Ball Centered for coordinated turn right!?!

[Will.iam]

I always thought keep ball centered in a banked turn was coordinated flight. I just watched a video about flying a multiengine baron and the guy stated the ball should always be pointing straight down in a turn. I thought that was called a slip.  

[DonMuncy]

Straight down in relation to  the plane, or straight down toward the earth?

[Vance Harral]

Did this have anything to do with one-engine-inoperative flight?  In a conventional twin with one dead engine, zero side-slip requires holding the ball slightly off center, see https://www.boldmethod.com/blog/und/how-does-zero-sideslip-work-in-a-multi-engine-aircraft/

[T. Peterson]

6 hours ago, Will.iam said:

I always thought keep ball centered in a banked turn was coordinated flight. I just watched a video about flying a multiengine baron and the guy stated the ball should always be pointing straight down in a turn. I thought that was called a slip.  

Centered is a coordinated turn. Bottom of the U is both straight down and centered. Anything else is slip or skid. 

[carusoam]

I’m pretty sure…

Keeping the ball centered, at the bottom of the U…

Is how we define coordinated flight…

At least in single engine Mooneys…

 

Otherwise…

Expect the trailing wing to stall first…?

If the ball isn’t centered… we step on the ball….   
 

For fun…  LBs have rudder trim… perfect for keeping the plane in trim during climb, cruise, and descent… where the AOA of the prop changes…. Requiring rudder inputs to stay nicely coordinated… in straight flight…

 

PP thoughts only, not a CFI…

Best regards,

-a-

[PeteMc]

17 hours ago, Will.iam said:

the ball should always be pointing straight down in a turn.

And where was the ball in the video you were watching???? 

Sounds like a pretty poor choice of words by the guy making the video, but guessing the ball was indeed "straight down" relative to the Coordination Indicator/Ball in the instrument.

[Pinecone]

It doesn't need actual knowledge to make a You Tube video.

And even the good ones get it wrong.

One popular Aviation You Tuber is sure that in a coordinated turn, the two wings are producing a different amount of lift.

[Shadrach]

10 minutes ago, Pinecone said:

It doesn't need actual knowledge to make a You Tube video.

And even the good ones get it wrong.

One popular Aviation You Tuber is sure that in a coordinated turn, the two wings are producing a different amount of lift.

Who? Come on spill it. No shame in outing a public personality that's offering misguided "expertise".

[Will.iam]

This is the video i was watching. The instructor talks about the ball being straight toward the earth multiple times. Starting at the 9 min mark of the video.  Yes it is in reference to twin engine operation with one engine out but i have never heard of letting the ball point straight to the earth as coordinated flight. 
Multi-Engine Training - Part 1: The Drill

 

[FlyingDude]

https://www.gleimaviation.com/2020/09/04/aerodynamics-of-turns/

"... deflecting the ailerons to increase or decrease the bank angle creates a phenomenon known as adverse yaw. The lowered wing produces less lift than the lifted wing due to the change in each wing’s angle of attack. The increased lifting force on the rising wing also causes more induced drag. " 

"As the angle of bank in a turn becomes steeper, the airspeed over each wing begins to vary greatly. This is because the outer wing travels a longer path than the inner wing, yet both complete their turns in the same amount of time. Therefore, the outer wing travels at a faster airspeed than the inner wing and, as a result, develops more lift. This creates an overbanking tendency that must be controlled by the use of the opposite aileron when the desired bank angle is reached. You will often experience this while performing steep turns. Once you set the steep bank angle, the aircraft will feel as though it wants to roll even further."

[Hank]

11 minutes ago, FlyingDude said:

https://www.gleimaviation.com/2020/09/04/aerodynamics-of-turns/

"... deflecting the ailerons to increase or decrease the bank angle creates a phenomenon known as adverse yaw. The lowered wing produces less lift than the lifted wing due to the change in each wing’s angle of attack. The increased lifting force on the rising wing also causes more induced drag. " 

"As the angle of bank in a turn becomes steeper, the airspeed over each wing begins to vary greatly. This is because the outer wing travels a longer path than the inner wing, yet both complete their turns in the same amount of time. Therefore, the outer wing travels at a faster airspeed than the inner wing and, as a result, develops more lift. This creates an overbanking tendency that must be controlled by the use of the opposite aileron when the desired bank angle is reached. You will often experience this while performing steep turns. Once you set the steep bank angle, the aircraft will feel as though it wants to roll even further."

