Why Do Aircraft fy? Flat Plate Lift Vs Bernoulli?
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Barit,
Yes the fuselage will provide some lift, but as it is (hopefully) symmetrical, it will provide as much of an upforce as a downforce. This is why you require a positive AoA to gain that small amount of lift. The fuselage is a source of lift in all scenarios, but is so small that it isnt talked about, except apparently here.
The lift coefficient alone wont be enough to allow most planes to fly straight and level at knife-edge, so certaintly cant be used as a standard example of flight. It requires additional thrust at a positive AoA to overcome the weight as illustrated by a harrier, rocket, helicopter.
Anyway, this thread is about how the force of lift is generated, and the fuselage in your example creates lift the same way that a wing creates lift normally, but due to the extreme AR of (most) a fuselage, lift generated will be insufficient for flight, requiring vectored diversion of thrust upwards to help overcome the weight.
That's all im trying to say
Yes the fuselage will provide some lift, but as it is (hopefully) symmetrical, it will provide as much of an upforce as a downforce. This is why you require a positive AoA to gain that small amount of lift. The fuselage is a source of lift in all scenarios, but is so small that it isnt talked about, except apparently here.
The lift coefficient alone wont be enough to allow most planes to fly straight and level at knife-edge, so certaintly cant be used as a standard example of flight. It requires additional thrust at a positive AoA to overcome the weight as illustrated by a harrier, rocket, helicopter.
Anyway, this thread is about how the force of lift is generated, and the fuselage in your example creates lift the same way that a wing creates lift normally, but due to the extreme AR of (most) a fuselage, lift generated will be insufficient for flight, requiring vectored diversion of thrust upwards to help overcome the weight.
That's all im trying to say
Last edited by cc2180; 26th Dec 2008 at 21:34.
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Is it not wrong as well as inaccurate to assume that all the effects that occur in a venturi will be the same if you were to cut the venturi in half, ie. a wing?
* An airfoil is not a Venturi nozzle. There is no phantom surface to produce the other half of the nozzle. Velocity gradually decreases as you move away from the airfoil eventually approaching the free stream velocity. This is not the velocity found along the centerline of a nozzle which is typically higher than the velocity along the wall.
* The Venturi analysis cannot predict the lift generated by a flat plate. The leading edge of a flat plate presents no constriction to the flow so there is really no "nozzle" formed. One could argue that a "nozzle" occurs when the angle of the flat plate is negative. But this produces a negative lift. The velocity actually slows down on the upper surface at a negative angle of attack; it does not speed up as expected from the nozzle model.
* This theory deals with only the pressure and velocity along the upper surface of the airfoil. It neglects the shape of the lower surface. If this theory were correct, we could have any shape we want for the lower surface, and the lift would be the same. This obviously is not the way it works - the lower surface does contribute to the lift generated by an airfoil. (In fact, one of the other incorrect theories proposed that only the lower surface produces lift!)
* The part of the theory about Bernoulli's equation and a difference in pressure existing across the airfoil is correct. In fact, this theory is very appealing because there are parts of the theory that are correct. In considering the pressure-area integration to determine the force on a body immersed in a fluid, if we knew the velocity, we could obtain the pressure and determine the force. The problem with the "Venturi" theory is that it attempts to provide us with the velocity based on an incorrect assumption (the constriction of the flow produces the velocity field). We can calculate a velocity based on this assumption, and use Bernoulli's equation to compute the pressure, and perform the pressure-area calculation and the answer we get does not agree with the lift that we measure for a given airfoil.
I wrote:
Difficult to find anything explicit in the literature. McCormick has some plots of Cl vs AoA at various Reynolds numbers, but they're not superimposed so it's difficult to see the effect clearly. But it shows a flat plate giving a lift coefficient of about 0.75 at Re = 420,000 but only about 0.55 at Re = 42,000. So a 10-fold increase in viscosity causes a small decrease in lift at the same AoA.
Abbot and von Doenhoff also have plots at Re = 3, 6 and 9 million. It's clear that the stall happens at a lower AoA for higher viscosity (lower Re) but it's very difficult to deduce the effect of viscosity on Cl at low AoA.
Beyond the trace of viscosity (present in every fluid that isn't a superfluid like helium 3) that is necessary for lift, lift generally decreases the more viscous the fluid, with all else equal. I'll see if I can dig up a graph.
Abbot and von Doenhoff also have plots at Re = 3, 6 and 9 million. It's clear that the stall happens at a lower AoA for higher viscosity (lower Re) but it's very difficult to deduce the effect of viscosity on Cl at low AoA.
