Need Help on Lift Coefficient
 

I need some help, and the sooner the better. I am trying to determine the lift of some models I have, hand made, before I test them in a wind tunnel; however I do not know how to find thelift coefficient.Can anybody give me an equation to find the lift coefficient, without already knowing the lift produced. Also any equations that relate the angle of attack, camber (including camber position), and thickness to lift would be most helpful. Accepting any equation, even if they involve advanced math, all I ask is thatyou supply: a link where I might find it on the internet; the name of the non-internet source were you got it from; or if its a derived equation from a well know equation, an explanation on how it was derived (This is because I am doing and IBO *International Baccalaureate Organization* extended essay on analyzing the affect that angel of attack, camber, and thickness have on the lift and drag of an airfoil/airplane)



Many Thanks


P.S. This message also applies to drag, seeing that I am having the same trouble with the drag.

RE: Need Help on Lift Coefficient
 

Welcome to the RCU forums!

Here you have some links:

http://www.mh-aerotools.de/airfoils/index.htm

http://www.free-online-private-pilot...in_flight.html

http://www.grc.nasa.gov/WWW/K-12/freesoftware_page.htm

http://www.ae.illinois.edu/m-selig/ads.html

Your questions don't have simple answers.

The lift and its coeficient depends on how the air reacts to the surface that moves thought it.
That reaction depends on the density and viscosity of the air combined with the dimension of the chord (Reynolds number), geometry (type of airfoil), position (angle of attack) and velocity.
Related math is very complicated; hence, calculators and simulators have been developed just for that, which complement wind tunnel experimentation.

Best luck with your project!

RE: Need Help on Lift Coefficient
 

You would be better off studying your books and doing the work yourself rather than asking total strangers to do your homework. What does your teacher think of what you are doing?

RE: Need Help on Lift Coefficient
 

First off Villa, this is not homework, It is an I.B. extended essay.Secondly I am reading through different sources that I have, and the most I have found 1 source say so far is, c_l=f(α,M_∞,Re), which is say that lift coefficient equals a function of angle of attack, free-stream mach number, and Reynolds number; past that it does not tell me the equation. And on top of all of this, I am not asking anybody to do my homework, I am a just asking people to be fellow scientists andenthusiastic aerodynamicists, and pass on any information theymay have came across. That is also why I requested where the sources where found. I am just asking for some feedback on this that is all. And I am sorry that you might be offended by this, asking other fellow scientists and aerodynamicists for feedback, you did not have to post your comment. But next time you are taking on 5 A.P. classes and 2 honors classes,participating in a sport,and writing a 3500-4000 word essay to begraded on par or above a college level class by specialists inthe field (and conducting an experiment with that essay), all the rigor of a college assignments and instead of only 15-18 hours of class a week having 35 hours of class a week (meaning less time to do assignments) and you ask for help (if you ever were smart enough to be in those classes); I will make sure i post a good word for you when you ask for some help.


P.S. This is me using my civil tongue.

RE: Need Help on Lift Coefficient
 

Thank You LNEWQBAN,

However most of those links I have looked at, but you talked about the related math part very briefly. I know I need all of those components, Ican find all of those components, I just need some way to link all of them together to find the lift coefficient. I do not care how complicated the math is, if you know an equation please tell me, those programs online wont do me much good, what I really need is the equations that those programs are bassed off. Please, all I need is the equation for the lift coefficient and/or the equation for the drag coefficient (the equations to find both, with out thelift orthe drag).

Thank You for your time

RE: Need Help on Lift Coefficient
 

I think you are misinterpreting the "equation": CL or CD = f(a,M,Re). If I understand your question correctly, you are asking: can somebody give me the function f()?

CL or CD = f(a,M,Re) is actually an extremely powerful statement. It says that , for a given wing/aircraft geometry, of all the possible things that could affect its lift or drag coefficient, only 3 dimensionless parameters apply. If you could come up with a simple (or even complex) mathematical relation for the function f(), you could make a lot of money. The reality is that the only "robust" way to find the relation is through experimentation or extremely complex computational methods (that involve modeling the wing/aircraft shape and solving the fluid flow equations for each condition of interest). There are less robust techniques, but they provide results that are less precise and less generally applicable.

