In the early days of aviation, engines were not very powerful, so there was a tendency to rely more on Bernoulli Lift, because it is more efficient regarding causing less Aerodynamic Drag. But in recent decades, extremely powerful (jet) engines have been developed, and aircraft have tended to be designed to rely very heavily on Reaction Lift. The results of this are far greater payload capacity, but also far greater Aerodynamic Drag.
It is almost hilarious regarding the OPINIONS of a lot of people who have NO organized education in Aerodynamics or Physics! It seems a lot like Politics where people hold intense passionate opinions, often without significant actual logical reason! Or religion, where at least three different (huge) groups of Christians each insist they KNOW what the future will be (Pre-Millennialists, Post-Millennialists, and Amillennialists) and they get into vicious arguments over screaming that the others are wrong! As far as I know, no one actually KNOWS the future, so each of their positions seems to have no actual basis (except for their INTERPRETATION of a few words in the Bible). WHY do they each feel it appropriate to scream insults at each other over a subject where NONE of them can actually know the absolute facts of the future? Hmmm!
Regarding this subject of why aircraft can fly, some people seem to remember a Grade School science book that said that it is because of Bernoulli Lift, and so they seem unwilling to tolerate any other viewpoint! Others have seen some TV program or web-site where someone has insisted that aircraft can fly because of Reaction Lift (also called Newtonian Lift) and they then seem willing to not tolerate any other view! It really is amazing! And then there are others who have become aware of more technical texts which refer to a concept (actually a theory) called Circulation, which is an immensely complex concept, and actually beyond anyone's ability to actually solve the equations except for trivially simple examples (in other words the speaker does not actually understand Circulation except that it sounds impressive!) and so that speaker claims that all other ideas are dead wrong and only Circulation is valid!
Human nature on display!
I received my education in Physics at the University of Chicago. The University seems to have done a good job and I believe that I have a solid understanding of the physics of aerodynamics. This page is meant to aid in providing an understanding of the subject to others.
It actually turns out that Bernoulli Lift IS a correct explanation, but only for PART of the lift at any instant. And Reaction Lift IS a correct explanation, but only for PART of the lift at any instant. And the theory of Circulation IS a wonderful mathematical way of expressing THE COMBINATION, but that the Circulation equations are all advanced Calculus, which require ASSUMPTIONS to be made in order to try to solve them. So ALL are right and yet all are somewhat deficient!
I feel that it is easiest to understand, and reasonably accurate to calculate, if BOTH Bernoulli Lift and Reaction Lift are calculated for any specific situation. This is informative because it then allows a reasonably accurage analysis of HOW MUCH of the Lift at any instant is Bernoulli and how much is Reaction.
Interestingly, there are a small group of people today who actually believe that there is no such thing as Bernoulli Lift! These extremely aggressive people clearly have no background in Engineering or Physics, and it is really strange that they believe such a thing. At first, it was amusing that people who think they are educated could be so mis-informed. But they are certainly incrediby aggressive and annoying! For them, and anyone else who is curious, I suggest a very simple experiment. Get two standard sheets of typing paper (without fold creases) and hold them up in front of your face edgeways, about 3" apart, so you can see between the two hanging sheets. If you now blow air gently between them, what will happen? Doesn't it seem that the pressure of the air you blow should push them apart? But, instead, they move together! And, the harder you blow, the more they move together! It's a simple example of the Bernoulli effect, and Bernoulli Lift. (Critics have no explanation for this effect!)
Of course, many people in various sports KNOW the effects of the Bernoulli effect and how to cause it! If you play ping pong, and ever put spin (English) on the ball, you easily see the effects! If you put sidespin on a ping pong ball, it curves to the side, because the two sides of the ball are now moving at different speeds to the room's air. This effect is generally referred to as the Magnus Effect, which is actually a very complex variant of the Bernoulli Effect. It is primarily different because the rotation of the object CAUSES motions of the air immediately adjacent to the surface. This Magnus Effect is therefore enhanced by anything that increases the frictional coefficient, such as seams on a baseball or microscopic irregularities in the surface of a ping pong ball. When the ball/object has very low mass, such as a ping pong ball, the effects can be quite substantial. (This Effect turns out to be a rather complex calculation, though, because it necessarily includes some factors regarding the smoothness of the surface of the ball, frictional effects, turbulence effects, and some other advanced concepts!) An interesting detail is that the fact that the ROTATING ball CAUSES local air motion, which has the effect of making it appear that the effect superficially seems to be the opposite that which would be expected by a simple Bernoulli Effect! This is an indication that such subjects are often far more complex than they first appear, and quite possibly might be a primary reason why many people seriously misunderstand the Bernoulli Effect.
There is also something called the Coanda Effect, which is also another complex variant of the Bernoulli Effect. Essentially the local low pressure caused by the Bernoulli Effect causes the surrounding fluid (air in this case) to follow around behind a curved surface, which then appears to have different effects. It is rather funny (and sad) when angry e-mailers tell me that this presentation is wrong in describing a Bernoulli Effect, as they claim that there is no such thing as a Bernoulli Effect and the Coanda Effect is operant instead! Such writers are ignorant of the fact that the Coanda Effect IS simply a type of Bernoulli Effect!
Long ago, when I was a little kid, there was a guy on PBS with a science show named Daniel Q. Posin. He was even a Physicist! One day he announced that there was NO SUCH THING as a curve ball in baseball! He insisted that the Bernoulli Effect was not big enough to cause any such measurable effect. However, just a couple weeks earlier, my cousin in AAA baseball had taught me how to throw a curve ball! I guarantee that it can be done! It is really rather cool to throw! Actually, the Bernoulli Effect also even more directly explains a different popular pitch, the Knuckleball. That pitch is thrown where the ball has no spin at all. As the ball proceeds the 60 feet to the plate, it encounters random natural tiny wind gusts, where a brief Bernoulli Effect to the left or to the right or up or down happens. The ball doesn't change very much, but for people familiar with the effect, it is often described as JUMPING one way or the other. Even though Knuckleballs are thrown rather slowly, and the batter thinks he has an easy solid hit, the fact that the ball CAN jump an inch or two in any direction in just the last few feet before the plate makes it a very difficult pitch to hit! The batter swings where he expects the ball to be, and it is not always there! It is also a psychological stress to be WATCHING that slow-moving ball jumping back and forth and up and down on the way from the pitcher! (If the wind is nearly calm, knuckleballs have the greatest effect. On windy days, they tend to have very little effect.) Even the Pitcher has NO idea what a Knuckleball might do!
(Posin did not seem to understand the variants of the Bernoulli effect which are called Magnus or Coanda, or else he would have both realized that it was real, and also then have been able to have calculated how much effect there would be.)
Ping-pong players ALL know about spin and the things they can cause a ping-pong ball to do!
When I became a semi-pro volleyball player, like other good players, I often used these sorts of effects. I had a "smoke" serve, that could never have gone in without the effect of spin. In fact, since I had also played decent level of tennis, I knew about both the American Twist and the Australian Twist serves, which also put ping-pong-like sidespin on the ball as well. I figured out how to do the compound (down and either side) action on my Smoke volleyball serve, where even excellent diggers sometimes totally whiffed my serve for an ace! Even most really hard spikes generally are given some wrist-snap topspin to increase the chance that they will land inbounds. Knuckleball (floater) serves are popular in high-level volleyball, too. If you have watched Olympic play, many teams rarely wail on the ball any more, but serve what appears to be easy and simple serves. They are like that because they are ALL knuckleball serves (or floaters, the name actually given them in the game). There are interesting psychological effects on the person waiting to receive such a serve, because you always know that it MIGHT suddenly jump a few inches one way or another and you will then look like a fool for shanking off such an easy-looking serve!
NASCAR and other racing USES the Bernoulli effect to create what they call Downforce. At racing speed, a 1200 pound vehicle can press downward on its tires with more than 3000 pounds of apparent vehicle weight! That effect allows the tires to stay in traction where the vehicle would otherwise have broken loose and gotten bent. The results are that they can drive around a curved track far faster than would actually be possible with the actual vehicle weight being on the tires. (Racing Vehicles DO often ALSO have angled Spoilers on top of the rear deck, which has a different effect, one essentially like the Reaction Lift discussed in this presentation, of forcing air UPWARD to cause a Reaction that is also a downforce. So such vehicles often use BOTH aerodynamic approaches).