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Bernoulli and Newton - Cause and Effect
Both the Newton (laws of motion, flat plate) and Bernoulli camps are more or less correct. Lift is created by accelerating mass downwards. In steady flight, the force created by accelerating mass (free air, engine exhasust) downwards is equal to the force on the aircraft due to gravitational attraction (ignoring minor effects such as buoyancy). The downwards deflection of the air is produced by the difference in pressure between the upper and lower surfaces of the wing predicted by Bernoulli's Theorem, although the mathematics describing the flow and its pressure differences is rather complicated.
(If we think of the example of a hosepipe playing on a flat plate, the plate slows down the water, so the pressure on the plate increases relative to that of the flowing water - which is the same as that of the surrounding still air, so the plate tends to move in the direction of the jet.)
Fifty years ago I was in the middle of a degree course in Difficult Sums which included, among many other things, a series of lectures on fluid dynamics. The years have eroded much of the detail from my memory, but the basic principles remain.
The partial differential equations that describe the steady three-dimensional flow of a real fluid are complicated, non-linear and do not have neat analytic solutions. When acceleration of surfaces in contact with the fluid is taken into consideration, the situation is even worse.
Without the assistance of modern high-speed computers, the accurate numerical solutions of the full equations for even simple cases are just not possible. The only feasible approach is to make simplifying assumptions, work out the numbers, and then perform experiments (for example with wind or water tunnels) to determine how closely the simplified theory matches reality.
The main sources of intractibility in the full equations are viscosity (or internal friction) and compressibility. So the simplest approach is to eliminate both, introducing the concept of the ideal fluid.
Solution of the simplified equations for two-dimensional flow round a circular object (equivalent to flow in three dimensions round an infinte circular cylinder) is (or was for me in the days of my youth) fairly easy. A simple trick (called conformal mapping) can transform this flow into the flow round an aerofoil shape. The difficult bit is finding a transformation that converts the circle into the aerofoil of interest.
This simplified model works well for some things. It predicts flows (and thus pressures) fairly well, so long as you don't look too close to the trailing edge of the wing. The pressures over most of the upper and lower surfaces tally well with the predictions from Bernoulli's equation. However this simplifies theory has one major drawback - it predicts zero lift (and drag). Introducing "circulation" into the theoretical flow can get out of this problem and produce acceptable predictions for many purposes.
However, the simplified system is not good for predicting flows near the trailing edge of the wing, or where the flow will separate from the wing with the resulting turbulence and increased drag. To model such things as flow separation and the onset of turbulence, the equations have to take account of viscosity, which increases the complexity of the computation dramatically. One of the complications is that there is a strong interaction between viscosity and typical lengths of objects in the flow. In one of the possible simplifications for viscous flow, it turns out that there is a characteristic number, the Reynolds Number, that identifies flows that are very similar though with widely different lengths and viscosities.
By varying viscosity as well as the scale of a model it is possible to set up an experiment in a relatively small space that can provide information about real flows past larger objects in fluids with different viscosity.
Reynolds Number modelling is applicable only where the fluid can be trreated as incompressible. It is initially a little surprising that air can be treated as incompressible for aerodynamic purposes up to speeds fairly close to the speed of sound. Beyond this, into the transsonic range and beyond, a different simplification of the general fluid flow equations is needed.
At subsonic speeds, the air can effectively "hear an aircraft coming" and move out of the way, resulting in relatively simple flow round the aircraft. At supersonic speeds, the aircraft arrives without warning and the result is a shockwave. The flow regime is quite different, and a wing designed for supersonic speeds is likely to be quite thin and symmetric, contrasting to the thicker and cambered low-speed wing.
Computational Fluid Dynamics (CFD) software typically will use very general forms of the fluid dynamics equations, modelling both compressibility and viscosity. Some simplifications may still be used, but fast computers permit much more detailed computations in a given time than are possibly with simpler tools.
So, rougly speaking, Bernuolli explains the cause of lift (the pressure difference), Newton explains the effect of the pressure difference.
(If we think of the example of a hosepipe playing on a flat plate, the plate slows down the water, so the pressure on the plate increases relative to that of the flowing water - which is the same as that of the surrounding still air, so the plate tends to move in the direction of the jet.)
Fifty years ago I was in the middle of a degree course in Difficult Sums which included, among many other things, a series of lectures on fluid dynamics. The years have eroded much of the detail from my memory, but the basic principles remain.
The partial differential equations that describe the steady three-dimensional flow of a real fluid are complicated, non-linear and do not have neat analytic solutions. When acceleration of surfaces in contact with the fluid is taken into consideration, the situation is even worse.