A very simple equation, that is remarkably accurate over a narrow angle of attack range is: CL = a_o(alpha - alpha_o). a_o is roughly equal to 2*pi for high aspect ratio configurations, and alpha_o is equal to zero for configurations with top/bottom symmetry.

RE: Need Help on Lift Coefficient
 

However I know for a fact that camber and thickness also affect the lift and drag in aerodynamics.That is the whole crux of my problem, I am trying to find a relation between A.O.A, camber, and thickness to lift and drag; and from what I understand they are related by C_l and C_d respectively. All am Ilooking for is some way to equate lift prior to doing testing, and this are hand-made wings, so unless anybody knows another way to find lift without the lift coefficient (keep in mind these are with subsonic speeds), I am looking for a way to find the coefficient of lift without doing the experiments. Another thing, Shoe, thats a good idea, however what you told me does not take into consideration the camber or thickness of the wings.

RE: Need Help on Lift Coefficient
 

Hi eronaay
I stand behind my suggestion and regret you chose the insult route. I studied Aeronautical Engineering in college but after 2 years switched to Mechanical Engineering because of the economy and available jobs, and graduated with a 3.5 average with a BSME. This was long before computers; the slide rule was the tool of the day.

RE: Need Help on Lift Coefficient
 

eronaay...the insult route was NOT the way to go. You're in High School. If you're having a hard time with that course load, put in your application at McDonald's and quit now. I graduated High School with a 3.8 unweighted, AP Scholar with Honors from the best Private School in the region (with the highest failure rate). My sports curriculum included qualifying for the Olympics in Hockey, International Basketball champions 2 of 3 years I played, semi-pro motocross (had the offer to go fully pro, but I had a bad wreck that scared me too badly to continue), and I still had time to kick back and play video games all senior year. Also, my sports were year-round....not 3-a-year. I got my second sponsor in MX, qualified for the International tournament in Basketball, and won the first round game of the hockey tournament in one day....the weekend before my finals started. I was also the best Delegate in the country for Model United Nations, the first year I did it. I also have friends that would put that to shame. Get off your high-horse, you're not that impressive.

Also, if you're going the insult way.....then that frees up my guilt to say this: if you're half as smart as you're trying to claim, you'd know that you can't calculate the lift coefficient numerically. Now, if you had experimental numbers giving you: lift force, density, wing area, and free-stream velocity then figuring it out would be a breeze. However, lift and drag coefficients for airfoils are NOT calculated....they are experimentally determined. In fact, I spent about 20 hours over two days in THE wind-tunnel that was used to experimentally determine that NACA values. Also, if you want a good approximation....you can plug in coordinates to X-Foil, but I'm not sure if you can understand it.

FWIW, I am a Sophomore Aerospace Engineer at Virginia Tech involved heavily with 3 airplane design teams. I run these numbers day in, day out, ad nauseum. Next time, I seriously suggest some humility.

RE: Need Help on Lift Coefficient
 

You are welcome.

Unfortunately, I don't know or ever read about the equations that you need for Cd and Cl.

My knowledge of Aerodynamics is very limited, but I know that the Euler and Navier-Stokes equations were used to develop the algorithm used in the computer program for one of the simulators that I have linked above:

http://www.grc.nasa.gov/WWW/K-12/airplane/nseqs.html

http://www.grc.nasa.gov/WWW/K-12/airplane/eulereqs.html

http://www.grc.nasa.gov/WWW/K-12/airplane/bernnew.html

Copied from those links:

“The amount of lift generated by an object depends on a number of factors, including the density of the air, the velocity between the object and the air, the viscosity and compressibility of the air, the surface area over which the air flows, the shape of the body, and the body's inclination to the flow, also called the angle of attack. In general, the dependence on body shape, inclination, air viscosity, and compressibility is very complex. One way to deal with complex dependencies is to characterize the dependence by a single variable.
For drag, this variable is called the drag coefficient, designated "Cd".
For lift, this variable is called the lift coefficient, designated "Cl". For given air conditions, shape, and inclination of the object, we have to determine a value for Cl to determine the lift. For some simple flow conditions and geometries, and low inclinations, aerodynamicists can now determine the value of Cl mathematically. But, in general, this parameter is determined experimentally using models in a wind tunnel. For thin airfoils, at small angles of attack, the lift coefficient is approximately two times pi (3.14159) times the angle of attack expressed in radians.”

