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