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# The yaw/slip thread (merged) aka Aerodynamics 101

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# The yaw/slip thread (merged) aka Aerodynamics 101

8th Sep 2004, 00:47
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Milt,

Now that's an interesting thesis ... "... ANY measure of asymmetric thrust will be sideslipping in straight flight whether wings level or banked....".

I have no difficulty with sideslip wings level as the horizontal fin/rudder force accounts for a lateral velocity to generate the slip.

However, if one banks while maintaining straight flight, then is there not a sideslip developed due to the bank - regardless of thrust asymmetry ? Depending on the sense of the slip due to bank, is it not either increasing or decreasing the magnitude of slip due to the asymmetry in thrust ? If this is the case, is there not going to be an angle of bank where the two will balance each other nicely and give nil slip ?

Or have I missed something along the way ?

8th Sep 2004, 09:14

Join Date: Oct 2000
Location: N. Europe
Posts: 436
Interesting. We agree that we have no rotation about the longitudinal (roll) axis in the turn, right*?

This leaves us with the pitch axis and the yaw axis on which to project the components of the turning motion, the axis of which is vertical.

For no yaw and with the roll axis removed from the equation, the entire rotation of the turn has to be around the pitch axis.

But the rotation is around a vertical axis. Ergo, the pitch axis has to be vertical which implies a 90-degree bank.

Does your definition of yaw differ from mine? I e “rotation about the yaw axis of the aircraft”.

Regards,
Fred

*) Not quite true unless the longitudinal axis is level, but let’s assume a flight condition providing this.

(Typo edit)

8th Sep 2004, 10:43

Join Date: Nov 2003
Location: Australia
Posts: 126
I'm under the same impression john_tullamarine - I thought the idea behind introducing a component of bank when there's assymetric thrust was to minimise the sideslip and therefore drag.

Milt?

8th Sep 2004, 12:48

Join Date: Oct 2000
Location: N. Europe
Posts: 436
Allright, my understanding of the situation:

The torque generated by the thrust difference has to be counteracted somehow with opposing torque. I can only think of one way to generate this opposing torque: The fin. We either change the camber of the fin (rudder) or the angle of attack of the fin (slip).

In either case, the force to the side of the dead engine has to be counteracted by another lateral force. Wings level, this will mean a slip into the dead engine. Rolling slightly into the live engine will give you the same effect without trying to shove the aircraft sideways through the air.

When we run into the end of the authority of the rudder as far as counter-torque generation goes, the only possibility to further decrease the speed or increase the power on the remaining engine will be to slip more towards the good engine, in order to increase the slip and thus the angle of attack of the fin.

Regards,
Fred

8th Sep 2004, 13:59

Join Date: Oct 2003
Location: Canberra Australia
Posts: 1,300
John Tullamarine and ROB-x38

That which you are overlooking is the resolved portion of lift from the few degrees of bank you are using to provide the horizontal force necessary to oppose the yawing moment being produced by the offset thrust.

Moment 1 - Thrust X arm to lateral centre of pressure, opposed by Moment 2 - Resolved lift X arm to lateral centre of pressure cancel out to give you straight flight but NOT along the aircraft axis. You can use parallelogram of forces here. Hence a small angle of sideslip which produced an opposite side force to cancel out the resolved lift sideforce. Total Drag balances the Total Thrust. Then a little extra lift please which with its extra induced drag added to the added drag for sideslip probably makes the two methods of slightly banked and wings level a push. This is one for the honours students doing their aero degrees to get their heads around.

Incidently weight and cg doesn't get a show in this area as it is all mostly in the horizontal and you cannot resolve the weight through 90 degrees. The implication of this is that Vmca is not affected by cg position contrary to what you see in many training publications.

Then you have a "form" of balanced flight and the navigator should estimate the sideslip angle to provide for more accurate navigation. Don't some handbooks provide an estimate.? I say "form" to indicate my reluctance to call straight flight while sideslipping balanced but indeed all the forces are in balance.

I guess you might determine the angle of sideslip without a vane on a boom by aligning a DG with an Inertial/GPS accurate heading reference and go asymmetric. You may see the difference between DG and Inertial/GPS when you stabilise.

