Please help me with Aerodynamics

[ArjenVdv 190]

Hello,

For Aeronautical Engineering I am studying Aerodynamics, and today I am getting totally confused about lift-induced drag, it is litterally driving me crazy.

 

Now, if you don't know anything about Aerodynamics, you better don't waste your time because things are about to get real complicated... :/

 

 

Now, lift-induced drag, inversed propertional to speed. Okay, I understand.

 

Lift is perpendicular to relative wind, and relative wind is opposite to the direction of flight. So if, like in my image, the relative wind line is under an angle, the plane is climbing, right?

 

Now the plane goes flying slower, so obviously lift-induced drag would be increased. Also, the angle of attack has increased to create enough lift at lower speeds.

Now I have these component vectors, the one perpendicular to the relative wind and direction of flight is my lift vector, my vertical component vector is the effective lift vector. The one right in between, should be my lift-induced vector. But this is where I am getting lost. When the plane flies slower, and the angle of attack is increased and thus my aerofoil drawing is tilted further backwards, my component vectors do not shift or change because they do not depend on the angle of the aerofoil but only on the relative wind. So my lift-induced component vector is not changing when I change the angle of attack?! This would mean the lift-induced drag is not dependant on the angle of attack. And this is of course conflicting information.

 

Now if the lift vector would simply be perpendicular to the chord line, it would be a whole lot more understandable: when the AOA changes, the lift vector would tilt further backwards, also increasing the lift-induced component vector. But of course lift is perpendicular to relative wind, and not to the chord line. 

 

I must be missing something, but at the moment things are not coming together because things are contradicting themselves...

[KevinAu 441]

You should try it with 3 vectors. The first one should be perpendicular to the cord line, your total lift vector. The second one that is vertical to represent the vertical component of lift. And the third one horizontally towards the rear to represent induced drag.

[ArjenVdv 190]

That is indeed what I mentioned, that would make things easier and more unstandable. But am I even allowed to put the vectors this way? Because as far as I know, the actual lift vector should always be perpendicular to the effective relative wind and NOT to the chord line.

 

Another question, this would clear things up, because it's probably this relative wind that is causing the confusion. There is relative wind (also called undisturbed stream), and EFFECTIVE relative wind, which is usually under and angle caused by the wing down-wash. Now, is the direction of flight parallel and opposite to the relative wind or effective relative wind. But if the second case was true, the plane would be climbing in all my pictures. I don't want it to climb, I want my plane to fly horizontally and the analyze the induced-drag caused by different angles of attack. 

[jcomm 5,890]

Pretty much what Kevin wrote:

 

http://img.tfd.com/mgh/cee/thumb/Wing-lift-and-drag-due-to-lift.jpg

 

http://www.theairlinepilots.com/forumarchive/principlesofflight/induceddrag.jpg

[ArjenVdv 190]

Pretty much what Kevin wrote:

 

http://img.tfd.com/mgh/cee/thumb/Wing-lift-and-drag-due-to-lift.jpg

In that image the lift vector is not perpendicular to the relative wind. That is what is making things confusing for me.

[jcomm 5,890]

In that picture, they name "lift" what is more correctly designated as "total aerodynamic force", composed of the "pure lift" which is indeed normal to the relative wind / free stream and the total drag.

[ArjenVdv 190]

In that picture, they name "lift" what is more correctly designated as "total aerodynamic force", composed of the "pure lift" which is indeed normal to the relative wind / free stream and the total drag.

Thank you, I think it's starting to be cleared up for me now. It seems to be the inconsistent designations in books and on the internet causing the confusion.

[mgh 89]

By definition:

lift is the force normal to the effective air flow

drag is the force parallel to the effective air flow.

 

Unfortunately some authors get this wrong!

[ArjenVdv 190]

By definition:

lift is the force normal to the effective air flow

drag is the force parallel to the effective air flow.

 

Unfortunately some authors get this wrong!

Okay, where did you get those definitions?

 

In my "Aerodynamics for Engineering Students" study book, it says this:

 

Lift is the force perpendicular to the direction of flight or undisturbed stream. 

 

You say lift is perpendicular to effective airflow. Effective airflow is not the direction of flight (or is it?). Very contradicting information, very confusing. But who is correct?

[mgh 89]

direction of flight = undisturbed stream =.effective airflow

[DaveCT2003 1,820]

I believe Effective Airflow merely takes into account any relative wind. It's a more accurate, or rather a more inclusive definition.