# Homework Help: Relationship between Lift and Centre Of Mass (aerodynamics)

1. Oct 1, 2006

### AussieDave

Hey here is a quick question. I have a question on an assignment that is asking me to define lift in an aircraft (done) and its relationship to the aircraft's centre of mass. I'm unsure how to do that second bit as lift acts through the centre of pressure...not the centre of mass (also known as centre of gravity ) Can someone more knowledgable please shed some light on this for me?

2. Oct 1, 2006

### andrevdh

If these two points do not coincide the two forces will also produce a couple that will rotate the body of the plane. If they do coincide the plane will rise, fall or stay at the same height without rotating about some axis. So yaw, pitch or roll is effected by offsetting the centre of pressure in the required direction with respect to the com.

3. Oct 1, 2006

### AussieDave

Ahh okay. Yeah well on aircraft the centre of pressure is always behind the centre of mass (correct me if I'm wrong) so I need to state how that even though the lift force doesn't act through the centre of mass, that it is still pulling the plane up from the centre of pressure and that it needs to be balanced (normally by a negative tail lift) so there isn't unwanted rotation as the points do not coincide. I've got all the yaw, pitch and roll stuff pretty down pat as they are basically rotations around the centre of mass with forces that go through the centre of pressure.

Here is a perhaps different question... On all basic diagrams of a plane flying level it always has the 4 arrors for thrust, drag, lift and weight. I'm not sure how to draw them on a plane that is ascending though... I have attached a picture showing the basic force diagram for a level plane in the top left that I see everywhere and 3 force diagrams of an ascending plane with 3 attempts to draw in the forces. Hopefully someone could tell me which one (if any) is correct?

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4. Oct 1, 2006

### andrevdh

The lines of action of the thrust and weight will act through the com of ( a single engine) plane. Not necessarily so with the drag and lift. To make the plane climb all that is necessary is to cause the upwards y-components of all of the forces to outweight the downwards y-components. By increasing the airspeed the lift will increase (and its point of application shift).

5. Oct 1, 2006

### AussieDave

What about in a Boeing plane which has 2 engines on either side, where does thrust act from then? I'm not neccesarily looking for how climbing is achieved by totaling the upwards y-components of the vectors....I'm basically looking for the direction of the individual forces.

The only one I'm sure about is Weight because it always points down no matter which way the plane is going. What I don't know is which way thrust, drag and lift are pointing during an inclination. Were any of those diagrams that I created on the attached picture close?

Thanks for your help so far :)

6. Oct 1, 2006

### Astronuc

Staff Emeritus
Thrust points forward, drag points opposite of velocity/thrust, and lift points upward. The drag is a consequence of momentum loss to the fluid in which the craft is flying (or for boat cruising/sailing).

The relationship between weight, lift, thrust and drag is shown in this -
http://www.grc.nasa.gov/WWW/K-12/airplane/smotion.html

Simple anatomy of an aircraft - http://www.grc.nasa.gov/WWW/K-12/airplane/airplane.html

Beginner's Guide to Aerodynamics - http://www.grc.nasa.gov/WWW/K-12/airplane/bga.html

Propulsion is discussed here - http://www.grc.nasa.gov/WWW/K-12/airplane/bgp.html

In a twin engine aircraft, each engine produces thrust. Ideally, the thrust of each engine is equal so the torque on the plane is zero. The thrust can be varied so that one can actually steer the aircraft by varying the difference in thrust between engines.

7. Oct 1, 2006

### AussieDave

Yeah I've kinda gone all through the nasa site yet all of their force diagrams are for planes that are level. when you say thrust points forwards, that is in the direction of the plane yes? so when climbing the angle between it and the weight force will be obtuse? When you say the lift points upward, is that at an angle perpendicular to the thrust and drag OR is it simply pointing up no matter which way the airplane is headed?

I've got all the basics of lift, thrust, drag and weight...except for their relative angles when a plane is ascending (that's why I created those diagrams in an above post attachment)

thanks for ya help :)

8. Oct 1, 2006

### andrevdh

The thrust of two engines can be reduced to a single force. The line of action of such resulting thrust will be parallel to the two engines and closer towards the engine with the larger thrust. It the two engines generate equal thrust the line of action will be midway between the two. A plane is designed so that it will fly level with no rudder, ailerons or flaps. At this point line of action of the centre of pressure will go through the com of the plane, if it did not the plane would have rotated. So even in such a case the lift need not point straight up. In any other case the direction and magnitude of the lift and drag can point in all sorts of directions, causing the plane to behave in certain ways. That is why each plane acts differently and it needs getting used to when flying it. That is learning how it acts under certain conditions and what the pilot need to do in order to get the required response from it. Generally a plane should be designed so that the thrust passes throught the com of the plane otherwise it would be quite unmanagable since it would tend to fly in a circle all the time!

9. Oct 1, 2006

### AussieDave

Okay so I'm beginning to understand why drawing a diagram for a plane while rising isn't as easy as it seems because there aren't universal directions for lift, thrust and drag.

The planes I'm normally talking about are big Boeings with two engines on each wing so, assuming they are equal, the point at which thrust acts from can be taken from a point inbetween the two wings as they are positioned evenly on the two wings...and even though this isn't either centre of mass or centre of pressure, it will be in a line parallel to them. If we take this total thrust force from the middle of the plane, not the individual thrust forces from each engine, it will be a sum total of all the individual thrusts yeah? like 20kN from engine right and 20kN from engine left, perfectly evenly spaced apart, will result in a total thrust of 40kN? (Not an average which would be 20)

Thanks mate, I think I have it now sorta :)

10. Oct 1, 2006

### Astronuc

Staff Emeritus
Those would be 747's then. Each engine provides its own thrust vector, and the resultant acts on the aircraft. Also, if straight flight is desired, the thrust of the engine(s) on one wing should balance (equal) the thrust of the engine(s) on the other wing so that there is no net moment or torque.

The thrust of the engines point backward, and the thrust imparted to the aircraft is forward. The forward thrust vector is the 'reaction' of the aircraft.

An aircraft can go up in three ways:

1. The thrust (aircraft reaction) vector points at an angle above horizontal, in which case there is a vertical component to thrust, as well as the horizontal forward. This happens when the attitude of the plane is pitched upward. This also increases drag.

2. The lift exceeds the weight. If the lift magnitude exceeds the weight magnitude, then there is a net upward force. This happens as the speed of the aircraft increases.

3. The airflow is deflected downward, so that the aircraft receives an upward force (reaction) to the downward momentum of the airflow. This is what happens at low speed when the flaps are extended downward behind the wings.

Last edited: Oct 1, 2006
11. Oct 1, 2006

### AussieDave

Ahh okay. So when climbing, the lift AND thrust are both acting upwards (have vertical components), not just the lift. I was thinking that thrust was merely a forward movement that generated the velocity needed for speed.

So when a plane is climbing, will lift be perpendicular to thrust? I wouldn't think so because that would mean lift is not acting directly upwards?

12. Oct 2, 2006

### andrevdh

The wings of an airplane experiences some aerodynamic force due to the air flowing over it. This resultant force can be decomposed into two components. The horizontal component acts towards the rear of the plane and is one of the drag components that the airplane is experiencing. The vertical component of this force is the lift that acts on the wings.