Sports-people rarely ever mention such effects, choosing instead to keep such things as secret as possible, in case some opponent is not aware of the advantages that can be had! But some (maybe a lot) of people who use such effects probably have no idea of the Physics behind what they are doing! They just do it because it helps them win and they know that if they don't use it, someone else who does WILL win!
Weigh and measure a ping pong ball, and find some way to measure the velocity (distribution) of air coming out of the vacuum exit port. With some math and some cute Posters, you have am impressive presentation!
It is even fairly easy to do, APPROXIMATELY. But there are different things that you need to separately calculate.
First, you need to use simple applications of Newton's Action-Reaction Law to calculate the necessary air volume flow and therefore airspeed which is required to SUPPORT THE WEIGHT of the ping pong ball, under the assumption that it is EXACTLY STRAIGHT UP above the air source. This is actually a variant of the Reaction Lift discussed in this presentation. Pretty easy to calculate. Gravity, the weight of the ball, its area/diameter, and you are pretty much there.
IF the ball always remained EXACTLY straight up, no Bernoulli Effect would even be necessary! Pure Reaction Lift would support the ball! (That actually determines how HIGH the ball would be suspended above the end of the nozzle.)
When it is NOT directly straight up (EXACTLY in the middle of the airflow), which is ALWAYS, then it gets more interesting and you have to calculate the Bernoulli Effect. You have to try to determine how the airspeed slows down across the width of the pattern of the blower output, the distribution of air velocity across the actual airflow. Make an accurate graph of that! Depending on how high above the nozzle you measure, this pattern is likely to be four or six inches wide.
Let's see what we have now! Say that we hold the vacuum output at an angle, maybe 10 degrees. Logically, it would seem that the ball should immediately fall off to the low side, due to gravity, and that would be the end of a very short demo! But that is NOT what happens! The ball SHOULD do that, meaning that you can use High School Physics (and geometry or trigonometry) to calculate the (sideways but slightly downward) gravitational force which certainly has to be working (since gravity does NOT stop just because you happen to want it to!)
This means that the Bernoulli Effect MUST NECESSARILY BE CREATING an inward-and-upward force to exactly balance what gravity is trying to do. When you look at the Bernoulli formula, you see that the local pressure is directly related to the velocity of the air there (which is actually what Bernoulli said and which was simply a specific way of saying Newton's Conservation of Energy).
So now you have the size of the ball, and from your graph, you have the (faster) air velocity near the center of the airflow, and also know the (lower) air velocity at a distance of one-ball-diameter away. You can then calculate the Bernoulli Effect (regarding the local air pressure) for EACH side of the ball. The side nearer the middle of the airflow is at the place of higher airspeed, and therefore Bernoulli shows that the local pressure there is lower. The HIGHER air pressure on the opposite side of the ball (AWAY FROM THE AIRFLOW) therefore has some extra pressure left after canceling out the lower (inner) pressure. Still with me??? This FORCES the ball to try to move TOWARD the middle of the airflow!
You now have the area of the ball AND the calculated pressure differential, which means that you now have the TOTAL FORCE acting on the ball due to the Bernoulli Effect (toward the middle). WHICH you have CALCULATED, based on your air-velocity graph. Before, you had calculated the gravitational force which should cause the ball to (fall) outward, and so now you have calculated the opposing force which must be exactly the same, to keep the ball in the airflow!
Cool, or what?
Using the weight of the ball, and the blower airflow info, and the angle that you have tilted the blower output, you NOW HAVE A MATHEMATICAL PREDICTION (what would be called a Theory if Bernoulli hadn't beaten you to it by around 200 years!)
So then you do the ping pong ball demo, and the fans will cheer!
MORE, everyone is always impressed at when you tilt the airflow to maybe 30 degrees (depends on the power and airflow of the vacuum). Oohs and aahs!
BUT you have already calculated (by Bernoulli) that at specific tilt angles, the ball actually is not quite centered in the airflow, but at a specific fraction of an inch away WHICH YOU HAVE MATHEMATICALLY PREDICTED.
I do not want to do any more for you here, to leave YOU the ability to actually have YOUR OWN Science Fair Project! I may have already given you too much, to make it all a little to simple and easy!
So now you will have calculated the predicted (UNIFORM) airspeed you will need to provide, which should provide sufficient Bernoulli Lift to raise that particular item up off the table. So you get a furnace blower and a variable speed control compatible with it, and maybe an air velocity meter (some are not very expensive). So you show your guests your calculations of how fast the air SHOULD need to be, and then show them the experiment where your furnace blower blows air at a particular speed across the top of each sheet of material, that confirms your Bernoulli calculations are decently accurate. Not quite as impressive as the Project suggested above, but still impressive. Of course, you need to be explaining to Judges exactly what is happening in your calculations and then in the experimental confirmation!
The sheets of material can NOT be tight to the table they are laying on! It is NECESSARY that there be at least a tiny airspace UNDER the sheet of material. Why? Do you know? It is because the Bernoulli Effect you are creating is causing a slight REDUCTION in the local atmospheric pressure. Nothing could then happen UNLESS the NORMAL atmospheric pressure is acting against the UNDERSIDE of the sheet of material. Actually, for things like paper and cardboard, they are never tight to a table and so there is always some air underneath them (unless the table is wet where that air cannot exist). But it is still best for such a Project to either make sure the table is not absolutely smooth and not wet, or even place the sheets of material on tiny spacers, such as the poker chips.
The boomerang is not actually held exactly vertical when throwing, but slightly tilted to the right. The rotational spin therefore creates the Bernoulli force vector that is slightly upward of being straight horizontal to the left. This small vertical component of the force vector overcomes the vertical weight vector of the boomerang, which keeps it from crashing down. Eventually, as aerodynamic drag slows down the boomerang's spin, the Bernoulli force vector also reduces. Once the vertical component of it drops to less than the weight of the boomerang, it falls and crashes. In these two paragraphs is everything there is to say about the Physics of boomerangs, and it is entirely due to Bernoulli Lift!
The uninformed people who insist on denying that Bernoulli lift exists are apparently also unaware that a properly shaped airfoil wing still has POSITIVE LIFT even when angled slightly downward (technically called a negative angle-of-attack). Logically, when the airfoil is aimed downward, the Reaction force of air hitting the TOP of the wing and being deflected upward SHOULD be forcing the wing downward, and that happens. But the upward Bernoulli Lift counteracts that effect, and the sum can still be an upward lift. In the case of standard airliner wings (NACA 4415 or NACA 4412 or NACA 4408 shape), they can have a negative angle-of-attack of more than 3° and still be creating upward lift. (See the graph just below.) (The limit for the NACA 4415 or 4412 shape is around -4° where the net lift is zero, where upward Bernoulli lift exactly matches downward reaction lift. For zero angle-of-attack, that specific wing shape has a sectional lift coefficient of +0.4) If you are ever confronted by anyone who insists that Bernoulli Lift doesn't exist, ask them to explain how and why the wings on airliners are still able to produce UPWARD lift when aimed 3° downward! According to their (partially correct but incomplete Reaction Lift) thinking, it should not just drop like a rock, but actually be accelerated downward FASTER than a rock! But they are definitely wrong! ANY Aerodynamicist could inform them about that, or they could look on page 490 or other pages of Theory of Wing Sections for the chart of the data for any NACA wing contour. We will briefly consider the NACA 4415 shape here.
Here is a copy of the NACA 4415 page in that book:
We will ignore the lowest line on this graph, as it presents an entirely different characteristic! The five other (angled) lines on the graph are as follows: The uppermost one only applies when near takeoff or landing where the airspeed is low, and the flaps are extended and tilted downward at 60°, which has the effect if increasing the lift but also tremendously increases the drag, requiring far more engine power. (The graph on the following page (491) in that book shows the drag coefficients, where it shows that extending the flaps nearly doubles the Sectional Drag Coefficient.)
