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Guest Ron Freimuth

Make Sure Your Aircraft Obeys This Law (Of Physics)

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When we have such astounding control of all aspects of the aircraft motion as in the air files today, it is easy to get carried away and make an aircraft that violates some laws of physics. I recently took off in an aircraft I have liked for some time and had just imported into FS9 when I found it seemed a bit slow turning through 90 degrees. I was aware of the laws governing turning flight but went back to 'the books' to make sure everything was done right. What I found was that the particular plane was taking twice as long to turn 90 degrees as it should have taken, using a moderate speed and a normal bank angle.By using this equation to check your aircraft's turn rate, you will be assured that it conforms, at least approximately, to the laws of physics.T90 = (V / tan :( / 12.14where V is the speed in KTAS and B is the bank angle. (Most calculators will use degrees for angles.) The normal autopilot makes a turn at 25 degrees. (I made an xml gauge and checked it.) T90 is the time in seconds it should take to make a 90 degree change in heading.I performed this test on many aircraft, default and custom, in FS9. I found that most conform well. But none conformed perfectly. It can be tricky doing the test. I suppose turning through 180 degrees would be a more accurate test. But 90 seemed good enough. At 175 KTAS, with a 25 degree bank, it should take 30.9 seconds. I saw values from 32 to 34 seconds. I consider 33 seconds good.The way I do the test is to set the aircraft in steady flight at a nice altitude with normal cruise power on a heading such as 300 degrees - 30 degrees above 270. Then I make it turn left to a heading of 150 degrees. I time the portion of the turn from 270 to 180. This avoids any unsteadiness at the beginning or end of the turn.In one case a 32-second turn took 60 seconds. Looking at the stability derivatives I found that Cn_r was -2.1387 while for a similar well-behaved aircraft the value was -0.100. That's 21 times bigger!!! The slow airplane became normal when I set this value to -0.10058.It may seem a little strange that such a simple formula can apply to all these fancy aircraft regardless of their dimensions, power, weight, moments of inertia, etc. But it is correct. When the aircraft flies a steady and level turn, the banked lift force has one vertical component that must balance the weight and one horizontal component that points inward toward the center of the turn and makes the turn happen. It bends the flight path into a circle. In the equations you start with weight and lift force which makes you think of angle of attack and lift coefficient, etc. But all that stuff drops out with a little algebra leaving the simple equationomega = 57.3*g*tan(:(/(1.689*V)where omega is the yaw rate in degrees per second, g is 32.2 and V is in knots true airspeed. To get T90 we just divide 90 by the yaw rate giving the formula shown above. This relation shows why all major changes in heading by a jet should be done at low altitude where true airspeed is low.In flying, you should be aware of what it takes to fly a "standard rate turn". This is a turn that takes one minute to go through 180 degrees such as on either end of a holding pattern. It is a method required frequently of pilots flying IFR. If you have a conventional turn and bank indicator, you make a standard rate turn by turning so the wings on the little airplane figure hold at the mark. That assures that the turn will take 60 seconds to go through 180 degrees. It assures that the bank angle is appropriate for whatever speed you are flying at so the turn is at the standard rate. In a fancy jet with no such indicator you will have to time your turn. It would help to know the bank angle needed for the speed you want to fly. Diddle with this equation until T90 = 30 and you have your answer.But a standard rate turn is only possible if the aircraft obeys this law of physics!

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Noted and TIPped....Felix/FFDSPegasus Aviation Design

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Hi.Thanks for that, and everything else. I am glad to see that some of us are taking this project seriously. In addition to that many gauges are grossly out of specifications. I

