How do airplanes fly with heavy weight and air resistance?

[rcgldr]

In flight school we were taught that lift is perpendicular to the chord line drawn from the leading edge of the wing to the trailing edge.

The definition of lift is the force perpendicular to the direction of travel, with respect to the air.

Bernoulli model

The problem with Bernoulli model is that it doesn't explain why the pressure and speed differentials form above and below a wing.

Explaing how lift is generated can be simplfied stating that a wing produces lift by moving through the air and diverting the relative (to the wing) air flow downwards. The air is diverted downwards because the wing has an effective angle of attack. On the bottom of the wing (assuming an angle of attack), the air is deflected off the surface. On the top of the wing, the air is drawn towards what would otherwise be a void (vacuum) along the upper surface of the wing, and if the transition is "smooth" enough the air flow tends to follow the upper surface as long as the pressure keeps decreasing, then as the pressure increases again, the flow transitions into turbulent flow and separates somewhat from the surface. If the angle of attack is too large or the surface of the wing is not smooth (too sharp of a curve for a given speed), then the air flow from in front of the wing tends to separate away from the surface then form large vortices (or one very large vortice) above a wing greatly reducing the amount of lift.

The total aerodynamic force equals the intergral sum of the components of mass of the affected air times the acceleration of those components. For a normal wing, most of this force will be downwards, related to lift, and some of it forwards, related to drag.

Caculating the lift and drag produced by a wing is very complicated. Using the wing as a frame of reference make this process simpler, since diversion of air flow doesn't require a change in energy from a wings frame of reference, so if a process can calculated air speeds across various surfaces of a wing above and below, Bernoulli can be used to approximate the overall pressure differentials that produce lift. Calculating drag is a bit more complicated, partly because one set of streamlines end at the leading edge stagnation zone, and another set begins at the trailing edge of a wing (where the stream lines from above and below merge).

 

[Traz 0]

The definition of lift is the force perpendicular to the direction of travel, with respect to the air.

I was unclear regarding lift, I suppose. I was referring to to lifting force, which has both a vertical component, I.e., lift, and a horizontal component, I.e. drag.

 

[Traz 0]

More specifically, induced drag, which is (was?) calculated as the vector portion of the lifting force acting opposite to thrust.

 

[rcgldr]

I was unclear regarding lift, I suppose. I was referring to to lifting force, which has both a vertical component, I.e., lift, and a horizontal component, I.e. drag.

That's the total aerodynamic force. The component of force perpendicular to the direction of travel is lift, and the component of force opposing travel is drag. See post #91 of this thread that explains induced drag for an ideal wing. (The m's with the dot above them represent mass flow, Δm / Δt).

post #91.htm

 

[Traz 0]

That's the total aerodynamic force. The component of force perpendicular to the direction of travel is lift, and the component of force opposing travel is drag. See post #91 of this thread that explains induced drag for an ideal wing. (The m's with the dot above them represent mass flow, Δm / Δt).

post #91.htm

And, now that we've clarified our terms, back to my original question: Is total aerodynamic force still calculated as perpendicular to the chord line?

 

[boneh3ad]

And, now that we've clarified our terms, back to my original question: Is total aerodynamic force still calculated as perpendicular to the chord line?

No. It is not in general perpendicular to the chord line.

 

[rcgldr]

And, now that we've clarified our terms, back to my original question: Is total aerodynamic force still calculated as perpendicular to the chord line?

The direction of the aerodynamic force is defined with respect to the direction of travel (with respect to the air), not the angle of the chord line. Note I updated post #91 to include induced drag as a funcion of lift for the idealized wing.

 

[rcgldr]

All of this is a based on various articles that I've read and feed back from a few people involved in aerodynamics (mostly the guys that design wings for radio control gliders).

If the vortices constantly carry air downwards

The vortices move downwards because there's a downdraft across the entire trailing edge of a wing (assuming the wing is producing lift), and the vortices are just part of that flow.

why hasn't the distribution of air in the atmosphere permanently changed due to a hundred years of airplane flight and millions of years of birds?

It has, the actual molecules of disturbed air are permanently displaced and the space those molecules left behind are now occupied by different air molecules. This can be seen by smoke in the air that gets disturbed by an aircraft flying through it, or in general, dispursed due to natural winds that occur in the air.

vortices actually are a result of drag, not lift.

