Post by Tom Goodrick on Aug 26, 2008 17:39:10 GMT -5
This is a text with illustrations that was buried on page 4 of the FD Development Thread which was on the 4th page of the FS2004 section of the old forum. It was hard to get to. We'll put it here under its own header so it is easier to find.
LONGITUDINAL STABILITY = PITCH STABILTY = SPEED CONTROL
We'll begin discussing stability, and how to adjust it within the .air file, by discussing the Longitudinal Stability which is also know as the pitch stability. many people confuse "stability" with "steadiness". They are very definitely NOT the same thing. Even an aerobatic aircraft or a fighter known for its lack of stability, could not fly at all without good pitch stability. This is ultimately the only way you can control airspeed. If you cannot control airspeed, You cannot fly even an "unstable" aerobatic airplane.
With this info, you can adjust stall speeds, level the aircraft in cruise and adjust the pitch motions during and following stall.
One important aspect of FS is that it presents aircraft models and lets them experience flight at any conceivable attitude relative to the earth and to the local realtive air velocity as the aircraft moves. Even though we will see that the aircraft normally flies at only a narrow range of angles, there are possible conditions that can put the aircraft at a very strange attitude. The stability relations in the .air file must allow the aircraft to return to its narrow range of controllable attitude, perhaps with some control input from the well-trained pilot. I was bothered when I started working with FS by the fact that all aircraft easily recovered from upsets. This is not true in the real world. There are many conditions from which recovery should be very difficult. by working in this area I have made many aircraft behave more realistically. In preparation for reading the rest of this articale, you should take the Baron 58, with my FD files for it from my web site, and "fool around with it". Stand it on its tail Put it into a turn and then pull the stick back as far as you can and hold it a while. (See what happens before you try to recover.) You will probably crash and burn a few times. The Baron is a very good airplane in real life. But it has also killed a few people who did not show it proper respect.
In flight we experience forces and moments. To fly in steady flight, we must balance all forces. In the vertical direction we adjust the lift so it balances the weight. In the horizontal direction we adjust the thrust so it balances the drag. Lift and drag forces are influenced by two basic things - airspeed and angle of attack. Aircraft are designed so that we can change the control settings to change angle of attack and then, holding those control settings, angle of attack will be held constant while we adjust the speed and the thrust to get the firces into balance. Curiously, holding angle of attack constant does not mean the aircraft won't vary in pitch attitude. Indeed, the aircraft will be seen to undulate over along period of time as lift gradually comes into balance with weight.
We can show how pitch stability controls speed and the importance of stability with a simple graph.
Look first at the how the colored and slanted lines cross the horizonatal axis (AoA) of this graph. For these lines, the vertical axis is CM or pitch moment and the sign of that value is such that a positive pitch moment causes a reduction in angle of attack. Consider the middle line (blue). It could be considered the "trim" line. It intersects the AoA line at Point 2. Now the concept of "stability" is that, if all controls are frozen, any oscillation in angle of attack will produce a pitch moment shown by this line. people who have seen similar charts will think this vertical axis is inverted. It is shown this way becuase that is how it appears in FS due to an unusual choice in sign convention. A negative pitch rotation is nose up. Moving AoA to the right from Point 2, moves up the blue line to a positive value of pitch moment. But that causes a rotation that moves AoA back to Point 2. If something causes the AoA to move left, a negative moment causes AoA to move right back to Point 2. We have superimposed a curve of lift coefficient, CL, on the graph also as a function of AoA that shows a particular value when the aircraft is at Point 2. If we give the aircraft time to reach steady state where all the forces balance, the fact that lift balances weight means the aircraft will be flying at a particular speed given by the equation:
V(kias) = 17.16 SquareRoot( ( W/S) / CL)
Now W is weight and S is wing area so they are essentially constant while we are flying. Thus the only thing that can change the speed is CL. If we are at a stable angle of attack, one where the curve of CM vs AoA is an upward straight line as it is here, the we stay at that angle of attack and the speed stays at the same value as shown for Point 2.
