NetHeads, Here are two messages I fished out of the KRnet archive from 2001. I just killed an hour sifting through that whole conversation. Quite interesting. For those interested, this thread will take you off the streets for a few days. I remember it well!
Richard Mole is a good friend and very sharp English aero engineer, and Bill Marcy was the aerodynamics consultant for Jeanette Rand on occasion when she needed some aero work done on the KR. Two different opinions, but definitely food for thought, either way. Hopefully I'm not opening a huge can of worms here. For those who want to get lost in that discussion, rather than building their own personal KR time machine , a trip back in time to early March of 2001 can be had by visiting the KRnet archive at http://tugantek.com/archmailv2-kr/search. This link is at the bottom of every email sent out from krnet at list.krnet.org . Hopefull ------------------------------------------- List-Post: krnet@list.krnet.org Date: Mar 8, 2001 3:28 PM Sender: Richard Mole Subject: Stability - ugh! - again - the last time - that's a promise! I felt that this post was required to try and clear the air. If you not a 'techie' its probably best to skip it completely. All the information in this posting is supplied without warranty of any sort implied or explicit. Aft cg limits shown here are calculated in good faith - but they have NOT been independently checked. They are not authoritative. They are one man's best shot. Results of own analysis; neutral points stick fixed and stick free. Datum: all aft of LE of stub wing kr2 Kr2S Stick fixed np 12.75" 13.5" Stick free np 11.8" 1.3 lbs/g at this limit 12.2" 1.3 lbs/g at this limit So there is very little difference, just 0.4", between the calculated aft cg for the kr2 and the kr2S. All numbers are power-off and the de-stabilising effects of power will bring them forward. Note that at least two Airworthiness authorities restrict the aft cg position: Australia aft cg limit is 12" aft of LE on stub wing (info posted by Malcom Bennet, krnet 23.12.98) South Africa aft cg limit is 13.44" aft of LE on stub wing (info posted by Kobus De Wet, 27.12.98) The stick fixed np is included in the table for interest only because the stick free case is always more stringent. It is possible to fly with the cg aft of the stick-free np but it is VERY dangerous and foolish to try this. The stick free manoeuvre margin is what makes it possible and this depends upon air density, so the margin reduces with density altitude. Bigger tails and moment arms both increase the tail volume and move the stick fixed np further aft. But this may be an illusory gain. What is really required is a rearward shift in the stick free n.p. The kr elevator floats with the relative wind because it has no aerodynamic balance. This floating tendency will always ensure that the stick free np is well forward of the stick fixed np whatever the tail volume may be. Aerodynamic balance is one (but only one) approach to improving the situation. Hence Dana's elevator horns. These horns add area and so they do improve the stick fixed np. More crucially, they reduce the tendency of the elevator to float with the relative wind. The stick free np is then much closer to the stick fixed np. It is hard to judge the correct horn geometry. Dana's horns are 'unshielded horns'. It is imperative to use the best data sheets available (ant to correct for the effects of the elevator cut-out). Do not try to eye-ball this for yourself as over-balancing is more dangerous than no balance. To do a longitudinal stability analysis requires a lot of work. These are some of the data that are required to be estimated to a high degree of accuracy. My full analysis covers 7 sides of single spaced paper. Estimates are required for: Wing lift slope a1 per rad (from Reynolds number, included angle at TE, transition point, Aspect ratio etc) Wing mean aerodynamic chord mac Tail lift slope a1t per rad (as for wing plus account of elevator cut out) Tail volume (from wing and tail areas, mac and tail arm) Rate of change of downwash with wing alpha Elevator lift slope a2 per rad Hinge moment rate due incidence b1 Hinge moment rate due elevator deflection b2 Stick free factor = 1- a2/a1t*b1/b2 Elevator gearing Longitudinal a/c relative density So it's a long haul and fraught with opportunity for unintended error and plain mistakes. The table at the start of this post is my best shot. It is offered in good faith. Richard -------------------------------------------------------------------------------- Then from Bill Marcy: List-Post: krnet@list.krnet.org Date: Mar 9, 2001 8:23 AM Sender: Bill Marcy Subject: tail stuff yet agan Tail Stuff again First things first: I have been challenged to knock off the discussion and publish the results of my calculations for the KR-2 and KR-2S. I did these