Aerodynamics: Center of Pressure

I am trying to figure out why it would not rotate around the center of pressure--for my on personal sanity! stuff like this drives me nuts. You should have seen this post back awhile ago called "True airspeed riddle"
 
Gotcha! :) I'll get you a reference but that will have to wait until next week. I'm not sure if that will make you feel more comfortable about the whole rotation thing.
Let's try something else. Would you agree that if the net force (force, not torque, you add the forces as vectors) is zero, the CG will not accelerate in any direction? That would also mean that if it's not moving up or down, it will continue to stay at the same height.

What I'm trying to get to is if we need to focus on proving that free objects rotate around the CG or on discussing if a flying airplane is such an object.
 
Adrock said:
The center of pressure (CP) on a wing is sort of like the center of gravity in that it is the center or concentration of forces. If one could attach a string at the center of gravity and suspend an airplane it would balance. If one attached a string at the station location where the center of pressure exists for a given flight condition (we know CP changes during flight) and an aircraft where suspended by this string the airplane would nose over due to the CG being ahead of the CP. Now visualizing the upward force as this string suspending the aircraft at its CP and the CG (ahead of the CP) as a string pulling down, one can see that the larger the distance (arm/leverage) between the two values the harder the tail has to work to overcome the nose down moment. Given this visualization I find it hard to believe that an aircraft pitches about its CG and not it’s CP. Go ahead guys, where did I go wrong?
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You are indeed over thinking it! Just think of the center of pressure as the "person sitting on the teeter totter". Thats all...
Of course then you have flight control surfaces that each have a center of pressure, the ailerons, rudder and elevators. This is why position of cg affects controllability relative to the cp of each surface that is creating movement; and affecting stability with reference to the center of pressure of the acutal lifting surface (the wing).
 
milski said:
You have it right, which makes me wonder how come you're having hard time with it. One thing to keep in mind is that the gravity goes directly down through the CG and does not contribute in any way to the pitching up/down rotation. So all that you have to balance, rotation-wise, is the torque created by the wing and the horizontal stabilizer. The arm of the stabilizer is much longer than the wing, so it needs to generate much more lift. Now all this gets you no rotation. To make sure that the airplane is not accelerating up and down, the sum of all these force has to be zero. So the sum of the weight and the downward lift generated by the tail has to be the same as the amount of lift generating by the wing. Does this help?
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BTW, not to split hairs, but because the horizontal stab is further from the CG, it actually does not have to produce more "lift" or tail down force, because its arm is longer its moments will always be greater!
 
milski said:
That's exactly correct - rotation happens around the CG. I think you're mixing the linear movement along any any of the axises with rotation around them. Pitching up and down is rotation along the lateral axis. What controls if and how much rotation happens is the sum of all the torques, where the torque is force x arm. Since the weight can be considered to go through the CG, its arm is 0 and thus its torque is zero as well.

Try to visualize the airplane as a bicycle wheel. No matter how much you pull it up or down by its axis, the wheel will not start turning. Now imagine that you pushed one of the spokes very close to the axis up - that will be your lift at the CP - it will make the wheel turn. If you wanted to prevent the wheel from turning, you could push on the same spoke but much further away from the axis. You'll need to push much lightly there - that's the force from the tail.

All this does not guarantee that the wheel will not fall up or down - only that it will not turn. To make it stay steady in the air you'll have to make sure that you're pushing on the spoke up hard enough to counteract for both the weight and whatever force you're using to push down at the far end of the spoke.
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The longitudinal axis, or roll axis does not necessarily intersect at the same point as the lateral and vertical axes. If your fuel is improperly balanced, then the axis, or longitudinal cg as it might be called, is offset and the aircraft will roll around that point...
 
Ziggyfuzz said:
BTW, not to split hairs, but because the horizontal stab is further from the CG, it actually does not have to produce more "lift" or tail down force, because its arm is longer its moments will always be greater!
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Right, that was a typo, you do need less force in the tail with the longer arm, not more. Thanks for catching it!
 
Ziggyfuzz said:
The longitudinal axis, or roll axis does not necessarily intersect at the same point as the lateral and vertical axes. If your fuel is improperly balanced, then the axis, or longitudinal cg as it might be called, is offset and the aircraft will roll around that point...
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Nope, the CG is a point. All rotation happens around an axis which goes through that point. In the case where your fuel is improperly balanced the longitudinal axis will move towards the heavier side together with the CG. In other words the axises of rotation are not going to be the same as the symmetry axises of the aircraft. Which is probably what you were saying too.
 
milski said:
Nope, the CG is a point. All rotation happens around an axis which goes through that point. In the case where your fuel is improperly balanced the longitudinal axis will move towards the heavier side together with the CG. In other words the axises of rotation are not going to be the same as the symmetry axises of the aircraft. Which is probably what you were saying too.
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Roger that!
 
