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This isn't a question of how a wing works -- vortex flow, Bernoulli's principle, all of that jazz. Instead, it's a question of why we need a wing at all. A wing produces lift, but why is that necessary?

I got to this by thinking of an airplane at a coarse level. The wing produces lift through some interesting physics, but it needs energy to do this. The engine is what ultimately provides all of this energy (let's assume no headwind, and in "ultimately" I'm not including chemical energy in the fuel, yadda yadda "it all comes from the sun"). That means the engine pushes enough air, and fast enough, to (a) offset gravity and (b) still propel the plane forward. So the question is: why can't we just angle the engine down a bit and get the same effect?

To slightly reword: why do wings help us divert part of an engine's energy downward in a way that's more efficient than just angling the engine?

One answer is that we can do exactly that; I'm guessing it's what helicopters and VTOL airplanes like the Harrier do. But that's less efficient. Why?

One analogy that comes to mind is that of a car moving uphill. The engine doesn't have the strength to do it alone, so we use gears; for every ~2.5 rotations the engine makes, the wheel makes one, stronger rotation. This makes intuitive sense to me: in layman's terms, the gears convert some of the engine's speed-energy into strength-energy.

Is this analogy applicable -- is the wing on a plane like the gearbox in my transmission? And if so, what's the wing doing, more concretely? If a gear converts angular speed to increased force, what X does a wing convert to what Y?

None of the answers I could guess at satisfied my intuition. If the wing converts horizontal speed to vertical speed, tipping the engine downward would seem to have the same effect. If it's changing the volume/speed of the air (more air blown slower, or less air blown faster), it would still have to obey the conservation of energy, meaning that the total amount of kinetic energy of the air is the same -- again suggesting that the engine could just be tipped down.

EDIT

In thinking about this more from the answers provided, I've narrowed down my question. Let's say we want a certain amount of forward force $S$ (to combat friction and maintain speed) and a certain amount of lift $L$ (to combat gravity and maintain altitude). If we tilt our engine, the forces required look like this:

vectored thrust

The total amount of force required is $F = \sqrt{S^2 + L^2}$. That seems pretty efficient to me; how can a horizontal engine + wing produce the same $S$ and $L$ with a smaller $F'$?

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I think you have the forces upside down. You need to tip the engine up to lift you up and make you go up. –  AJMansfield Jun 27 at 21:36
    
@AJMansfield Yeah, when I was drawing that image, I was drawing the direction that air gets pushed. The force on the airplane would be opposite to those vectors in both components (here, we're flying right-to-left). –  yshavit Jun 27 at 21:39
    
Your lift L is pointing downwards! The short answer is that we don't need to generate L using energy. The air below the wing will provide L for free, by resisting the wing's attempt to move downwards. –  joeytwiddle Jun 28 at 17:28
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Wings do a much better job converting gravitational potential energy into not crashing into the ground. Unlike engines. See "glider" -- a machine which can fly for hours using only a few minutes of pulling by an engine. To keep a wing in level flight, only enough force to overcome drag need be applied. To keep an engine in level flight, both drag and gravity must be overcome. –  Eric Towers Jun 28 at 18:08
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Note that a propeller blade IS typically an airfoil, and thus is itself a "wing". –  keshlam Jun 29 at 3:52
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13 Answers 13

up vote 17 down vote accepted

Let's look at the relationship between momentum and energy. As you know, for a mass $m$ kinetic energy is $\frac12mv^2$ and momentum is $mv$ - in other words energy is $\frac{p^2}{2m}$

Now to counter the force of gravity we need to transfer momentum to the air: $F\Delta t = \Delta(mv)$

The same momentum can be achieved with a large mass, low velocity as with small mass, high velocity. But while the momentum of these two is the same, THE ENERGY IS NOT.

And therein lies the rub. A large wing can "move a lot of air a little bit" - meaning less kinetic energy is imparted to the air. This means it is a more efficient way to stay in the air.

This is also the reason that long thin wings are more efficient: they "lightly touch a lot of air", moving none of it very much.

Trying to replicate this efficiency with an engine is very hard: you need compressors for it to work at all (so you can mix air with fuel and have the thrust come out the back) and this means you will have a small volume of high velocity gas to develop thrust. That means a lot of energy is carried away by the gas. Think about the noise of an engine - that's mostly that high velocity gas. Now think of a glider: why is it so silent? Because a lot of air moves very gently.