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>When we have such astounding control of all aspects of the>aircraft motion as in the air files today, it is easy to get>carried away and make an aircraft that violates some laws of>physics. I recently took off in an aircraft I have liked for>some time and had just imported into FS9 when I found it>seemed a bit slow turning through 90 degrees. I was aware of>the laws governing turning flight but went back to 'the books'>to make sure everything was done right. What I found was that>the particular plane was taking twice as long to turn 90>degrees as it should have taken, using a moderate speed and a>normal bank angle. People also set physically unreasonable aerodynamics by having 1101:50 inconsistent with TBL 404, incidence and twist (when the later two work -- before FS9). It is also common to see unrealistic Mach Drag at low Mach numbers to adjust climb rates, etc. Clearly, when real aerodynamic effects are fudged to fix one problem other things will come not come out correctly, no matter how much else one messes around.>By using this equation to check your aircraft's turn rate, you>will be assured that it conforms, at least approximately, to>the laws of physics.>>T90 = (V / tan :( / 12.14>>I performed this test on many aircraft, default and custom, in>FS9. I found that most conform well. But none conformed>perfectly. It can be tricky doing the test. ...........>>In one case a 32-second turn took 60 seconds. Looking at the>stability derivatives I found that Cn_r was -2.1387 while for>a similar well-behaved aircraft the value was -0.100. That's>21 times bigger!!! The slow airplane became normal when I set>this value to -0.10058. I expect any AC will turn at the correct rate if there is no Slip. I think you are seeing the effect of uncoordinated flight. Which can be difficult to know since the 'ball' seems to move back to the center even with slip. At last, before FS9. AFSD displays Turn Rates for 'Coordinated Turns'. When I adjusted the rudder for near zero Slip the two values displayed coincide. However, I watch 'beta', not the questionable FS 'ball'. Many AC have an 'inverse' 'Roll Moment - Yaw Rate' that requies some rudder input. It is intrinsic to having the vertical stabilizer above the Centerline. AC with the Yaw Control below the centerline are probably more coordinated. An example is the RQ-1 Predator UAV. I set some SD's to the opposite sign of normal to account for the 'low rudder'. It is really an inverted V tail, but that can be resolved into vertical and horizontal components.>This relation shows why all major changes in heading by a jet>should be done at low altitude where true airspeed is low. Turning the Concorde adds a lot of induced drag unless turns are made very slowly. >In flying, you should be aware of what it takes to fly a>"standard rate turn". This is a turn that takes one minute to>go through 180 degrees such as on either end of a holding>pattern. It is a method required frequently of pilots flying>IFR. I have practiced holding patterns in real and FS aircraft. The idea is to hold the turn indicator needle at the correct place. Then, one will turn 180 degrees in 1 minute. I think it's another minute of straight flight, then another 1 minute turn to change direction by another 180 degrees. I noted the GPS holding pattens that can be conrolled by the FS9 GPS work poorly. The GPS tries to follow the oval, rather than setting bank for a 2 minute (360 deg) turn. The holding pattern ovals will only be tracked if one is at the TAS they are displayed for. The correct way to fly them is by turn rate and timing. With further adjustments if there is an X-Wind. I also assume pilots are to fly them at the designated altitude and a limited range of airspeeds. A slow AC would trace a much smaller oval than a jet, but controllers probably assume an AC can be anywhere within the oval. The danger would be flying a jet at too high a (true) speed, since it would then require a larger boundary holding area than otherwise. Ron

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>Hi.>Thanks for that, and everything else. I am glad to see that>some of us are taking this project seriously. In addition to>that many gauges are grossly out of specifications. I

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>But a standard rate turn is only possible if the aircraft obeys this law of physics!In addition to that many gauges are grossly out of specifications. I