Tell me where I might have lost my marbles. They are rattling around in my head!

8th Sep 2004, 15:03

Mach 3

Join Date: Aug 1998
Location: Stratosphere
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\tan(\alpha)=u/V & \sin(\beta)=v/V

where

V = ui + vj + wk &

V =\sqrt[u^2+v^2+w^2]

The way I see it is once you've got an assymetric condition you've got two options once you've noticed it, whereupon by definition you've got an angle of sideslip, and depending on the stability derivative C_l_\beta (& C_l_r), some roll angle. Which one you use is a matter of preference in most cases but in critical cases where you've let the angle get large and configuration and performance considerations come into play you best choose one not the other:

1) Jump on the appropriate rudder to arrest the yaw. C_n_\beta i.e., static directional stability requirements tend to ensure the contribution of the fin is to oppose any increasing sideslip, and with the effective fin angle of attack increased by the rudder deflection, a flight path with a characteristic \beta will develop where the forces and moments are in balance. Its a dirty flight condition and unless C_l_\beta ~=0, you need an initial amount of aileron to re-gain wings level. The actual value of sideslip that develops is merely a function of how much load you choose to apply to the rudder.

However, if you want to continue in straight flight, the lateral loads on the aircraft must also sum to zero whereupon the value of \beta will probably be fixed and unique.

2) Accomplish the above, but now you've got an aft CG condition and you're at MTOW and you've let \beta get large (on Sector 4, Day 6, 0200Z perhaps?) at 200' when a donk lets go off R/W32 @ AGP, 32C and 975mb. This is approaching a V_mca condition.

JAR 25.149 requires no more than 150lbs/667N of force be applied to the rudder controls in order to restore directional control in this condition and continue in straight flight. Neither may thrust be reduced.

The proviso for no more than 5 degrees angle of bank is presumably because if one supposes that full rudder deflection is required to counteract the asymmetric yawing tendency, you have lost the ability to control the path of the aircraft in azimuth through space via expedient use of the rudder. Hence the allowance for use of bank. Since the lateral component of lift due to bank is proportional to \sin(\gamma) you now have ~=9% of the aircraft lift to aid the process.

The aerodynamic advantages of the use of bank are numerous, and again, because the vertical component of lift whilst banked is proportional to \cos(\gamma) you now still have ~=99.5% of the original lift available for performance at 5 degrees of bank.

My concern is that for the purposes of calculating RTOW's at speeds approaching V_mca (or for that matter any speed), the performance will clearly be affected by whether or not you choose to employ some bank angle. Oddly, there is no performance requirement to be met associated with V_mca.

For presumably 99% of the time, you needn't concern yourself with this matter, but in the interests of discussion, if the only way you can meet a climb gradient requirement is by flying in a particular configuration, it becomes paramount to ensure you do so.

Now if only I could fly within +/- 5 degrees of bank.

PS: V_mca certainly is affected by CG location.

From JAR 25.149:

(c) VMC may not exceed 1·13 VSR with –
(1) Maximum available take-off power or
thrust on the engines;
(2) The most unfavourable centre of
gravity;
(3) The aeroplane trimmed for take-off;
(4) The maximum sea-level take-off
weight (or any lesser weight necessary to show
VMC);
(5) The aeroplane in the most critical
take-off configuration existing along the flight
path after the aeroplane becomes airborne, except
with the landing gear retracted;
(6) The aeroplane airborne and the
ground effect negligible; and
(7) If applicable, the propeller of the
inoperative engine –
(i) Windmilling;
(ii) In the most probable position
for the specific design of the propeller
control; or
(iii) Feathered, if the aeroplane has
an automatic feathering device acceptable
for showing compliance with the climb
requirements of JAR 25.121.
It affects the length of the tail moment arm, a crucial component towards directional stability.

Last edited by SR71; 8th Sep 2004 at 15:15.

8th Sep 2004, 17:07

Join Date: Dec 1998
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Two separate discussion going on now. One about yaw (or not) during a turn, and the other about sideslip (or not not) during asymmetric flight.

