Lift Coefficient

[marfish]

Started flying models 40 yrs. ago (now I feel old) and last fall, after a 15 yr. hiatus started up again. This time around I'm trying to learn more about the physics of flight.
Can someone give me a "rule-of-thumb" guide to calculate at what lift coefficient a model flies when:
1. Straight and level?
2. During a relatively serious turn?
3. During a full-blown, high-speed, high-alpha turn that's just above a stall?
I know that alot depends on the wing loading and airspeed. Maybe a better question would be: HOW DO I DERIVE THE C/L FOR ANY OF MY PLANES?
I know that different airfoils will yield different capabilities, but I'm also looking for generalities. Like: Do symmetrical foils fly at different C/L than semi's and other non-symmetricals?
Can I find a C/L I like and build a wing based on the polars, or what other conditions do I need factored in?

See? Just a couple simple questions. :p
Marlan

[BMatthews]

It's not what the model is doing but more about the speed it's doing it at.

For straight and level if it's just hovering near the stall the Cl will be very high. But if it's scooting along at high speed then the Cl will be low, often VERY low.

For G loads in a turn the Cl goes up depending on the G load and the amount of lift needed. It's quite possible for the model to be flying at it's max speed but turn so tight that the Cl is very high and if it's high enough the model will stall despite the high speed. We call this snapping out of a tight turn.

The max Cl reached just before a stall will depend on the airfoil charactaristics. A thin symetrical airfoils will stall earlier than a high cambered style of airfoil.

Up to the stall the airfoils will all generate the same lift for the same lift coefficient. However they will generate the induced drag based on the polars. So for example a pylon racer wants an airfoil that has a wide Cl range but where the low drag "bucket" or area of most vertical shape reaches down to a Cl=0 and extends as high as it can. This let's it do the straights on the course with minimal drag at the very low Cl's but in the turns generate the least drag it can get away with at hopefully a higher Cl than the opposition. Or the SAME Cl but less drag. Either means less speed bleed in the turns and lower lap times.

Do a search on google for Foilsim. If you set it up for a wing size of the model you want to make and tailor the airfoil to suit the rough parameters that you want to use you can alter the angle of attack and flying speed to simulate your actual model. The readout is switchable between lift and Cl. So set it to a speed and angle that provides the expected model weight as lift then switch to Cl to see the value. Figure out how many G's you'll pull in a tight turn and up the lift with the angle of attack to simulate the lift needed in the high G turn. Then see the Cl. Play with the airfoil camber and see how it all changes.

But all this doesn't show you the drag created by the camber. For that you still need your polar charts.

[Sparky Paul]

The variables in the equation for Cl are Lift (weight)... Airspeed and wing area.
Planes with the same weight and wing area at the same speed will have the same Cl. The angle of attack that delivers that Cl is likely to be different.
There's no one "good Cl".. these depend on the purpose of the plane, and where it is in the flight envelope.
For super efficiency designers look for a Cl that is optimum for a specific flight condition, and accept any variations from optimum off the specific condition, while keeping any changes as smooth as possible off the optimum point.
Thermal duration gliders will look for a lower Cl than a 3D aerobat, which will most often ignore Cl altogether, and just cram on power to get performance.
What you can see when flying is alpha, the angle of attack. That's more under your direct control than Cl.

[marfish]

Thanks guys: Awesome.
That is very good info indeed.
Actually I've been "sandbagging" in that I have the full version of PROFILI. I've been having fun calculating some polars for various conditions, speeds, and RE's. What I don't have a firm grip on is where I should expect to find any model, real or theoretical in the curve from C/L=0 through C/L =1. Neutral lift is a given, but after that, am I needing to know the speed and cord(RE)? As an example, my F3F Nyx flying level at 10 lbs. and 40 mph is...... where in the lift and "drag bucket"? No camber on the airfoil (HN785TC).
In other words:
1. what do the vertical numbers on the Polar graph (C/L) equate to? G-force? I think NOT.
2. what do the horizontal values mean for C/D? Percentages?

Lotsa lift,
Marlan

[Ollie]

What you need besides Profile is PC-Soar (it's free):
http://my.athenet.net/~atkron95/pcsoar.htm

[Batmanwpg]

http://www.flyingsites.co.uk/downloads/index.htm
http://www.amadistrictii.org/cjrcc/wing2/wing.html

[marfish]

Thanks all, for the help.
Lotsa lift,
Marlan

[yoyoML]

Nonono... CL is mostly not a function of lift, nor G load, nor airspeed, nor wing area....

CL is a function of angle of attack (alpha), and is a function of aspect ratio, wing sweep, wing profile. Basically it's a function of alpha plus all the parameters describing the wing shape, excluding wing area.

You can see this from how we "use" CL:

Lift = CL(alpha) * (wing area) * 0.5 * (air density) * (airspeed)^2

And then,

Lift = Mass * G load (like in F=ma)

For a basic CL versus alpha graph, the vertical axis is CL without unit (pure number) and the horizontal axis is alpha in degrees (physically, angle has no unit, either).

