What am I missing about aerodynamics?
August 2, 2007 11:36 AM   Subscribe

How does a plane that generates less thrust than weight stay in the air? Assuming in level flight that thrust=drag and lift=weight, where is the lifting force coming from, if not from the drag on the wings?

My understanding is that the lift genrated by the wings is a result of drag.

Shouldn't any lift come out as a drag force on the airplane equal to or greater than the lift?

If the force pushing up on the plane's wing is not coming from drag force, where is the exta force coming from?

I know I must be missing something, but I'm not sure where it is.
posted by OldReliable to Science & Nature (23 answers total) 2 users marked this as a favorite
My understanding is that the lift genrated by the wings is a result of drag.

That's what you're missing. It's not. Read up on how an airfoil works here.
posted by cerebus19 at 11:41 AM on August 2, 2007

In straight and level flight, drag and thrust are equal and balanced, and lift and weight are equal and balanced, separately. Induced drag is the component of drag that comes from making lift, and can be less than the lifting force. Lift-to-drag ratio.
posted by exogenous at 11:51 AM on August 2, 2007

Drag and Lift come together, but they are not generally equal.

Consider a glider, which has no thrust whatsoever.

Demonstrating lift is fairly easy. Hold a piece of paper with both hands, near the bottom. Let the top fall away from (in front of) you toward the floor. If you blow across the gentle arc that has been created, the paper rises to meet your wind.
If you weren't holding the paper, it would also be blown away from you due to drag, of course, but the lift is still there. Getting the most lift, but as little drag as possible, is pretty much what an airfoil is for.
posted by Chuckles at 11:51 AM on August 2, 2007

Evolution of the lift-to-drag ratio over time, with real numbers. If I had more time I would put this in the wikipedia article - it's nice to have real examples.
posted by exogenous at 11:57 AM on August 2, 2007

Response by poster: I'm not explaining the nature of my confusion properly:

Where is the energy to lift the plane coming from? The wing is essentially taking the continuous downward force of gravity on the plane and putting that momentum into the air, I get that part.

At any given instant, the engine is putting forward force on the plane that is less than its weight, but the wing is mysteriously generating an upward force that IS equal to the weight of the plane. How is this possible even from a conservation of energy standpoint?

So what is wrong with this model? What am I missing? Can an airfoil do better than unity? Or am i misunderstanding something about the Physics terms for thrust, drag, force and energy?
posted by OldReliable at 12:04 PM on August 2, 2007

The only time that the thrust/weight equation is an issue is if you're flying vertically, gaining altitude. Then you're essentially in a rocket ship, where your wings aren't really generating any lift. If you don't have more thrust than weight you'll eventually slow to a stall, because your engine can't overpower the strength of gravity.
posted by craven_morhead at 12:04 PM on August 2, 2007

Response by poster: OP Here again:

Let me be much more specific, because I am an aviation enthusiast and I know a lot about airplanes in general, but I do not have the background in physics to tie the pieces together.

Very specifically:

How can a wing have a L/D ratio higher than one? How is the upward force generated by the wing greater than the force needed to make it cut through the air? Why are you not getting something for nothing?
posted by OldReliable at 12:13 PM on August 2, 2007

Best answer: OldReliable: I don't know much about aerodynamics or airplanes, but I think you question isn't about aerodynamics, but about conservation of energy.

Force is not energy. force * distance = work (which is energy). Essentially you have a weird kind of mechanical advantage here where you can provide a smaller force over a greater distance (you're moving fast) and have it applied to overcome a larger force over a smaller distance (you're gaining or losing altitude slowly).

This is how come it's possible that you can get more lift than drag. Drag is the side of the block and tackle you're pulling on, and lift is the side with the anvil on it.
posted by aubilenon at 12:16 PM on August 2, 2007

Where is the energy to lift the plane coming from?

Hold a 100 lbs dumbell weight for a while, you will find it is extremely exhausting. You are spending all this energy to fight gravity. Yet, according to the physics, you are not doing any work. There is no energy involved but waste heat.

Compare with putting the same 100 lbs weight on the ground. It is the same situation as above. Yet your floor has no trouble holding the weight up against gravity with no energy expense at all.

the wing is mysteriously generating an upward force that IS equal to the weight of the plane.

So is the floor. The floor is generating a 100 lbs force against the weight with no energy expense at all.

How is this possible even from a conservation of energy standpoint?

Acceleration requires energy, but not force.

W = FD, work equal force times distance. The place is not moving vertically, so lift requires no work, and no energy aside from waste air motion.
posted by gmarceau at 12:21 PM on August 2, 2007


I think part of the confusion is coming that in picturing the situation you're consolidating the four forces at play--lift, weight, thrust, and drag--into just two, lift and drag. And...that doesn't really work.