I tried to stay away from the math but hope the principle is clear from this.

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Simple and clean answer. One could also, as a matter of principle, consider the case of the rocket engine. But it needs high speed to avoid eating too quickly the mass of the vehicle. Wings are a bit like ramjet ... and do not work in empty space, like ramjet. They rely on outside matter for reactive mass. It is actually interesting to study various kinds of moving bodies, including bacteria in nutriant: is the energy from internal or external source? Is reactive mass from internal or external source. –  babou Jun 30 at 10:53
    
The distinction between momentum and energy makes sense. But then, what about a tilted prop engine with long, thin wings -- something approaching a helicopter or Osprey. Presumably those aren't as efficient as fixed-wing aircraft, at least at high speeds (a couple hundred mph, let's say). –  yshavit Jun 30 at 21:04
    
@yshavit - I am guessing the idea behind the Osprey is to make it possible to get some "large area lift" from the wings when it is moving forward - making it a helicopter that's more efficient when moving fast. A conventional helicopter moving forward has half the rotor moving at a speed of "rotor plus chopper" which increases the drag. The Osprey at least can tip its rotors into the vertical plane (horizontal thrust) when cruising. So it tries to be "a little bit of both". But in most engineering situations, tradeoffs mean compromises in performance. –  Floris Jun 30 at 21:20
    
I wonder if it's also that the aircraft you have to build in order to get a "prop engine" above the center of mass (ie, a helicopter where the "prop engine" is the main rotor) is going to have a less aerodynamic design overall? –  yshavit Jun 30 at 21:27
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Yes - that's exactly the idea behind the high bypass. –  Floris Jul 1 at 5:14
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The key point is that wings allow you to "tilt the engine" much more efficiently than actually tilting it. Tilting an engine converts the power only at 1-to-1 ratio, but wings do it better - a Boeing 747 has a lift/drag ratio of 17 at cruise speed, the wing is generating 17 times more lift than the applied engine power.

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It's not really the wings that do the tilting, but the elevators at the tail - a missile has no wings, but will change the direction the engine points by adjusting the pitch ( vertical angle between flight path and fuselage centre line ) using tail fins equivalent to elevators. But +1 for the lift/drag ratio. –  Pete Kirkham Jun 28 at 12:23
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It is merely a long comment but hopefully it gets your intuition on the right track. I try to detail the physical part of the reason why having fixed wings is a good thing:

You basically ask, why are airplanes more efficient (hence people still produce them despite their less nice maneuverability)

well you probably noticed helicopter rotors work pretty much as wings too. But for the most efficient flight you want to optimize your wing for some average flight scenarios, say flying straight 1000 km/h. Now, when it comes to optimizing the "good" thing a wing can do is provide lift, and the "bad" thing it does is provide drag. So you want to optimize for highest lift-to-drag-ratio. But your problem is that helicopter wings dont always face the direction of your flight speed. it spends a lot of time going backwards(relative to the aircraft at least) so that cannot receive air flows at the same speed as the rotor blades that go forwards, yet they are at exact same blades with the exact same same angle as the ones going backwards(facing slower air flow)

notes:

  1. If you think about it, this applies to any aircraft you could imagine that relies on "rotating wings" for lift.

  2. So it basically means that aircraft don't really need static wings for staying in the air, only when going at high speeds.

  3. Airplanes are arguably more resilient in general then helicopters so they cost less in insurance and maintenance, which makes them overall less costly besides being better optimizable(which I attempted to detail in the main text).

If you have questions fell free to comment. I hope I helped.