Wing tip vortices are caused by the higher pressure air below a wing flowing around the wing tips towards the lower pressure above a wing. Small turbulent vortices can occur in the boundary layer when there is separation of flow, and these travel backwards across a wing surface. If a wing's angle of attack is in the stalled regime, a very large vortice can form. Trailing edge vortices can also form depending on how the streams from above and below a wing merge at the trailing edge. Leading edge induced vortices can occur at higher angles of attack, which usually results in separation and a stalled state, except for delta wings which can take advantage of the low pressure vortices and avoid stalling at angles of attack up to 20° or so.

If you span a wing across a wind tunnel, there are no voritces and no lift-induced drag.

If the wind tunnel is "tall" enough to not restrict vertical air flow, then a wing that spans a wind tunnel diverts the flow downwards, and this results in induced drag even for an ideal wing that diverts the air flow with no change in speed. You can see the downwash in videos of wings in "tall" wind tunnels with smoke generators. The horizontal component of air flow after diversion is speed x cos(θ) (where θ is the angle of diverted flow), and the reduction in horizontal speed is speed x (1 - cos(θ)). This reduction in speed corresponds to induced drag. I did the math back in post #91.

I'm not sure of the conditions that result in turbulent vortices formed at the trailing edge of a wing that spans a wind tunnel, other than it does occur if wind speed and angle of attack are high enough. As an extreme example, a vertical flat plate spanning a wind tunnel will generate vortices at it's top and bottom edges.

 

[Traz 0]

The direction of the aerodynamic force is defined with respect to the direction of travel (with respect to the air), not the angle of the chord line. Note I updated post #91 to include induced drag as a funcion of lift for the idealized wing.

And how is angle of attack accommodated in that equation?

 

[rcgldr]

The direction of the aerodynamic force is defined with respect to the direction of travel (with respect to the air), not the angle of the chord line. Note I updated post #91 to include induced drag as a funcion of lift for the idealized wing.

And how is angle of attack accommodated in that equation?

The angle of the diversion of the relative air flow is related to the angle of attack, the air foil, air density, the relative air speed, the length of the wing chord, ... (Reynolds number is related to speed and wing chord). Since cambered airfoils can produce lift at zero physical angle of attack (which is based on leading and trailing edges), the effective angle of attack, which is defined to be zero when zero lift is created, can be a more useful way to describe angle of attack.

Note that equation is for an idealized wing. Using the wing as a frame of reference, for a real wing, the overall mechanical energy of the air is reduced, reducing lift and increasing drag compared to an idealized wing. In addition, the angle of diversion of air flow decreases with distance from a wing, so using a single value for the angle of diversion is based on an averaged effect, but it's useful for trying to explain lift and induced drag.

 

[Traz 0]

The angle of the diversion of the relative air flow is related to the angle of attack, the air foil, air density, the relative air speed, the length of the wing chord, ... (Reynolds number is related to speed and wing chord). Since cambered airfoils can produce lift at zero physical angle of attack (which is based on leading and trailing edges), the effective angle of attack, which is defined to be zero when zero lift is created, can be a more useful way to describe angle of attack.

Note that equation is for an idealized wing. Using the wing as a frame of reference, for a real wing, the overall mechanical energy of the air is reduced, reducing lift and increasing drag compared to an idealized wing.

"Leading and trailing edges" Isn't that how I defined wing cord?

"Air foil" do you mean the cross-section of the wing?

"Air density" We pilots have to factor air density into performance tables (ultimately reduced to 'density altitude') but I've never heard that it can change the dynamics of wing response.

It sounds like you're saying that everything I learned in flight school was wrong. Amazing that I'm still alive.

 

[rcgldr]

"Leading and trailing edges" Isn't that how I defined wing chord?

Wing chord is a straight line from leading edge to trailing edge. Camber line is a curved line that is 1/2 between the upper and lower surfaces of a wing. The camber line gives a better idea of the coefficient of lift versus angle of attack for a cambered air foil.

"Air foil" do you mean the cross-section of the wing?

yes.

"Air density" We pilots have to factor air density into performance tables (ultimately reduced to 'density altitude') but I've never heard that it can change the dynamics of wing response.

Reduced density requires higher actual air speed for most dynamics. In an aircraft you're probably going by Indicated Air Speed (IAS), which already compensates for air density. For example, stall speed is based on IAS, which takes air density into account.

It sounds like you're saying that everything I learned in flight school was wrong.

The only thing "wrong" was the flight schools definining lift relative to angle of attack as opposed to direction of travel (relative to the air). The Newton versus Bernoulli debate isn't as important as what a pilot needs to know to fly safely, such as how to avoid a stall, takeoff and landing procedures, avoiding wake turbulence from large aircraft, compensating for high altitude and/or high temperature takeoffs or landings, and little things like landing at the correct airport on your first cross country flight, ...

