Lift and Drag Coefficients

[noodle]

Okay, please excuse me if this is a dumb question, but here goes:

I would like to know how the lift and drag coefficients relate to actual lift and drag values. For instance, if a certain airfoil has a lift coefficient of 1 and a drag coefficient of .015 at a 5 degree angle of attack, how can I figure out the actual amounts of lift and drag produced by a 48" wing with an AR of 6 traveling at 60 mph with that airfoil?

Oh, on a side note, I downloaded Profili V2 light off the website, and whenever I try to open it on my computer I get a message that says "Could not initialize installation(CRC)" Anyone else had this happen?

Thanks,

noodle

[Ollie]

Cl = L / (A * .5 * r * V^2)
L = Cl * Area * .5 * air density * Velocity^2

Cdo = Do / (A * .5 * r * V^2)
Cdi = (Cl^2)/(3.14 * Aspect ratio * efficiency factor)
Cd = Cdo + Cdi
D = Cd * Area * .5 * air density * Velocity^2
Assume efficiency factor as one.

Depends on units like:
velocity (feet per second)
area (square foot)
density (pounds per cubic foot)

[noodle]

Wow, thanks a bunch. That's very useful info.

noodle

[noodle]

I just noticed that you didn't say what units lift and drag are measured in. I assume it's pounds, but I'm not sure.

noodle

[Ollie]

Force (Pounds)

[space_case]

You gotta watch the units. Density will never be measured in lbs/ft^3 because by definition it is mass/length^3. There is often confusion between lbm, lbf, and slugs:

1 lbf = 1 lbm 32.2 ft /sec^2 = (1/32.2)slugs (32.2 ft/sec^2)

I would highly recommend working in the metric system and going from Newtons -> pounds at the end if need be.

Also you have an airfoil section lift coefficient and Cl mentioned by Ollie above is a three dimensional coefficient (usually noted as CL), which may or may not be too different. There are ways to estimate this but it usually calls for a 'span efficiency factor' which is a function of the geometry of the wing.

If you get stuck, let me know and I may be able to produce some numbers for you, but YMMV...

[Ollie]

space_case,
Thanks, for correcting me on density units.

For a standard air density at sea level altitude, you can use 841 density (slugs per square foot).

The 'span efficiency factor' is a range from 1.0 to zero depending on the aspect ratio, taper ratio, twist, and sweep back. In case, the Cl is 0.15 and the aspect ratio is 6. The induced drag coefficient is (0.0225)/(3.14 * 6 * e). Assuming an efficient lift distrubiton for the wing design the 'span efficiency factor' is very close to one. The induced drag coefficient in this case is 0.0012 compared to a much larger profile drag coefficient (Cdo). With an airfoil angle of attack at 5 degrees and a Cl at 0.15 it means the airfoil has camber about 2 to 4% . This implies a large Cdo.

[funfly2]

You gotta watch the units. Density will never be measured in lbs/ft^3 because by definition it is mass/length^3. There is often confusion between lbm, lbf, and slugs:

1 lbf = 1 lbm 32.2 ft /sec^2 = (1/32.2)slugs (32.2 ft/sec^2)

I would highly recommend working in the metric system and going from Newtons -> pounds at the end if need be.

...Hi,
Could you please show the formula for lift using the metric system?
And what Cdo, Do and Cdi stand for?
Thanks.

[Ollie]

Cdo and Cdi have no units. Drag has Newton force.

See MKS units:
http://scienceworld.wolfram.com/physics/MKS.html

Physics is fun, in the rest of the whole world, except the USA.

[space_case]

Here is one estimation equation I placed in a recent document regarding a new UAV. I have the reference at work, so I don't remember the assumtions - I think an unswept wing may be one. Anyways here it is with your aspect ration in there,

>> AR=6

>> e = 1.78*(1.0 - 0.045*AR^.68) - 0.64

e = 0.8691

Here is a way to convert your 2D lift coefficient to 3D,

Cl = 1

>> CL=Cl/(1+1/(pi*AR*e))

CL = 0.9425


or you could use thin airfoil theory (http://www.aerospaceweb.org/question/aerodynamics/q0136.shtml) or lifting line theory (http://www.aerospaceweb.org/question/aerodynamics/q0184.shtml) assuming you have certain additional info about your airfoil. good luck.