My view:

1. Yaw vs turn.

At 0deg AoB the a/c can be turned using 'all rudder' ie a flat turn. In this case the a/c is yawing but not pitching.

At 90deg AoB the a/c can be turned using 'all elevator'. In this case the a/c is pitching but not yawing.

The a/c can't instantly switch from one case to the other. It's a smooth change from one condition to the other, with yaw reducing & pitch increasing as AoB increases.

2. Slip vs asymmetry.

I think we all agree that in a wings level steady heading asymmetric condition there is some amount of slip. The Rel Airflow will be from the 'dead side' as a result of the rudder/fin sideload.

If an a/c is banked it will start to slip in the banked direction ie the relative airflow will have a lateral component (relative to the a/c axes) from the low wing side. This still applies in the asymmetric case. Imagine an asymmetric a/c at a very large AoB. It *will* start to slip towards the low wing. The slip will then result in a yaw towards the low wing. If the low wing is the live engine side then there will be a sufficient AoB that will counter the thrust asymmetry as a result of the relative airflow approaching from the live engine side causing a yawing moment towards the live engine.

It's possible to have sufficient bank that NO rudder at all is needed - ignoring some incredibly high thrust engine that could make the a/c do cartwheels...) albeit at a very high cost in drag. Not much good for performance then. On the hand, Vmc would be nice & low since the rudder hasn't reached its maximum deflection. In fact, it hasn't moved at all... Large angles of band are good for the manufacturer when it comes to certification since many things are related to Vmc so a low Vmc is 'useful'. Not so good for the pilot since it means unusual handling is required - hence the 5 deg AoB certification limitation.

Note the difference in the two cases above. Case 1 (wings level, only rudder used to oppose the asymmetry) the Rel. Airflow has a component from the 'dead side'. Case 2 (AoB, no rudder used to oppose the asymmetry) the Rel. Airflow has a component from the 'live side'.

As AoB increases towards the live side the component from the dead side must reduce until there is no sideslip, then increase again but this time from the live side.

So, it is possible to fly asymmetrically with zero sideslip and this AoB is where best performance will occur. This typically occurs at ~2-3 deg AoB. Any more than this and there will be a small sideslip towards the live side, any less than this and there will be a small sideslip towards the dead side.

8th Sep 2004, 19:18

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Location: La Belle Province
Posts: 2,122

In any practical, stable, banked turn, the aircraft will have roll, yaw and pitch rates simultaneously, even though the bank angle and pitch attitude will be fixed and it appears that the only attitude angle change is in heading.

This is because the roll, yaw and pitch rates are defined in an axis system which is fixed in the aircraft, and the bank angle, pitch attitude and heading (yaw attitude) are all defined by the relationship of that aircraft-fixed axis system to the earth-axis system.

The trick is that rate of change of bank angle is NOT mathematically the same as roll rate; nor for the other axes. Those are approximations which hold good for a given level of accuracy, but not to the ultimate.

If you had no angle of attack, such that the aircraft x-axis - about which we measure roll rate - was perfectly aligned with the velocity vector, you'd have no roll rate, but that's all. You'd still have a yaw rate and a pitch rate.

Having spent many happy hours explaining that, no, the simulator is working properly, those rates on the IRU are REAL, down to digging out the relevant equations of motion, I'm pretty sure of that lot.

9th Sep 2004, 02:32

Join Date: Oct 2003
Location: Canberra Australia
Posts: 1,300
SR71

Thanks for the hieroglyphics and the erudite discussion.

Unfortunately you didn't explain, in the banked case, how a horizontally derived portion of lift acting laterally on the fuselage can fail to cause sidslip. The contra force resulting from the sideslip is the balancing force is it not?

So I say again with some conviction
ANY imbalance in thrust on a multi, not having centre line engines, which is then flown straight by either rudder or bank or a combination inevitably results in sideslip. It is unavoidable
Then you refute the obvious in believing and stating that there can be an effect of cg position on Vmca. Derive all the weight you can to the horizontal and what do you get !!