The four other lines are nearly identical. They present the lift coefficients for different Reynold's Numbers, which essentially means different velocities of the aircraft.
We want to point out several details here. First, find the (horizontal) graph line of ZERO (Sectional Lift Coefficient). You can see that it intersects those four angled lines at around -4° angle-of-attack. This shows that this particular wing shape can be AIMED DOWNWARD by 4°, where it would have zero total lift. Any AOA HIGHER than -4° therefore has POSITIVE LIFT!
Now look at the (vertical) graph line of ZERO° AOA. It intersects the angled lines at around +0.4 Sectional Lift Coefficient. THIS actually identifies the AMOUNT of BERNOULLI LIFT that this wing shape has. In fact, if we could somehow separate the Bernoulli and Reaction Lift components, we would see a (nearly) HORIZONTAL LINE at +0.4 that would represent the Bernoulli Lift. This is due to the fact that the Bernoulli Lift is not very dependent on the angle of attack.
Given that fact, we can see that the Reaction Lift would therefore be exactly the angled lines, EXCEPT that the entire graph would be shifted DOWNWARD by that 0.4. if there were no Bernoulli lift. At an AOA of 0° (flat) the Reaction Lift Coefficient would therefore be zero. The straigness of that angled line then shows that the Reaction Lift is very close to being PROPORTIONAL to the angle of attack.
We can therefore see BOTH effects in this graph! The Bernoulli Lift simply is an UPWARD SHIFT of the graph lines, and the Reaction Lift is the angle (slope) of the lines themselves.
Regarding the Reaction Lift, we might think that those lines are STRAIGHT at a constant slope. That is actually not quite true! The slope is actually a slight curve, actually a mathematical sine curve. For the small angles that wings operate at, the sine is the nearly straight line graph we see.
We can also see that if we tilt the wing up above around +12° AOA, the lift curves rather suddenly drop off. This shows the effect of Stalling, where the wing rather quickly loses its lifting ability. The REASON this happens is a new effect! The Reaction Lift would continue to slope upward, and even the Bernoulli Lift would not change very much. But there develops a huge amount of TURBULENCE, above and behind the wing. That large turbulence has two major effects, of greatly increasing DRAG and of greatly counteracting the beneficial effects of both the Bernoulli and Reaction Lifts.
The word STALL became associated with this phenomenon in the 1920s and 1930s, when pilots who survived such events always said that the aircraft seemed to suddenly STOP moving forward! That was technically not true, but it certainly slowed down immensely, and very quickly.
The Graph refers to SECTIONAL Coefficients! That is because nearly all real wings have complex TWISTED shapes (for many technical reasons that we will not address here.) Our discussion has generally assumed that the wing has a constant shape and constant AOA, for the simplicity of the discussion. Actual design of aircraft wings requires mathematically Integrating the Sectional Lift contributions for the entire surface area. There are also other adjustments that have to be made, regarding the ENDS of the wings, which have some odd characteristics, effects near the fuselage, etc.
(Down below, we will note and discuss the obvious fact that all modern airliners have wings that are clearly tilted upward. THAT has NOTHING to do with Bernoulli and actually hurts that effect a little! That is done by aircraft designers because all aircraft (except gliders) are now expected to carry the heaviest payloads possible within safety constraints, and as long as you have really powerful engines, the other, REACTION Lift process has far greater lifting benefits at the slow speeds of takeoffs and landings. Modern aircraft are therefore simply designed to take greatest benefit of BOTH methods of Lift, with the slanted wings being the most obvious factor of REACTION Lift and the airfoil shape of the wings themselves being the most obvious factor of BERNOULLI Lift. At SLOW speeds of takeoff and landing, nearly ONLY Reaction Lift commonly applies, even though it is immensely wasteful of fuel. At CRUISING speeds, as much of the load as possible is designed to be carried by Bernoulli Lift, as it is FAR more efficient regarding needed thrust and therefore fuel economy. So aircraft designers essentially have to design TWO separate wing concepts, for slow and cruising speeds, and then choose the best intermediate design to actually get built.
There is another form of energy, which is of importance here. It turns out that you can COMPRESS a gas such as air or carbon dioxide and in the process store some energy, which gets released when the compressed gas is released. In fact, that energy usually first converts to kinetic energy of the gas moving at high speed, whether from an air compressor hose nozzle or a fire extinguisher outlet nozzle. Those uses convert the energy stored in COMPRESSED gas into kinetic energy.
In fact, Newton's Conservation of Energy allows us to calculate what the change of pressure is and what the resulting air or gas velocity will be. It is a very simple problem, simply keeping all other forms of energy constant and only considering the energy present in a (stationary) compressed gas and the energy present in a moving gas. The first man to rigorously apply Newton's Laws to this situation was named Bernoulli, almost three hundred years ago.
Down below we will show and discuss the simple formula that Bernoulli derived directly from Newton's Laws, where he used the already known formula for kinetic energy and the other already known formula for the energy in a compressed gas. All Bernoulli did was to say that nothing else is allowed to be changed, so that the total of those two forms of energy must necessarily stay constant.
Presto! Bernoulli elegantly provided the math to prove it, but you can already see that if the kinetic energy increases (due to faster speed) then the energy-of-pressure must necessarily get less, which means that LOWER PRESSURE MUST THEREFORE OCCUR.
This is essentially a statement of what is called the Bernoulli Effect, where if air is made to move faster (such as over the top of a bulged-out top part of a wing) then that faster moving air must necessarily have LOWER INTERNAL PRESSURE when compared to air that is going slightly slower along a straighter (and therefore shorter) path under that same wing. This then results in NORMAL air pressure pressing against the bottom side of a wing, but a SLIGHTLY lower air pressure existing in the space just above the wing. Therefore, there is a PRESSURE DIFFERENTIAL, and that results in an UPWARD FORCE on the wing as a result, which is what we call Lift.
It seems that extremely few people are aware of how TINY the Bernoulli Effect actually is for things like aircraft wings! People, especially critics, seem to think that ferociously powerful upward force is claimed as Bernoulli Lift. Not even close! For an actual airplane wing, the air going over the top of a wind only goes around THREE PERCENT FASTER than the air which goes under that wing! And below, we will see that results in a Bernoulli Lift which is less than 1% of atmospheric pressure. It is almost disapointing that the effect is so small!
Below, you will be shown how to calculate the actual pressure differences between below and above a wing. In Grade School, you learned that atmospheric pressure is 14.7 pounds per square inch. PER SQUARE INCH! Think about that! For a SQUARE FOOT, that is 2,100 POUNDS (as we will see and calculate below). A well-designed (small) airplane wing may have 10 pounds per square foot in design lift (at cruising speed), where 200 square feet of wing surface would then be able to provide a total of 2,000 pounds of Bernoulli Lift which would then fully support a small aircraft.
Are you getting the main point here? Out of 2,100 pounds per square foot of natural atmospheric pressure pressing against the bottom side of that airplane's wings, the Bernoulli Effect only has had the rather pitiful effect of reducing the top pressure to 2,090 pounds per square foot (to get the desired 10 pounds per square foot of actual net Bernoulli Lift of the wing). That is only lowering the pressure along the top of the wing by less than HALF OF ONE PER CENT!
Under normal conditions, it might be considered as too small an effect to even be worth the trouble! Except that it has allowed us to FLY for the past 100 years! So it is seen as quite remarkable. It really is. But the EFFICIENCY of using the Bernoulli Effect seems really disappointing, at only 0.5%, and this after a hundred years of countless thousands of great minds trying to advance aviation! Interesting!
