Are lift and Drag proportional?

[MAraujo]

So, Im new to aerodynamics which makes this a beginner's question. To make things simple lets assume a given airframe flying level with constant thrust. The way I understand flight is that there are four major force vectors: thrust, drag, lift, and gravity. In order to make the airframe accelerate, the drag vector must be less than the thrust vector. To maintain altitude the lift vector must be equal (or close) to that of the force of gravity. As the airframe increases its speed, both the lift and drag vectors grow in magnitude. At some point the drag will equal thrust (which stayed constant) and no more forward acceleration (or lift) is possible. Now thats the setup. Here are the questions:

Do lift and drag grow at the same rate with respect to air speed?

If we hold a constant speed, does the proportionality change when we raise/lower air pressure?

For simplicity Im trying to make this the most ideal model, so most other factors i.e. fuel weight, atmospheric gradients, gravity gradients, should drop out.

 

[Urwumpe]

No. But they are closely related. Lift for example creates lift-induced drag. Also, in real aerodynamics, you can have effects of supersonic air flow, in which drag increases much stronger than lift and finally settles at a lower lift factor and a slightly higher drag factor for higher Mach numbers.

 

[MAraujo]

could you imagine a situation where lift grows faster than drag?

 

[Kozak]

Are lift and Drag proportional?

No. There's such a thing called "aerodynamic polar line". Here's an example for a small plane:

Cy is lift coefficient, C = Cx - drag coefficient.

At 4deg AOA here you have maximum aerodynamic efficiency, at 16deg. (?) - maximum lift.

Any real aircraft design begins with creating such diagram, either by manual computations, either by using CFD software.

 

[mjl1966]

:hmm:

could you imagine a situation where lift grows faster than drag?

Friction generating more force via lift to overcome its own effects. Yep, another entropy "you can't go there" deal. 3rd law of thermodynamics is a real sweetheart, you just can't get away from her.

Besides, it would be pretty scary riding in a 737 that takes off and rotates to 88 degrees. :hmm:

 

[MAraujo]

Thankyou all very much for the insight!

I am however still looking for an answer regaurding air pressure. Is an airframe optimized for a given air pressure? or conversly, would a different air pressure merely require an adjustment in speed to maintain level flight? To put it more clearly, an airframe at a given altitude has a certain ratio between lift and drag. At a higher altitude (lower pressure) would one only need to increase speed to make up for the difference in lift, and would drag still increase with the same ratio to lift as it did at the lower altitude?

Again, this is an ideal model, ignoring how altitude affects thrust.

 

[Urwumpe]

You have many factors in the optimization of the airframe, not only just one. Depending on which is more important, you can have Mach number, Reynolds number, maximum L/D at a speed or even just being so ugly that it gets repelled by Earth.

 

[Linguofreak]

could you imagine a situation where lift grows faster than drag?

Well, you have two types of drag: Induced drag and parasite drag. Induced drag is highest at high angles of attack, and lowest at low angles of attack. Parasite drag increases with airspeed. Lift increases with angle of attack up to the point where the aircraft stalls. So at low airspeeds lift is high and drag is high. As airspeed increases, drag drops off and lift gets higher. Then, past a certain point, drag starts getting higher again.

 

[Kozak]

Is an airframe optimized for a given air pressure? or conversly, would a different air pressure merely require an adjustment in speed to maintain level flight?<...>

Cx and Cy (and their ratio correspondingly) don't directly depend on pressure, they depend on Mach number, that's why it's widely used. You need to derive explicit functions Cx = f(AoA, Mach) and Cy = g(AoA, Mach) - they will show you everything, without it you'll not get anything but forum experts talk.

A general advice: don't mix flies and beefsteaks. First make everything clear with aerodynamics, then think of flight strategy.

 

[Juanelm]

Do lift and drag grow at the same rate with respect to air speed?

Someone correct me if I'm wrong, but the answer depends on if you are assuming straight and level flight (therefore the AoA will lower as speed increases in order to maintain a constant lift and constant altitude;straight and level flight), or if you are assuming a constant AoA (and therefore the aircraft starts to climb as you get more airspeed; no straight and level flight).

If you are assuming the first case, then the answer is no, they do not grow at the same rate, and what happens is what DarkWanderer pointed out. If, however, you are assuming the second case, then, in theory, they both grow at the same rate (proportional to square of velocity).