 

[A.T.]

The only thing "wrong" was the flight schools definining lift relative to angle of attack as opposed to direction of travel (relative to the air).

Yes, usually the force components relative to the cord line are called "normal force" and "axial force": See also:
http://www.aerospaceweb.org/question/aerodynamics/q0194.shtml

Difference between lift (L) and drag (D) versus normal force (N) and axial force (A)

Another common source of confusion: When dealing with propellers/turbines "axial force"/"drag" can also refer to the component parallel to the rotor axis, instead of parallel to the cord line / relative flow at the airfoil.

 

[sophiecentaur]

This is the part that is wrong: Yes, which is why helicopters are much, much less efficient than airplanes.
Flip the issue over: If the vortices constantly carry air downwards, why hasn't the distribution of air in the atmosphere permanently changed due to a hundred years of airplane flight and millions of years of birds?

Also (not as important): the vortices actually are a result of drag, not lift. If you span a wing across a wind tunnel, there are no voritces and no lift-induced drag.

Is there some transition between the way a helicopter wing and a fixed wing works, then? The difference in efficiency is just a difference in detail - it doesn't have to he 'in principle'. In fact, how can it be? The only difference is surely that the helicopter blade effect is hundreds of times more on the same local region of air around it.

They don't and it goes without saying; air goes down and air goes up (long after the plane has passed). The motion is spiral and energy gradually dissipates. The shapes of the vortices would not be 'circular' and I have no idea about the details. That doesn't matter. The initial effect of the deflected air is spread out and, as the speeds reduce with radius, a vortex is the natural result But their effect is in a region far outside any region that you are discussing in your Bernouli analysis. The total weight of air plus plane in a corridor ten miles wide is the same, whether the plane is flying or on the ground. The plane flies because of its interaction with a local region of air and it leaves behind, in the vortices, the result of this interaction. You are dismissing this by saying the vortex is just due to drag. Can you give a reference about it?

There is a fundamental problem with what you are saying about behaviour in a wind tunnel though. (A wind tunnel is not the same as a plane, flying through the open air, for a start. It's a tool to help with design and understanding.) If what you say is true then the total weight of the wind tunnel plus wing would have to reduce when the air is flowing. As you cannot think that (??), what is the alternative to some extra pressure on the floor when in operation? Newton 3 again has to apply; if not, we have invented the antigrav machine.

Finally, if there is no net air deflection, how does a fan, with an aerofoil section - just like a wing - work? What essential difference can you suggest between fan and wing?

If we were discussing some Illusionist trick we'd seen on TV, you would never be prepared to ignore Newton 3 in any explanation. Why do you dismiss it as irrelevant in this context? Maybe, the Bernouli calculations give you an accurate enough prediction about behaviour but they can't be relied on to 'explain' the whole thing. This is similar to the analysis of a receiving radio antenna. It's a bit of a frig from beginning to end, making assumptions about current distribution etc. but delivers good results and no one complains - except when the question "what actually happens" is raised.

 

[sophiecentaur]

So, I'm getting a bit lost here, but, I have an additional question. In flight school we were taught that lift is perpendicular to the chord line drawn from the leading edge of the wing to the trailing edge. Which makes sense under the Bournoulli model we were also taught. Is this still considered true? And, if not, how was this missed by aerospace engineers, who must surely rely on such calculations?

Flight school teaches you to fly. Just like a seagull, if you spent your time worrying about the Physics of how you stay up there, you'd fall out of the air.
Many years ago I did a parachute jumping course, along with a group of fellow (very bright) research Engineers. The (Army) instructor just couldn't cope with our constant and very interested technical questions. ("I'm afraid I'm losing you guys.") In the end, we just did it by numbers - as he wanted - and we got on fine.

 

[rcgldr]

Is there some transition between the way a helicopter wing and a fixed wing works, then? The difference in efficiency is just a difference in detail - it doesn't have to he 'in principle'. In fact, how can it be? The only difference is surely that the helicopter blade effect is hundreds of times more on the same local region of air around it.

There are several reasons for helicopter rotor inefficiencies. One issue is that the relative speed at the inner part of the rotor is much less than the outer speed. Another issue is that a cambered airfoil produces a downwards pitching torque that would put too much stress on a rotor blade and it's support, so a helicopter rotor uses a nearly symmetrical airfoil. Similar to a propeller, there is washout, and the washout near the outer tips is set to reduce lift and the associated vortices that would otherwise be generated.