Adrock said:
I am trying to figure out why it would not rotate around the center of pressure--for my on personal sanity! stuff like this drives me nuts. You should have seen this post back awhile ago called "True airspeed riddle"
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The CG is the fulcrum, the aircraft is the lever, and aerodynamics are the forces acting on the lever.
 
inventor said:
The CG is the fulcrum, the aircraft is the lever, and aerodynamics are the forces acting on the lever.
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A fulcrum is a supporting point of a balancing system. There is no way you can argue that the cg is fulcrum withouth a cyclical argument claiming that "it is a fulcrum because that is where rotation occurs."
 
The CG is not supporting the system, the Center of Pressure is. therefore the CP is the fulcrum
 
Adrock said:
The CG is not supporting the system, the Center of Pressure is. therefore the CP is the fulcrum
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There is no 'support' in the system - the airplane in that case is a free body. There is no difference between the gravity force and the lift force, except where they are applied and the direction. Neither acts as a 'support.' To have a fulcrum, you need a physical object touching the airplane at a certain point. The landing gear when on the ground would be a perfect example for that.
 
No, and no. A fulcrum does not have to be a physical object. A fulcrum represented as a physical object, is a simple way of explaining a lever. A fulcrum is precisely like a point, it's a definition, not necessarily something that has a physical existence. CG is specifically, the definition of a fulcrum.
 
Air is a physical object. Air has mass and if accelerated it creates a force. If a small powerful jet of air held up a balsa wood board the balsa board would rotate around that jet of air, because that jet of air would be a fulcrum.
 
If one suspended a ruler by a string in the middle and added weight to the front and added the appropriate amount of weight to behind the sting to make the ruler balance then any weight added would cause a rotation around the string. The ruler system's CG while balanced would be at the same location as the string. I think we can all agree on this?

NOW, if you added weight to one end of this balanced system you would be causing the CG to move (if you add weight to the front of the ruler, you have just moved the CG ahead of the string attach point) yet the rotation that would result would still occur about the string.
 
The ruler suspended from the string is not the same as the airplane flying. Moving the point where the string is attached down introduces additional force from trying to lengthen the string. The harder you pull down on the string, the larger that force becomes (until you tear the string). There is no similar force when the CP of a flying airplane moves down - the lift generated by the wing is the same, no matter if the wing is up or down by a few feet.

In the post where we talk about the air being object - replace physical object with a rigid object.
 
Adrock said:
The CG is not supporting the system, the Center of Pressure is. therefore the CP is the fulcrum
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Wrong again! First of all, a system is self supporting, it is the sum total of all masses/energies in the system. In this case the system is the air, the aircraft, gravity, drag, and thrust. The CP is the point along the chord line of the wing where lift is concentrated. The CP is the focal point of the force that causes an aircraft to pitch nose down about the lateral axis that intersects the CG, the point where gravitational force is focussed. Gravity is ultimately the force, at an acceleration of 9.8 m/s, that we are trying to over come. That force is focussed at the CG due to the distribution of mass along the longitudinal axis (axis perendicular to gravitational force), lift acts behind the CG at the CP to overcome the acceleration of weight, creating that nose down moment (pitch around the lateral axis).THis is why tail down force is needed. If the CP was the fulcrum, there would be no need for the horizontal stab to produce the balancing force we call "tail down force"! Also, when dealing with a "system" in physics, we are talking about the conservation of energy and the sum total of all forces in that system. As milski pointed out, an aircraft in equilibrium has a net force of zero. (downward forces=upward forces and forward forces=rearward forces: these are not just lift, weight, thrust and drag, it is acutally more complicated than that. You have components of thrust and wieght that actually act vertically and horizontally as well. THis can get pretty messy and involves some trig.)
 
Try thinking of it this way. Let's say you have a dumbell. It has a 10 lb weight on one end and a 1 pound weight on the other end. In space (to discount all distractions) if you spin it, it will spin around its CG, which will not be the center of the dumbell, but at a spot closer to the 10lb side. If you try to spin it at the center of the dumbell (by holding it in the middle) it will feel off balance, and as soon as you let go, it will correct itself to its equilibrium again. This is because the physics of a rotating body are that both sides produce an outward force (it's actually centripetal acceleration, but don't get me started), and nature abhors an imbalance, so the system will tend to go to neutral (both opposing forces are equal). A free spinning object can (and will) ONLY spin around its center of mass(weight). The lift is only a force 'acting' on the CG and not part of the CG itself, so it has no bearing on the center of rotation (other than giving it the direction of rotation). So an airplane can ONLY rotate around its center of mass (which is the CG). Clear as mud?
 
Adrock said:
Air is a physical object. Air has mass and if accelerated it creates a force. If a small powerful jet of air held up a balsa wood board the balsa board would rotate around that jet of air, because that jet of air would be a fulcrum.
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Yes, but when we talk about accellerating air over a wing, we are speaking relatively, it is the wing that actually is accelerated to produce the effect we desire. The air itself is static, it is the medium.
 
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