In steady straight flight forces in the horizontal act around the lateral centre of pressure - NOT the cg. The cg can be anywhere until manoeuvre comes into the act..

Consider the directional stability of a twin engined dirigible having no apparent weight. Vmca when asymmetric ???

Looks like JAR 25.149 was prepared by someone having the same misconceptions and it may be important that we take steps to correct.

Hope you are enjoying this as much as I am.

We may have to fit a vane on a boom and do it all over again !!

Come in NATPS ETPS USNTPS Edwards NASA

9th Sep 2004, 05:14
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Isn't this all jolly good fun ?

Milt, was speaking with JL last weekend .. now that I know to whom the username relates .. I shall continue to read your words with the considerable respect they deserve.

Mind you, though, I think we might continue to disagree on the slip question.

9th Sep 2004, 07:40

Join Date: Aug 2000
Location: UK
Posts: 3,646
Anybody in Canberra prepared to take Milt for a ride in a twin with a slip string attached?

9th Sep 2004, 19:11

Mach 3

Join Date: Aug 1998
Location: Stratosphere
Posts: 622
Well if empirical flight test results demonstrate otherwise, the mathematics requires amendement. One should ensure the facts work with the hypothesis not vice versa!

I see this as essentially a lateral/directional stability problem. Normally these calculations are resolved about the CG.

It is the load on the fin that counteracts the component of the lift along the inertial y-axis, thereby allowing straight flight inspite of the bank angle.

Lets assume an a/c with C_l_\beta ~= 0 and where the No 1 eng fails. In this case the roll DOF is not important - we can assume wings level. Assuming the rudder has sufficient authority to counteract the assymmetric yaw, an equilibrium position will develop where the a/c is sideslipped away from the live engine. Unfortunately relative to inertial space, the a/c cannot maintain the runway centreline because resolving the thrust vector and fin load, they both in the same direction.

In order to arrest the azimuthal drift, you need to reverse the sense of the sideslip. This is done via judicious use of the rudder.

However, in reversing the sense of the sideslip, the rudder is now working hard. Not only must it balance the component of thrust resolved in the relevant axis, but its natural propensity to generate a load in the same direction courtesy of the sideslip.

Now assume by this judicious use of rudder, whereupon I'm able to change the flight path vector in azimuth, I've regained the runway centreline.

One way of off-loading the rudder is merely to incline the lift vector in order to generate a component in the direction of the inertial y-axis i.e., bank.

If I do this without reducing the sideslip, i.e., the load on the rudder, the aircraft will now drift in azimuth away from the runway centreline in the direction of the live engine.

Reduce the sideslip and it should be possible to balance the forces again all the way until you have a zero sideslip condition.

You are merely balancing the thrust component, the lift component and the fin sideload along the inertial y-axis via a combination of sideslip and roll angle.

That said, I don't believe you can have a nil sideslip, nil rudder force, angle of bank /= 0 condition and maintain the runway heading because the fin is symmetric. In this case, the only way to counter the tendency of the a/c to drift in the direction of the bank is to counter with rudder. This effectively cambers the rudder whereupon you get a sideload.

As for V_mca....

The way I understand it, you can change the available moment necessary to counteract asymmetric yaw due to an ENG OUT situation via modification of the force or the distance that the opposing aerodynamic surface generates.

Whereupon my conclusion that the CG location is intimately acquainted with the concept....

10th Sep 2004, 05:44

Join Date: Oct 2003
Location: Canberra Australia
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SR71
CC John Tullamarine for your further delight.

Would be most presumtuous for me to claim the maths are wrong. Haven't checked them lately!

And SR71 - I see that you are now starting to see how it all works by saying that "It is the load on the fin that counteracts the component of lift along the y-axis, thereby allowing straight flight inspite of the bank angle". Partially correct. The only way I know of to get a side force from the fin, rudder central, is with sideslip. So - yes - the fin is probably the biggest contributor aided by the rest of the sideslipping fuselage.

My concern is with the few mYths that continue to perpetuate.