Without the assistance of modern high-speed computers, the accurate numerical solutions of the full equations for even simple cases are just not possible. The only feasible approach is to make simplifying assumptions, work out the numbers, and then perform experiments (for example with wind or water tunnels) to determine how closely the simplified theory matches reality.
The main sources of intractibility in the full equations are viscosity (or internal friction) and compressibility. So the simplest approach is to eliminate both, introducing the concept of the ideal fluid.
Solution of the simplified equations for two-dimensional flow round a circular object (equivalent to flow in three dimensions round an infinte circular cylinder) is (or was for me in the days of my youth) fairly easy. A simple trick (called conformal mapping) can transform this flow into the flow round an aerofoil shape. The difficult bit is finding a transformation that converts the circle into the aerofoil of interest.
This simplified model works well for some things. It predicts flows (and thus pressures) fairly well, so long as you don't look too close to the trailing edge of the wing. The pressures over most of the upper and lower surfaces tally well with the predictions from Bernoulli's equation. However this simplifies theory has one major drawback - it predicts zero lift (and drag). Introducing "circulation" into the theoretical flow can get out of this problem and produce acceptable predictions for many purposes.
However, the simplified system is not good for predicting flows near the trailing edge of the wing, or where the flow will separate from the wing with the resulting turbulence and increased drag. To model such things as flow separation and the onset of turbulence, the equations have to take account of viscosity, which increases the complexity of the computation dramatically. One of the complications is that there is a strong interaction between viscosity and typical lengths of objects in the flow. In one of the possible simplifications for viscous flow, it turns out that there is a characteristic number, the Reynolds Number, that identifies flows that are very similar though with widely different lengths and viscosities.
By varying viscosity as well as the scale of a model it is possible to set up an experiment in a relatively small space that can provide information about real flows past larger objects in fluids with different viscosity.
Reynolds Number modelling is applicable only where the fluid can be trreated as incompressible. It is initially a little surprising that air can be treated as incompressible for aerodynamic purposes up to speeds fairly close to the speed of sound. Beyond this, into the transsonic range and beyond, a different simplification of the general fluid flow equations is needed.
At subsonic speeds, the air can effectively "hear an aircraft coming" and move out of the way, resulting in relatively simple flow round the aircraft. At supersonic speeds, the aircraft arrives without warning and the result is a shockwave. The flow regime is quite different, and a wing designed for supersonic speeds is likely to be quite thin and symmetric, contrasting to the thicker and cambered low-speed wing.
Computational Fluid Dynamics (CFD) software typically will use very general forms of the fluid dynamics equations, modelling both compressibility and viscosity. Some simplifications may still be used, but fast computers permit much more detailed computations in a given time than are possibly with simpler tools.
So, rougly speaking, Bernuolli explains the cause of lift (the pressure difference), Newton explains the effect of the pressure difference.
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So, rougly speaking, Bernuolli explains the cause of lift (the pressure difference), Newton explains the effect of the pressure difference.
As you alude to, you cannot attempt to model each and every particle going over different sections of an aerofoil. At some point certain generalisations have to be made.
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Lift
I wrote a couple of interesting articles for Associated Content that were helpful. The amount of disagreement on this topic is surprising. The shape of the wing and pressure differences are of course important (Bernoulli), but I don't think an aircraft would ever take off without the downward deflection of air via AOA of the aircraft and control surfaces (Newton).
How an Airplane Wing REALLY Generates Lift - Associated Content
How an Aircraft Wing Generates Lift - Associated Content
Bernoulli's Principle - Associated Content
How an Airplane Wing REALLY Generates Lift - Associated Content
How an Aircraft Wing Generates Lift - Associated Content
Bernoulli's Principle - Associated Content
Last edited by deHavillandDave; 31st Dec 2008 at 00:59.
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rubik101 - My model aeroplanes fly quite well with flat tailplanes and fins (ususally made out of 1/82 or 1/4" balsa wood). A few of my small 'planes have "flat" wings too and they fly OK. Having tailplanes and fins with "sections" doesn't seem to make much difference so far as models are concerned.
Maybe everything changes on "full-size".
Maybe everything changes on "full-size".