This disappointing performance caused me to build myself a very peculiar device in May 1999. In its one and only experimental flight, I had hoped to achieve 3% to 5% efficiency of the Bernoulli Effect, which would have been quite significant. When I later examined and studied the videotape I made that morning, it turned out to have had over 21% efficiency, and that from a VERY crudely made basement contraption! Well, prior to that morning, yes, I could see where some people might be skeptical about a physical process which only ever showed 0.5% performance when everything went as 100 years of Aeronautical Engineering had desired. But having seen that brief (10 second and uncontrolled) flight, I have since simply smiled when people who think they know what they are talking about claim that there is no such thing as Bernoulli Lift! (Only a very small area of the device was arranged to have this effect, which resulted in roughly a 1.0 G vertical acceleration (extremely briefly). The fact that my strange device only used a standard 3.5 hp lawnmower engine (unmodified) greatly restricted its rate of climb so that acceleration almost immediately ended, once the thing got up to a maximum vertical speed, within around a second! After that, the puny engine power limited it to roughly 3,000 feet-per-minute "rate- of-climb", which still was a lot better than virtually any aircraft can ever do. Not bad for an old lawnmower engine!
And even though I was remarkably full-of-myself for that truly cool experiment, and my head was probably somewhat larger for a couple weeks, I saw what I felt was a very dark side to the picture. I was not really sure whether my extremely peculiar device could ever have been converted into anything that would represent anything that could have been used as an aircraft, but I realized that others a lot smarter than me might have done that. But what I DID realize was the astounding performance of a very small aircraft that only used a non-modified standard 3.5 hp lawnmower engine for power. If I had FULLY prepared the entire surface of the thing with the modification, then a vertical acceleration of greater than 20 Gs seems possible and even likely. (No human could withstand such G fprces!) Physicist friends of mine at the time had mentioned that DARPA and other government projects had long been trying to develop very small remote-controlled aircraft. One description of a goal that I was told about was that they hoped to develop a tiny aircraft which might fly in a house window at 200 mph, stop on a dime, fire a gun at people inside or drop a hand grenade, and then zoom out of a window again at 200 mph. If they are ever able to achieve that, the residents of that building would not even have one second to know that they were about to be killed.
I am a Peace-loving person, even prior to having become a Christian Pastor in 1996. I would NEVER, NEVER, NEVER want to have participated in providing what sounds like an ultimate killing machine, to anyone. And even if the US government insisted that THEY ALONE would protect such a device, as they have proven hundreds of times before that they cannot keep ANY secrets for more than a few years. So, IF DARPA or the others ever actually develops what they spend billions of our tax dollars to do, they might have some kind of strategic advantage for a few years, but soon every criminal gang would get the same capability. Well, my mind got tangled on the image of a peaceful family watching TV and being exterminated in a second by some irate neighbor who happened to have access to such a device, where I did not see how ANY person on Earth would then be safe.
Therefore, during June 1999, I dismantled and destroyed the strange device that I had made, and also burned and destroyed all the sketches, notes, videotape, and floppy diskettes that had anything related to it. UNLESS some dangerous adversary some day shows usage of such a device, I will have nothing to do with again making or advancing such a device. It just seems far too dangerous to me, something I had not realized in May 1999 when I was so puffed up about it. I do NOT believe the world should have such a device. From past experiences, I know that these comments, even 9 years later, will cause large numbers of people to send me vicious notes, where they will DEMAND that I provide THEM the capability of having such a device. THIS was actually the reason that I had chosen to never even mention my Spring Adventure for all these years. There is actually little value in doing so even now, EXCEPT that I happened to have had that personal experience regarding how spectactularly the Bernoulli Lift can actually perform. I guess I have gotten sick and tired of the irresponsible clowns constantly annoying me for many years in claiming that there is no such thing as Bernoulli Lift, while I had done an actual experiment to prove that they were fools! I guess I have sprung a leak now and have felt the need to vent some bile! I apologize for this ranting over a device which will never be confirmed, supported or defended! You are free to deny that any such device can or did ever exist!
From before powered flight actually occurred until about twenty years ago, the actual lift of an aircraft was generally popularly attributed to Bernoulli lift. Within the past twenty years, most descriptions now entirely discard Bernoulli lift and instead credit Reaction lift. Both of those "explanations" are actually wrong! The reality is that both forms of Lift are always acting. Very large modern aircraft generally are designed to create about 4/5 Reaction Lift and 1/5 Bernoulli Lift, in order to carry the heaviest possible loads. Smaller aircraft generally have a more even proportion, say 2/3 Reaction Lift and 1/3 Bernoulli Lift. Birds, also, fly as a result of a combination of both types of lift. Both types of lift are important, but for rather different reasons. Given the way aircraft are designed, the Reaction Lift is capable of far greater amounts of lift, but the phenomenon is naturally unstable (therefore potentially unsafe) and it is also naturally wasteful of energy (therefore fuel). If you have ever seen video of a racing boat or a racing car have its nose slightly lift up, reaction lift starts acting on the underside of it. As the angle gets a little greater, the lift gets a LOT greater, and the angle quickly gets very large. The boat or car almost always quickly points straight up and all other directions, and extreme danger is involved. That is described as an unstable lifting effect, and that is the NORMAL situation with Reaction Lift. Actually, technically, it can usually be somewhat controlled, by VERY careful attention to the angle of the wings (called angle-of-attack or AOA) as during the flight of aircraft, and then it is called meta-stable. The Bernoulli Lift for practical aircraft wings does not produce such great amounts of lift, but that phenomenon is naturally stable (therefore far safer) because the amount of Bernoulli Lift created is fairly constant for various wing angles. Also, Bernoulli Lift generally creates far less turbulence in the air, so it is much less wasteful of energy and therefore is more efficient regarding fuel use.
In the case of your hand in the car, if the car is traveling at 60 mph (to the air and not necessarily the ground) (which is 88 ft/sec), then the stagnation pressure is: 1/2 * (1/13 pound/cu.ft) * (88)2 / 32, or about 9.3 pounds per square foot. (the 32 was necessary to convert the weight in the density into a mass unit, 32 being the acceleration due to gravity). The actual pressure on your hand is a little higher than that, because air that had hit the windshield also has to move past the area where your hand is, so more air is passing through that space and so it has to move faster than 60 mph, and so the actual pressure there is higher.
If, instead of holding your hand vertically, you tilt it forward, your hand will feel a Reaction Lift. Essentially, air that then hits your angled hand gets deflected downward, giving the air a new downward motion along with its remaining rearward motion. Newton's action-reaction (in an up-down direction) tells us that your hand experiences an UPWARD motion as a result. For small angles of your hand from horizontal, an analysis of the pressures involved is pretty simple. The available stagnation pressure is simply multiplied by the sine of the angle of the tilt from horizontal. For example, if your hand if angled 15° from horizontal out that car window, the Reaction Lift pressure on your hand would be about 9.3 pounds per square foot * (0.2588) or around 2.4 pounds per square foot vertical lift force.
If your hand and lower arm weigh less than this, you find it necessary to HOLD your hand down! But kids are able to find some particular angle, where there seems to be no arm force necessary upward or downward. At that angle, the UPWARD Reaction Lift is exactly equal to the DOWNWARD gravitational weight force on the hand and lower arm.
For an airplane flying at 500 mph (730 ft/sec), in the less dense air at 30,000 feet altitude, the stagnation pressure is easily calculated at around 260 pounds per square foot.
The process of Reaction Lift is naturally unstable. If you tilt your hand at more of an angle, there is both a lot more force now, especially due to a larger area presented to the wind, pressing against your hand, and it also has greater leverage angle, so it tends to want to both tilt and raise your hand even more. The fact that there are TWO different effects which both cause greater lift (each proportional to the sine of the angle of incidence) is the reason this process is unstable. You have to stiffen your arm muscles to keep that from happening. There actually IS one specific angle where your hand tends to be able to remain (called meta-stable) but a tiny wind gust or mis-estimate of the exact angle will quickly upset that temporary stability.
Therefore, for the range of relatively small angles which are actually practical for aviation, Reaction Lift is proportional to the square of the sine of the AOA (angle-of-attack).
Reaction Lift is sort of a "brute force" lift. It relies on the availability of a lot of (engine) power to create strong windspeeds, since it essentially creates Reaction Lift by deflecting that air downward, which uses up a lot of power. It is also naturally unstable. Because modern aircraft have very powerful engines, all modern large aircraft primarily rely on Reaction Lift for the majority of their total aerodynamic lift.
