Problem solving forces with pressure integration

[Jurgen M]

Angle theta is different for every place at airfoil surface, so it can't be one theta from leading edge to trailing edge.
Can please someone explain pressure integration in depth, step by step?

 

[Arjan82]

I'm happy to answer a specific question if I can, but I'm not in the business of making free tutorials...

So, please be very specific in your question, show us what you've done so far yourself and where you get stuck...

[edit] And don't expect us to look at 16 minute youtube films in which at some point some important part of your question is shown... or whatever your intent was with the video[/edit]

 

[Jurgen M]

I'm happy to answer a specific question if I can, but I'm not in the business of making free tutorials...

So, please be very specific in your question, show us what you've done so far yourself and where you get stuck...

[edit] And don't expect us to look at 16 minute youtube films in which at some point some important part of your question is shown... or whatever your intent was with the video[/edit]

Angle theta is different at every place at airfoil contour, so to know angle theta at every single place at airfoil we need have f(x) function of airfoil top and bottom contours. We must know inclination of local surface where pressure is act, to decompose pressure in normal and parallel component to x co-ordinate..
Where is this function here?

Or just post one complete example where lift and drag is calculated from given pressure distribution over airfoil section.

 

[jbriggs444]

Where is this function here?

You are the one asking the question. You tell us.

Watching the video...

We have a hand-drawn airfoil (or cross-section of an airfoil) which is claimed to be symmetric.

The author lays out coordinate axes with x going left to right from leading edge to trailing edge on the horizontal and y vertically at right angles.

The origin appears to be at the midpoint on the leading edge. A chord is drawn clumsily -- visibly curved so that it arches toward the top surface. The author indicates that this is not intentional.

The author draws a vector indicating the flow direction of the free stream. The free stream is angled upward (the air foil has a positive angle of attack). But, as above, we are using coordinates anchored to the air foil so it is at least notionally the free stream that is angled upward and the airfoil that is horizontally aligned.

The author proceeds to parameterize the upper surface so that ##S_u## denotes the path length along the airfoil surface from the leading edge to a particular point on the top surface. Similarly, ##S_l## denotes the path length from the leading edge to a particular point on the bottom surface.

One assumes that this is setting up so that ##S_u## and ##S_l## will be the variables to integrate over.

The author proceeds to talk about pressure as a function of ##S_u## and about the angle between a normal to the surface and the vertical also expressed as a function of ##S_u##. So we have ##P(S_u)## and ##\theta(S_u)##.

The force element on an incremental surface element is now simple to state, though the author has not done so yet. Yes, he is definitely setting up for an integral.

[At this point we are 3:02 into the video]

The author goes on to define a shear force (or shear "distribution") which is tangent to the surface. This is obviously at angle ##\theta(S_u)## with respect to the horizontal. But you do not care about shear, so neither will I.

The author repeats, talking about a point on the lower surface with pressure and shear as functions of ##S_l## in the obvious manner. No surprises there. Just repetition to make sure it sinks in.

[This takes us to 4:29 in the video]

At this point is is blindingly obvious that we can integrate over the upper surface to get the vertical component of the pressure force and also [though perhaps less significantly] the vertical component of the shear force. Similarly, we can integrate over the lower surface to get the vertical component of the pressure force and of the shear force.

The [vector] sum will give us lift.

It is also blindingly obvious that we can do essentially the same integrations to get the net horizontal components and arrive at a vector sum for drag. Just need to swap sines for cosines and vice versa.

The required inputs to this process are a pressure field parameterized in terms of path length along the surfaces and a shear field parameterized the same way.

Without watching the rest of the video, it is not clear whether the author will attempt to derive either input from the flow field. [Skipping forward, it looks like he spends the rest of the video talking about the sines and the cosines and making sure the sign conventions are right]. He's just setting up the integrals in the obvious way.

 

[Arjan82]

Where is this function here?

Right here, in the very video you've quoted yourself! (video below starts exactly at the functions your are presumably referring to):

 

[Arjan82]

Or just post one complete example where lift and drag is calculated from given pressure distribution over airfoil section.

Now you are letting us do all the hard work while you can just sit back and relax while your answer is being generated. I'm not going to make a tutorial or chapter in a book for you only to find out that that wasn't actually really the question you had. The question I think you have is answered in the video, but if it is not, then please be more specific in what you are asking...

 

[Arjan82]

You are still not answering my question: please be more specific. 'The complete procedure' is not specific enough. If you want that, find a textbook on the matter. It is quite some work for us to find a good example and work you through the entire procedure step by step (There are entire chapters written on that). (You say you didn't mean me to calculate it, but crunching the actual numbers is 1% of the work, showing you what numbers to crunch is all the work).

Besides that, you pointed yourself to a video doing 95% of the work. The last 5% is just calculus. So make an effort yourself: come up with an airfoil shape (Some NACA profile could be a start). Then come up with a pressure distribution (Usually not easily computed analytically, but if you want to do do that, look at the Joukowsky airfoil, you can also compute it numerically using XFoil, otherwise, you can just assume something, but then it is hard to check if your answer is correct). And once you have these two, do the math. If you get stuck, come back here and show where *exactly* you get stuck.

 

[russ_watters]

Duplicate thread closed.