the AC". The AC, for all practical purposes, does not move. That's the key difference between it and the older concept of "Center of Pressure", which does move quite a bit. Quote:
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One of the most difficult things to predict, especially at low Re's, is stall behavior, and the qualities you will need will depend a great deal on the relative stall characteristics between the wing and canard. That's not something that's likely to happen by accident or just by analysis (NONE of the commonly available airfoil programs are likely to make reliable predictions of that), and it's likely to involve some serious blood, sweat and tears before you get it just right. Quote:
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What a beginner needs more than anything else is time to think. That means you need to have something slow. I personally recommend indoor models, such as our Roadkill Series Piper Cub: http://www.djaerotech.com/dj_product/roadkill_cub.html or a GWS Slow Stick or Tiger Moth, or a low wing loading two meter sailplane such as a Gentle Lady or our 2meter Chrysalis: http://www.djaerotech.com/dj_product/chrysalis2m.html, particularly the electric version. Quote:
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[quote]• Given the limited power, and the minimum cord length, the canard will be close to 50% of the total wing area (probably around 40%), and the A.R. for both the main wing and the canard will be relatively low.[quote] Depends on what you mean by "relatively". In general, your statement above seems to jump to quite a few conclusions unnecessarily quickly. In general, a canard aircraft will have the best overall efficiency if the canard is as small as possible, so the greatest possible percentage of the plane's weight is supported by the wing, not the canard. This can be achieved by using a long moment arm for the canard. This is also the best thing possible for dynamic stability, which is at least as important for handling qualities. A short span, low aspect ratio wing will be likely to have poor roll damping. Quote:
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Sweep does tend to unload the root and load up the tips, inviting tip stalling. Also, there is a balance between wing dihedral (including the dihedrallike effects of sweep) and fin authority. To much fin/not enough dihedral gives you spiral instability. Too much dihedral/ not enough fin gives dutch roll problems. Given that most canard aircraft tend to have very short moment arms for the vertical tail, and therefore tend to have atrocious vertical fin authority and yaw damping, as a group they tend to be even more sensitive to these problems. Adding significant amounts of sweep to the wing gives you what amounts to a variable dihedral airplane. It's very possible you could end up with significant spiral instability at higher airspeeds and low Cl, and also have serious amounts of dutch roll at low speeds and high Cl, such as during final approach and the flair for touchdown on landing. Quote:
If you could get them vertically that far apart, the relative drags of the wing and canard are now going to start influencing pitch trim in ways that are normally small enough to be ignored. The span loading and Reynolds number issues are likely to make these effects destabilizing in pitch. Quote:
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I like the "shoe analogy" for this issue. Yes, it's important to have a shoe that's well designed and well constructed, but what is even more important is how well that shoe fits your personal foot. Michael Jordan's shoes on your feet are not likely to help you be a better basketball player, unless your feet are exactly the same size and shape as his. Quote:
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The first red flag is that any source that seems to recommend a 1416% thick airfoil for an Re = 50K application should immediately be viewed with great suspicion, if not discarded as invalid right at the beginning. Quote:
Here's where I really start to get serious heartburn with that source. They use a program that's based on the old Eppler program to do their airfoil predictions. Eppler is good at Re = 500K, not so good at Re = 250K, starts getting pretty shaky at Re = about 150K. It does not iterate on the boundary layer, which becomes very important at low Re's. It's one thing to generate a performance prediction for Re = 50K. It's another matter entirely to generate a performance prediction that's actually any good at that Re. Even if the overall performance predictions are accurate (which in this case I find EXTREMELY doubtful), the predictions of stall behavior, both the angle and especially the characteristics, are likely to be utter nonsense. There are no public domain programs that do a good job of predicting stall characteristics at even moderate Re's, and the lower the Re the worse they get. Quote:
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At Re = 50K, a 1416% thick airfoil will ave less max lift than one about half that thickness. At all angles of attack, large portions of that thick airfoil are likely to have separated flow, which also invite the possibility of aerodynamic hysteresis as those separated areas move around with changes in alpha. The actual stall characteristics, as I indicated above, are likely to bear little resemblance to those predictions. About the only thing we can say with much certainty is that those airfoils at Re = 50 100K will have terrible L/D's. Yes, they will probably have what appears to be gentle stall characteristics, but only because they are already, at all angles of attack, operating in a condition of what amounts to a partial stall. What the exact details of that stall look like, and the angles where those details occur, will be very difficult to nail down with any certainty or precision. In general, at lower Re's (such as the 5080K region), you need low thickness (below about 8.5%), modest camber (12% or less) and the max thickness point around 2325% aft of the leading edge. Quote:
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Let me suggest another. You have a lot of unknowns here, some serious technical risks (even with some appropriate airfoils), and the probability of some significant design iterations required before you end up with something acceptable. I suggest doing some smaller models to sort out the issues and answer some questions, before investing in the bigger one. Start with small (maybe 10"12", 30 cm) balsa freeflight scale models of your design, fly them in your living room. Thin out the airfoils to about 34% thick for these to allow for the effects of Reynolds number. Start with glider versions, don't worry about power till you have the basic C/G, flying surface arrangements, etc. sorted out. You can also cut the control surfaces out, use aluminum foil to reattach them, and then experiment with things like incidences, flight trim and control responsiveness. By the time you actually invest big time and bucks in your model, you will have already identified most of the real problems you face, as well as having a decent handle on the effectiveness of your proposed solutions. 