So now you want to know what the red lines are for. These show how we can use the stick to shift the pitch line left or right. We can only be on one of these slanted lines at a time. Consider that, with no stick input, the trim setting has us on the blue line. Hold the stick forward and we are on the left red line which intersects AoA at Point 1. But that point is below the CL curve at a lower value than before. So now we have a lower value of CL in our equation. That makes a higher speed. The plane will speed up. Of course while it is doing that we have to increase the thrust to keep thrust balancing drag. If we pull back on the stick and hold it, we are shifting from the blue line to the right red line so our new stable point is Point 3. That has a CL value that is higher so we will slow down. Again we have to adjust the thrust to balance drag. We can also consider that, by adjusting the pitch trim, we can slide the blue line either left or right. We will have a new trim speed where the stick has no force when left at the center and new red lines can be drawn on either side of the new trim line showing what will happen if we push or pull on the stick.
The slope of this curve can determine the "strength" of the stability. A steep slope is very strong causing the aircraft to lock in quickly on a new angle of attack.
In discussing pitch stability we often talk of the two different types of stability - "angle of attack stability' and "path stability". In responding to a control change as we have discussed above, the change is normally very rapid. As a pilot move the control, the angle begines to change and reaches the stable value at the time the pilot stops moving the control. There is essentially no oscillation. But once that change is ineffect, the angle of attack is locked in but the forces are not yet balanced so an oscillation of the flight path continues. This secondary oscillation is sometimes called the "phugoid" oscillation. It can last for a few minutes. Pilots often develop varius ways of damping it with little stick motions.
216.180.4.173
Tom Goodrick
Administrator
-------------------------------------------------------------------------------
PITCH STABILITY OF THE CESSNA CRUSADER
The Cessna T303 Crusader is a twin with six seats and turbocharged engines of 250 hp. It has a curve of CL vs AoA as shown below (This is from table 404 of the .air file.) The horizontal axis is AoA in radians. Multiply by 57.3 to get degrees. Note that, as far as I know, there is no .air file editor that lets you add or subtract points to one of these tables. That is a shame since tables for different aircraft do come with different numbers of points.
To make sense of this it helps to have a model of an airplane that you can hold at various angles. But anything with distinguishable top, bottom, front and back ends will do such as a TV remote. The left of this curve is where the aircraft is upside down and backwards. To get to the center of the graph, rotate the object nose down and forward so it ends up facing you with the top up. That is the left half of the graph. Now raise the nose 16 degrees. That takes you across the portion where the curve shoots up to a peak. This is the entire normal range of flight for the vehicle. At zero lift, it would dive very fast. At some positive lift it would cruise and do most of its flying. At the peak it would fly the slowest just before stalling. The act of stalling rotates the AoA into the region where the lift curve drops significantly. Some people make these curves with very little reduction in lift. In reality, the lift drops off significantly for most aircraft. This basic shap is true for most aircraft. If you continue to rotate the plane nose-up relative to the moving air, its lift will go to zero and then below zero. An actual curve would be fairly complex, moving above and below zero and having minor peaks as it reaches tail-first flight. It may come apart from the nasty loads. You'd certainly experience a nasty ride.
There are three adjustments we must commonly make in this CL vs AoA curve (Table 404). First the max value of CL will determine the clean stall speed (if the pitch moment adjustments discussed below allow stability near this point). The peak in the curve comes at AoA=0.2793 or 16 degrees. the value is 1.62177. The wing loading (W/S) is 27.25 lb/sq ft. The stall speed calculates as 70.3 KIAS. The flaps-down stall speed is determined by the flaps lift increment in the .air file in Section 1101. For the Crusader it is 0.6711. It will be added to the max lift coefficient in table 404 to get the total max lift coefficient from which stall speed can be calculated using the same formula shown above. It shows 59.16 KIAS, close to the specs (68 kias clean and 62 KIAS with flaps.) You're right. These CL values could be adjusted. Indeed we could calculate the required CL values first and set them into the curves. When you click the mouse on a pint on the curve, you see the values in boxes below the graph. Then you can type in a desired value.
The second way this table 404 can be used is to level the aircraft in cruise. We used to be able to do that by simply changing the wing incidense angle. But the idiots at MS took that simple adjustment away when they brought out FS9. Now to lower the nose we have to shift all points on this curve between about -.1 and ,3 to the left by reducing them by about 0.02 radians.