I remember that in the rental Cessna that I took lessons in. I do not remember it happening in my Mooney . . . . . I just keep holding the yoke over and go round and around without overbanking and with no opposite aileron.

[FlyingDude]

2 minutes ago, Hank said:

I just keep holding the yoke over and go round and around without overbanking and with no opposite aileron.

Well we all know that Mooneys are strange.  Isn't that why we're flying them??  Opposite aileron can be needed at steeper turns (60deg), I believe...

[Vance Harral]

6 minutes ago, FlyingDude said:

As the angle of bank in a turn becomes steeper, the airspeed over each wing begins to vary greatly. This is because the outer wing travels a longer path than the inner wing, yet both complete their turns in the same amount of time. Therefore, the outer wing travels at a faster airspeed than the inner wing and, as a result, develops more lift

This is one of those things that is technically true, but is so overstated as to arguably be false for a typical GA piston aircraft.

Consider a Mooney with a 35' wingspan, flying an "aggressive" 60-degree banked turn at 120 knots.  The handy calculator at https://calculator.academy/aircraft-turn-radius-calculator/ tells us the radius of the turn is 738 feet.  That means the centerline of the aircraft is 738 feet from the centerpoint of the turn.  The path traversed by the inboard and outboard wingtips do not differ by the full wingspan, because of the bank angle.  Employing some trigonometry, cos(60)=0.5 and therefore the wingtip paths of a 35' wingspan aircraft are only 17.5' feet apart relative to the center of the circle in a 60 degree bank.  Specifically, the inboard wingtip traverses a path of 729.25', and the outboard wingtip traverses a path of 746.75'.  Circumference of a circle is 2*pi*R, so the circumference of the inboard and outboard wingtip paths are 4582' and 4692', respectively.  That's a path difference of 2.3%, therefore the airspeed difference is 2.3% as well.  Bear in mind this 2.3% is only the difference at the wing *tips*, not the effective difference across the whole wing, which will be smaller.  I don't have a formula handy for that, but across the whole wing we're probably talking about a difference in effective airfoil speed on the order of 1%.

So yeah, the outboard wing is moving faster than the inboard wing and generating more lift.  But not enough to make any noticeable difference, and certainly not enough to be the primary cause of over-banking tendency in the turn.  Extreme cases, like a glider with an enormous wingspan flying very slow and tight in a thermal, experience the airspeed delta effect to a greater degree, but you're not going to get that scenario in a typical Cessna/Piper/Mooney/Bonanza/etc.  Overbanking tendency in steep turns is caused by many things, and the airspeed difference between the two wings is almost never the primary cause.

[FlyingDude]

I would think 2% difference in airspeed would amount to something.  As lift is ~velocity squared, that'd mean 4% greater lift there. 

Let's assume it's 1% difference in airspeed.  So, there is 2% higher lift in one wing.  

Let's pull numbers from our pockets and assume that in a 2500lb = 1130kg Mooney, the wings (filled with 90gl fuel) amounts to 500kg and the fuselage is 600kg.

Moment of inertia of a cylinder rod (fuselage that's 1.5m wide)= m/2 * r^2 = 169 kg.m^2

Moment of inertia of a rod rotating around the center (wings) = 1/12 m x L^2 = 1/12x500x10.6^2 = 4681 kg.m^2.  

Total =~ 4850 kg. m^2.

The plane is lifting 2500 lbs.  2% = 50lb.  Let's assume that's at the wing midpoint.  The torque will be 50lb = 225 N at half wingspan.  1125 N.m

Torque = moment of inertia x angular acceleration => 1125N.m = 4850 kg.m^2 x alpha.

Alpha = 1125/4850  = 0.23 rad/s^2. 

2 seconds into the turn, the wing would be further lifted up by 1/2 0.23rad/s^2 (2s^2) = 0.46 rad, which is 26 degrees.

Like @carusoam usually ends his posts:

Electrical engineer recalling highschool physics.  Not a mechanical or aerospace engineer

[PeteMc]

Ah...  Twin Engine with an engine OUT...

So not a reference for a single engine Mooney.  Not a twin driver, so no clue how true it is for a engine out scenario.  I didn't listen much past the 9 min mark, but sort of get the half ball on the line.

[Shadrach]

1 hour ago, FlyingDude said:

I would think 2% difference in airspeed would amount to something.  As lift is ~velocity squared, that'd mean 4% greater lift there. 

Let's assume it's 1% difference in airspeed.  So, there is 2% higher lift in one wing.  