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..............>Indicators that are not even close to what they should>indicate in pitch attitude etc.<>>TV, I can confirm that the pitch info is incorrect on the FS9>747.>Recently, after reading a forum topic at Simflight about the>FS9 747s' excessive nose up pitch in cruise, I set about>changing the cruise pitch to better reflect the real aircraft>and found that the EADI pitch info was 2-3 degrees too high>when compared to AFSD. The Digital Pitch reading is the correct value. Some .mdl's also appear to have an incorrect LG articulation and place the nose too low for TO. That is pitch is very important and should be correct in the .mdl.>I see a topic at the MSFS General Discussion forum with links>to two job opportunities with the MS Aces' Game Studio working>on Flight Simulator.>>Hopefully this is in response to a long needed pruning of the>deadwood responsible for the current state of MSFS, and that>two of their most egregious and incompetent persons are now>ex-employees and will no longer be drawing a paycheck there. Gossip I was unaware of. But, it's not the quantity, it's the quality that counts.>>Clearly, when real aerodynamic effects are fudged to fix one>problem other things will come not come out correctly, no>matter how much else one messes around.<>>How true! I'm going to print this, have it framed, and hang it>over my desk to remind me to do it right the first time, ad>initium - and avoid having to do it over and over, ad>infinitum! The problem is it's not easy to understand all that is involved. I've been at this for years and slowly understand and improve the basics. Getting the significant distances in aircraft.cfg correct is quite important. I'm still confused about some things. Engineering drawings show the MAC and important distances. Operating Manuals are mainly concerned with how much space it takes to hanger the AC. None I have give the location of the wing or center of lift. >>I think you are seeing the effect of uncoordinated flight.>Which can be difficult to know since the 'ball' seems to move>back to the center even with slip. At last, before FS9.<>>You may be right about the slip Ron. But Tom is probably using>his digital XML gauge that displays incidence beta, and not>relying on the coordination ball in the turn coordinator. He didn't say. I also display Beta in my XML test gauge, AFSD does also. AFSD now displays three Body velocities. With small slip, the side velocity of my Concorde could be 20 ft/sec. > I just found that the FS2002/FS9 autopilot isn't cabable of>executing a coordinated turn in the default C-172. The A/C>slips in the turn, as reported by AFSD and the highly suspect>MS slip/skid ball. I knew "auto-rudder" only locked the 'ball' and rudder input. It does not reduce slip. A true autorudder would be similar to a Yaw Damper - which will help coordinate a turn. No wonder big jets are flown 'no rudder' other than when landing. Regardless, my jets do hold bank better than my small AC, and they require little if any rudder input in climb/cruise. Proably due to the high speeds giving higher aerodynamic forces relative to the other factors. But I'm not seeing the ball move back to>center when the A/C is slipping, not in FS2002 or FS9 (MS>C-172). It takes a skid to center it! Still, I think that what>Tom is saying about high Cn_r may be valid, although I haven't>tested it yet. Generally, all AC have similar Stability Derivatives. They are normalized to MAC and Wing Span. That is the advantage of useing the normalized parameters! Different configurations, such as a Canard or 'bottom tail' reverse some signs. Thrust and MoI's can also be normalized. In fact, it would be easier to do some calculations and see if things were 'typical' if thrust and MoI's were normalized. But, also make them less intuitive. Regardless, Trust/HP per sq-ft of wing area is commonly given. And, easy to calculate if desired. Wing Loading, W/S, is also commonly given.>>AFSD displays Turn Rates for 'Coordinated Turns'. When I>adjusted the rudder for near zero Slip the two values>displayed coincide. However, I watch 'beta', not the>questionable FS 'ball'.<>>So do I, and after testing the MS C-172 in FS2002 and FS9, I'm>seeing a constant sideslip of 2-3 degrees when using the>autopilot to make a "coordinated" turn. The ball remains>deflected about 1/2 width to the inside of the turn, and it>requires bottom rudder and a skid of about 3 degrees (-3.6) to>center it. However, there is still a disagreement between the>turn rate and coordination rate even with beta at 0. The MS>slip/skid ball - I'm starting to realize - is completely>screwed up. When we understand the details of the individual components of velocity, etc. we might find some problem. It's easy to calculate the 'co-ordinated' turn rate. One calculates the 'centrifugal' component of Lift by simple Trig. That should be balanced by F=((2Pi*V)^2)*r. Setting the centrifugal wing component to the F at the right, one can calculate radius 'r' for a given TAS, 'V'. Speed has to be in ft/sec for such calculations. 'G Force' = 1/COS(Bank). 2 G at 60 deg. One can take Sin (60) = 0.866 and multiply it by that 2.0 G to get the radial inward G force: 1.73. Multiply by 32.2 ft/sec for 1 G and it comes to 55.8 ft/sec^2 inward acceleration. Which is what r * (2PI*V)^2 should equal. The G force is independent of the speed, but the turn radius, r is dependent on TAS, V. I used a formula I remember from Freshman Physics for 'F', but anyone who can draw simple triangles should be able to get an idea of how force components, etc. change with AC attitude. Ron

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Ron, you have the equations but have not worked with them long enough to resolve them. The equation I presented comes directly from those equations. The radius of turn drops out when you use the relation r = V/omega.I don't think it makes any difference whether the turn is coordinated or not. All that matters is that it must be very steady - steady altitude, steady bank angle and steady true airspeed. When steady, the path will be circular and these relations apply.Here are the results of my first test that proved that the 'Brand B' aircraft was set wrong.AIRCRAFT__________T90cal_________T90obs______Cn_rMS King Air 350: 39.0____________39__________-0.500MS Baron 58:____35.9_____________38__________-.10009'Brand B':______33.9_____________58__________-2.13867I just noticed that I had earlier made some adjustments to the Baron 58. The original value of Cn_r was -0.97656 and I changed it to several values ending with -0.10009. I did not test the Baron for turn rate with that original setting. I also made some slight adjustments to the King 350 but did not keep notes.The point here is clear. Cn_r generates a yaw moment that resists turning. The developer of 'Brand B' set this value intentionally because he wanted the aircraft to turn gracefully. Indeed some of us liked the way he set the plane up. He later had second thoughts and intended to change this setting but did not get to it before it was distributed. I can certainly feel empathy with that.Variations between T90cal and T90obs of 10% or so are easily explained by technique and by the approximations used in the sim. But when the error is nearly a factor of TWO, there is a big mistake.

