Coefficient of Lift

[Zipper730]

You need to use consistent units: in SI, newtons for force or weight, kg per cubic meter for density, square meters for area, meters per second for velocity.

Newton is 1kg*m/s^2?

In US Customary, pounds for force or weight, slugs per cubic foot for density, square feet for area, and feet per second for velocity.

And a slug is 1 lbf*s^2/ft?

So, you'd have Cl = L / A*0.5*r*V^2 and in metric you'd have for a wing-area of 35 m^2 or 376.737 ft^2, a speed of 50 m/s, or 164.042 fps, or 118.847 mph at sea-level you'd have in metric, either...
Cl = L / ((35 m^2)(0.5)(1.225 kg/m^3)(50 m/s)^2), or Cl = L / ((35 m^2)(0.5)(101,325 Pa)(50 m/s)^2).
I'm not sure which one is right, and for imperial you'd have
Cl = L / ((376.737 ft^2)(0.5)(0.0023769 slug/ft^3)(164.042 f/s)^2) correct?

 

[Zipper730]

Yes, I know math is not my strength

 

[swampyankee]

Newton is 1kg*m/s^2?
And a slug is 1 lbf*s^2/ft?

So, you'd have Cl = L / A*0.5*r*V^2 and in metric you'd have for a wing-area of 35 m^2 or 376.737 ft^2, a speed of 50 m/s, or 164.042 fps, or 118.847 mph at sea-level you'd have in metric, either...
Cl = L / ((35 m^2)(0.5)(1.225 kg/m^3)(50 m/s)^2), or Cl = L / ((35 m^2)(0.5)(101,325 Pa)(50 m/s)^2).
I'm not sure which one is right, and for imperial you'd have
Cl = L / ((376.737 ft^2)(0.5)(0.0023769 slug/ft^3)(164.042 f/s)^2) correct?

That looks right. Be nice if we could write math -- or at least superscripts* -- here.



* If there is a way, I've not found it, and I looked, but maybe hard enough.

 

[Zipper730]

That looks right. Be nice if we could write math -- or at least superscripts* -- here.

Agreed, many places have that feature

 

[Zipper730]

Since it's been a very long period of time since I've done math with multiplied units, I just ran it through the google calculator feature and based on the figures I put in earlier...
CL = L / ((35 m^2)(0.5)(1.225 kg/m^3)(50 m/s)^2)
I got...
CL = L / 53593.75 newtons...
...and I guess if CL was 2, then lift would be either 107187.5 newtons

If I'm wrong, be glad I'm not building a plane you might one day fly

 

[Ivan1GFP]

Hello Zipper730,
I think some of the more technical folks are getting a little too hung up on the exact calculations and units and I believe all you were really looking for was the concept of what Coefficient of Lift is about.

Here is how I see it: (Apologies in advance if I sound condescending.)
Moving Air has what is called a dynamic pressure (as opposed to static or ambient air pressure).
The faster the air moves, the higher the pressure.

The formula for calculating Dynamic Pressure is 1/2 * Rho * V^2
where Rho is air density and V is Velocity.
This dynamic pressure is typically abbreviated as "q".

A Wing has an area that we will call S. (I don't know why it is "S" but that is what folks use.)

When we take the Pressure which is in units of perhaps Pounds / Inch^2 (or Pounds per Square Foot)
and multiply it by the Area of the Wing which is in Feet^2,
we get a Force in Pounds.

The Coefficient of Lift is a Ratio of the Force of Lift that the Wing supplies as compared to this calculated Dynamic Force.

- Ivan.

 

[Zipper730]

I think some of the more technical folks are getting a little too hung up on the exact calculations and units and I believe all you were really looking for was the concept of what Coefficient of Lift is about.

Yes

The Coefficient of Lift is a Ratio of the Force of Lift that the Wing supplies as compared to this calculated Dynamic Force.

So a CL of 2 would mean twice the lift to dynamic pressure or force?

 

[Ivan1GFP]

So a CL of 2 would mean twice the lift to dynamic pressure or force?

If I understand you correctly then Yes.
A CL of 2.0 is not very typical from numbers I have seen.