A hovering helicopter has to deal with it's own induced wash, and for some helicopters, it's unsafe to vertically descend into the downwash because there's not enough power to stop the descent. For a helicopter in forward flight there's much less induced wash, and forward flight takes less power than hovering.

The core principle is the same, lift is the result of accelerating air downwards, via diversion of the flow relative to a rotor blade, propeller blade, or a wing.

energy gradually dissipates.

but not the impulse. The impulse may get spread out over a large area, but the magnitude of the impulse does not diminish over time or distance until some other force or impulse opposes it. As pointed out in several posts, the average force that the atmosphere applies to the surface of the Earth is the sum of the weight of the atmosphere and the weight of any aircraft (or hovering balloons) that the atmosphere is supporting, it's a closed system.

behaviour in a wind tunnel though.

Wind tunnels that are too "short" prevent vertical air flow, and essentially model a wing in a combination of ground effect and "ceiling" effect (air prevented from flowing downwards from above).

 

[boneh3ad]

...then as the pressure increases again, the flow transitions into turbulent flow and separates somewhat from the surface.

As an aside, this is true but misleading. The change in the sign of the pressure gradient and the transition to turbulent flow often do occur in the same region but the relationship is not necessarily causal. In this case, the adverse pressure gradient tends to destabilize certain instabilities in the boundary layer and help speed transition along, but this is not necessarily always the case. The primary instability mode on a swept wing is actually stabilized by an adverse pressure gradient, oddly enough. Also, a turbulent boundary layer won't separate from the surface until quite a bit later than were the boundary layer laminar the whole way.

Calculating drag is a bit more complicated, partly because one set of streamlines end at the leading edge stagnation zone, and another set begins at the trailing edge of a wing (where the stream lines from above and below merge).

That's not really the reason that drag is more difficult. Really, it comes down to a couple things. For one, many times people just grab the drag spit out by inviscid solvers using a panel method, which gives you induced drag but ignores other forms of drag, particularly viscous drag. Viscous drag can often be the dominant form of drag on an airfoil section moving at subsonic speeds, so it is quite important to get it right and many codes ignore it for the sake of simplicity. The next complicating factor is the fact that the location of transition is currently impossible to predict in general. The only truly accurate way to get drag is to do wind tunnel testing at this point in time and scale it. You can, of course, use wind tunnel tests to determine the laminar-turbulent transition properties of a wing and then use that knowledge to feed back into your codes and get a much, much better idea from your codes, and that happens a lot.

You just have to know the limitations of your tool. Some, like XFOIL, go a bit beyond simple inviscid panel methods in order to model the boundary layer and correct for its effect, which improves accuracy in drag prediction. Even XFOIL still uses a very rudimentary transition prediction criterion (though it is about as good as it can get without solving the full Navier-Stokes equations given current knowledge on the subject).

Wing chord can be a straight line or it can be a curved line that is 1/2 between the upper and lower surfaces of a wing. The curved line gives a better idea of the coefficient of lift versus angle of attack for a cambered air foil.

No, wing chord is the straight line from leading edge to trailing edge. The line half-way between the two surfaces is the camber line.

Wind tunnels that are too "short" prevent vertical air flow, and essentially model a wing in a combination of ground effect and "ceiling" effect (air prevented from flowing downwards from above).

If the experiment is designed properly, this isn't an issue. Most of the time in a wind tunnel, either you use a wing small enough to avoid this problem or else you use a wing at such an angle of attack that it produces zero lift (which serves multiple purposes, though funding agencies don't like it much since it is "unrealistic"). Generally, more fundamental studies tend to be in zero-lift situations, negating the issue entirely, and more realistic studies are carried out with a combination of large enough wind tunnels and small enough models assuming the researchers are competent.

 

[Traz 0]

Reduced density requires higher actual air speed for most dynamics. In an aircraft you're probably going by Indicated Air Speed (IAS), which already compensates for air density. For example, stall speed is based on IAS, which takes air density into account.

Actually, density altitude is used to calculate expected aircraft performance, such as, will my plane be flying when I reach the end of this runway or will I be driving into those trees. Also, rate of climb, fuel use, etc.

 

[Traz 0]

Flight school teaches you to fly. Just like a seagull, if you spent your time worrying about the Physics of how you stay up there, you'd fall out of the air.
Many years ago I did a parachute jumping course, along with a group of fellow (very bright) research Engineers. The (Army) instructor just couldn't cope with our constant and very interested technical questions. ("I'm afraid I'm losing you guys.") In the end, we just did it by numbers - as he wanted - and we got on fine.