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>Ron, you have the equations but have not worked with them>long enough to resolve them. The equation I presented comes>directly from those equations. The radius of turn drops out>when you use the relation >r = V/omega. I was just showing some of the relationships. In fact, my equation for force, 'F' was really for radial acceleration. One would have to add mass, m, to get a force. Though, mass cancels out later. I remember two equations for 'centrifugal acceleration': a_radial = (V^2)/r a_radial = w^2 * r; where 'w' is 2Pi*f, f=1/period One follows from the other. Further, F_radial = m * a_radial. And, that Force must be provided by the radially inward AC Lift. I remember at 60 degrees Bank one should see 2 G's. However, the AC has to be at a constant altitude and in a constant turn. Note one can bank an AC and apply opposite rudder to fly a straight track. Bank alone doesn't guarantee 'turning'. Further, one can skid around a turn. Keep the AC wings level and use the rudder. In that case one would feel a side force similar to turing in an auto at the same rate. Rather than an increase in G directly into the seat.>I don't think it makes any difference whether the turn is>coordinated or not. All that matters is that it must be very>steady - steady altitude, steady bank angle and steady true>airspeed. When steady, the path will be circular and these>relations apply. A steady turn in a circle requires that a centripal force be present. That inward force can come from a combination of many aerodynamic forces. Most which result in 'uncoordinated' flight (slip not 0). >Here are the results of my first test that proved that the>'Brand B' aircraft was set wrong.>>AIRCRAFT__________T90cal_________T90obs______Cn_r>MS King Air 350: 39.0____________39__________-0.500>MS Baron 58:____35.9_____________38__________-.10009>'Brand B':______33.9_____________58__________-2.13867>>I just noticed that I had earlier made some adjustments to the>Baron 58. The original value of Cn_r was -0.97656 and I>changed it to several values ending with -0.10009. I did not>test the Baron for turn rate with that original setting. I>also made some slight adjustments to the King 350 but did not>keep notes. I have linear stability derivatives for quite a few AC. I see -619 for my 727. That's -0.302 in real values. Somewhat high, but Jets tend to be unstable in Yaw in MSFS. And, the Yaw damper doesn't do much. However, higher Yaw damping shouldn't affect steady state flight. While Cn_p "Yaw Moment - Roll Rate" is responsible for the initial Yaw (ball off the center) when one rolls into a turn. And, Cl_p "Roll Moment - Yaw Rate" continues to roll the AC as long as there is Yaw. I think using only the rudder (above the center line) to Yaw an AC tends to roll the wings in the opposite way one wants to turn. But, as the Yaw Rate drops the Yaw Moment eventually changes the turn to the way expected. Due to Dihederal and/or other effects. There is also 'adverse yaw' due to the ailerons, but this is often neglible in 'normal' AC. The signs of the SD's in the AIR file are not all consitent with published values. Normally, they should be the same sign as good AIR files have. >The point here is clear. Cn_r generates a yaw moment that>resists turning. The developer of 'Brand B' set this value>intentionally because he wanted the aircraft to turn>gracefully. Indeed some of us liked the way he set the plane>up. He later had second thoughts and intended to change this>setting but did not get to it before it was distributed. I can>certainly feel empathy with that. I set much lower values for Cn_r in my jets than MS and others. Real jets are rather unstable if one kicks the rudder. That's why Yaw Dampers are added!RonPS: Work is advancing on displaying Turbine Ram Drag and also Net Thrust. I've programmed what should be the appropirate Theta's and Delta's into my Jet Test gauge, but this only gives factors for TBL 1506, 1507, and Intake Area.

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I'm curious if there have been more developments on this subject.I found turning radii out of whack: 747 by a factor of ~3, 737 by ~2 and the Mooney by 10% in FS9.It would be interesting to hear from real-life pilots - they might have ideas with turning into the approach and flying holding patterns. It might be interesting to hear what academics & engineers have to say. You

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Evan, why are you "replying" to a post that is now FIVE years old?Do you think things may have changed a bit since then? ;)

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