“For given air conditions, shape, and inclination of the object, we have to determine a value for Cd to determine the drag. The drag coefficient is composed of two parts; a basic drag coefficient which includes the effects of skin friction and shape (form), and an additional drag coefficient related to the lift of the aircraft. The additional source of drag is called the induced drag and it is produced at the wing tips due to aircraft lift.
The induced drag coefficient is equal to the square of the lift coefficient (Cl) divided by the quantity: pi (3.14159) times the aspect ratio (Ar) times an efficiency factor (e). The aspect ratio is the square of the span divided by the wing area. Lifting line theory shows that the optimum (lowest) induced drag occurs for an elliptic distribution of lift from tip to tip.”

RE: Need Help on Lift Coefficient
 

I am apologize Villa, it was out of line for me to say what I did. I was just a little on edge at the time and it kind of pissed me off when you called it homework, it felt like you were belittling me, but seeing as you had a right to, I apologize. Victor, I can determine everything, such as free-stream velocity; density; and wing area, prior to conducting the experiment. All I was asking if there was a way to determine the lift coefficient without knowing the lift, or at least conducting the experiment. I was reading through one of my resources, and it talked about Lift=Weight (if it was at an angle, then it would be Lift=Weight *cosine angle); thus that is one way to determine lift. I do however have acouple question for you Victor; the source said that Drag=Thrust my question however is, because the book was very explicit; Ifan experiment was being conducted in a wind tunnel, could the free-stream velocity be considered the thrust? Second, how does the camber and thickness affect the lift (such as an equation)? Lastly, when did you ever have time to sleep with all that you did?

Some say humility is a virtue, but its very hard to have some humility. However, Iapologize, for my what I said, and looking back (actually even when Iwas writing it)I agree with Villa,the post sounds like a kid who doesn't want to do work; what I was looking for was some feed back and I realizedto have feed back I have to pose a situation or a question, instead of just asking people.

I'll take some humble pie if anyone's got some.

RE: Need Help on Lift Coefficient
 

Hum...the answer is NO. You have to be able to measure lift to determine CL. That is why wind tunnels have mass balances that measure lift. If you know lift (or weight) the equation is simple. L=CL*Q*S or CL=Q*S/L Now if you don't know lift you have one equation two unknowns ...can't be solved. This is why wind tunnels spend millions of $ on mass balances.

Now if you can get the "wing" to fly in a wind tunnel straight and level and just balance out (like a plane in flight) then L=W and you have only one unknown.

So the answer is "No"
Steve

RE: Need Help on Lift Coefficient
 

Well, once you get those variables PLUS the lift, then the equation is simple. Lift coefficient = (2*Lift)/(wingarea*density*freestreamvelocity) Metric units are: (Newtons, meters, kg, s), English units are: (slugs, ft, s, lb).


Short answer, no. That's why they do wind tunnel tests!

That is for banked flight. If you think about it, the vertical component of lift has to equal weight no matter what...and it's always that weight=lift*cos(bankangle). When bankangle=0, then cos0 = 1. The horizontal component of lift is force used for turning (centrifugal acceleration). Simple enough to process.



No. Drag=thrust for constant velocity, constant altitude, straight&level flight. ONLY then. That relation is mainly used to calculate the flight envelope. If you're given a thrust, then you can figure the drag polar using the same force....which would give you the induced portion of drag (given that you know the parasitic drag) and that would then solve your lift coefficient, lift, velocity, etc. However, free stream velocity is NOT a thrust. Thrust and drag are forces, velocity is not. If you measured the drag force on the system then yes you can, given that you know the parasitic drag. You can achieve that by measuring the drag when the lift force is 0. Then the Drag Poler = Thrust = cd0 (zero-lift drag coefficient) + k*cl^2 (where k = 1/(pi*e*AR) and cl is the lift coefficient). If you are doing an airfoil and not a wing, then k = 1.

Camber and thickness, for lowspeed subsonic airfoils, don't effect your equations...they only effect things physically. But generally, camber increases your Cl and thickness helps the airfoil stall later (both are to a point, of course). Camber increases the pressure difference between the top of your wing and the bottom, giving you lift. I'm really not that well versed on what thickness does (outside of a structural standpoint).