As an example, I am working on a flight model for the P-39D/F Airacobra for an old simulator.
A simple observation of the Wing Root airfoil suggests that CL would be about 1.3 for a NACA 0015 section.
A NACA test report states that the maximum CL is about 1.4.
The Manual states that the stall speed clean (Flaps Up) is about 105 MPH (Useful to calculate Dynamic Pressure).
The Gross Wing Area (which includes the section inside the Fuselage) is 213 Square Feet.
At Stall Speed, the Wing is developing its Maximum CL which multiplied by Wing Area and Dynamic Pressure should equal the Weight of the Aircraft.
My estimate for the loaded weight for the P-39 series without external stores is around 7650 - 7700 pounds.

When all these numbers are plugged in to a spreadsheet I wrote to check, what I got was a CL of about 1.28.
Note that an exact speed is critical for this calculation to work. If I remember right, a reduction of stall speed to 102 MPH brings the CL up to 1.36.

Note that with Flaps down, Stall speed drops to around 95 MPH which works out to a CL of 1.56 which is +0.28 over the CL with Flaps Up which is fairly typical.

Note also that we are using Gross Wing Area. The actual Wing Area not including the area within the Fuselage is only about 175 feet^2 if I remember correctly. Then again, it is pretty hard for the Wing without its center section or fuselage to do any useful flying.

The Spreadsheet I wrote is pretty simple and if you want to play around with it, just send me your email address in a PM and I can send it to you. I can tell you if you like working in Metric, you won't like it.

- Ivan.

 

[fliger747]

Where are the Slugs when we need them... Yes HH Hurt, Aerodynamics for Naval Aviators is an excellent basic reference, though the Naval aviators may feel like the title suggest Aerodynamics for the complete idiot series. My favorite reference when I "forget stuff".

 

[Zipper730]

While we're at this, what's coefficient of drag? Let's start by keeping it simple before going into a whole bunch of math stuff

I Ivan1GFP 's explanation for coefficient of lift
"The Coefficient of Lift is a Ratio of the Force of Lift that the Wing supplies as compared to this calculated Dynamic Force."
Was a great explanation.

 

[PStickney]

Where are the Slugs when we need them... Yes HH Hurt, Aerodynamics for Naval Aviators is an excellent basic reference, though the Naval aviators may feel like the title suggest Aerodynamics for the complete idiot series. My favorite reference when I "forget stuff".

"Aerodynamics for Naval Aviators" was created to explain a rather technical subject to Aviation Cadets, who didn't necessarily (or often) have a deep technical background.
It's an excellent reference for "Why does this" questions.
Note that one of the alternate titles (From the Engineering Side) is "Aerodynamics for English Majors".
If you don't have a copy, I recommend that you find one.

 

[Ivan1GFP]

While we're at this, what's coefficient of drag? Let's start by keeping it simple before going into a whole bunch of math stuff

Hello Zipper730,
Thanks for the comment.
I can tell you in advance that Coefficient of Drag will get just a little more complicated but hopefully not too much worse.

Let's start off first with something other than aeroplanes, say perhaps a car.

At a particular speed, there is a certain amount of Drag due to Air Resistance.

The forward speed of the car creates a Dynamic Pressure. (Calculated by 1/2 * Air Density * Velocity^2)
For a car, the Reference Area would typically be something like the Frontal Area of the car. (Makes sense so far, right?)
The Coefficient of Drag is how the Drag compares to this Reference Area multiplied by the Dynamic Pressure.

Drag = Coefficient of Drag * Reference Area * Dynamic Pressure

.....Now let's switch to Aircraft.

With Aircraft, the typical Reference Area is usually the WING AREA which is usually represented by the letter S.

That is really all there is to it.
The idea of Coefficient of Drag (Cd0) sometimes doesn't tell the full story when comparing very different aircraft as we tend to do around here. What happens when we compare two aircraft with very different Wing Areas?

Let's go back to the general formula.
Drag = Coefficient of Drag * Reference Area * Dynamic Pressure

Drag is a force.
Dynamic Pressure * Area is a force.
The Coefficient of Drag is really a scaling factor so that we can use our Reference Area and get a correct equation.

How about we do this instead:
Drag = Equivalent Flat Plate Area * Dynamic Pressure

By using something called "Equivalent Flat Plate Area", we still get a correct equation and the amount of this Area is proportional to the actual Drag. Thus we can compare the Actual Drag between two objects and difference in Wing Area doesn't give misleading numbers.

The important thing to remember here is that Equivalent Flat Plate Area does not represent the drag of an actual flat plate of that size. An actual flat plate would have much higher drag; ITS Equivalent Flat Plate Area is normally about 1.3 times its actual area.

Hope that makes sense.
- Ivan.