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Airplanes are generally more resilient than helicopters I disagree, but this is very, very subjective. Helicopters don't need much of a landing strip, for example. Otherwise, +1. –  Renan Jun 27 at 20:26
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I think this may have been the missing piece for me! If I'm reading it right, the idea is that the backwards-moving of the blade is a big loss in efficiency (it's basically working against a major tailwind). If you have a prop plane or even a turbojet, then it's the same principle, just to a different degree. But if you have a horizontal engine, its blades never move backwards relative to air, and are thus always at full efficiency. This increased efficiency more than offsets whatever extra drag the wings provide. Is that about it? –  yshavit Jun 27 at 20:58
    
@yshavit exactly, yes. –  Jani Kovacs Jun 27 at 21:41
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Hm, though now that I think of it... wouldn't the tailwind on the backwards-moving blades be offset by an equal headwind on the forwards-moving blades? –  yshavit Jun 27 at 21:45
    
@yshavit there is no tailwind if you consider only the wind generated by the blades. –  Renan Jun 27 at 22:00
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The important quantity in determining the effectiveness of a wing is its lift to drag ratio. It turns out that the key contributer to a large lift to drag ratio is a large wing span ($b$ in the below equation). As such the large wings on the aircraft can be far more efficient at generating maximum lift with minimal drag that the smaller "wings" of the engine.

The key equation for the theoretical maximum lift to drag is:

$(L/D)_{max}=0.5 \sqrt{\frac{\pi\epsilon}{C_{fe}}\frac{b^2}{s_{wet}}}$

where $(L/D)_{max}$ is theoretical maximum lift to drag ratio, $C_{fe}$ is the equivalent skin friction coefficient, $b$ is the wing span $S_{wet}$ is the wetted area and $\epsilon$ is the span efficiency factor (a number near to 1 in the optimal case.

Refs:

  • Loftin, LK, Jr. "Quest for performance: The evolution of modern aircraft. NASA SP-468".`
  • Raymer, Daniel (2012). Aircraft Design: A Conceptual Approach (5th ed.). New York: AIAA.`
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So as I read the OP, the question is "why don't we just angle the engines to begin with?" You've answered "Given that the engines are pointed perfectly horizontally, large wings give us the needed lift with the least amount of drag." But why not angle the engine so as to not need lift at all? This is after all similar to what a helicopter does (if we think of its blades as an engine). –  Chris White Jun 27 at 22:19
    
@ChrisWhite You need the lift one way or annother (gravity isn't going away). You can provide that with the "big wings" on the side of the plane or you can provide it with the "small wings" in the engine but one way or annother you have to provide it –  Richard Tingle Jun 27 at 22:22
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To illustrate the importance of L/D ratio : If an engine provides 1 lb thrust, and a wing has L/D of 10 - the engine alone can lift 1 lb off the ground, but the wing can convert 1lb of thrust to 10lbs of lift. –  Brian Drummond Jun 27 at 22:35
    
Ah, this makes a lot of sense, too! So the idea is that you don't need to be super efficient in producing horizontal force (it's okay if we only go 250kmh at takeoff), but you had better be pretty darn efficient about vertical force (a 777 taking off needs to be in the air, and soon, if you don't want a visit from the NTSB). –  yshavit Jun 27 at 22:43
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Why is an airplane better than a rocket? Because the plane grips the medium.

For a rocket to remain at a fixed altitude, it must continually thrust upwards in order to counteract the fall caused by gravity. It does this by pushing down a large amount of air and fuel each second.

An airplane can create this same upward force to counteract gravity, but in a more efficient way, by pushing against the local medium of air. Forget for a moment about the shape of the wing providing lift, just think about how the flat planar shape cutting horizontally through the air keeps the altitude from dropping.

The wing pushes down on the air below it, and the air briefly resists, pushing back upwards against the wing. A motionless plane would quickly begin to fall because the air below it would soon stop resisting, and would begin to travel downwards with it or move out of the way. But when an airplane is moving, it is getting a continual fresh supply of static medium. And all this fresh air resists the attempt of the wing to fall downwards.

A similar effect is used by the keel or centerboard below a sailing boat when it is tacking perpendicular to the wind. The planar board has the effect of "gripping" the water as it cuts through it, preventing the boat from being pushed downwind (leeward) in the axis perpendicular to the motion.

This effect is present even when the boat or airplane is not moving, but is far more pronounced the faster the plane is cutting through the medium. So the faster you go, the less horizontal area your wing needs. (Consider the relative area of the wings on a biplane versus those on a modern jumbo jet.)

You can also consider how a glider can achieve much greater distances than a rocket, whilst expending no energy at all! Or how a flat sheet of paper falls more slowly than a rolled (or crumpled) sheet of paper.

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I think You have Your intuitions a bit scrambled.

Engine and wings do not have the same function.