You may have noticed that Reaction Lift does not depend at all on the actual shape of the wing. A flat board, tilted, creates Reaction Lift as well as any complicated curved airplane wing would. And, of course, the bottom surface of a wing using Reaction Lift MUST be tilted to get the lift effect.
Bernoulli Lift is entirely created due to the SHAPE of the wing. The upper surface of the wing is always bulged out more than the lower surface is, which is what actually creates Bernoulli Lift. As described below, Newton's Conservation of Energy causes any fluid flow to have (slightly) lower pressure if it is moving faster. The air molecules that are together before the front edge of a wing, but separate above and below, MUST get past it, to MEET UP AGAIN after the wing has gone by. (That statement is ONLY absolutely true for laminar flow, and when there is turbulence, as there usually is in real applications, they do not necessarily meet, and EITHER could be there before the other!) The bigger bulge of the top side of a wing (airfoil) means the air has to move a little faster, to cover the longer distance, than air that went under the wing where the path was straighter. Bernoulli Lift is simply the effect of this (slight) difference of pressure above and below a wing. It ONLY depends on the shape of the wing, the velocity of the air and the density of the air. It has no dependence on the angle of the wing to the air motion. Remember that the actual maximum Bernoulli Effect which exists in all aircraft is only around HALF OF ONE PERCENT of the available pressure, so the Bernoulli Effect is actually somewhat pitiful from a scientific perspective. And yet it has helped enable millions of very heavy metal aircraft to fly!
Bernoulli Lift does not require the massive engine power that is necessary for Reaction Lift. Gliders are designed to use nearly completely Bernoulli Lift because of this. But since large modern aircraft all have powerful engines, great reliance on Bernoulli Lift has faded. The discussion below shows that modern airliners commonly fly with 1/6 Bernoulli Lift and 5/6 Reaction Lift. At lower airspeeds, both types of lift become far less (both depending on the square of the velocity of the air), but massive aircraft can remain in the air by extending "flaps" along the rear edge of the wings and tilting them downward, which greatly increases ONLY Reaction Lift. Slow speed performance of the very heavy airliners is therefore especially unstable, which explains why nearly all airliner accidents occur during takeoffs or landings.
Most people that do not want to believe that Bernoulli Lift even exists tend to claim that the ONLY way that anything could have Lift is if air is "thrown downward". They cite Newton's action-reaction reasoning, and are actually quite correct in describing how Reaction Lift occurs. However, Newton also described many other things to us! Specifically, that there is Energy in any "compressed fluid" which generally means to us either water or air. As small children, we learned that there is Atmospheric Pressure, of around 15 pounds per square inch. We generally never think about the fact that it is incredibly important that we also have air INSIDE us, which is also at that same pressure! Otherwise we would instantly squish! Some science teacher may have done a fun demo for you as a student where a (metal, for safety) (with a screw cap) can has a little water placed in it and it is placed on a (Bunsen burner) fire. The water boils, which drives much of the air out of the container. The cap is screwed on tightly and the fire turned off. Once the water vapor inside condenses into water again, there is no longer anything that can withstand the atmospheric pressure on the outside of the can, and it crumples up into a small mess!
Well, if you take a one-foot-square thin board, and just hold it up in the air horizontally, we therefore know that there is a total of 144 square inches times 14.7 pounds/square inch, or over 2,100 pounds of force pressing DOWN on top of that small board! But YOU are so strong you can hold it up! Impressive! Well, not really! Because pressure is such that it works equally in all directions, and there is actually also 2,100 pounds of force pressing UP on the bottom of that board due to atmospheric pressure. It works out that these two values are always the same! EXCEPT for when Bernoulli effects apply!
Do you see? Say that by some "magic" you are able to reduce that top downward force to 2099 instead of 2100 pounds, while the bottom force stays the original 2100 pounds. There is now a NET UPWARD FORCE (of only one pound, granted). If that board weighed less than one pound, that board might then be able to HOVER (thinking about the ping pong ball yet?) We are NOT talking about making spectacular changes in the pressures on top and bottom of that board. In fact, for that situation, we would only be talking about (1/2100) * 15 or 0.007 PSI difference in pressure, (top to bottom) to have that board "hovering".
First, WHY is there the "atmospheric pressure" of 14.7 pounds per square inch or 2116 pounds per square foot pressing in on everything? Do you know? It is actually very simple! If you look exactly straight up, imagine a column of air, exactly one foot by one foot, all the way to the top of the atmosphere (hundreds of miles above). Wanna guess at how much all that air weighs inside that column? Yup, exactly 2116 pounds! That is all that atmospheric pressure actually is, the pressure due to that much weight of air stacked above!
Now, if I tell you that roughly 13 cubic feet of air weighs one pound, can you now figure out if I climbed up on a ladder and imagined the same column of air, but now starting 13 feet above before, how much air is above me? Yup, again, now 2115 pounds! We "passed up" 13 feet of the atmosphere, so we now have slightly less atmospheric pressure on us.
Now, one pound difference per square foot is a microscopic difference in the 14.7 PSI the way it is usually described, and we do not notice it. But in a rapid elevator ride, your ears might pop as a result of you passing up some of the atmosphere! Also, going to Pike's Peak or any high mountain, it is quite noticeable that it is harder to breathe enough, which is because there is less air pressure up there.
Getting back down to Earth, let us now consider a "box" (actually a balloon!) which is really sturdy but that does not have any weight, and which is one foot square and 13 feet tall. We first hold it up, vertically, filled normally with air. There is pressure against the top of the box, which is the 2115 pounds total downward force, as we discussed above. There is pressure against the bottom of the box (13 feet lower in the atmosphere) which totals 2116 pounds upward force.
This is starting to sound good, we apparently have a net upward force of 1 pound on our box! BUT, we have it filled with exactly one pound of air, remember! Since the upward force is therefore exactly the same as the (downward) weight of the air in the box, it doesn't go anywhere, it just stays there. We are actually just describing here why UNboxed air, even though having weight, does not all constantly fall!
NOW, imagine that we remove HALF the air inside the box. Well, we have 0.5 pound DOWNWARD weight and 1.0 pound net UPWARD atmospheric force, so it will rise. In fact, we could now even have our box weight anything up to 0.499 pound and it would still rise (but more slowly).
Unfortunately, nearly any box is too flimsy to withstand the enormous pressure of the atmosphere, so any REAL box like that would have to be extremely strong (and heavy).
However, it turns out that there are some gases, specifically Hydrogen and Helium, which have lower densities than air does. AND they still are able to have their own PRESSURE to withstand the crushing pressure of the atmosphere. So, hundreds of years ago, people discovered that if they filled a balloon with Hydrogen gas, and if the balloon was not particularly heavy, the weight of the balloon and the hydrogen were still less than the air that used to take up that volume, and it would rise! A hundred-fifty years ago, Helium was discovered which did the same. It was actually earlier known that heated air also had lower density than cool air, which also enabled a balloon to rise, but not as well as with either Hydrogen or Helium.
Why is this important here? We are pointing out that the reason a balloon rises or not, and even how fast it would rise or fall, is easily calculated based on the TOTAL ATMOSPHERIC FORCE ON TOP PUSHING DOWN and the TOTAL ATMOSPHERIC FORCE ON THE BOTTOM PUSHING UP. The ONLY other fact needed is the actual total weight of the balloon and its contents, which needs to be less than the difference of forces so that it would rise. (This description is essentially exactly the same as for Bernoulli Lift).
OK. Now imagine our 13-foot tall, foot square box with some tubes inside and an airpump! (For complicated reasons, the following is far harder to actually do than it sounds!) Imagine that we have our airpump set up so that it SUCKS air from just above the box and sends it out just below it. In fact, we can calculate just how much air we would need to suck and blow, to create "differential pressures" both above and below our box. Say that we get an airpump set up so that it removes enough air above the box so that the pressure on the top of the box gives 2114 pounds total force rather than the normal 2115 pounds we have discussed. And at the same time, we are adding air underneath so that the pressure there is increased slightly so that the total upward force on the bottom is now 2117 pounds.
Remembering that our box has 1 pound of air in it, and maybe another pound due to our airpump and pipes. But we now have a NET upward force on the box now of THREE pounds, while the total weight is TWO pounds. The entire box would now rise!