The third way this table 404 is used is to adjust the reduction of lift that follows stall. It should be a fairly direct decrease but you can change the slope just after the peak to make it easier to handle as in many Piper aircraft.
Now we get to a very interesting aspect of FS. There is a basic pitch trim curve in table 473 that works for the aircraft through the entire range of angle of attack, corresponding to the angles shown for the lift curve.
This shows the pitch moment, CM as a function of AoA from -3.1416 to 3.1416 (-180 to 180 degrees). Note the simple positive slope just right of zero AoA and the abrupt reduction after the peak. Normal operation is within the region of zero to the peak. This gives strong positive stability in that region. Consider this like the blue line on the introductory chart. Stick changes can produce stability about any angle in this region. With so few points to work with, you can't get very fancy with this curve. But this shape does a good job both for normal flight, for stall and for any weird tumling you may want to do. The extremes give zero moment so that, during an extreme upset, momentum will carry you past the extremes and into the areas where there is control. The original curve had the point outside the stall region going higher and then increasing positively toward the right and negatively toward the left. This means the same backwards orientaion produces very different moments depending on which route you take to get there. Make sense? At stall, which is the point where the curve on the right cuts downward, you want to have a positive moment pushing the nose down. But this can be reduced at stall from the moment that it had just before stall. When it was increasing at this point, the aircraft had a weird slapping action. It would raise to stall and then slap down to a lower angle of attack and come back up - so it went up and down indefinitely in pitch - very weird. It drove my wife and bird nuts as the stall warning came on and off, on and off! Dropping it down as it is makes it do a little shudder and then go into a deep stall but recovery is easy. Push the nose down and it resumes flight.
You'll see a much more complicated situation when we go over the Baron 58 shown below. With more points on the pitch curve it is possible to make secondary stability conditions that tend to produce flat, deep stalls that are difficult to recover from.
« Last Edit: Aug 20th, 2007, 12:41pm by Tom Goodrick » 216.180.4.173 216.180.4.209
Tom Goodrick
Administrator
--------------------------------------------------------------------------------
PITCH STABILITY OF BEECH BARON
I adjusted the pitch stability of the Beech Baron 58 after reading a report on a crash in which a group of people road a Baron to the ground in a flat spin. They were all killed or seriously injured. If you fly the aircraft properly, maintaining airspeed well above the stall speed, you will have no trouble. But, if you are confused flying in clouds and not aware that your airspeed has decreased substantially, you can get into serious trouble from which recovery may not be possible. This is not unique to the Baron. Many fast twins are in the same category. They should be flown by professional pilots who fly regularly if not daily.
The FD for the Baron that include these figures are in the download #6 on my web site. (Click left icon under photo.)
The figure above shows the lift coefficient versus AoA from table 404. (There really should be a comparable table of parasite drag. A plane flying at 90 degree AoA has a much higher parasite drag than one flying at zero AoA. But there isn't such a table.) I was anticipating secondary stable points near half Pi either side of zero so I put the lift coefficient through zero at those points. Note also the abrupt drop in lift after the stall. Perhaps this drop should even be greater.
This figure shows the pitching moment for the same complete range of AoA from -Pi to +Pi or -180 to 180 degrees. There were enough points in this graph so I could set it up with two offset stable points in addition to the main stable point at zero. Remember that stick motion can create parallel lines near these stable points that will move the points a little bit. With the sign convention used in FS, we need both a zero pitching moment and an upward slope at a point to make it a stable poiint. Consider also that in a dynamic state, momentum can carry a rotating aircraft through one region into another. Consider the region from the left edge to the point where the curve passes down through zero for the second time. That entire region is a stable region with a stable point at about -90 degrees where the curve first rises through zero. If the aircraft were to start with zero momentum at an AoA within that range, it would stay in the range. It would difficult, if not impossible, to get out of that range into the normal range. The same can be said of the region in from the right edge. But each of thee regions has an inner boundary with such a steep slope down through zero, that it is likely that any substantial momentum will carry the plane past the boundary into the central area of normal flight.
