For the eggheads: The math behind an uncoordinated turn
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For the eggheads: The math behind an uncoordinated turn
I'm trying to determine, mathematically, if the aircraft is in a Skid or Slip condition while turning.
Does anyone know the math?
Does anyone know the math?
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In a coördinated turn at true airspeed V the bank angle φ is given by:
tan φ = V * ω /g
where ω is the rate of turn and g is acceleration of gravity (in consistent units).
tan φ = V * ω /g
where ω is the rate of turn and g is acceleration of gravity (in consistent units).
Centrifugal force is the "equal and opposite reaction" of the airplane to the change in direction and acts equal and opposite to the horizontal component of lift.
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That was when lecturers were sufficiently unsophisticated in their understanding of physics to be unable correctly to perform an analysis of forces in a rotating frame. Thankfully things have improved since then.
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Knuckles & yaw
Mr Fly, in order to avoid a rap across the rudder in the rotating frame, rudder must surely be applied to keep the aircraft pointing in the tangent direction, which I guess the tendency to depart from, the ruler-wielder would attribute to a coriolis force.
Last edited by awblain; 3rd Dec 2012 at 14:47. Reason: i before e except after c. Rap.
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Remember the days this was so simple? Keep the ball in the middle and you were in a coordinated turn. No formulas required. I saw a skidding turn in a Bonanza out of Burbank, Ca. one day and it ended up in a fiery crash with 4 dead from 300 feet on take off with an engine malfunction. The pilot didn't keep the ball in the middle, simple as that. He rolled over when he stalled and went straight into the ground at the departure end.
That was when lecturers were sufficiently unsophisticated in their understanding of physics to be unable correctly to perform an analysis of forces in a rotating frame. Thankfully things have improved since then.
Must be missing something here! Where does the 'centrifugal force' come from? The only forces are weight and the total aerodynamic reaction. The latter is at right angles to the wing and has two components - vertical, which in a level turn equals and opposes weight and horizontal towards the centre of the turn which is the centripetal force which makes the ac turn.
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so after all of these years.. the dynamics of an aircraft in a turn...wow...
this discussion should be coupled with the theory of lift discussion...
I will throw in another mf to the discussion. A turn is a rate of change. As the ac goes from level, to the bank required to make the desired turn, the rate of change is constantly changing, hence the definition of a spiral.
I have had to deal with this on a frequent basis designing RNP turns. As one notes, RNP procedure turns are a simple radius. If one looks at turn on final, the transition between level and full bank limited by the ac or criteria, is a spiral. One has to be very careful with that transition, hence the slip takes the ac out of containment.
havent 'those days been a while! 
this discussion should be coupled with the theory of lift discussion...
I will throw in another mf to the discussion. A turn is a rate of change. As the ac goes from level, to the bank required to make the desired turn, the rate of change is constantly changing, hence the definition of a spiral.
I have had to deal with this on a frequent basis designing RNP turns. As one notes, RNP procedure turns are a simple radius. If one looks at turn on final, the transition between level and full bank limited by the ac or criteria, is a spiral. One has to be very careful with that transition, hence the slip takes the ac out of containment.
In the days when lecturers were prone to administer a rap over the knuckles with a ruler to encourage learning, I seem to recall that mention of "centrifugal force" was a sure way to get one.
Last edited by FlightPathOBN; 4th Dec 2012 at 19:49.
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Where does the 'centrifugal force' come from?
Probably better to keep oneself nice by thinking of centripetal acceleration (and force) with an opposite centrifugal reaction ?
Probably better to keep oneself nice by thinking of centripetal acceleration (and force) with an opposite centrifugal reaction ?
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bubbers44:
As a recent PPL holder 48 years ago, I was taught that lesson in an old Ryan PT-22. My instructor (Purdue's Irwin Treager) talked me through a couple routine stalls and slowflight maneuvers, then suggested I hold a little rudder (cross-control) to see what goes.
Well, about 1-2 mph above the expected stall speed, we did the prettiest snap roll! Happened so fast that by the time I could respond, we were shiny-side up again. A lesson not soon forgotten.
I saw a skidding turn in a Bonanza out of Burbank, Ca. one day and it ended up in a fiery crash with 4 dead from 300 feet on take off with an engine malfunction. The pilot didn't keep the ball in the middle, simple as that. He rolled over when he stalled...
Well, about 1-2 mph above the expected stall speed, we did the prettiest snap roll! Happened so fast that by the time I could respond, we were shiny-side up again. A lesson not soon forgotten.
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Don't try that in a high wing-loading swept wing jet mate - it's called departure.
One question comes to mind though - 23 July 1983, Air Canada Flight 143 (The Gimli glider) - The captain had glider/sailplane experience, found himself a bit high on approach, and dared to slip that 767 on final.
Was he merely lucky not to depart the regime of positive roll control, or did he have some insight beyond his seat-of-the-pants about how far to push the beast?
Last edited by barit1; 5th Dec 2012 at 15:05.
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You can slip, either forward or side slip in any airliner as long as you have the proper speed. All my crosswind landings in airliners were side slips to compensate for the drift, the forward slip is the same except the nose is not positioned lined up with the runway. The aerodynamics are exactly the same, one is used to compensate for crosswind and land straight, the forward slip is to cause fuselage drag to increase drag and descent rate.
I heard a story of a 737 operator doing it when idle power didn't work and landed just fine. I wouldn't advertise I did it however.
For us that use the side slip to have the plane land straight and not in a crab to not abuse the landing gear on touchdown we also know we need to have the proper speed. It is quite simple.
I heard a story of a 737 operator doing it when idle power didn't work and landed just fine. I wouldn't advertise I did it however.
For us that use the side slip to have the plane land straight and not in a crab to not abuse the landing gear on touchdown we also know we need to have the proper speed. It is quite simple.
Yes, and in fact the PT-22 has 2 or 3 degrees sweepback, which undoubtedly
aggravated this behavior.
aggravated this behavior.