Now plot a straight line between two points (-20 degree, -2.2) and (20 degree, 2.2). *This is the CL curve for an infinitely long, symmetric, straight wing! This is the region of alpha where the wing is not stalled. Beyond the stall (alpha>20 or alpha<-20) the curve goes toward 0 quite erratically.

For finite length wings (finite aspect ratio), the slope is lowered (the curve is flatter) and CL reaches almost the same max value (2.2) but with somewhat larger alpha.

For assymetric wing profiles, the whole plot is to be shifted to the left so that CL intersects the horizontal axis at a negative alpha, instead of 0 degree. Now the CL is positive at alpha=0.

Remember, CL is a function only of alpha and wing shape.

[Andrew McGregor]

Right, so what you really want to do is calculate from the airspeed and known weight of the model what CL it had to be flying at:

CL(alpha) = 2*weight*load/(area*density*(airspeed^2))

Which if you know the polar also lets you know what alpha was.

[Sparky Paul]

Nonono... CL is mostly not a function of lift, nor G load, nor airspeed, nor wing area....
....

Remember, CL is a function only of alpha and wing shape.
.
The computation for Cl has to note the airspeed, the weight, and the wing area.
Then, polars are examined to find the wing profile that will give the Cl needed for the condition.
First you find the Cl, then you look for alpha.

[marfish]

LoL. Great sites Ollie and Batman.. Haven't had time to look closely at them. I will look closer because I'm wanting to compare foils for a 60" sloper/racer and am wondering what the C/L at level flight, high speed, would compare to the high/alpha turn at the pylons.
How do I determine the proper A/R, considering C/L and such?
More later,
Marlan

[Andrew McGregor]

Well, look at it this way: in a pylon turn, you want maximum G possible, right? But you want to maintain a margin away from the stall, because acclerated stalls are bad. So you're going to be flying at about 80% of CLMax. Now look at your wing area and work out the actual lift. Now you know how many G you're pulling (by dividing by the weight). Now level flight at that same speed will be 1G, so divide 80% of CLMax by the loading in the turn, that's CL for level flight at turn speed. Then you can adjust for airspeed changes using the formulae above.

[yoyoML]

There's an easy way to prevent accelerated stalls, and stay safe below critical alpha.

Simple version:
Note the elevator stick position (%) that stalls the plane. At any speed is fine. Then limit elevator throw to that % either by linkages or by transmitter. You won't ever stall again.

Long version:
The main wing's alpha is simply proportional to the stab incidence angle (incidence from nuetral, where 0 G is pulled). *Note that airspeed does not affect main wing alpha, nor does mass or G load, only stab incidence does. The proportionality constant is:

alpha/incidence = A2(cg-x2) / (A1(cg-x1)+A2(cg-x2)),

where A1 is main wing area and A2 is horizontal stab area; x1 is main wing's 25% MAC position and x2 is horizontal stab's 25% MAC position; cg is cg position.

The trick here, is to 1) limit max stab incidence, or 2) increase stab area/ decrease main wing area, or 3) move cg forward, so that even max elevator deflection does not bring the main wing beyond critical alpha. Then you can safely pull full elevator without stalling no matter the speed, attitude, no matter what.

For a full flying stab the incidence is just the elevator deflection. For a conventional stab/elevator combo, the stab leading edge plus the elavator trailing edge makes an angle to the fuselage, which is approximately the incidence.

[Andrew McGregor]

Yup, that works. So that gives you a possibility of using more than 80% in my calculation before.

[Ollie]

The airfoil polars are for two dimensions of air flow. A real wing has three dimensions of air flow. So you must account for induced angle of attack, induced drag, aspect ratio, sweep, twist (washout), etc.

For model sizes and speed (reynolds number) the airfoil dimensions have along with them the boundary layer. The flow around the airfoil changes along the chord from liminar to separation bubble to turbulent.

Most simiple formulas assume a straight line between negeative stall to positive stall for Cl vs alpha. Some airfoil measurements show the Cl vs. alpha polar is kinked in the straight line because of the separation bubble moves and its size changes with alpha and Cl.

My advise is to read "Model Aircraft Aerodynamics" by Martin Simons. Its worth your time.

[yoyoML]

The airfoil polars are for two dimensions of air flow. A real wing has three dimensions of air flow. So you must account for induced angle of attack, induced drag, aspect ratio, sweep, twist (washout), etc.

For model sizes and speed (reynolds number) the airfoil dimensions have along with them the boundary layer. The flow around the airfoil changes along the chord from liminar to separation bubble to turbulent.

Most simiple formulas assume a straight line between negeative stall to positive stall for Cl vs alpha. Some airfoil measurements show the Cl vs. alpha polar is kinked in the straight line because of the separation bubble moves and its size changes with alpha and Cl.

My advise is to read "Model Aircraft Aerodynamics" by Martin Simons. Its worth your time.

Indeed, indeed. The straight line CL curve is very crude, but still very useful especially for symmetric airfoils. Induced AoA can be very apparent at times, and aspect ratios aren't always high enough to justify using 2d flow.

Anyway, I think it'd be better if you supplied some practical methods to account for the factors, which we "must" account for.