So you are flying the Baron at high angle of attack near stall. What happens to get you into bad trouble? You might be rotating nose up with enough momentum to carry you over the peak in the moment curve (which coincides with the peak in the lift curve) so that you lose lift and continue to rotate past the peak and the steeep decline in corrective moment into the region of negative moment that starts pushing your rotation to even larger angles to the stable point at 90 degrees. Doing nothing will keep you trapped there until impact. You can try pulling the stick hard back as you find yourself passing through 90 degrees AoA to rotate even faster through that area. Then you start from the other edge where you are in another trap.
There are two solutions. The best is to recognize the signals that tell you the aircraft is starting to stall and take corrective action immediately. Avoid the deep stall and you avoid the problem. But if you find yourself in a deep stall at 90 degrees, either erect or inverted, try asymmetric power, full rudder and ailerons. You may be able to roll out of it into a dive. You'll generally get into a flat spin if any turning was done before the stall.
To examine this aspect of flight do what the US Navy calls "Departure Tests". They have test pilots flying out of Patuxent NAS that do these tests regularly with several types of Navy aircraft. The term "departure" means departing the relm of normal flight. They get some speed and plenty f altitude and then pull up into vertical flight and hold that attitude while cutting the power so the plane flies back onto its tail. They let the motion develop for a little while and then try to recover.
Good luck!
« Last Edit: Today at 4:29pm by Tom Goodrick » 216.180.4.176 216.180.4.5
Tom Goodrick
Administrator
--------------------------------------------------------------------------------
I did some tests with the Baron using different loadings. In all cases I had 120 lbs in the aft cargo area. For a forward CG, I had two 220 people in the front seats. The CG was at 15.75%. I had no problem in the tests.
Then I put a 200 lb person in the middle seat on the right side and a 200 lb person in the rear seat on the left side. This put the CG at 22.23%. I still had no trouble
Finally I put the copilot in the right rear seat. I got into a stall from which I could not recover. I knew I was in trouble when I saw 4000 fpm down and zero airspeed in a flat attitude. I tried my usual nose-down push which had been working fine. It had no effect. I put one engine at idle and full power on the other. That started a yawing motion but we hit before any good came of it.
LONGITUDINAL STABILITY = PITCH STABILTY = SPEED CONTROL
We'll begin discussing stability, and how to adjust it within the .air file, by discussing the Longitudinal Stability which is also know as the pitch stability. many people confuse "stability" with "steadiness". They are very definitely NOT the same thing. Even an aerobatic aircraft or a fighter known for its lack of stability, could not fly at all without good pitch stability. This is ultimately the only way you can control airspeed. If you cannot control airspeed, You cannot fly even an "unstable" aerobatic airplane.
With this info, you can adjust stall speeds, level the aircraft in cruise and adjust the pitch motions during and following stall.
One important aspect of FS is that it presents aircraft models and lets them experience flight at any conceivable attitude relative to the earth and to the local realtive air velocity as the aircraft moves. Even though we will see that the aircraft normally flies at only a narrow range of angles, there are possible conditions that can put the aircraft at a very strange attitude. The stability relations in the .air file must allow the aircraft to return to its narrow range of controllable attitude, perhaps with some control input from the well-trained pilot. I was bothered when I started working with FS by the fact that all aircraft easily recovered from upsets. This is not true in the real world. There are many conditions from which recovery should be very difficult. by working in this area I have made many aircraft behave more realistically. In preparation for reading the rest of this articale, you should take the Baron 58, with my FD files for it from my web site, and "fool around with it". Stand it on its tail Put it into a turn and then pull the stick back as far as you can and hold it a while. (See what happens before you try to recover.) You will probably crash and burn a few times. The Baron is a very good airplane in real life. But it has also killed a few people who did not show it proper respect.
In flight we experience forces and moments. To fly in steady flight, we must balance all forces. In the vertical direction we adjust the lift so it balances the weight. In the horizontal direction we adjust the thrust so it balances the drag. Lift and drag forces are influenced by two basic things - airspeed and angle of attack. Aircraft are designed so that we can change the control settings to change angle of attack and then, holding those control settings, angle of attack will be held constant while we adjust the speed and the thrust to get the firces into balance. Curiously, holding angle of attack constant does not mean the aircraft won't vary in pitch attitude. Indeed, the aircraft will be seen to undulate over along period of time as lift gradually comes into balance with weight.