Drag is an effect of the airplane pushing forward through the air; it only directly opposes the thrust of the engines. The dynamics of the air passing over and under the airfoil generates the lift, which is only directly opposed by the weight.
posted by Drastic at 12:25 PM on August 2, 2007

Response by poster: So what you are telling me, gmarceau, is that I have to sweat like a dog to hold a weight at the end of my arm, using valuable calories to do what a physicist calls no work(in lbs/ft or something) but an airplane can overcome gravity indefinitly for a fraction (L/D) of the upward force needed to keep it aloft?

I like the pulley analogy, mechanical advantage seems about right, but I am still trying to wrap my mind around where the force comes from.
posted by OldReliable at 12:36 PM on August 2, 2007

Best answer: The pressure differential on an airfoil isn't the best explanation for why it produces lift. The airfoil is curved and the friction caused by the surface moving through the air causes the air to follow the shape of the airfoil. This is causing a change in the momentum of the air, which the airfoil must equal in the opposite direction (conservation of momentum). So, airfoil pulls air down, airfoil goes up. The friction (among other things) also causes your induced drag.

The reason the engine doesn't need to put out as much thrust as the weight of the airplane is the same reason you can stand on roller skates and push against a wall without using an amount of force equal to your weight to get you moving.
posted by backseatpilot at 12:36 PM on August 2, 2007

Force and energy are two different things. Force is not energy.

Weight, drag, thrust, and lift are all forces. For a plane flying level and at constant velocity, the forces are balanced: weight (downwards) and lift (upwards) are balanced. Thrust (forwards) and drag (backwards) are balanced.

If the opposing forces aren't balanced, the plane won't be flying level and at constant speed. If weight is greater than lift, the plane will descend. If lift is greater than weight, the plane will ascend. If thrust is greater than drag, the plane accelerates. If drag is greater than thrust, the plane decelerates.

Note the previous two paragraphs have all talked about these forces in opposing pairs: thrust vs. drag, and lift vs. weight. Nothing about drag vs. lift.

The drag and the lift are each dependent on the plane's airspeed, each in a complicated way depending on the aerodynamics of the plane. There's no particular reason they would be equal. Since drag and lift are perpendicular to each other, not opposed to each other, they also don't need to be equal for the plane to fly level and at a constant speed. Conversely, there's no particular reason why the thrust would have to be equal to the lift: they're perpundicular forces, not opposing forces.

The final bit that may be helpful: There is no "conservation of force" law. (There's conservation of energy, of course, but energy is not force.)
posted by DevilsAdvocate at 12:45 PM on August 2, 2007

There is a pretty good explanation here, particularly starting with the section "Lift requires power."
posted by exogenous at 12:50 PM on August 2, 2007

Compare with putting the same 100 lbs weight on the ground. It is the same situation as above. Yet your floor has no trouble holding the weight up against gravity with no energy expense at all.

Sort of. There's strain energy in the floor. That is to say, the floor deflected ever so slightly when the weight was applied. The energy is stored in this deflection.

Anyways, lift is the magic of fluid dynamics, and has nothing to do with conservation of energy. Whether you look at it as a pressure differential or as a momentum change, the airfoil shape has been carefully constructed to maximize the lift (perpendicular to the direction of motion) and minimize drag (opposite to the direction of motion). At a first approximation, the amount of lift depends on the shape of the wing and the relative speed between the wing and the air. It does not matter how that relative speed is generated.
posted by mbd1mbd1 at 12:52 PM on August 2, 2007

Consider the difference between a weight sitting on the floor, holding it above your head with arms locked, and holding it out in front of you at a right angle. There is no mechanical work being done in any of those cases, but..

To keep the weight steady on the floor, you don't have to do anything, to keep it above your head with arms locked takes some energy, and to keep it in front of you at 90 degrees takes a huge amount of energy. This is because with arms locked above your head, your skeleton is bearing most of the weight, your muscles are mostly only maintaining balance. When your arms are out in front holding the weight, the entire weight is being born in muscle tension. Muscles require a lot of energy to stay in tension, and the more tension, the more energy.

A plane flying straight and level is somewhere between the arms locked position, and the weight sitting on the floor.
posted by Chuckles at 1:11 PM on August 2, 2007

How is the upward force generated by the wing greater than the force needed to make it cut through the air? Why are you not getting something for nothing?

Force is not conserved. This is true; it was one of the most puzzling aspects of elementary physics for me.
posted by ikkyu2 at 1:54 PM on August 2, 2007

Response by poster: Thanks for the info guys, now let me see if I get this straight.

The friction of the air against the wing imparts downward momentum to the air as it cuts through. In order to conserve momentum, the wing gets moved upwards. In a perfect world, this action would require no energy because there is no change in the potential of the system. On an actual plane, the inefficiency and waste comes out as the incidental drag.

Thus the only force that the engine needs to counter to keep the plane aloft is the relatively small amount of drag that is the waste of pushing the wing through the air. That is the power that the engine needs.

How does that sound?
posted by OldReliable at 2:33 PM on August 2, 2007

If you are going to use the momentum argument, think of the millions of air molecules, each colliding with the wing. As they collide, they bounce off based on the angle of the wing and the direction of the wind.