I slept quite well, actually. It's NOW that my sleep is getting limited. I'm actually working on Aircraft Performance homework right now, so most of the equations you want (and MANY equations you don't) are sitting in front of me right now :D.

RE: Need Help on Lift Coefficient
 

Couldn't it be said that in level flight the force of lift equals the force from the weight? Also, if lift and weight were the same throughout the whole flight wouldn't the plane not increase in altitude? (wrote second question fast, still doesn't seem complete to me)


Logically, can it be thought as if the plane had a thrust that enabled it to go at a speed that the free-stream wind would be comingtowards the plane at50 m/s (example), that there would be some relation to the thrust the plane is exhibiting?

RE: Need Help on Lift Coefficient
 

.
Increasing the power makes the plane go up.
The elevator controls the airspeed.
A plane trimmed at one airspeed will climb when the power is advanced.. descend when power is reduced.

.
Wind speed and airspeed... The plane flies -in- the wind at an airspeed. In calm conditions, it may require x amount of thrust to fly at y airspeed. The elevator will be at a particular angle for level flight.
In a wind equal to y airspeed, and x power, the plane will not move forward. Ground speed is zero, airspeed is y, wind speed is -y.
To move forward, the elevator trim is changed, or to move the plane back, while facing forward.
Gliders do this naturally.
The airspeed comes from the elevator trim angle.
On the slope, it is easy to place the plane in the wind so that the plane is not moving forward at all.
With power planes and strong winds, the same is possible.
And fun. :)

RE: Need Help on Lift Coefficient
 

Well put, Paul.

eronaay: Logically, can it be thought as if the plane had a thrust that enabled it to go at a speed that the free-stream wind would be coming towards the plane at 50 m/s (example), that there would be some relation to the thrust the plane is exhibiting?

No. It cannot. Speed and thrust are NOT in anyway related. Thrust is a force, not a velocity. Speed is a velocity, not a force. The units of thrust are (in metric) kg*m/s^2 (kilogram-meter per second squared) or Newtons. The units of speed are (in metric) meters per second. Thrust is a function of mass and acceleration. Also, you can be going backwards with TONS of forward thrust. You can also be going forward FAST with no thrust at all. They are NOT the same. They're not even close.

Also: Couldn't it be said that in level flight the force of lift equals the force from the weight?
Yes, it is. W=L*cos(bankangle). In level flight, bankangle=0 and cos(0) = 1. Therefore, W=L. It's just easier to say that W=L*cos(bankangle) because it's a perpetually true statement.

Tall Paul answered the second part of that question better than I could, thanks again Paul!

RE: Need Help on Lift Coefficient
 

If Thrust is needed to have drag, then where is the drag coming from when its a model in the wild tunnel? If this model is just suspended in the wind tunnel then what is producing the drag if there is no thrust from the model? Thus doesn't the "thrust" the model exhibts have to be due to the free-stream velocity (the wind coming in)? And I know that Thrust is a force, but I typed that at about 5:45 in the morning and i was still half asleep, so the fact that i was camparing two things with different units did not pop out at me. Yet, the air does still exert a force on the plane, so there must be some correlation between the force exerted on the plane via the free-stream velocity, and the force acting back against the free-stream velocity from the plane.

Also just to clarify, I will not be messing around with elevators and tail flaps as that would give to much variablity to the lift; I think accounting for change in A.O.A, camber, and thickness; is good enough for one paper.

RE: Need Help on Lift Coefficient
 

(quotes added by moderator for clarity)


You do NOT need thrust for drag. You need a force opposing drag for the model to be stationary. However, that number is NOT thrust. Thrust, in fact, should NOT be factored into any equations you're dealing with. The equations you're talking about should simply NOT involve thrust in any way. Thrust is really only used in more advanced performance equations.

In fact, why do you keep thinking you need thrust???

Oh, and the force exerted on the plane via the free-stream velocity and the force acting back against the free-stream from the plane is the same thing. It's the wing's specific drag polar. Find the cd0 for a wing, then add that to the induced drag. The induced drag is: (lift coefficient)/(pi*oswald efficiency <typically .8>*the Aspect Ratio). For an airfoil (infinitely long wing), there is not second term (induced drag). The parasitic drag is the cd0 term, and is the drag coefficient when the wing is producing zero lift. If you find the drag when there is no lift, then use: Drag = cd*.5*density*v^2*S to find the cd value, and then that's cd0. cdi is the induced drag and it follows k*cl^2 (k = 1/(pi*e*AR)).