We can show how pitch stability controls speed and the importance of stability with a simple graph.
Look first at the how the colored and slanted lines cross the horizonatal axis (AoA) of this graph. For these lines, the vertical axis is CM or pitch moment and the sign of that value is such that a positive pitch moment causes a reduction in angle of attack. Consider the middle line (blue). It could be considered the "trim" line. It intersects the AoA line at Point 2. Now the concept of "stability" is that, if all controls are frozen, any oscillation in angle of attack will produce a pitch moment shown by this line. people who have seen similar charts will think this vertical axis is inverted. It is shown this way becuase that is how it appears in FS due to an unusual choice in sign convention. A negative pitch rotation is nose up. Moving AoA to the right from Point 2, moves up the blue line to a positive value of pitch moment. But that causes a rotation that moves AoA back to Point 2. If something causes the AoA to move left, a negative moment causes AoA to move right back to Point 2. We have superimposed a curve of lift coefficient, CL, on the graph also as a function of AoA that shows a particular value when the aircraft is at Point 2. If we give the aircraft time to reach steady state where all the forces balance, the fact that lift balances weight means the aircraft will be flying at a particular speed given by the equation:
V(kias) = 17.16 SquareRoot( ( W/S) / CL)
Now W is weight and S is wing area so they are essentially constant while we are flying. Thus the only thing that can change the speed is CL. If we are at a stable angle of attack, one where the curve of CM vs AoA is an upward straight line as it is here, the we stay at that angle of attack and the speed stays at the same value as shown for Point 2.
So now you want to know what the red lines are for. These show how we can use the stick to shift the pitch line left or right. We can only be on one of these slanted lines at a time. Consider that, with no stick input, the trim setting has us on the blue line. Hold the stick forward and we are on the left red line which intersects AoA at Point 1. But that point is below the CL curve at a lower value than before. So now we have a lower value of CL in our equation. That makes a higher speed. The plane will speed up. Of course while it is doing that we have to increase the thrust to keep thrust balancing drag. If we pull back on the stick and hold it, we are shifting from the blue line to the right red line so our new stable point is Point 3. That has a CL value that is higher so we will slow down. Again we have to adjust the thrust to balance drag. We can also consider that, by adjusting the pitch trim, we can slide the blue line either left or right. We will have a new trim speed where the stick has no force when left at the center and new red lines can be drawn on either side of the new trim line showing what will happen if we push or pull on the stick.
The slope of this curve can determine the "strength" of the stability. A steep slope is very strong causing the aircraft to lock in quickly on a new angle of attack.
In discussing pitch stability we often talk of the two different types of stability - "angle of attack stability' and "path stability". In responding to a control change as we have discussed above, the change is normally very rapid. As a pilot move the control, the angle begines to change and reaches the stable value at the time the pilot stops moving the control. There is essentially no oscillation. But once that change is ineffect, the angle of attack is locked in but the forces are not yet balanced so an oscillation of the flight path continues. This secondary oscillation is sometimes called the "phugoid" oscillation. It can last for a few minutes. Pilots often develop varius ways of damping it with little stick motions.
216.180.4.173
Tom Goodrick
Administrator
-------------------------------------------------------------------------------
PITCH STABILITY OF THE CESSNA CRUSADER
The Cessna T303 Crusader is a twin with six seats and turbocharged engines of 250 hp. It has a curve of CL vs AoA as shown below (This is from table 404 of the .air file.) The horizontal axis is AoA in radians. Multiply by 57.3 to get degrees. Note that, as far as I know, there is no .air file editor that lets you add or subtract points to one of these tables. That is a shame since tables for different aircraft do come with different numbers of points.