There is the one about our present subject and others such as the 95% pilot belief that aircraft rudders opperate in the correct human instinctive sense.
Right NOW we have many heavy pilots rolling out after touch down using rudder in one direction to hold centre line before he changes over to use nose wheel steering, usually in the form of a wheel, and operating the nose wheel steering control in the reverse sense to achieve the same result. He may even be uncoordinated enough to be doing that simultaneously. But we humans are very versatile and it didn't really take more than an hour or two to suppress our prior learning on billy carts, bicycles, cars and motor bikes to operate the damn thing in the aircraft the other way round - did it?

But how we came to accept reverse operation of rudders is a bit like some switches being up for on and across the pond they are down for on. Subject for another thread.

Same with our mental picture of an aircraft's cg position. It seems to take on its own personna when we are considering it in the pitching/longitudinal sense. Long stab is where we first learned about the balance of forces and all that. Then we transferred our attention much later to directional considerations and found it very convenient to bring along that mental picture of the cg. It just doesn't exist in the unaccelerated horizontal. Certainly you can push it sideways a bit by having an unbalanced transverse load. But so what with our present thoughts?

But I remain perplexed that in the case being considered of straight balanced unaccelerated flight most of you still want to consider forces acting around a point which is totally irrelevant to the unaccelerated horizontal situation. Vital yes to the vertical situation.

Too few of us have thought much about the lateral centre of pressure of a body moving through the air. Total drag can be said to concentrate from that point just as we represent total lift in the vertical through a point for ease of reference. But it's damned important to keep that point down the back. Otherwise our aircraft will want to turn around and go backwards.

In considering a stable horizontal situation move the cg anywhere you want. Take moments about the tip of the nose if you want. Makes no difference to the balance of the steady horizontal forces. I know - some of you aren't convinced of that yet. So I must insist that you only look at the horizontal only because that is what this discussion is all about.. Strange I didn't have the problem before when comprehending the vertical situation. There was no flow over then from the horizontal to the vertical unless the cg moved sideways. Don't give up - it gets simpler.

Having convinced you that the position of the cg doesn't matter, I will now proceed to examine the horizontal forces for the case of an asymmetric aircraft having some bank into the side having most thrust. Keep it simple - it's a twin.

All of the HORIZONTAL forces involved can be simplified, I hope you will agree, into thrust component, drag, horizontal lift component and the one that most of you want to ignore which is the horizontal force generated by sideslip. In the wings level case that sideforce was obvious because it just must be there. I absolutely know that the rudder is deflected.. But roll over a little and you replace that force largely produced previously by the rudder with total fuselage sideslip so that you can now have a close to central rudder. May look neater to some.

What are the simple moments and how do they get into balance to give us straight "balanced" flight?

1. Thrust component X arm to the line of total drag. OK those two forces, thrust and drag, balance but are endeavouring to yaw the aircraft mightily and spoil your day. Quickly lets have contra yaw to keep us on the straight and narrow. Let's use the next moment.

2. Horizontal lift component X arm to ?? Whoops - where is the opposing force. It has to be around someplace or we have to go sideways and yaw at the same time. So sideways we start to go until the sideforce generated by the sideslip builds up to equal the horizontal lift component. Hey we are back in balance.

Do I see flashes of inspiration towards a better understanding of asymmetric directional stability.

Will you now join with me in my crusade to start a new religion based on the lateral centre of pressure.? OR

Please someone show me where I may be wrong before I take up hydrodynamics instead to see how they do it with boats and dirigibles.

Had to edit to correct spelling of asymmetric which is impossible to spell correctly all of the time - just like parallel - that doesn't look right either.

Smooth landings

10th Sep 2004, 07:21

Join Date: Aug 2000
Location: UK
Posts: 3,646
The only way I know of to get a side force from the fin, rudder central, is with sideslip.
No one is suggesting that the rudder is central for zero sideslip. It may be a little less than for the wings level case, but there's still substantial force coming from the vertical tail surface (without sideslip).

All of the HORIZONTAL forces involved can be simplified, I hope you will agree, into thrust component, drag, horizontal lift component and the one that most of you want to ignore which is the horizontal force generated by sideslip.
And you want to ignore the force at the vertical tail...