Silly flight school. They wanted us to understand aerodynamics. Lol

Also, that wing cross-section diagram posted a few entries ago does show "normal force" as acting perpendicular to the chord line, which IS as I was taught. And, so, again my initial question: Is this still considered the proper model for diagramming wing function? Or is it a rough approximation that's good enough for government work?

 

[cjl]

Silly flight school. They wanted us to understand aerodynamics. Lol

Also, that wing cross-section diagram posted a few entries ago does show "normal force" as acting perpendicular to the chord line, which IS as I was taught. And, so, again my initial question: Is this still considered the proper model for diagramming wing function? Or is it a rough approximation that's good enough for government work?

Notice that it has a normal force and an axial force in that frame of reference though - the total force is not perpendicular to the wing. That's just a different frame of reference (which is seldom used - the lift and drag components are usually more useful for calculations). If you really wanted, you could break the force down into any pair of normal vectors you wanted - you could define one as 45 degrees from the chord line for example (and it would be completely correct, just not very useful).

 

[rcgldr]

The change in the sign of the pressure gradient and the transition to turbulent flow often do occur in the same region but the relationship is not necessarily causal.

I had the impression that an adverse pressure gradient usually (but not always) triggers a transition to turbulent flow (assuming turbulent flow hasn't already begun due to other factors).

drag - partly because streamlines end, new ones begin ...

That's not really the reason that drag is more difficult.

I thought that the streamlines ending and beginning were an issue for profile drag (the "partly" part), like a bus traveling down a highway, where the stagnation zones front and rear do not have the smae pressure, and most of the profile drag is usually due to the lower pressure aft of an object (depending on the shape).

No, wing chord is the straight line from leading edge to trailing edge. The line half-way between the two surfaces is the camber line.

I thought I fixed that. It's fixed now.

 

[boneh3ad]

I had the impression that an adverse pressure gradient usually (but not always) triggers a transition to turbulent flow (assuming turbulent flow hasn't already begun due to other factors).

Like I said, it is a related pair of phenomena but not one in the same. At the risk of digging too deep into this topic, I will try and clarify fairly succinctly here what I mean. As an example, the boundary layer on a flat plate will transition to turbulence without the action of an adverse pressure gradient. Boundary layers are essentially very complicated, nonlinear dynamical systems, in many ways like a mass-spring-damper system, only more complicated, and instead of being governed by Hooke's Law and some damping, they are governed by the Navier-Stokes equations.

Much like their simpler counterparts, they have various instability modes that can grow and eventually get large enough to transition to turbulence. It turns out on a flat plate, the instability mode that leads to turbulence is a streamwise wave called a Tollmien-Schlichting wave. On a flat plate, these will eventually grow large enough to transition to turbulence. As it also happens, they are dominant on a 2-D wing. They are also remarkably unstable to an adverse pressure gradient, so when you get farther downstream on a wing and they encounter the adverse pressure gradient, they grow much faster than usual and it leads to early transition. They don't need the adverse pressure gradient in order to cause transition, but the adverse pressure gradient does speed the process along. In this case, your understanding is correct.

For a swept wing, Tollmien-Schlichting waves exist but are not dominant. In those situations, you have what is called the crossflow instability that dominates. That instability, it turns out, is actually made more stable by an adverse pressure gradient. However, on most practical swept wings in service, it transitions well before the adverse pressure gradient occurs anyway. In other words, most commonly-used swept wings actually transition independently of the adverse pressure gradient, and the pressure gradient itself would actually delay the transition somewhat.

I thought that the streamlines ending and beginning were an issue for profile drag (the "partly" part), like a bus traveling down a highway, where the stagnation zones front and rear do not have the smae pressure, and most of the profile drag is usually due to the lower pressure aft of an object (depending on the shape).

That's true enough, but that only occurs on an airfoil when you have separation. Otherwise there is no issue of the streamlines not meeting up neatly. On a bus, you have that massive separation.

 

[sophiecentaur]

Silly flight school. They wanted us to understand aerodynamics. Lol

Also, that wing cross-section diagram posted a few entries ago does show "normal force" as acting perpendicular to the chord line, which IS as I was taught. And, so, again my initial question: Is this still considered the proper model for diagramming wing function? Or is it a rough approximation that's good enough for government work?

I think so. They can hardly expect a specialist flier to be a specialist Physicist at the same time (or vice versa ).
The meaning of the word 'understanding' is very wooly. I am sure that the flight school course didn't require you to do more than be 'comfortable' with the techinical stuff at a reasonable level. What they told you would probably not have been sufficient for you to have designed a wing, for example.