calculations six years ago at the request of Jeannette Rand in response to concerns by the Australian CAA. The stick fixed, power off neutral point of the KR-2 is 7.24 inches aft of the wing 25 percent mean aerodynamic chord, or 31.06 inches aft of the aft face of the firewall. This is 3 inches further aft than the aft limit shown in the KR-2 manual I have had since about 1988. The stick fixed, power off neutral point of the KR-2S is 7.12 inches aft of the wing 25 percent mean aerodynamic chord, or 33.18 inches aft of the aft face of the firewall. This is a bit more than 5 inches behind the aft limit in the Rand manual (I assume the c.g. limits for the -2 and -2S are the same). The difference between the two locations is almost entirely due to the 2.0 inch difference between the locations of the 25 percent mean aerodynamic chords of the two airplanes, and this difference is due to the increased wingspan and reduced tip chord of the KR-2S relative to the KR-2. Note that within the accuracy of calculation, the neutral points are exactly the same distance behind the 25 percent mean aerodynamic chords of the two airplanes.( Incidentally, don?t take the .01 inch accuracy of the numbers too seriously, they are probably no better than about .15 inches.) For those who want to check my neutral point calculations, here are the numbers. For the KR-2: wing area 74.22 square feet wing span 20.21 square feet mean aerodynamic chord 3.52 feet aspect ratio 5.50 lift curve slope 4.401 per radian location of 25 percent mean aerodynamic chord 24.06 inches aft of the firewall aft face fuselage length 174 inches fuselage width 38.12 inches horizontal tail area 10.94 square feet horizontal tail span 20.21 feet mean aerodynamic chord 3.52 feet aspect ratio 3.20 lift curve slope 3.482 per radian location of 25 percent mean aerodynamic chords 121.05 inches aft of the firewall aft face and 30 inches above the zero lift plane of the wing. downwash derivative at the horizontal tail 0.36 degrees per degree angle of attack For the KR-2S: wing area 81.15 square feet wing span 23.54 feet mean aerodynamic chord 3.28 feet aspect ratio 6.83 lift curve slope 4.707 per radian location of 25 percent mean aerodynamic chord 26.06 inches aft of the firewall aft face fuselage length 190 inches fuselage width 38.12 inches horizontal tail dimensions are the same as KR-2 except the location of the 25 percent mean aerodynamic chord, which is 137.05 inches aft of the firewall and 34 inches above the wing zero lift line. In response to another question, I have not and am not building a KR, and I have never flown one of any kind. My personal airplane is a large, comfortable, very stable, ponderous, slow, and inefficient 1947 Navion; I have owned it since 1977. I have no axe to grind one way or another. However, I do lean toward improvements to the airplane that can be made by builders who are already flying. This is the reason I have stated that , as Dana Overall stated: stability is determined by the location of the center of gravity in relation to the center of pressure (lift). That is a qualitative, but nevertheless true, statement. More precisely, I will quote from NACA Technical Report No. 971, Appreciation and Prediction of Flying Qualities, by William H. Phillips, published in 1948: An airplane that is stable with stick fixed requires a forward movement of the stick to increase speed (same thing as decreasing angle of attack or lift coefficient) and a rearward movement of the stick to decrease speed (same thing as increasing angle of attack or lift coefficient). As the center of gravity moves aft toward the point of neutral stability, it takes less and less stick motion to pitch the airplane through its full range of lift, until at the neutral point, no motion at all is required, and aft of the neutral point the motion is reversed. This is a definition that anyone who flies can understand. Next, Phillips defines the stick-free stability: An airplane that is stable in pitch with its stick free requires not only forward motion to increase speed, but also requires that the stick must need a push force to move it forward and must need a pull force to move it aft. Because the elevator generally tends to float with the relative wind, the effective stabilizing area of a tail with the elevator free to move is less than with the stick fixed, and the aft limit of the center of gravity with stick free is more forward than the aft limit with stick fixed. This can result in a condition that appeals to the aerobatically inclined: there is a center of gravity that is slightly stable with stick held fixed, but that lets you move it back and forth with no resistance. This can be fun for awhile, but it gets tiresome if you are trying to fly straight and level on a cross country. Incidentally, stick free stability is what the FAA requires; in