Until you actually need something that requires thrust, IGNORE IT.

RE: Need Help on Lift Coefficient
 

Thanks, I wasn't going to really worry about it, until Icame across some places that said the opposing forces on an airplane, where lift and weight, and thrust and drag. Then one of my sources said talked about thrust, and also said that the maximum lift versus drag ratio (i.e. best efficiency) would result in the minimum thrust required.

RE: Need Help on Lift Coefficient
 

Your friend is quite right. But you confusing a powered aircraft in flight, and trying to calculate the lift and drag coefficients of an airfoil in a wind tunnel. One of these things is the end result of quite a bit of engineering, the other is practical measurements of an experimental shape. Yes, you need to know the Cl and Cd of the shape in order to provide part of the design answer for the other, but realise that the wind tunnel experiment will not give you absolute answers, and the answers you get might be quite different from what is found in full size. If you are concentrating on model sized foils, then you will find that nearly all of them will have a Cl of 1. In other words, the actual shape makes very little difference to the amount of lift generated. It has all been done before and a little search on the web will supply all the answers you need, without you having to do all the experiments again. As for drag, that is one of the results of lift, you can't have one without the other. To which you also have to add the drag of the shape the foil is attached to, and realise that it is all changing as the speed and direction of the shape compared to the airflow changes. But the variety of opinions about what is actually happening...!
Evan, WB #12.

RE: Need Help on Lift Coefficient
 

I hate thissystem, I had a good point to make, and then when I pushed okay a message came up saying that my session ended or something.

Whatever the main points where that I am making the models by hand, and that this was an IBO extended essay paper so i had to do the experiments. And that Drag is just a name given to the force component in the opposite direction of the forward force in the planes flight direction; as well as, that Drag is inversely related to lift (if drag was a result of lift, the L/D ratio would never change).

RE: Need Help on Lift Coefficient
 

Drag is partially a result of lift (induced drag)...but it's based off the square of the lift coefficiemt. As Cl increases, Cd increases exponentially. If drag weren't tied to lift somehow, L/D wouldn't ever change. The other part of Drag is the profile drag (parasitic drag). This is a "constant" for the wing/airfoil and can be found by setting the wing at a zero-lift setting and finding the DRAG at that point. Then, you can use a simple equation to find cd0.

RE: Need Help on Lift Coefficient
 

The lift, drag and pitching moment measured on a airfoil in wind tunnel are found because the test item is attached to a balance which reads the reaction of the test item to the incoming wind.
In theory, a plane can be flown in a wind tunnel, as gliders do outside, by the usual flight control positioning.
Any mistakes though result in the model going "down the tunnel".
Many tunnels have scars from when models do this. :)
Such flights usually include tethers to the model to reduce the damage when things go wrong.
But measuring any of the forces on the model isn't practical unless the model is restrained by the attachment to the balance.

RE: Need Help on Lift Coefficient
 

Some additional math and practical vs. theorical Cd values here:

http://books.google.ca/books?id=1iPE...rfoils&f=false

RE: Need Help on Lift Coefficient
 

It is interesting to note..:
If you put a powered plane into a windtunnel with "no power" you won't get the correct drag. Why would that be? Well, the flow around the aircraft changes with power! Then you put power on the model..(but what is the power?). Well you can measure the power of the engine (on a dyno)...and you can possibly calculate the efficiency of a prop...(or measure it in the wind tunnel)....so you can measure the thrust...but it is uninstalled. With blocking of the cowl and inaccuracies in your engine model you end up getting a different thrust than what you think...so what do you do? Well, you get the model the best you can...and you measure the (T-D) or excess thrust and find out where the forces balance out and all is good untill the airplane doesn't go fast enough or have a high enough rate of climb....then what happens is the airframe company says that the engine is not producing power....and the engine company says the darn plane is draggy....and all heck breaks loose...lol. Then the airframer cleans up the plane aerodynamically and asks for some more power...and the engine company says we will give you more power for some more $. The person who buys the plane pays more and everyone is happy...:D

Steve