Let's pull numbers from our pockets and assume that in a 2500lb = 1130kg Mooney, the wings (filled with 90gl fuel) amounts to 500kg and the fuselage is 600kg.

Moment of inertia of a cylinder rod (fuselage that's 1.5m wide)= m/2 * r^2 = 169 kg.m^2

Moment of inertia of a rod rotating around the center (wings) = 1/12 m x L^2 = 1/12x500x10.6^2 = 4681 kg.m^2.  

Total =~ 4850 kg. m^2.

The plane is lifting 2500 lbs.  2% = 50lb.  Let's assume that's at the wing midpoint.  The torque will be 50lb = 225 N at half wingspan.  1125 N.m

Torque = moment of inertia x angular acceleration => 1125N.m = 4850 kg.m^2 x alpha.

Alpha = 1125/4850  = 0.23 rad/s^2. 

2 seconds into the turn, the wing would be further lifted up by 1/2 0.23rad/s^2 (2s^2) = 0.46 rad, which is 26 degrees.

Like @carusoam usually ends his posts:

Electrical engineer recalling highschool physics.  Not a mechanical or aerospace engineer

I would bet a 2% lift delta per side to be close to allowable manufacturing tolerances.

[Vance Harral]

1 hour ago, Shadrach said:

I would bet a 2% lift delta per side to be close to allowable manufacturing tolerances.

Agreed; and while not disputing FlyingDude's math, 50 lbs of differential force (which is likely not at the wing midpoint but further inboard, at least on a Mooney, but I digress...) is on the same order as differential forces due to completely normal asymmetry in passenger and fuel loading.  50 pounds is about 8 gallons of avgas, and is also much less than the weight difference between children, petite adults, and beer-gutted, aging pilots (which I can say, because I am one).  Yet none of the differential-speed explanations of overbanking mention it being eliminated/doubled by having an odd number of passengers, or burning an hour of gas out of one tank before rolling into the turn.

Whether a piston GA airplane exhibits overbanking in "steep" turns or not, is mostly a function of the airframe design.  Things like wing dihedral, keel area, and CG are typically the dominant factors in spiral instability, rather than the differential speed going around the circle.  This explains why some airplanes exhibit more or less of it, despite executing the same turn, vs. other airplanes that exhibit less.

[jaylw314]

4 hours ago, Vance Harral said:

This is one of those things that is technically true, but is so overstated as to arguably be false for a typical GA piston aircraft.

Consider a Mooney with a 35' wingspan, flying an "aggressive" 60-degree banked turn at 120 knots. 

I think overbanking is the sort of thing that would be more noticeable in trainers in steep turns at 70 knots?  According to that theory, there should be no overbanking tendency in a 90 degree bank 

AFAIK, if the ball is 'pointing straight at the ground' it by definition means you're not turning (or changing heading, to be precise).  In ANY proper constant-heading slip, the ball will do so, whether you're single-engine or twin with one engine out.

Edited November 3, 2022 by jaylw314

[Vance Harral]

32 minutes ago, jaylw314 said:

I think overbanking is the sort of thing that would be more noticeable in trainers in steep turns at 70 knots?

The difference in path length is certainly greater at slower speeds, due to the smaller turn radius.  But there is a practical limitation: the slower you go, the less steep of a level turn you can maintain without exceeding critical AOA and stalling the airplane.  Vs1 in a 172 is 44 KCAS.  In a 2G turn, that increases to 44 * 1.4 = 62, so you're probably not going to find a lot of instructors willing to fly a 60-degree banked turn at 70 knots even in a 172.  Private pilot "steep" turns are spec'd at 45 degrees, and the steeper commercial pilot turns are typically taught by entering at maneuvering speed to provide margin against an accelerated stall.  Those lower bank angles and/or higher speeds increase the turn radius, and therefore decrease the magnitude of the effect we're discussing.

To be clear, I'm not saying the simple explanation is wrong and speed differential between inboard and outboard wings never matters; just that several factors affect spiral (in)stability, and in most piston GA scenarios, the speed differential effect is negligible relative to design and loading factors.

[PT20J]

A couple of different effects have been discussed in this thread...

1.  Zero sideslip for a twin operating on one engine: When flying straight and level with two engines operating, the ball is in the center and "points" straight down. Now, shut down the left engine. The asymmetric thrust will cause the airplane to yaw to the left. To counter this we apply right rudder which creates a counteracting yawing moment to stop the yaw. But the sideways force on the tail now causes the airplane to fly sideways slightly to the left. To balance out that force and fly with zero sideslip, we bank the airplane a few degrees to the right which tilts the lift vector slightly so as to oppose the side force from the tail. Now, the airplane flies straight with zero sideslip and the ball is about a half ball width to the right and pointed straight down. 

