Posted: Mon Feb 16, 2009 2:05 pm Post subject: Lift Formula Debate
It was a bit of a tease, but only because its so widespread.
The formula L = CL 1/2 rho V squared S is a two dimensional formula to start with, it doesnt make any account for how the air behaves at the edges of the airfoil. For now I will call it the aeroplane lift formula.
The rotor blades of a heliopter are wings that spin about an axis and in simple terms the nearer the axis the slower the blade is going in linear terms the V squared term is not rotational velocity but linear so we need to split the blade down into tiny slices or elements and at this level pretty much the formula does apply.
The CL is dependant upon angle of attack even if you assume the inflow (downwash) velocity to be the same across the whole disc in the hover the inflow angle is changing along the blade. From negative (Relative airflow from above) in the center to shallow positive near the tips. Angle of attack being pitch angle + inflow angle - any washout along the blades at the radius we are looking at.
The CL is also dependant upon reynolds no which means (with out all the complicated crap) that as you go slower (near the centre) the CLs will different for the same angle of attack if you were going faster with the same blade chord..
if you try to apply the formula to a blade where do you chose V squared or CL (most people choose the tips) but the actual AOA and V squared is different from everywhere else on the blade.
The way to calculate the forces involved is to work out the force for a tiny element of the blade and the one next to it and so on and add them all up a process most of use were introduced to in high school called integration at which point most of us gave it a damn good ignoring.
The reason the aeroplane wing formula seems to work is that once we chose arbitrary figures for CL and V Squared the addition or reduction of speeds seems to work, up makes the result go up and down makes the result go down.
On the retreating side if we move into forward flight the aeroplane lift formula doesn't hold at all, how do we deal with the region of reverse airflow, part of the airfoil is going backwards and drag near the centre of the disk is huge compared to the same place on the advancing side.
Once again picking a number and reducing V squared seems to work as it reduces the lift force and fits the aeroplane explanation.
Some of this is perhaps too much for PPL teaching but I think it should be understood by instructors, once again it helps with the explanation of flapback, inflow roll, aerodynamic precession (my term) (don't get me started on gyroscopes, we'll leave that for another day).
Joined: Mar 29, 2006 Posts: 289 Location: Scotland
Posted: Mon Feb 16, 2009 2:35 pm Post subject:
Nice post. I absolutely agree with you on the whole there.
However, most of us are mere mortals, I know i am, and not aviation Gods with a degee in aerodynamics. Therefore until we get an easy to use model that encompasses all the effects on a blade during its cycle, then i'm afraid we are stuck with the simplified versions.
I realise I have used the abovementioned formula in one of my discussions, and in simplified terms, it works well to illustrate my point, that is not to say it would stand up to a more indepth look. Hence why I agree it is a very controversial view.
But then I do love a good group discussion, and if we all take the easy group consensus, then we never have to think for ourselves and these idaes never see the light of day.
Loving to hear someone giving the whole gyroscopic precession in rotor systems a hard time, hallelujah. (at least I think thats where you're going). _________________ Generally wrapped in rubber, be it in the air or on the water.
Its set up to simulate an R22 blade element in the top dagram and then the blade as a whole in the bottom ones.
Its geometrically accurate, uses Lift and Drag coefficients from NASA for the 0012, 0015 and 0018 aerofoils and needs all kinds of things added to make it more user friendly but if you persever with it, it serves a purpose.
It needs scales and some explanation for each dagram which I will get around to.
For the moment it assumes an Inflow Velocity the same as in the hover for all speeds which is wrong but better than nothing.
The primary reason I put it together is that from diagrams that drawn in flying schools that i've seen they never get drawn to scale so no one would ever know if they were right or not , and its easy to make what we are told fit what we teach if we know no better.
It is still under development but I will be using it illustrate the point for some of my ramblings soon.
The way it has been written it doesn't steam the pictures yet so it may get confused if more than one person uses it at once, diagrams are saved with the same name for each user so you may get someone elses
Last edited by veeany on Mon Feb 16, 2009 3:07 pm; edited 1 time in total
Because of the compressed scale its hard to see but the spike is at about 15/16 degrees the traditional place we expect to see the CL start to decrease and we determine stall to begin, there end the traditional teaching and if you plot the curve from -180 to 0 to + 180 degrees aoa thats what it looks like, start increasing again after the steep fall at 15/16 degrees.
I'll add a link to the expanded version of the curves with a table fo the CL vs AOA for each of CL and CD, all the data is there so its not overly difficult to do.
Thats for a rotating wing in still air, it has to be, in which case the blade isn't retreating or advancing it's just spinning about a root axis.
if you add a relative airflow from a fixed single direction the results would change as, in my simple and uneducated description, the advancing blade would be travelling fast and the retreating blade would be travelling slow.
Fast = more drag Slow = less drag
or iz i jus fik???
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