Otherwise, I think that is about right.
There are some interesting subtleties you can add, at this point, like induced drag (mentioned above) vs. parasitic drag.. Induced drag is a necessary bi-product of lift, so it is a fundamental physical limitation, but parasitic drag can always be reduced just a little further with improving design.
posted by Chuckles at 2:55 PM on August 2, 2007

When I think of "waste" or "inefficiency" in an engineering setting, I think of unrecoverable heat energy that dissipates to the environment. So I'm not sure I'd choose to phrase it that way.

Think of an infinitely thin rigid string that sits there in place of the airfoil wing. Imagine yourself pushing that string through the air. It's not difficult to push that through the air at all. Because the string has no cross-sectional area, it does not generate any drag, nor does it perturb the air that it's moving through. It cuts through like a hot knife through soft butter.

However, it *is* more difficult - takes more work - to push an airfoil through air than it is to push an infinitely thin string through the same air. It's surprisingly complicated - non-elegant - to describe exactly what is going on in terms of the air, its different velocities and pressures and viscosities, turbulences, etc, as the airfoil passes through; "it's the Bernoulli effect" is only a primitive first approximation. But because of the shape of the wing and the properties of air, some of the work that was applied to push the wing forward ends up being redirected to lift the plane. That work does not help accelerate the plane forward; it instead accelerates it upwards.

If you think of the airplane engines as "work generators," and you think of the plane as something that can accelerate either forward or upward due to these work generators, and you run the numbers, you find that most of the work generated by the engines is used to accelerate the plane forward. A lesser amount of work generated by the engines is used to accelerate the plane upward. This is really a restatement of the fact that the L/D ratio is greater than 1.

It's also why the wikipedia article separates out "induced drag" (drag caused by the airfoil's tendency to lift) and "profile drag" (drag caused by the work needed to move the airfoil's cross-section forward through the air), though in reality there is no distinction between the two. In the case of an airplane neither causes "waste;" they are both necessary for the plane's function.
posted by ikkyu2 at 3:12 PM on August 2, 2007

In straight and level flight, the engines do not accelerate the plane at all. The plane is flying at a constant velocity, both horizontally and vertically and therefore there is no acceleration. The acceleration is zero; therefore the sum of the forces is zero. F=ma=0. Lift = weight, thrust = drag. The power generated by the engines is exactly equal to the amount to overcome drag at the velocity you are moving. P= drag * velocity.

Likewise when a plane is climbing, there is no acceleration. The plane moves at a constant velocity upward, you feel no acceleration as the plane climbs to 30,000 feet, therefore again the sum of forces is zero. The plane climbs, not because of excess lifting force, but because there is an excess of power over what is needed to support the airplane in level flight. The excess power, instead of accelerating the air downward, goes into potential energy moving the airplane upward. But there is no acceleration and the forces are zero. The lift on a wing is no greater when it is climbing than when it is flying level. In both cases the lift is exactly equal to the weight. In this case, however, power is greater than drag velocity. P > drag * velocity. The excess power is exactly equal to the weight * upward velocity. So P = (drag * horz. velocity) + (weight * vert. velocity).

When P > (drag * hoz. velocity) you go up. When P < (drag * horz. velocity) you go down. and when p exactly equals (drag * horz. velocity) you fly level.br>

This is similar to the forces in an elevator. You feel acceleration very briefly when the elevator starts and when it stops. For this brief moment when the elevator accelerates, the force is greater than your weight and you can feel it in your legs. But once the elevator is moving, there is no excess force. The lifting force is exactly equal to your weight. F= ma = 0. In fact if there were no floor numbers flashing by, it would be impossible to determine if you were moving or stopped. Your weight would feel exactly the same. But power is being applied to move you upward even though the forces are still zero.
posted by JackFlash at 10:25 PM on August 2, 2007


That sounds pretty good. I wouldn't necessarily describe it as "friction," however. There's some interaction between the air and the plane that results in momentum transfer. People argue about the relative importance of specific mechanisms, but it's not important for this question.

The net momentum per unit time transferred from the air to the wing in the vertical direction is the lift; in the horizontal direction it's the drag. Without further specification, however, there's nothing relating the vertical momentum transfer to the horizontal momentum transfer. Planes are shaped the way they are because it results in a good bit of the former--enough to take off/counter the weight at cruising speed--with relatively little of the latter. The engines are designed to counter the drag and then some.

gmarceau: Acceleration requires energy...

This is a bit pedantic, but it's a common error. Acceleration parallel to the velocity of an object results in a change in the object's kinetic energy. Acceleration perpendicular to the velocity does not.
posted by dsword at 8:47 AM on August 3, 2007

Along similar lines, we humans can accelerate vertically - stand up from a squat, and/or can even jump, demonstrating that our legs can generate more thrust than our weight. So why wouldn't this be a great idea?
(This is a rhetorical question - thought-prompting rather than answer-seeking :-)
posted by -harlequin- at 9:37 PM on August 4, 2007

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