If You need to make a parallel then wings have the same function of wheels on a car: they provide an efficent way to remain above ground by pushing down on some medium.

Wheels push on ground and have no problem keeping your car above it even when the car is still.

Wings, on the other hand, manage to produce an high pressure on their underside and a low pressure on the overside, this difference of pressure converts in a net force keeping the plane from falling. Unfortunately to maintain this difference of pressure the wing has to move in the air (somewhat less solid than ground) at least with a certain speed ("stall" speed); below that airflow is not laminar anymore and the plane becomes a paperweight. Energy has to be provided to maintain the speed against friction; that's the purpose of the engine.

Wings are very efficient in their job: an albatros can fly for thousand miles without moving their wings (with no "engine") just using the tiny difference in windspeed before and after oceanic waves.

Using brute force to keep airborne, as hummingbirds do, needs MUCH more energy even if you use wings. It's the same difference between a suitcase with or without weels.

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I've wondered about this a bit before. I think it's good to hugely simplify things to think about it. Incidentally, I'm absolutely not a source of authority here. I'm just thinking it through from what seems apparent to me.

A falling plate

You've said specifically that you don't want to think about how wings work, so let's not. Forget about the wing. Forget about the airplane. Forget about the thrust, rocket or otherwise too.

Think about a plate of flat, rigid, fairly light material. It "magically" doesn't tip: it remains parallel to the ground. I can only slide up and down.

I'm pretty sure you'll agree that this will "fall" a lot slower than a ball of the same weight? And yet, it is a completely passive device – it does not require energy or expel thrust.

It falls more slowly because, to fall, it must move air molecules out of the way, or squashed them up under it. Both of these require force to be applied, which it must supply, resulting in an equal and opposite force providing it a gradual descent.

It's easy to see that making the plate larger (and keeping the same weight) will increase the staying-in-the-air quality. Changing its shape in other ways will have other effects that are beyond me to speculate on, because I'm not a real physicist or aeronautical engineer.

In air, a falling thing has a terminal velocity. The terminal velocity of our plate will be small. Much smaller than a solid ball the same weight. If it's terminal velocity if v_fall, and it is "launched" from a height h, it will take at least t=h/v_fall seconds to fall to the ground (I am neglecting any time required to accelerate to its terminal velocity).

Adding thrust

Let's attach something that provides thrust. Our plate will slide along, and again, magically stay parallel to the ground. Provided there is no significant friction created by sliding the plate through the air, and provided that the thrust source isn't heavy, we'll have got t completely free seconds of "flight" (or, if you prefer, falling with style) from the plate. That sounds pretty good! It the trust pushes us at v_thrust, we'll travel t.v_thrust before we start sliding on the ground.

Flying

But what if we start on the ground, and we want to travel for longer than the t seconds?

If we are on the ground, we could angle our plate just a touch so that as it is pushed along, the fall (from the plate's terminal velocity in air) just matches the amount that the plate climbs (due to it being pointed up a bit rather than parallel to the ground) as it is pushed along. If we did that, we'd lose some of our forward speed. We'd end up with:

v_forward^2 = v_thrust^2 - v_fall^2

(Pythagorus, right?)

If we can decrease v_fall, perhaps by making the plate bigger, then we can make make v_forward (the useful bit) bigger.

Just an engine

Without the plate at all, v_fall would be large – whatever the thrust source's terminal velocity is, in fact. So v_forward (the useful bit) would be much smaller.

Real Wings

Real wings, living in the real world, don't have access to magic to maintain their necessary pitch. They have to be built from available materials instead of ideal ones, and they need to contend with slipping through a fluid that adds drag. For these reasons and probably many more, they have a clever shape.

Obviously, everything here is grossly simplified.

I'm not claiming the tiny amount of maths here is useful for modelling reality and would be extremely surprised if it is! Nor am I claiming the lift producing mechanism of a real wing works in this way (presumably, it works better).

However, I am claiming that by working with an extremely simplified model, you can see that an airplane's wings achieve something that thrust alone does not. They provide an extremely "cheap" source of lift that would otherwise require much more of the thrust to be diverted downwards.

You could probably summarise their function as being a parachute that is rigid enough to push through the air :-) Further support that cheap lift is available comes from engineless gliders, sycamore leaves, and dandelion seeds.