The point being made here is that there is no downward air blast necessary to do this, and in fact there is an advantage in having the exiting air travel straight sideways! So Newton's Action-Reaction does not directly apply here! We are simply using properties of fluids that Bernoulli first discovered, shortly after Newton.
With such a box and airpump as described, we could rise, hover or sink as desired, simply by adjusting the speed of the airpump.
Well, as said earlier, it turns out that this approach is impractical and mechanically very difficult to do. But Bernoulli's Law and his equation provided a different way of creating that SLIGHTLY lower pressure above. The discussion above pointed out that in order to Conserve Energy, if a gas is sped up (more kinetic energy), its internal energy of pressure necessarily has to get less by the exact same amount. Voila, the airfoil wing shape! Air going over the top of the bulged surface NECESSARILY has to have a slightly lower pressure in it!
Our discussion with our box and balloons has shown us that we do not require MASSIVE changes in that pressure, that remarkably small pressure differentials are fine. For common aircraft wings that have an effective Bernoulli lift of around 10 pounds per square foot, that is only meaning that our 2116 got lowered to 2106, a remarkably small difference! The real situation is that the NORMAL atmospheric pressure of 14.7 PSI might apply on the underside of a wing and one ounce less, 14.63 PSI local pressure applies above it. And that tiny difference is enough to produce ALL the Bernoulli Lift in all aircraft! It's sort of amazing!
We want you to note here that for a Bernoulli Lift to provide 10 pounds lift per square foot of wing surface, that is really saying that the total downward force on the top of a square foot of the wing was reduced from 2116 to 2106 pounds. This is actually just a local air pressure reduction above the wing which is 0.07 PSI less than the 14.7 PSI standard atmospheric pressure that is still pushing upward on the bottom of the wing. That tiny amount of pressure difference, is ALL that actually exists in the Cruising flight of nearly any modern aircraft!
The "magic" we required above is actually not much magic at all, of only finding a way to reduce the pressure above the wing by 0.07 PSI as compared to the bottom. And THAT is what Bernoulli showed us applies! That there was a way to cause that very minimal pressure differential, and Bernoulli showed us that all we need to have is (relative) airspeed!
By the way, at low aircraft speed, Bernoulli Lift is minimal, as it is speed dependent. So during the low speeds of takeoffs and landings, nearly all the lift is provided by Reaction Lift.
In order that the total energy of a mass of flowing fluid be constant (which Newton had proven), any increase in the speed of the fluid must therefore be matched by an appropriate decrease in the pressure. Newton had shown that the total energy is given by
E = mgh + 1/2mv2 + Ju + pv
the four terms being: potential energy; kinetic energy; internal (chemical) energy; and pressure energy. Once this total is known, it must remain constant, by Newton's Law of Conservation of Energy.
Bernoulli considered the situation where there is no chemical change occurring to an object (and no temperature change). This simplifies Newton's equation above,to:
E = 1/2mV2 + pv + mgh
Bernoulli knew that this equation is true for each of any two
situations, and that for an incompressible fluid, volume does not
change, so therefore:
E = 1/2mV12 + p1 * v + mgh1 = 1/2mV22 + p2 * v + mgh2
Dividing all terms by mg and calling 'h', 'z', we get:
V12/2g + p1 * v/mg + z1 = V22/2g + p2 * v/mg + z2
or, since the quantity mg/v is defined as Specific Weight (essentially
density) (called either g, or r), this can be written:
V12/2g + p1/g + z1 = V22/2g + p2/g + z2
In this form, the equation is called Bernoulli's Equation, and we have seen that it is simply Newton's Conservation of Energy for a steady moving, frictionless, incompressible fluid. It turns out that this same equation can be derived in a different way, from an analysis of all the forces which apply to each tiny bit of the fluid, from what is called the Equation of Motion (by Differentiating it). For a given fluid (commonly air or water) this equation always applies since it really is just saying that Energy is Conserved as Newton said. Notice that, on either side, if the velocity increases, that term gets bigger, but the total must remain the same, which requires the pressure term to get smaller, which explains why the Bernoulli effect describes fast moving air or water creating lower local pressures. If the velocity is the same, then there is no pressure difference. But if either velocity is greater, then you can see that ITS pressure has to be a little less. (Real aircraft examples are below.)
Newton had established the Laws of Motion for discrete objects. Bernoulli applied those laws of motion to fluids and found (from above) that the (differential) pressure in a moving fluid P (where there is no significant height difference, so no difference in the z terms) is given by 1/2 * r * V2, where r is the density of the fluid. It's simply Newton's Conservation of Energy as applied to fluid flow!
The Bernoulli Equation is simply a statement of Newton's Conservation of Energy for a fluid. It is certainly real, and valid, and easily confirmed. Science Project!: If you weigh a sheet of paper lying on a desk, you can easily use this Bernoulli equation to calculate what speed air would have to pass over it to cause it to lift up off the (rough surface) desk. Simple Bernoulli Lift would counteract the gravitational weight of the paper! You would have used Bernoulli's Equation to PREDICT the Bernoulli Lift that would raise that weight of paper! (I said rough surface for a reason! Air has to be able to get UNDER the sheet in order for that 2,115 pound per square foot atmospheric pressure to be there to push upward on it. A glass-surfaced desk is so smooth that air may not be able to get under the paper, and the experiment will then NOT work! Slightly crumpling the sheet of paper also works!)
It is unfortunate that there are many, many, many alleged descriptions of the Bernoulli Effect or of Bernoulli Lift or about how airplanes fly, which are not accurately correct. Usually, the reasoning described in such descriptions contains misstatements and even logic flaws, and so I suppose that skeptics might see cause to doubt everything. Well, at various times, I discovered that commonly available descriptions of Ocean Tides, of the Earth's Precession, of how an automobile engine works, of aerodynamic lift, etc, seemed to need a Physicist's touch, and so I write these sorts of web-pages.
It is also true that modern aircraft are intended to carry the heaviest payload possible, and that has resulted in a design usage of mostly Reaction Lift, ESPECIAALY at takeoff, but Bernoulli Lift, ESPECIALLY AT CRUISING SPEED (for far better fuel economy) still contributes!
As a thought experiment, which I hope no one ever actually tries, it WOULD be possible to replace the wings on a Cessna with simple slabs of constant thickness wood or aluminum or plastic. Such an aircraft would have NO possibility of creating any Bernoulli Lift! But it would still be able to fly, assuming its engine was strong enough.
Such an aircraft would be nearly impossible to fly, because it would be so unstable. The slightest wind gust would require than an instant correction, up or down, regarding AOA would have to be made. Otherwise, once the AOA changed very much at all, the unstable aspects of pure Reaction Lift would cause an uncontrollable stall or nosedive.
In addition, such an aircraft, which would have to constantly be producing Reaction Lift during Cruising, would require several times as much fuel to do that, as compared to a standard Cessna that relies greatly on Bernoulli Lift at Cruising speed.
But it certainly would be physically possible. The pilot might have an extremely short life, very much like the countless accidents like those which occurred in the first years of powered flight, where many people did not yet know to need Bernoulli Lift and they made aircraft that were entirely dependent on Reaction Lift. Movies of some show that, yes, they were right that there was lift, but there was also no control whatever, and often the crash killed those pilots.
Powered flight really only became realistic once people like the Wright brothers realized that Bernoulli Lift provided some self-correcting characteristics, where it actually was safe to try to fly.
An airplane wing is always bigger, curvier, on top and flatter on
the bottom. There is a reason for this! Imagine two molecules of
air that are right next to each other to begin with. And it is important
to imagine that you are WITH the molecules (in THEIR reference
frame, and not that of the wing which whizzes by).
A wing (or a knife or any other object) comes
by and separates them, but once it has completely gone by, they would again
be right next to each other. We are discussing here a SMOOTH flow,
which is called Laminar Flow. IF, instead, we sent a cubic block of
wood through, there would be DRAG and TURBULENCE, and that WOULD
cause some of the air to get PUSHED ahead of the block of wood. Laminar
Flow can be thought of as extremely slippery, where the object was
able to pass through without doing any permanent damage or effects.