Hold your hand palm down out of the window of a moving car.Tilt the angle of your hand up ,your whole hand then raises.Tilt your hand down,your entire hand moves down.
for understanding of this subject
I recommend that one has familiarity with two dimensional flows, Navier Stokes solutions, spherical harmonics, Curl, Gradients, Flux, Divergence, volume elements, vector math the Laplacian the Legendrian and slope fields, as well as {Oiler's}
theorem
here one method to arrive at your answer from Abbott and Van Doenhoff
xe =1/Ux ^8.210* INT[U^8.210] dx
Sheesh
Happy New Year Pprune
PA
I recommend that one has familiarity with two dimensional flows, Navier Stokes solutions, spherical harmonics, Curl, Gradients, Flux, Divergence, volume elements, vector math the Laplacian the Legendrian and slope fields, as well as {Oiler's}
theorem here one method to arrive at your answer from Abbott and Van Doenhoff
xe =1/Ux ^8.210* INT[U^8.210] dx
Sheesh
Happy New Year Pprune
PA
Last edited by Pugilistic Animus; 2nd Jan 2009 at 00:41. Reason: spelling--as usual
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Heya "Tarq57" (post 24) well not really, because I had said "Haven't you ever heard of the passenger theory..." plus if I was going to quote my source, that would mean me providing my email address and password and isp website, and well, I'd kinda rather not do that. So pretty much you're saying, when I repeat a joke to anyone, I should be stating my source otherwise its plagiarism? I dont think many people mind to much.
"What did the police man say to his tummy?.....You're under a vest!" - Christmas Cracker from 2008 Christmas lunch (sorry not sure the date of manufacture or factory this Christmas Cracker came from)
"What did the police man say to his tummy?.....You're under a vest!" - Christmas Cracker from 2008 Christmas lunch (sorry not sure the date of manufacture or factory this Christmas Cracker came from)
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lift
An aeroplane flies because of velocity and angle of attack of the aerofoil,
cause and effect are in play here purely down to Newtons theory, Bernolli has only a small part if any to play here.
Think of this, if an aeroplane really was sucked into the air then all those really big aircraft will have to have very strong rivited sheeting to hold hundreds of tons up aloft, also how could an aeroplane fly upside down and not be sucked into the ground (and don't talk about centre of pressure), also the comments above are correct there is no such thing as pulling or sucking it's another matter of cause and effect a common mis-conception, I will try to explain another time.
cause and effect are in play here purely down to Newtons theory, Bernolli has only a small part if any to play here.
Think of this, if an aeroplane really was sucked into the air then all those really big aircraft will have to have very strong rivited sheeting to hold hundreds of tons up aloft, also how could an aeroplane fly upside down and not be sucked into the ground (and don't talk about centre of pressure), also the comments above are correct there is no such thing as pulling or sucking it's another matter of cause and effect a common mis-conception, I will try to explain another time.
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I propose a simple explanation. Lift is caused by differential velocity between a flat plate solid and a Newtonian fluid. The amount of lift (and drag) is caused by the pressure ratio which may be varied by changing the angle of incidence between fluid and fp solid, and/or the shape of the solid.
In trying to figure this out I have a couple of facts I cling to in order to understand:
1. On fixed wing aircraft, the engines provide a fraction (like 1/2, 1/3 whatever) of the force needed to lift the aircraft. I realize a few aircraft actually produce more thrust than weight.
Question is, where is the extra force coming from? It would seem a conservation principle is violated here.
2. Helicopter engines produce enough HP to lift their max weight at 1 g if they were on a cable. I.e. their "thrust" is equal or greater than their weight. I believe this allows hovering.
3. In level flight of a fixed wing, the weight of the aircraft is equal to the mass of the air being accelarated downward. (Newton)
Am I close? Or should I just go back to playing MSFS?
Therefore, I guess that the column of air collapsing into the lower pressure area behind the aircraft adds the missing force in the case of fixed wing aircraft with less thrust than weight.
1. On fixed wing aircraft, the engines provide a fraction (like 1/2, 1/3 whatever) of the force needed to lift the aircraft. I realize a few aircraft actually produce more thrust than weight.
Question is, where is the extra force coming from? It would seem a conservation principle is violated here.
2. Helicopter engines produce enough HP to lift their max weight at 1 g if they were on a cable. I.e. their "thrust" is equal or greater than their weight. I believe this allows hovering.
3. In level flight of a fixed wing, the weight of the aircraft is equal to the mass of the air being accelarated downward. (Newton)
Am I close? Or should I just go back to playing MSFS?
Therefore, I guess that the column of air collapsing into the lower pressure area behind the aircraft adds the missing force in the case of fixed wing aircraft with less thrust than weight.
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Fakepilot,
1.Please see my short post above. The lift is caused by the forward motion of the wing through the air (the differential velocity). The forward motion is caused by the thrust of the engine, which does not need to equal or exceed the weight/mass of the a/c.