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Wings have a much larger surface area than engines, so they are better at preventing a plane's gravitational potential energy from being converted into downward kinetic energy. A plane with gliders instead of wings and engines pointed downward at an angle should be just as energy efficient as a regular plane. The glider might be less practical because the engines would need to be more powerful in order to produce enough thrust to lift the glider by themselves.

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How about this explanation (not that detailed, but simple):

The reason is that, if force of lift and force of gravity cancels each other out exactly, then staying airborne requires zero energy. Basically, energy and force are different things. A helium balloon can stay in the air indefinitely, without needing energy to do so, and without the air supplying any energy. The air pressure just supplies force, which is enough.

We know lift can be generated either using wings or using engines. Generating a constant upwards force using engines requires a constant expenditure of energy. But if you use wings, you can generate a strong upward force for a fraction of that cost, provided that you don't try to convert this upward force into energy (i.e. you can't climb for free with wings, you need engines (or an updraft), but you can maintain a constant altitude without engines, disregarding drag).

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I don't think wings would allow you to stay airborne without engines. You said "disregarding drag" but isn't that drag exactly what provides the upward lift of the wings? –  Jonas Jun 28 at 16:51
    
@Jonas: drag is made up of a frictional part and a part from diverting air momentum downwards. By making the wings very big and airflow slow, you can minimise both arbitrarily so it's indeed "possible" to stay airborne without engines... theoretically. In practise, big wings also come with big mass and sacrificing speed is only reasonable up to a certain point – when it becomes simpler to just build an airship. –  leftaroundabout Jun 28 at 17:07
    
@Jonas: yeah, I suspected someone might say that, but I wanted to keep it simple. Drag is a necessary side effect of the dynamics of a wing, but is not what actually creates the lift. However, if you like, the gearbox analogy can be used: wings is a device that converts drag, which has a small force but can take significant energy to overcome, into lift, which has a large force but almost no energy. –  Ove Jul 3 at 15:18
    
I should probably clarify that the energy lost in drag, though significant on large aircraft at high speeds, is typically much less than the energy it would take to produce the thrust it would take to lift that same aircraft without help from the air. Common aircraft engines usually aren't even powerful enough to do that. –  Ove Jul 3 at 15:51
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You can also consider how a glider can achieve much greater distances than a rocket, whilst expending no energy at all!

Ah, no. One expends energy in the launch phase - an aerotow or winch launch being typical - and gains energy in slope, wave, dynamic or thermal lift and then expends it in overcoming drag. Energy management is one of the most important factors in high performance gliding and if you're not good at it you won't do well in competition!

Simply 'not having an engine' does not equal 'expending no energy'. Not by a long way.

And I think the Apollo crews might argue that they covered rather greater distances than any glider flight is likely to manage.

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That sounds like a challenge. Ten times around the world without touching ground and no refueling. Hm... –  Mr Lister Jun 29 at 8:18
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There are planes that tilt the engine down to take off those are called VTOL (vertical Take Off and Landing). These are usually military fighter craft.

The reason why they aren't used for general aviation is multifold:

First every regulation aircraft must be able to touch down safely after losing an engine, if the engine is what provides the lift then the craft turns into a falling brick (a helicopter uses the rotational energy stored in the rotor to touch down safely).

Second you need a large thrust to weight ratio (>1 to even lift off) creating an engine that powerful isn't cheap especially when you want to transport cargo.

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The lift of a wing is proportional to the square of the air velocity passing over it. If you have a wing it is thus very easy to get a lot of lift just by increasing your speed. In this way, rather than using engine force to lift the aircraft directly, you use the engine force to push you in the direction you want to go as fast as possible. This means you get there faster, because more of the engine's force is used to push you forward rather than push you up (which the wings are doing for you as a by product of moving forward rapidly).

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Consider helicopters, which are simply aircraft whose wings go in a circle.

Then consider those flying platforms consisting of a fan pointed down.

enter image description here

The only real difference is whether the wings are big and slow versus small and fast.

Lift consists of the momentum (per second) of air directed downward. Momentum is $mv$. That air has kinetic energy proportional to $mv^2$. You can get the same lift for less energy by directing more air mass $m$ with less $v$.

If you want to see an aircraft intermediate between a fixed-wing and a helicopter, whose engines tilt, look at the Osprey. enter image description here

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