(Anything else (for Laminar Flow) would cause a net horizontal acceleration and massive energy transfer to ALL of the air above or below a seam where the wing had passed through, which would also give ALL that air (above) a new velocity where it would have to continue. Essentially, such an effect would TRANSFER kinetic energy to that air, and Conservation of Energy means it would have to come from somewhere, in what is called Aerodynamic Drag, and therefore from an engine. The very definition of Laminar Flow is that there is NO kinetic energy transferred to the surrounding fluid (air or water).
Such an effect of transferring that kinetic energy to the surrounding air (which many people insist on!) is simply not Physical, EXCEPT due to undesirable TURBULENCE, in essentially causing a TEAR in the air immediately behind the airfoil! It is easier to visualize this in water as a submerged (THIN) hydrofoil blade BRIEFLY zooms by. Could ALL the tons of water which happened to be above where that hydrofoil passed through all be shifted forward or rearward? Not a chance! That would require MASSIVE transfer of kinetic energy to the water just above where it passed through. It would also cause a TEAR in the water if such a thing happened. Simple calculations show the immense amounts of kinetic energy which would have to ACCELERATE all that water very quickly to get it to a new location in a fraction of a second, for the water to have physically MOVED all the water above where the hydrofoil had passed through forward or rearward like that! Just because a skinny piece of material had whizzed by for an instant, the entire upper portion of an ocean or lake is NOT all moved forward or rearward! Those people might THINK they have a logical idea and they may even have seen one of the videos presented on the internet which APPEAR to show such a thing. In an amusing note, there are about an equal number of such videos which show the air above being moved FORWARD and being moved REARWARD!
In Physics, we tend to rely a lot on Calculus, and it is very helpful here. We would do such calculations for an airfoil of thinner and thinner thickness, and we would quickly see that for an infinitely thin airfoil or hydrofoil, there can be NO transfer of energy to the surrounding fluid at all. Then we analyze the effects of making the foil shape thicker again, and we would see that, except for turbulence factors, the shape is still able to slide through the fluid smoothly and easily, with no kinetic energy transfer to the fluid.
A Physicist sometimes sees it as amusing that non-Physicists do not see the obviousness of such things! In general, non-Physicists seem to ASSUME that there is ONLY ONE reference point to view from, the wing itself. A Physicist knows that there are an infinite number of EQUIVALENT reference frames, as long as they are not accelerating in regard to each other. Specifically, we choose the reference frame of the molecule just below where the wing will pass through. The animation above demonstrates this (for really big molecules!)
An analogy might be useful here: Imagine that you are in an enormous crowd of 200,000 people, and you are in a hurry to get to the bathroom! You could try to RUN through the crowd, essentially like a football Running Back. You WOULD knock a lot of people down and drive many others along with you in the process! THAT is akin to what can happen in (fast motion) turbulent flow. However, most people would instead try to squeeze their way BETWEEN people, without knocking anyone down and without PUSHING anyone ahead of them! THAT is akin to Laminar Flow, and the point here is that THE CROWD IS ESSENTIALLY UNCHANGED after you have passed through it. Yes, you momentarily caused some individuals to have moved a few inches sideways as you passed, but as soon as you were past, they were able to go right back to where they were to start with. See the point? In this second case, you did NOT force a husband or wife to wind up ten feet ahead of the spouse, but in the first case, you MIGHT have caused that effect. They are quite different.
If the relative velocity is above a certain speed, the Reynold's Number indicates that any laminar flow will have changed into turbulent flow. (Even walking through a crowd of people!) In turbulent flow (nearly all of real situations), the wing unintentionally creates turbulence, which greatly complicates everything by causing such accelerations of EVERY INDIVIDUAL PORTION of the air, which is called Drag. That really complex situation drags the air along, BOTH above and below the wing, depending on how clean and smooth each surface is and the relative curvature present. We are examining HERE the situation called Laminar Flow where no turbulence and extremely little drag is created. Essentially by definition, laminar flow enables the airfoil to slip by without disturbing much, except for spreading the fluid apart for an instant so that it could slip by, but then the fluid returns to its original places once it has passed. Because the effects seen in such videos are due to that turbulence, they have about an equal chance of showing forward or rearward shifting of SOME of the air.
Now, since the two molecules begin together and end together, a requirement then exists: We will look at this from two different reference points. First, the reference point that is stationary with the molecules: The lower molecule does not move at all, and the upper molecule simply got pushed straight upward and then back downward, to permit the body of the wing to squeeze through. (we are simplifying by assuming absolutely no drag here which would have DRAGGED the top molecule FORWARD with the wing). The Bernoulli concept is really obvious in this rest-frame since the bottom molecules virtually does not move at all!
Now the second reference view, that of being on the wing: The path followed by the upper molecule must have been longer, because of having to have gone the longer path, higher and farther to get around the bigger upper part of the wing, than the shorter, more direct (nearly straight line) path followed by the bottom molecule. They both have to wind up next to each other again, (as is obvious when the first reference of the stationary-with-the-air view is considered) so they must take the same amount of time to make their trips! This means that the bigger size of the upper part of a wing guarantees that the air going OVER it must go a little faster than the air that goes UNDER the wing!
For sixty years, the length of the (laminar) path above and below every NACA airfoil shape have been known and used. We will use such data momentarily below.
Bernoulli's Equation, being an expression of the Conservation of Energy, says that the total energy in the (molecules of) air above and below the wing must be the same. The TOTAL cannot change for either of them, at any time. The air that went over the top had to go farther, in the same time, so its velocity was a little higher FOR A WHILE. The Bernoulli Equation then says that the air PRESSURE above the wing must be slightly less than the air pressure below the wing, because of this difference in the speeds, and because the total energy must be conserved.
We can apply some numbers now! An airliner flying at 550 mph can also be described to be flying at about 810 feet per second. For a common shape of wing used on airliners, the NACA data on the wing shape dimensions shows that the upper path is 1.0590 times as long as the straight distance across the chord of the wing, so the air must go at an average speed of 810 * 1.0590 or about 858 feet per second past the top of the wing. The lower path is 1.0241 times the length of the straight wing chord, so that air must travel at an average speed of 810 * 1.0241 or about 830 feet per second past the bottom of the wing.
The density of air r at around 33,000 feet altitude is around 1/1260 slug/cu.ft. (don't ask! It is also around 1/39 lb/cu.ft.) The difference in the pressure below and above the wing is therefore (by Bernoulli)
Punder - P over = 1/2 * r * Vover2 - 1/2 * r * Vunder2 or 1/2 * r * (Vover2 - Vunder2).
In our case, this is
Punder - P over = 1/2 * 1/1260 * (8582 - 8302)
or 1/2520 * (736164 - 688900) or about 18.75 pounds per square foot.
In case you are curious about that EQUIVALENT REFERENCE FRAME, we can do the same calculation in the rest-frame of the molecules! In this case, the lower molecule moves DOWN about 2.5 feet and the upper molecule moves around 5.5 feet UP and then each returns to its original spot (so each went a total distance of twice these numbers). And since the wing is traveling at around 810 feet per second, and the wing chord (effective) may be around 36.5 feet, and the wing passes by in about 1/22 or 0.045 second. Therefore we would have:
Punder - P over = 1/2 * 1/1260 * ((11/.045)2 - (5/.045)2)
This is Punder - P over = 1/2 * 1/1260 * (2442 - 1112)
or 1/2520 * (59589 - 12312) or about 18.76 pounds per square foot.
Either reference frame gives the same net result of the Bernoulli Effect!
Notice that this calculation did NOT depend on the AOA at all! THIS is the reason that Bernoulli Lift is so stable. The amount of Bernoulli Lift present essentially does NOT change when the pilot or wind gusts cause changes in the AOA.
This is the amount of Bernoulli lift that exists, for that specific airliner and at that specific Cruising speed. Every square foot of wing surface creates that much Bernoulli lift (approximately, because the shape of a wing is complex). A Boeing 747 has around 5,500 square feet of wing area, so this creates a total (Bernoulli) lift, at that speed and at that altitude, of around 103,000 pounds.