To make sense of this it helps to have a model of an airplane that you can hold at various angles. But anything with distinguishable top, bottom, front and back ends will do such as a TV remote. The left of this curve is where the aircraft is upside down and backwards. To get to the center of the graph, rotate the object nose down and forward so it ends up facing you with the top up. That is the left half of the graph. Now raise the nose 16 degrees. That takes you across the portion where the curve shoots up to a peak. This is the entire normal range of flight for the vehicle. At zero lift, it would dive very fast. At some positive lift it would cruise and do most of its flying. At the peak it would fly the slowest just before stalling. The act of stalling rotates the AoA into the region where the lift curve drops significantly. Some people make these curves with very little reduction in lift. In reality, the lift drops off significantly for most aircraft. This basic shap is true for most aircraft. If you continue to rotate the plane nose-up relative to the moving air, its lift will go to zero and then below zero. An actual curve would be fairly complex, moving above and below zero and having minor peaks as it reaches tail-first flight. It may come apart from the nasty loads. You'd certainly experience a nasty ride.
There are three adjustments we must commonly make in this CL vs AoA curve (Table 404). First the max value of CL will determine the clean stall speed (if the pitch moment adjustments discussed below allow stability near this point). The peak in the curve comes at AoA=0.2793 or 16 degrees. the value is 1.62177. The wing loading (W/S) is 27.25 lb/sq ft. The stall speed calculates as 70.3 KIAS. The flaps-down stall speed is determined by the flaps lift increment in the .air file in Section 1101. For the Crusader it is 0.6711. It will be added to the max lift coefficient in table 404 to get the total max lift coefficient from which stall speed can be calculated using the same formula shown above. It shows 59.16 KIAS, close to the specs (68 kias clean and 62 KIAS with flaps.) You're right. These CL values could be adjusted. Indeed we could calculate the required CL values first and set them into the curves. When you click the mouse on a pint on the curve, you see the values in boxes below the graph. Then you can type in a desired value.
The second way this table 404 can be used is to level the aircraft in cruise. We used to be able to do that by simply changing the wing incidense angle. But the idiots at MS took that simple adjustment away when they brought out FS9. Now to lower the nose we have to shift all points on this curve between about -.1 and ,3 to the left by reducing them by about 0.02 radians.
The third way this table 404 is used is to adjust the reduction of lift that follows stall. It should be a fairly direct decrease but you can change the slope just after the peak to make it easier to handle as in many Piper aircraft.
Now we get to a very interesting aspect of FS. There is a basic pitch trim curve in table 473 that works for the aircraft through the entire range of angle of attack, corresponding to the angles shown for the lift curve.
This shows the pitch moment, CM as a function of AoA from -3.1416 to 3.1416 (-180 to 180 degrees). Note the simple positive slope just right of zero AoA and the abrupt reduction after the peak. Normal operation is within the region of zero to the peak. This gives strong positive stability in that region. Consider this like the blue line on the introductory chart. Stick changes can produce stability about any angle in this region. With so few points to work with, you can't get very fancy with this curve. But this shape does a good job both for normal flight, for stall and for any weird tumling you may want to do. The extremes give zero moment so that, during an extreme upset, momentum will carry you past the extremes and into the areas where there is control. The original curve had the point outside the stall region going higher and then increasing positively toward the right and negatively toward the left. This means the same backwards orientaion produces very different moments depending on which route you take to get there. Make sense? At stall, which is the point where the curve on the right cuts downward, you want to have a positive moment pushing the nose down. But this can be reduced at stall from the moment that it had just before stall. When it was increasing at this point, the aircraft had a weird slapping action. It would raise to stall and then slap down to a lower angle of attack and come back up - so it went up and down indefinitely in pitch - very weird. It drove my wife and bird nuts as the stall warning came on and off, on and off! Dropping it down as it is makes it do a little shudder and then go into a deep stall but recovery is easy. Push the nose down and it resumes flight.
You'll see a much more complicated situation when we go over the Baron 58 shown below. With more points on the pitch curve it is possible to make secondary stability conditions that tend to produce flat, deep stalls that are difficult to recover from.
