jonnyjetprop

Because the nose tends to drop as you increase your pitch. You don't have the power available to hold altitude.

Cubdriver

Yes, I should have said something like that instead. Bank angle shifts the lift vector to the side according to the trigonometric relations you gave, except you need to swap the words cosine and sine in your equations. Sine of the lift vector gives the vertical component of lift, while cosine of the lift vector gives the horizontal component of lift during a banked turn. This is true for any angle of bank up to 89+ degrees or multiples thereof at which point the equation goes to infinity and becomes useless. This incidentally is why Quaternions are used for flight simulation instead of Eulerian angles.

Cubdriver

You guys didn't study this?

shdw

Interesting, thanks. And yah I did that in my head real quick, wasn't sure if it needed to be the reverse. I did test it on a calculator though: cos 60 = 0.5, we know a 60 degree bank requires double the lift to equal weight. That is why I thought that was right. Hmm?

Cubdriver

Lift at zero degrees of bank is defined as being 90 degrees from the horizontal plane; so <sin (90 degrees) = 1>. This means 100% of the lift is going in the vertical direction at zero degrees of bank. <Cos (90 deg) = 0>; so 0% of the lift is going to the horizontal axis in level flight. At 60 degrees, (.5) or 1/2 the lift goes to the horizontal axis of flight and at 90 degrees of bank, ALL of it goes to the horizontal. That is a big change over a small number of degrees (30), so we call that an exponential relationship.

shdw

Got ya, changing it now and thanks.

MrWalk

Hahaha.

As Cubdriver so intelligently pointed out, this is an unstable flight mode to begin with. The bank angle does not have to pass 90 degrees in order for pulling back on the yoke/stick to be detrimental. Once the spiral dive develops, pulling back "tightens" it, i.e. brings the aircraft in toward the center of the spiral it is drawing in the sky rather than arrest the descent and decrease the airspeed.

"While descending turns are commonly performed by pilots as a standard flight manoeuvre, the spiral dive is differentiated from a descending turn owing to its feature of accelerating speed" [source: wikipedia "Aircraft Dynamic Modes]

What makes a spiral dive a "graveyard" spiral is the failure to recognize the situation and apply the correct remedial action. You lose situational awareness and fail at energy management.

Sines and cosines apply to a snapshot of this process. But, like so much in flying, the key is in the trend. By definition, you are in a situation where the horizontal component of lift is going to get the lion's share of the energy you direct with the increased AOA/lift, while airspeed continues to build and the decent remains unarrested. Therefore, it is the wrong action to take.

You end up waging war with centrifugal force until you rip the wings off with either Vne+ or overstress or else hit the planet.

nciflyer

I think most of the issue rises from the PHAK assuming, without stating directly, that tightening a turn means a mixture of g-load, an airplanes aerodynamic overbanking tendencies, and spatial disorientation factors. I'm not saying these are the only factors that define a graveyard spiral. Although they should be considered as a part of the system and can contribute to a graveyard sprial.


Of course as discussed already if you're pitch attitude low in a steep turn it is much harder to correct this solely by the elevators merit rather than leveling the wings a little first. I figure the PHAK is assuming the plane is in a large descent and bank angle where a normal amount of force applied to up elevator will not reduce the increasing trend of airspeed and sink rate. Since a disoriented pilot in such a banked dive would not see the sink rate and airspeed trends improve they would naturally command more up elevator worsening the g-load problem.


Secondly, the effects of a steep turn can cause the plane to overbank, hence the reason opposite aileron to keep bank angle constant in such a turn. I've noticed in steep turns when up elevator is applied overbanking will increase. Overbanking also gets worse at steeper bank angles, lower speeds, and longer wings. All such factors contribute to the wing on the outside of the turn to have a higher airspeed than the inside wing which makes the outside wing produce more lift imparting a roll. So now figure that when a disoriented pilot, who thinks he/she is wings level & nose down, applies up elevator to decrease the descent bank angle could increase without any movement of the ailerons. Since overbanking does not make the plane roll very rapidly it is likely it'll go unnoticed since the pilot does not know which way is up.


Also consider the pilot may be getting "the leans" where the plane feels bank level due to a prolonged banked turn, which is essentially a graveyard spiral situation. If a significant uncommanded roll happens and reduces the aircraft bank angle the pilot could perceive that as departing from level flight and apply corrective action therefore worsening the spiral.


To demonstrate graveyard spirals to student I'll initiate a turn to where overbanking will occur then set ailerons neutral and from there on out only apply up elevator. Further elevator is only applied after overbanking has increased the bank and time has allowed for the nose to drop due to the increased bank. Then I add up elevator slowly as bank builds enough to increase g-load without reducing the descent rate too much and continue until the g-load is uncomfortable and my point is clear. This can be tricky though and of course this lets them see it with their eyes and makes them think how easy it would be to prevent/recover, which is not reality under imc. So, I'll usually follow up by making them close their eyes and command a series of right/left banks to specific bank angles which will send them into a spiral all on their own merit. Then I'll get them to do the same thing to me so they can laugh at someone else getting disoriented and truly see how useless we are without our eyes and a horizon.

sellener

[quote=MrWalk;731533]Hahaha.


The bank angle does not have to pass 90 degrees in order for pulling back on the yoke/stick to be detrimental. Once the spiral dive develops, pulling back "tightens" it, i.e. brings the aircraft in toward the center of the spiral it is drawing in the sky rather than arrest the descent and decrease the airspeed.


I think that describes it better than how the PHAK did. Pulling back would tighten the spiral and G loads, and disorientation and would not have an effect decreasing rate of descent due to g loads nessesary to decrease rate of descent in this situation.

"pulling back on the yoke increases the rate of descent" just doesnt describe the situation accurately.

shdw

Very nice non mathematical description: shows understanding and doesn't conflict with physical law. I like!



Nciflyer: Just wanted to add to your demo some stability, physiological, fixation/distraction, and disorientation. We let go of the controls to demo that directional being greater than lateral stability can lead to the start of this. We discuss how this leads to disorientation because it happens too slow for your inner ear to realize, so with poor visual cues you are left thinking this bank is straight and level. Discuss how it happens because of distractions or fixation. Finally, discuss and demonstrate the disoriented pilots response you explained. It takes about 5 minutes to get into it, so plenty of time to discuss these things.