2. Horizontal lift component X arm to ?? Whoops - where is the opposing force.
At the vertical tail...

Certainly you can push it sideways a bit by having an unbalanced transverse load. But so what with our present thoughts?
I sympathise with your concern that unquestioningly resolving everything about the C of G is unhelpful. However, in the case of the horizontal component of lift, there's a reason for considering the C of G. The total (mainplane + horizontal tail) lift on the aircraft must act at the C of G, otherwise there would be an unbalanced couple with the weight. Thus the horizontal component of lift also acts at the C of G and the C of G position is therefore of significance in assessing asymmetric control.

10th Sep 2004, 11:01

Join Date: Oct 2003
Location: Canberra Australia
Posts: 1,300
bookworm

Thanks for highlighting the bits you don't understand.

A sideforce from the fin, rudder central without sideslip ??? You have discovered something unknown in aerodynamics. Patent it quickly.!!

How can you possibly say " there's still substantial force coming from the vertical tail surface (without sideslip)" when there will be absolutely zilch except drag unless there are inequalities in the shape of one side with the other. I'll concede that slightly different airflows along the vertical tail resulting from one engine operating and the other closed down may have some effect. But skip this for now as it only complicates the case on which we seek a conclusion.

For ease of further discussion, which must be very illuminating to the thread visitors, let us just look at the wing down case where we have carefully adjusted the bank to result in a centralised rudder whilst we maintain balanced straight flight.

You say "And you want to ignore the force at the vertical tail..."

Please tell me how I am ignoring it when I have just said "and the one that most of you want to ignore which is the horizontal force generated by sideslip."

Does this not equate to your "the force at the vertical tail.."

This IS the force at the vertical tail which is ONLY achievable from sideslip unless we have a gremlin out there giving it a shove.

Don't forget that there is a reasonable contribution of force from the side of the fuselage to the balancing force at the vertical tail.

If the above does not convince please tell me where I have failed. I have a thick skin.!

We agree on one fact. That is that the total lift acts through the cg (ignoring any vertical component of thrust.)

Pardon me on my insistence on the use of cg intead of CG. It's the same as using MM for mm and maybe I'm a long way behind on an update.

The combination of a relatively small horizontal lift component and the small permissable fore and aft cg range results in there being insignificant effects of cg position on the stabilising couple with the tail force resulting from the sideslip. Because of its insignificance I have taken the liberty of ignoring it for the sake of simplicity.

Perhaps someone will come up with some typical numbers to illustrate that insignificance to satisfy the purists. That will involve complex multiple hieroglyphics.

Wings level, that insignificance disappears.

Incidently have you handled asymmetric situations?

10th Sep 2004, 15:36

Join Date: Aug 2000
Location: UK
Posts: 3,646
A sideforce from the fin, rudder central without sideslip ???
One more time: the rudder is not central.

Incidently have you handled asymmetric situations?
Yes, in aircraft in which if you don't eliminate the sideslip you don't get a rate of climb at blue line!

10th Sep 2004, 15:55

Join Date: Oct 2000
Location: N. Europe
Posts: 436
The total (mainplane + horizontal tail) lift on the aircraft must act at the C of G, otherwise there would be an unbalanced couple with the weight.
I'd like to modify that to say that "the vertical lift of the mainplane and the vertical lift of the tail must act at the CoG". After all, the vertical aerodynamical force on the tailplane is not directly linked to the force in the aircraft z direction.

I'm almost scared to put myself in the middle of all of this but hey, this place is usually civilized.

Regards,
Fred

10th Sep 2004, 18:00

Join Date: Aug 2000
Location: UK
Posts: 3,646
For ease of further discussion, which must be very illuminating to the thread visitors, let us just look at the wing down case where we have carefully adjusted the bank to result in a centralised rudder whilst we maintain balanced straight flight.
Ah, perhaps this is the cause of the crossed wires.

If you hold the wings level and use rudder to correct the asymmetry, the aircraft will slip towards the dead engine.

If you use wing down to correct the asymmetry to the extent that you're able to centralise the rudder, the aircraft will slip towards the live engine.