Don,
I always find your aerodynamic lessons very enlightening  one reason why I continue to lurk on this thread despite not having any Canards planned at present. You give two different criteria for static pitch stability. Firstly the dCl/dalpha argument: Quote:
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I must admit though that I tend to think of the cg ahead of ac giving a negative pitching couple which, in level flight, has to be counteracted by a positive pitching moment from the combined flying surfaces. So, if the model pitches down, I imagine the corrective force resulting not in direct response to change in attitude but rather in response to the subsequent change in airspeed which would increase the upward pitching moment from the flying surfaces. I know this is dangerously close to the old concept of longitudinal dihedral but it is the best mental model I can manage! If our models really do generate corrective forces in response to changes in attitude (as opposed to changes in airspeed), I really would like to get my head around it in a qualitative way  much as I have always loved calculus! Trevor 






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Probably another significant factor here is that the whole airspeedrelated explanation is most likely quicker to tell and easier for the "civilians" to follow, so it gets used more than the angleofattack explanation, even thought the angleof attack explanation is probably more technically complete. It's a little like the Bernoulli vs. Newton debate about how a wing makes lift, both are focusing on the same problem, but coming at it from different directions. Both are valid, at least within the range of common designs. Quote:
In the case of a conventional tail, the C/G is forward enough that the moment change from the tail has proportionately more effect than that of the wing, resulting in a net correcting moment. In the case of a canard, the C/G is far enough forward that the change in moment from the wing has proportionately more effect than the change in the lift of the canard. It's a leverage thing. Wait  did anyone notice that the same phenomenon is occurring for BOTH? In both cases, the leverages work out such that the change in lift at the aft surface dominates, bringing the pitch attitude back towards the original setting. As I've said before, there is fundamentally no difference between a canard, a tandemwing and a conventional layout. All represent different points along the continuum of "twosurface aircraft". OK, let's look at it again through another example. Consider an arrow, maybe one of those hunting arrows with the big wide triangular blades on the head, like a set of delta wings on the front of the arrow. Let's say it was in stable flight, but has just passed the apogee of its flight. Its attitude is horizontal with the ground, its inertia wants to hold it there (or if it was pitching, to continue pitching at the same rate, regardless of whether or not that kept it aligned with the flight path and airflow) but its flight path is now changing to downhill, causing the "relative wind" to hit it from slightly below. This angle of attack causes an upward lifting force on both the head and the feathers. The angle is different from what existed before by the same amount at both ends of the arrow. At opposite ends of the shaft, the head and the feathers BOTH begin making lift forces in an upward direction. Is the arrow going to realign istelf with the airflow, or will it pitch up to even greater pitch angles, and eventually tumble out of control ?? !!! Will it continue to its target, or turn completely around in mid flight, go back the other way, and skewer the person who originally fired it ??? !!!! Inquiring minds want to know !!! The answer is "it depends". If the head was really big and the feathers too small, that would favor a tumble. If the head was really light, and some misguided (pun intended) person made the feathers out of steel in hopes they would be more durable in service, the C/G of the arrow might be way too far aft, giving the feathers little leverage and the head way too much, again favoring a tumble. However, maybe the head on this arrow is metal and the "feathers" are  well  feathers, so the C/G of the arrow is well forwards, giving the feathers more leverage and the head less leverage. Maybe the feathers are large enough that their lift force is greater than the head. Maybe some of the above, or all of the above. Be it due to greater lift force, or greater leverage, or both, the feathers dominate, and the arrow begins to align itself with the now downhill flight path. As it does so, thanks to gravity it also starts picking up airspeed. The lift forces on the head and the feathers increase, while the inertia of the arrow that resists changes in its rate of pitch change stays constant. We've already established that in this example, not because of any inherent property of all arrows, but rather because this particular arrow was designed and made correctly, the correcting forces of the feathers are dominant. As the airspeed increases, the correcting forces become even more dominant, straightening out any discrepancies in its attitude even quicker, and the arrow continues on its course even more straight and true. LOOK OUT BAMBI !!!! mmmmm...venison for dinner tonight! Quote:



Last edited by Don Stackhouse; Nov 12, 2010 at 06:35 PM.





Thanks Don, I think the penny's dropped now! Another way of describing the attitudesensitive corrective effect is to say that, if the aircraft pitches up, the downward couple exerted by the weight acting through the cg and the lift acting through the AC will immediately increase due to the extra lift caused by the change in angle of attack.
I should be able to sleep tonight now. Trevor 





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On afttailed airplanes with this problem, such as the Republic SeaBee or the Lake Amphibian, they place the horizontal tail (and the rudder too) squarely in the middle of the propwash. As long as there is enough authority from that induced flow, it works fine. However, I know of cases where they wanted to install bigger engines in planes like these, and found there simply wasn't enough authority from the elevators to keep the plane from trying to visit the fishes. In your case it's going to be even more difficult. Keeping the longitudinal moment arms as long as possible would probably help, as well as keeping enough volume in the nose for good buoyancy. However, that will cut into your yaw stability. Good luck, and remember, if it was easy, someone else would have done it already. 






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Thanks Don. I've got a plan to increase the size of the nose and add 'chine rails' (is that the right word?). Also a bigger canard to get some ground effect at an early stage. I've noticed with flying boats that you need to be very gentle with the throttle at the beginning of the takeoff run. However, though I have flown my canards from water, it's never really been easy yet. cheers Nick 






Thank you Don. By showing me which of my initial assumptions are not valid you have done me quite a service. I won’t worry about a bit of rain if you don’t – I have been wet before. I am still waiting for materials to arrive (balsa etc), so I have the time to indulge in a protracted design process – and find out which of my assumptions definitely belong in the garbage can.
I have encountered a great deal of conflicting information on the subject of airfoils. If I understand you correctly, the model used for the data on the Krauss website is not able to make extrapolations of test data that are reliable for low Reynolds numbers. I thought I was going to be able to have my cake and eat it too: airfoils with excellent aerodynamic characteristics at low Re #’s that are thick enough to make building light, strong wings fairly easy. Oh well, such is life ) I didn’t write down all of the links in the chain of reasoning that resulted in the decision to use a tractor engine. Since I had already committed to a lower limit for chord length, the front wing would be a fairly large fraction of the total lifting area (for any reasonable span/AR). The motor has to go somewhere, and since the front wing will be producing a substantial amount of the total lift, placing the motor at the front makes one or two things easier without creating any difficulties in getting the centre of lift and the centre of mass in the same place. I looked up the definition for aerodynamic centre, and discovered that the concept that I was looking for is closer to the centre of pressure. For an airplane in unaccelerated level flight, all aerodynamic forces (thrust, drag, lift) must resolve to one vertical force, equal to the weight of the airplane, and acting through the centre of mass. This is not aerodynamics – it is basic physics. If we resolve all forces to vertical and horizontal components (2 dimensional model), and assume that any torques (referenced to the centre of mass) associated with horizontal forces are small and resolve to 0 (not an unreasonable assumption for a simplification of an airplane in level flight), then all of the torques created by vertical forces (aerodynamic, gravity) must also resolve to 0. If we postulate three vertical forces, and stipulate that no two can operate through the same point, then my reasoning regarding irreducible elements holds for unaccelerated level flight. The torque associated with the force of gravity is 0, and therefore the torques created by the two aerodynamic forces must be equal and opposite. I agree with your point that for static stability, it is more accurate to speak in terms of rates of change. If these torques are modeled as functions of AoA, then the second derivative of f(AoA)  torque must be more negative for the forward most positive lift producing surface if there is to be static stability – thank you for straightening me out on the difference between static and dynamic stability! This of course ignores any other torques that might be a function of AoA, or values of AoA outside the limited range associated with normal flight – but this is a simplification. Time to go to bed ) 

