Great information....and correlation with my theory about the mac and the corresponding cg range. My wings are going to be stretched so I have to be very careful with the cg and that is causing me to relook at what was done before. On Aug 16, 2013 10:39 PM, "Mark Langford" <ml at n56ml.com> wrote:
> 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 <http://tugantek.com/archmailv2-kr/search>. This > link is at the bottom of every email sent out from krnet at list.krnet.org . > Hopefull > ------------------------------**------------- > > 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: > > 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 > ------------------------------**-------------------------- > > > ______________________________**_________________ > Search the KRnet Archives at > http://tugantek.com/**archmailv2-kr/search<http://tugantek.com/archmailv2-kr/search> > . > To UNsubscribe from KRnet, send a message to KRnet-leave at list.krnet.org > please see other KRnet info at http://www.krnet.org/info.html > see > http://list.krnet.org/mailman/**listinfo/krnet_list.krnet.org<http://list.krnet.org/mailman/listinfo/krnet_list.krnet.org>to > change options >