Between the two is a zero-sideslip, wing-down, non-central-rudder scenario.

10th Sep 2004, 19:56

Join Date: Jul 2003
Location: An Island Province
Posts: 1,080
I do not wish to enter such an expert discussion, but if it helps, please see two somewhat more practical articles – with diagrams here: Turboprop PSM+ICR, “asymmetric flight.pdf” and “Asymmetric flight at low airspeed.pdf” The related articles indicate the flight results if you do not get the rudder and bank sorted out.

11th Sep 2004, 03:29

Join Date: Oct 2003
Location: Canberra Australia
Posts: 1,300
bookworm , ft, alf5071h
Where are you SR71?
Still with us J T ?

Great to have you joining the fray. You will find yourselves reviewing a lot of aerodynamic basics and may also come to grips with a major myth that has been perpetuated regarding directional stability for far too long.

Most text books continue to make the mistake that the horizontal forces on an aircraft in steady flight have someting to do with weight and the cg. Well in this case only a smidgen.

A few basics first to re-establish the detail of what we are discussing. That is Sideslipping when Asymmetric.

1. The horizontal forces on a twin engined aircraft in steady straight unaccelerated level flight can be accumulated and represented by just two distict forces familiar to us.

1.1 Component of Thrust - Acts straight along an aircraft centre line assuming equal thrust from engines. Vertical positioning of thrust line irrelevant to horizontal. NO relationship to weight or cg

1.2 Total Drag - Acts straight along an aircraft centre line. Equals Thrust. Vertical positioning of drag line irrelevant to horizontal. NO relationship to weight or cg

2. The horizontal forces on a twin engined aircraft having asymmetric thrust flying in steady straight unaccelerated level flight, wings level, can be accumulated and represented by just three distinct forces familiar to us.

2.1 Component of Thrust - Acts along a line parallel to an aircraft centre line. Vertical positioning of thrust line irrelevant. NO relationship to weight or cg.

2.2 Total Drag - Acts parallel to an aircaft centre line. Equals Thrust. Vertical positioning of Total Drag line irrelevant. NO relationship to weight or cg.

2.3 Fuselage Sideforce - Acts from the lateral centre of pressure normal to the aircraft centre line and towards the engine having least thrust. Verical positioning of Fuselage Sideforce line irrelevant. NO relationship to weight or cg.

3. The horizontal forces on a twin engined aircraft having asymmetric thrust flying in steady straight unaccelerated flight, small bank angle, can be accumulated and represented by just four distinct forces familiar to us.

3.1 Component of Thrust - Acts along a line parallel to the aircraft flight path. Vertical positioning of thrust line irrelevant. NO relationship to weight or cg.

3.2 Total Drag - Acts parallel to the aircraft flight path. Equals Thrust. Vertical positioning of Total Drag line irrelevant. NO relationship to weight or cg

3.3 Component of Lift. Acts from an obscure point along the vertical line from the cg and normal to the flight path horizontally towards the side having greatest thrust.Vertical positioning of Component of Lift force line irrelevant. Point of origin related to cg, NO relationship to weight.

3.4 Balancing force to Component of Lift. Acts from the lateral centre of pressure normal to the aircraft flight path and towards the engine having the greater thrust. Verical positioning of Fuselage Sideforce line irrelevant. NO relationship to weight or cg.

Note. 1 bookworm. Deliberate no mention of rudder to keep it simple. Don't care where it is and incidently there is no way for you to accurately trim rudder to nail the min drag you have been chasing in a performance climb. Re-engined Caribou was a classic. Difficult without a boom and vane. Yaw string too gross.

Note 2 The vertical levels/planes of the above forces do not coincide. Resulting vertical moments are well cared for by the aircraft's longitudinal stability. We are strictly horizontal here.

Now - can someone please explain where we can generate that balancing force to the Component of Lift ?? I can assure you that it does not come from the strengths of a family of Gremlins, Fiffinellas and their proginy - Widgets.

Challenge to all who pass this way.

Watch this space for the next exciting discourse on aerodynamics !!