I am however still looking for an answer regaurding air pressure. Is an airframe optimized for a given air pressure? or conversly, would a different air pressure merely require an adjustment in speed to maintain level flight? To put it more clearly, an airframe at a given altitude has a certain ratio between lift and drag. At a higher altitude (lower pressure) would one only need to increase speed to make up for the difference in lift, and would drag still increase with the same ratio to lift as it did at the lower altitude?

I believe thats right; at higher altitude you just need a faster airspeed. The drag polar (which describes the relation between coefficients of lift and drag at different AoA) depends only on the geometry of the aircraft and on reynolds number. A higher altitude would mean a lower density and therefore a lower reynolds, but you would just need to raise the speed to attain the same reynolds as before and therefore the same drag polar and the same Cl/Cd relation.

 

[MAraujo]

Thanks Juanelm, you put it beautifully. I appreciate all the input from everyone, Im new to orbiter forums but have been playing for years, its awsome to see such a community of people surrounding this seemingly obscure but brilliant software.

 

[ex-orbinaut]

Ummm. In straight and level, unloaded flight, lift is equal to weight, no matter what the speed is. It has to be, that's its purpose. And that´s why you have to vary the AoA to adjust the Cl. I take it we ARE allowing the AoA to alter in the hypothetical question, yes?

In a level turn, however, load factor comes into it. It is equivalent to 1 / cos of bank angle. Stall speed goes up by the square root of the load factor.

Now, drag, is different. It has all what you in the know of it above have been saying. Rule of thumb, parasite drag goes up by approximately the square of the velocity; remember the formula (D=1/2 x V^2 x Rho x Frnt Area x Cd). Twice the speed, 4X the P drag.

This is not counting, of course, induced drag. An approximation can be obtained by calculating the sin of the AoA x Lift, but it is actually a little more, as it's considered origin is at the center of pressure, perpendicular to local airflow, and the local airflow there is already (slightly) on the way down the upper camber, and not paralel to the general relative wind. Induced drag decreases, as velocity is increased (Ie; AoA decreased), assuming unloaded flight conditions.

Basics here, only, people. Or I will end up rewriting here in english the manual I have just finished writing in spanish.

Thanks, all the best...

 

[cjp]

If, however, you are assuming the second case, then, in theory, they both grow at the same rate (proportional to square of velocity).

They both grow approximately proportional to the square of velocity, so if there is any difference, the devil must be in the details: any secondary effect that makes one of them grow in a different way from the other will become important. Unfortunately I'm not an aerodynamics expert, so I can't tell you about these secondary effects.

If they both continue to grow with the same rate, this allows for some interesting concepts. One concept I invented was to attach an air-breathing, solar-powered VASIMIR ion engine to a sail plane. My idea was that if both lift and drag are proportional to air density times the squared velocity, you can achieve the same 'force balance' by flying both higher and faster. Because of the good L/D ratio of a sail plane, only a minor force is required to actually increase altitude and airspeed. This could provide an efficient way into LEO.

Unfortunately, my idea turned out to be impossible for other reasons. The (calculated) efficiency of my engine was not incredibly high, and the required power could not be generated by covering the wings with solar panels.

One thing that could become important at higher speeds is the effect of transsonic and supersonic airflow. I'll leave this to the experts.

 

[tblaxland]

If they both continue to grow with the same rate, this allows for some interesting concepts. One concept I invented was to attach an air-breathing, solar-powered VASIMIR ion engine to a sail plane. My idea was that if both lift and drag are proportional to air density times the squared velocity, you can achieve the same 'force balance' by flying both higher and faster. Because of the good L/D ratio of a sail plane, only a minor force is required to actually increase altitude and airspeed. This could provide an efficient way into LEO.

This is a bit like the way the DGEX gets to orbit. Just remember that once you hit the von Karman line, you need to be at orbital speed in order to generate enough lift to keep you aloft. That is why the von Karman line is considered the boundary of space - where areodynamics leaves off and astrodynamics takes over.

 

[ex-orbinaut]

So, Im new to aerodynamics which makes this a beginner's question.

The question is pretty basic. Some references and the best complete answers are at;

http://www.faa.gov/library/manuals/aviation/pilot_handbook/

Chapter 3, 4 and 5.

And I have a space related question for you all to put me the wiser, but I am posting another thread for it.