2. Overbanking tendency: Technically this is called "rolling moment due to yaw rate" A level turn is a combination of a pitch rate and a yaw rate. You can see this by imagining a 90 degree bank turn of zero radius and note that the airplane is constantly rotating about the pitch axis. Next, imagine a level turn of zero radius and note that the airplane rotates constantly about the vertical (yaw) axis. So an airplane in a banked turn of finite radius has a pitch rate and a yaw rate. Whenever the airplane is yawing, one wing has higher airspeed than the other and thus more lift. Note that the effect is entirely dependent on the yaw rate. At higher airspeeds and shallow bank angles, the yaw rate is low (3 degrees per second for a standard rate turn) and the effect is negligible. At slower airspeeds and higher bank angles, the effect is more pronounced, but it is still not all that significant and most pilots learn to compensate for it automatically so that we don't even notice it after the first few hours of flight training.

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EDIT: According to Bill Crawford (p1.5) http://www.flightlab.net/Flightlab.net/Download_Course_Notes_files/ManeuversFlight Notes.pdf , rolling moment due to yaw rate increases with angle of attack, is decreased by wingtip washout, is decreased by flap extension, increases with aspect ratio and decreases with wing taper.

 

Edited November 4, 2022 by PT20J
Added info from Bill Crawford's paper

[PT20J]

6 hours ago, Vance Harral said:

Things like wing dihedral, keel area, and CG are typically the dominant factors in spiral instability, rather than the differential speed going around the circle.  This explains why some airplanes exhibit more or less of it, despite executing the same turn, vs. other airplanes that exhibit less.

You're on the right track. Aircraft have several types of stability. Two important ones are directional stability and lateral stability. Airplanes with greater directional stability than lateral stability tend to be spirally unstable whereas airplanes with greater lateral stability than directional stability tend to Dutch roll. Most airplanes are designed to damp the Dutch roll because it is an uncomfortable motion. However, whether the resulting spiral mode is divergent or not depends on other considerations such as longitudinal stability and roll damping (and probably a bunch of other stuff).

In my M20J, if I trim straight and level at maneuvering speed and let go of the controls the airplane will eventually roll off one way or the other and the nose will drop and the airspeed will increase nearly to redline. But, as the speed increases the phugoid kicks in and the nose starts to come up and the airspeed slows almost to stall and then the nose comes back down. This repeats for about two and a half cycles, each of lower amplitude than the previous, until the airplane settles into a nose low, 45 degree bank, constant airspeed descending turn.

[carusoam]

Holy cow!

You guys are good GREAT!

1) Subject knowledge…

2) Ability to explain things mathematically…

3) Slow the explanation down verbally for everyone else…. (Thank you!)

4) Supplying Mooney examples…

5) supplying the extra effort so even I can understand…. 

Thank you!

Go MS!

Best regards,

-a-

[Will.iam]

I’m glad you understand. I’m still stuck on that ball pointing straight down. I don’t do it in a single engine plane and in a twin jet i don’t do it either. We train to center the beta to include while turning. Maybe it’s an underpowered piston twin thing to have the ball displaced and that is now coordinated floght but I don’t see it. Luckily I don’t own or operate a piston twin bird so I don’t have to worry about it. I was just curious if that was correct to do in a piston twin. 

[carusoam]

Will’s up late tonight!  

One thing… I think…  the ‘author’ of the video…  chose an odd way to describe his use of the inclinometer…

I couldn’t understand what he meant by straight down…

Easy to interpret in two different ways… one of which has to be wrong…

That made the whole video something I couldn’t learn from…

 

Bummer…

Best regards,

-a-

[PT20J]

8 hours ago, Will.iam said:

I’m glad you understand. I’m still stuck on that ball pointing straight down. I don’t do it in a single engine plane and in a twin jet i don’t do it either. We train to center the beta to include while turning. Maybe it’s an underpowered piston twin thing to have the ball displaced and that is now coordinated floght but I don’t see it. Luckily I don’t own or operate a piston twin bird so I don’t have to worry about it. I was just curious if that was correct to do in a piston twin. 

Light piston twins generally do not have much performance on a single engine. Flying with zero sideslip versus ball centered can often be the difference between a small ROC and a descent. Jets have a lot of excess thrust and, in the case of tail-mounted engines, not much yaw on a single engine.

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