« Last Edit: Aug 20th, 2007, 12:41pm by Tom Goodrick » 216.180.4.173 216.180.4.209
Tom Goodrick
Administrator
--------------------------------------------------------------------------------
PITCH STABILITY OF BEECH BARON
I adjusted the pitch stability of the Beech Baron 58 after reading a report on a crash in which a group of people road a Baron to the ground in a flat spin. They were all killed or seriously injured. If you fly the aircraft properly, maintaining airspeed well above the stall speed, you will have no trouble. But, if you are confused flying in clouds and not aware that your airspeed has decreased substantially, you can get into serious trouble from which recovery may not be possible. This is not unique to the Baron. Many fast twins are in the same category. They should be flown by professional pilots who fly regularly if not daily.
The FD for the Baron that include these figures are in the download #6 on my web site. (Click left icon under photo.)
The figure above shows the lift coefficient versus AoA from table 404. (There really should be a comparable table of parasite drag. A plane flying at 90 degree AoA has a much higher parasite drag than one flying at zero AoA. But there isn't such a table.) I was anticipating secondary stable points near half Pi either side of zero so I put the lift coefficient through zero at those points. Note also the abrupt drop in lift after the stall. Perhaps this drop should even be greater.
This figure shows the pitching moment for the same complete range of AoA from -Pi to +Pi or -180 to 180 degrees. There were enough points in this graph so I could set it up with two offset stable points in addition to the main stable point at zero. Remember that stick motion can create parallel lines near these stable points that will move the points a little bit. With the sign convention used in FS, we need both a zero pitching moment and an upward slope at a point to make it a stable poiint. Consider also that in a dynamic state, momentum can carry a rotating aircraft through one region into another. Consider the region from the left edge to the point where the curve passes down through zero for the second time. That entire region is a stable region with a stable point at about -90 degrees where the curve first rises through zero. If the aircraft were to start with zero momentum at an AoA within that range, it would stay in the range. It would difficult, if not impossible, to get out of that range into the normal range. The same can be said of the region in from the right edge. But each of thee regions has an inner boundary with such a steep slope down through zero, that it is likely that any substantial momentum will carry the plane past the boundary into the central area of normal flight.
So you are flying the Baron at high angle of attack near stall. What happens to get you into bad trouble? You might be rotating nose up with enough momentum to carry you over the peak in the moment curve (which coincides with the peak in the lift curve) so that you lose lift and continue to rotate past the peak and the steeep decline in corrective moment into the region of negative moment that starts pushing your rotation to even larger angles to the stable point at 90 degrees. Doing nothing will keep you trapped there until impact. You can try pulling the stick hard back as you find yourself passing through 90 degrees AoA to rotate even faster through that area. Then you start from the other edge where you are in another trap.
There are two solutions. The best is to recognize the signals that tell you the aircraft is starting to stall and take corrective action immediately. Avoid the deep stall and you avoid the problem. But if you find yourself in a deep stall at 90 degrees, either erect or inverted, try asymmetric power, full rudder and ailerons. You may be able to roll out of it into a dive. You'll generally get into a flat spin if any turning was done before the stall.
To examine this aspect of flight do what the US Navy calls "Departure Tests". They have test pilots flying out of Patuxent NAS that do these tests regularly with several types of Navy aircraft. The term "departure" means departing the relm of normal flight. They get some speed and plenty f altitude and then pull up into vertical flight and hold that attitude while cutting the power so the plane flies back onto its tail. They let the motion develop for a little while and then try to recover.
Good luck!
« Last Edit: Today at 4:29pm by Tom Goodrick » 216.180.4.176 216.180.4.5
Tom Goodrick
Administrator
--------------------------------------------------------------------------------
I did some tests with the Baron using different loadings. In all cases I had 120 lbs in the aft cargo area. For a forward CG, I had two 220 people in the front seats. The CG was at 15.75%. I had no problem in the tests.
Then I put a 200 lb person in the middle seat on the right side and a 200 lb person in the rear seat on the left side. This put the CG at 22.23%. I still had no trouble
Finally I put the copilot in the right rear seat. I got into a stall from which I could not recover. I knew I was in trouble when I saw 4000 fpm down and zero airspeed in a flat attitude. I tried my usual nose-down push which had been working fine. It had no effect. I put one engine at idle and full power on the other. That started a yawing motion but we hit before any good came of it.