2. Helicopters have rotary wings. The lift is produced by the differential velocity of the blades (or wings) moving through the air. Directional thrust and speed is produced by tilting the blades.
3. Yes, but what about drag. Do you think that should be added to the weight? Concerning the second part of this question, I think that the answer is no, as there is no 'missing' force.
I hope that this helps.
1.Please see my short post above. The lift is caused by the forward motion of the wing through the air (the differential velocity). The forward motion is caused by the thrust of the engine, which does not need to equal or exceed the weight/mass of the a/c.
2. Helicopters have rotary wings. The lift is produced by the differential velocity of the blades (or wings) moving through the air. Directional thrust and speed is produced by tilting the blades.
3. Yes, but what about drag. Do you think that should be added to the weight? Concerning the second part of this question, I think that the answer is no, as there is no 'missing' force.
I hope that this helps.
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My hand produces lift
Yes, its true. My hand actually creates lift. I suck it outta the car window, and the harder i pressed the accelerator pedal, the higher my hand went.
Thats all i really need to know about that!
Thats all i really need to know about that!
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fakepilot -
The relationship between thrust and lift is identical to the relationship between drag and lift. We call this the lift/drag ratio, or L/D. The number can range between 5 and 50, depending on the cleanliness of the design. Sailplanes might exceed 50 - and the Harrier etc. might be much lower than 5.
The L/D can also be called the glide ratio. If a plane can glide, power off, for 20 miles while losing 1 mile in altitude, then its L/D is 20.
barit1
(aeronerd)
The relationship between thrust and lift is identical to the relationship between drag and lift. We call this the lift/drag ratio, or L/D. The number can range between 5 and 50, depending on the cleanliness of the design. Sailplanes might exceed 50 - and the Harrier etc. might be much lower than 5.
The L/D can also be called the glide ratio. If a plane can glide, power off, for 20 miles while losing 1 mile in altitude, then its L/D is 20.
barit1
(aeronerd)
Last edited by barit1; 28th Jan 2009 at 01:01. Reason: wiki reference
The technical answer you are looking for is found in The Kutta Condition
just a method of laying siege to certain second order differential equations-provided certain conditions are met or assumed
in airfoil design--- certain equations have been found to approximately model the lift or drag characteristics of a wing section but nevertheless the WIND TUNNEL remains the reall proving grounds as aerodynamics is an empirical science that lends itself to a more mathmatical --as opposed-- to verbal discussion--
Let's not even attempt a discussion of high lift devices
I propose a simple explanation. Lift is caused by differential velocity between a flat plate solid and a Newtonian fluid. The amount of lift (and drag) is caused by the pressure ratio which may be varied by changing the angle of incidence between fluid and fp solid, and/or the shape of the solid
absolutively
PA
Well Mr Bernoulli -
What rule of physics, mathematics, or horticulture states that two air molecules which seperate at the leading edge of a wing, ever meet up again in the future?
What rule of physics, mathematics, or horticulture states that two air molecules which seperate at the leading edge of a wing, ever meet up again in the future?
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Well Mr Bernoulli -
What rule of physics, mathematics, or horticulture states that two air molecules which seperate at the leading edge of a wing, ever meet up again in the future?
What rule of physics, mathematics, or horticulture states that two air molecules which seperate at the leading edge of a wing, ever meet up again in the future?
rgds pf
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A Physical Description of Lift
Try this link article by D Anderson.You will find that Newtons second law prevails when considering the mechanism of lift from a physical standpoint. The classical Bernoulli explanation is quite misleading if not downright wrong. (The Bernoulli diff pressure effect is present alright but fails to account for bulk amount of lift generated and is therefore secondary) It is the Coanda effect which is responsible for the bending of the flow around an aerifoil resulting in the downwash which by reaction momentum exchange produces lift. Lift is not a free lunch, the power required can be nicely calculated by this Newtonian approach.
D Anderson's book is basic but very good written by a blend of a physicist and pilot.
Try this link article by D Anderson.You will find that Newtons second law prevails when considering the mechanism of lift from a physical standpoint. The classical Bernoulli explanation is quite misleading if not downright wrong. (The Bernoulli diff pressure effect is present alright but fails to account for bulk amount of lift generated and is therefore secondary) It is the Coanda effect which is responsible for the bending of the flow around an aerifoil resulting in the downwash which by reaction momentum exchange produces lift. Lift is not a free lunch, the power required can be nicely calculated by this Newtonian approach.
D Anderson's book is basic but very good written by a blend of a physicist and pilot.