If the aircraft only weighed 103,000 pounds, we would have now shown that it was flying entirely due to Bernoulli lift! But remember that a fully loaded Boeing 747 weighs much more than that, as much as 775,000 pounds. This makes it obvious that we must now consider the SECOND source of aerodynamic lift!
For this effect to exist, the wing or your hand must be tilted upward, at an angle that is called the "angle of attack". Because of the high speed of the car or the airplane, a lot of air constantly hits the bottom surface of the wing or the palm (bottom) of your hand. After that air has hit that angled surface, it gets deflected downward, pretty much at the angle of the angle of attack. Therefore, the air now has a new VERTICAL movement downward due to the collision, which occurs due to a downward FORCE being applied to it. Newton said that there must therefore be an equal and opposite UPWARD force on the wing / hand.
Knowing the density of air and the velocity, it is possible, and pretty easy, to calculate these things! It is simplest to first define something called the stagnation pressure which is given by 1/2 * r * V2, much like above. For the case of a car, at 60 mph (88 fps), this comes out to around 9.3 pounds per square foot. For our airplane at the altitude and speed we have been discussing, it is around 260 pounds per square foot.
Let's say for a moment that the wing of our Boeing 747 was at that speed and altitude, and was tilted so the effective angle of attack was 4°. When air molecules BOUNCED OFF the bottom of that wing, we know that individual molecules have to have equal angles of incidence and reflection, so the air molecules actually gets deflected downward at TWICE that wing angle, or 8°. (The observed airflow does not show this, because so much other air is rushing by that it causes the reflected molecules to immediately be carried much closer to being along the surface of the wing, but the actual (microscopic) Physics is that each molecule definitely has to reflect off at that doubled angle (in order to Conserve Linear Momentum). And that greater angle is the one that determines change of Momentum in the air which is deflected downward and therefore the REACTION force on the wing upward! We will determine the VERTICAL component of that change of momentum, because that quantity has to be the same as the Linear Momentum imparted vertically to the wing in order to Conserve Momentum.
The "frontal area" of the bottom of the wing that was "visible" to the air ahead, would just be the total wing area time the sine of the angle of attack. However, the bottom of the fuselage of a 747 is designed to be nearly flat, so that it also has the same Reaction Lift effects. Much of the 231 foot length is 20 feet wide, so we have an additional 4,000 square feet of Reaction Lift area. Therefore we have an actual 9500 square feet of total underside area times that sine of 4°. This is 9500 * .0697 or 663 square feet of frontal area exposed to the oncoming air.
Each of those square feet experiences that stagnation pressure of 260 pounds/sq.ft. The Momentum in that moving air is therefore 260 pounds/sq.ft * 663 square feet * 810 ft/sec / 32 or about 139 million feet-pounds per second.
But the air is REFLECTED downward at double that 4° angle or 8°. Therefore, once the molecules of air are all deflected downward, they are given a VERTICAL Momentum of this 139 million feet-pounds per second times the sine of 8° which is then 19.4 million feet-pounds per second. We then divide this by 32 (the acceleration due to gravity in the equations) to get a result of 607,000 pounds of vertical Reaction Lift.
Newton taught that Momentum is Conserved, and when all those air molecules are reflected or deflected DOWNWARD at double that AOA, there is necessarily an UPWARD Momentum which gets applied to the wing of the same exact amount.
The entire amount of lift acting on our Boeing 747 is the total of these two independent lift components, or 103,000 + 607,000 or 710,000 pounds of lift. If the Boeing 747 was nearly fully loaded with fuel and passengers and luggage, its total gross weight could be 710,000 pounds at the beginning of a flight, so this situation would permit stable horizontal flight at constant speed, as long as the engines provided thrust to overcome air resistance (drag). During takeoff, at an angle of around 30° upward, the four engines running flat out and each producing around 43,000 pounds of thrust would also be providing an UPWARD net force (4 * 43,000 * .5000) of around 86,000 pounds of vertical lift, which actually provides most of the ability to gain altitude then!
We trust that you noticed that the 747 is therefore designed to use around SIX TIMES as much Reaction Lift as Bernoulli Lift under those circumstances!
For each vehicle weight, altitude and speed, there is some specific angle of attack that provides exactly the correct total amount of lift to enable horizontal flight. As an airliner continues on a long trip, the total weight reduces significantly, and so the necessary angle-of-attack becomes less. The airliner actually flies more efficiently as the fuel is used up and a smaller angle-of-attack is necessary, since the total aerodynamic drag also reduces.
A 747 uses up fuel at about one gallon per second while cruising. That's about 3600 gallons per hour, around 7 gallons per mile. After a 5,000 mile long trip, that is around 35,000 gallons of fuel that is no longer carried in the airplane, around 210,000 pounds of fuel. So, near the end of a long trip, when the aircraft remaining weight might now be around 500,000 pounds, our situation is that we still have the 103,000 pounds of Bernoulli Lift but now we only need around 397,000 pounds of Reaction Lift. The necessary AOA has now dropped to around 2.5°. The airplane should have leveled out by around 1.5° during that ten-hour flight. Photos of a 747 while cruising seem to confirm this. The wings themselves seem to be attached to the fuselage at an angle of around 4°.
Lift = CL * 1/2 * r * V2 * Area
If CL for a NACA 1408 wing at an AOA of 4° is 0.55, this equation gives a TOTAL lift of around 787,000 pounds for the situation we have discussed above. It gives a credibly accurate number, but remember that it is based on a number which was experimentally determined and not from any theory (as the previous discussions of Bernoulli Lift and Reaction Lift have been.) Our analysis above which is based on the SEPARATED theories of Bernoulli Lift and Reaction Lift gave us a value of 710,000 pounds, which is in relatively good agreement.
If an aircraft attempts to fly extremely slowly, a pilot finds the need to increase the angle of attack to get enough Reaction Lift to remain flying. At some speed, the required angle of attack becomes a stall situation, so that is described as being the stalling speed of that particular aircraft. All aircraft have a stalling speed, and every pilot must be very aware of it, particularly during landings.
This sort of demonstration confirms everything we have described here. If ONLY Bernoulli Lift existed, no upside down flight would be possible. If ONLY Reaction Lift existed, then an aircraft could use the same angle-of-attack either shiny side up or upside down. The fact that maybe 1/3 greater angle-of-attack is necessary suggests that around 1/3 of the normal lift is probably provided by Bernoulli Lift (for that speed and altitude) while the other 2/3 is normally provided by Reaction Lift.
However, actual USAGE of Circulation Theory to real airfoil shapes involves immensely complex mathematics, and many ASSUMPTIONS must be made in order to be able to solve even the simplest of problem sets!
It is always quite amusing when someone sends an e-mail in that demands that all other descriptions be scrapped and ONLY Circulation Theory be presented! It seems a virtual certainty that those e-mailers have NO idea of what Circulation Theory actually is or the remotest capability of ever solving the extremely advanced Calculus equations.
(I had considered reproducing here some of the Circulation equations, but there really is no point! IF you happen to think that you can understand that and even solve those equations, you probably already own a copy of Theory of Wing Sections and otherwise, they probably would just seem like a bunch of funny-shaped symbols!
Because modern airliners are operated by companies that intend to make money, they try to have the heaviest payload that is safe. This is why purely Bernoulli Lift aircraft are commercially impractical. It has been found by practice that a combination of Bernoulli Lift and Reaction Lift, where the Reaction Lift predominates, especially at low speeds, represents the most cost-effective and safe choice.
In a sense, Bernoulli Lift might be thought of as representing stability and consistency, while Reaction Lift might be thought of as more brute force lift that is less easily managed.
The equations used above apply for any situation as long as you don't get too near the speed of sound, where many complications develop. But they apply equally for Boeing 747s, for Cessnas and Piper Cubs, and for hang-gliders and kites, and sheets of paper on a desk! If you choose to use them, keep in mind that the density of air (r) changes greatly with altitude, being only around 1/3 as much at 33,000 feet as at sea level.
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C Johnson, Physicist, Physics Degree from Univ of Chicago