fact, it requires that the stability margin be high enough and control system slop and friction be low enough that with the airplane trimmed to zero stick force at any speed, it will return to within 10 percent of that speed if the stick is pushed or pulled for a moment and then released. Nothing here says that the only way to get more distance between the center of gravity and the stick-fixed or stick-free neutral points is by moving the neutral points to the rear. The same effect can be gotten by balancing the airplane so its center of gravity is more forward. Now, just how far forward can the center of gravity be? First, for a taildragger especially, it can?t be so nose heavy that it falls over when brakes are applied. Second, it can?t be so nose heavy that the tail can?t balance it throughout its speed range. The landing gear problem can be solved by tilting the gear legs forward, so let?s look at the tail effectiveness, starting with the condition for maximum lift. S.F. Hoerner in his book, Fluid Dynamic Lift, lists the max lift coefficient of the RAF 48 as 1.45. For the KR-2S wing, the angle of attack for this coefficient is 1.45/4.71 = .308 radians or 17.6 degrees. Including 3.5 degrees incidence, the zero lift line of the wing is approximately 3 degrees nose down, so the airplane angle of attack at maximum lift is 14.6 degrees. This should be the angle of attack of the horizontal tail, but that neglects the downwash behind the wing. The stability calculations gave the downwash as 36 percent, so the true angle of attack of the tail is 14.6 degrees minus 0.36 times 17.6 degrees, which equals 8.3 degrees. The max elevator deflection is 30 degrees up, and the elevator effectiveness, assuming 50 percent chord ratio, is about 65 percent. This means that 30 degrees elevator deflection is equivalent to 20 degrees angle of attack. Subtract 8.3 degrees from that, and the down tail load is what can be produced by 11.7 degrees angle of attack. The tail lift curve slope is 3.482, so the tail lift coefficient is -0.711. The area of the KR-2S tail is 10.94 square feet, and the dynamic pressure at max lift (1050 lb weight) is 8.94 pounds per square foot. Then the maximum tail down load with 30 degrees up elevator at maximum lift is 69.5 pounds. The 25 percent mean aerodynamic chord of the tail is 8.08 feet aft of the wing 25 percent mean aerodynamic chord, so the nose up moment at the 25 percent wing chord is 562 foot pounds. The airplane weighs 1050 pounds (in this example), but you can?t get a full forward center of gravity with two persons, so we should subtract 170 pounds. This reduces the dynamic pressure at stall to 7.49 pounds per square foot, so the maximum down load at the tail can only be 58.2 pounds and the nose up moment can only be 471 pounds. Then the furthest forward the center of gravity can be is 562/1050 = 0.535 feet, or 6.42 inches forward of the 25 percent wing mean aerodynamic chord. This is 17.6 inches aft of the aft face of the firewall. My KR-2 construction manual (NOTE: KR-2, not KR-2S) gives the forward limit as 8 inches aft of the wing leading edge, or only 4.0 inches forward of the 25 percent mean aerodynamic chord. So these calculations let you have 2.4 inches more forward center of gravity than specified in the plans. However, be aware that I have neglected the tail down load required to counter the nose-down moment of the wing-fuselage combination that is due to camber; I have neglected any power effects, and I have used an elevator effectiveness curve that ignores the gap between the elevator and the stabilizer. I have included all the details of this calculation to give you all an idea of what is involved in analyzing an airplane design. Note that I have not done the calculation of the tail angle of attack, elevator deflection, and down load required for the high speed dive condition, because I don?t have the zero lift pitching moment coefficient for the RAF 48. However, all this is mere discussion. The proof of the pudding is that dozens of KR-1?s and KR-2?s, and not a few KR-2S?s, have been built and flown for hundreds of hours. This does not mean it can?t be improved. The early Bonanza revolutionized the post WWII aviation market, but compared to the Bonanza that has evolved since 1946 it is completely outclassed. Let?s do the same for the KR. Well, I?ve gotten carried away by enthusiasm again. I had some other stuff but I will put it off until I get some feedback on what I?ve given you here. Now I?ve got to get cracking on static test loads for Chris Kogelmann. Keep the airspeed up and the dirty side down, guys! Bill Marcy old paper and pencil engineer -------------------------------------------------------------------------------- Mark Langford ML at N56ML.com website at http://www.N56ML.com --------------------------------------------------------