Full blown CFD and flight test / wind tunnel data are really the way to go but we can't all do that. Some of this stuff can get pretty close, but it depends on the aircraft.

[space_case]

Hi,
Could you please show the formula for lift using the metric system?
And what Cdo, Do and Cdi stand for?
Thanks.

Same formulas - google 'sea level density' or 'atmosphere density' if you are high.

You'll get something for kg/m^3 - use Ollie's website for general info on units - V = xx m/s S = yy m^2 - etc..

[funfly2]

Thanks for your attempts but I don't think I've got it yet...

For example, I assume that:
Cl = lift coefficient
L = lift
Cd = drag coefficient
D = drag

but:
Do = ?
Cdo = drag coefficient?
Cdi = drag coefficient?

[space_case]

Thanks for your attempts but I don't think I've got it yet...

For example, I assume that:
Cl = lift coefficient
L = lift
Cd = drag coefficient
D = drag

but:
Do = not sure about this notation - it would seem to indicate minum drag force, but you really need Cdo - see below
Cdo = drag coefficient? minimum drag - see a polar plot to get this - plot Cl vs Cd to get this plot
Cdi = drag coefficient? induced drag - drag due to lift -> Cdi=f(Cl) you can't get more lift without incurring more drag

[funfly2]

space_case,
It seems much clear to me now, thanks a lot for your patience. :)

[Ollie]

"but:
Do = ?
Cdo = drag coefficient?
Cdi = drag coefficient?"

Do is the drag force due to the airfoil.
Cdo is the drag coefficient due to the airfoil 2D flow. The two dimensional flow without spanwise flow.
Cdi is the induced drag coefficient due to 3D flow around the wing. It is mainly due to vortex flow near the tip.

[funfly2]

Thanks a lot Ollie, I've got it now. :)

[space_case]

There are a dozen different ways to represent these values. This NASA site (http://www.grc.nasa.gov/WWW/K-12/airplane/dragco.html) says:

------------------------------------------------------------------------
The total drag coefficient Cd is equal to the drag coefficient at zero lift Cdo plus the induced drag coefficient Cdi.

Cd = Cdo + Cdi
------------------------------------------------------------------------

And actually I was reading Cdo to be Cdmin in the following:

Cdi = (Cl^2)/(3.14 * Aspect ratio * efficiency factor)
Cd = Cdo + Cdi

which really would be :

Cd = Cdmin + (Cl - Cl@Cdmin)^2/(3.14 * Aspect ratio * efficiency factor)

It depends on what Cd(!) you have. Is it Cdo as the above site sees it? Is it Cdo as Ollie views it? Or is it actually Cdmin as I first perceived it?

Where are you guys getting these numbers? Websites? Xfoil? Your brother's mother's best friend's cousin? Once we know what you have available to you, then we can help you calculate the end product.

[noodle]

Lots of great information, guys. I can only understand part of it :rolleyes: but I'm learning. :)

Any thoughts on the Profili question? Or should I start a different thread for that?

noodle

[space_case]

Any thoughts on the Profili question? Or should I start a different thread for that?

Instead, try using xfoil (http://raphael.mit.edu/xfoil/) and/or AVL (http://raphael.mit.edu/avl/)

[Ollie]

See the analysis by a discrete vortex Weissinger computation:
http://aero.stanford.edu/WingCalc.html

[noodle]

Alright, I'll give those a try. :)

[YOGEVKAT]

Hello

My name is yogev a student from Israel

And I have a question about the calculating of the drag force.

For example I need to calculate the drag fore on a 60 degrees area that is against the air flow.

So the lift force in this case is zero? it mean that I have only need to know the cdo coefficient at zero lift?

How can I know it?

Tank you !