It is truly amazing that our modern technology has progressed as it has in so many ways. If one had not actually seen it happen, it would be difficult to accept a stranger claiming that it was possible to build a very large metal object, which weighed as much as 250 automobiles (775,000 pounds - a loaded Boeing 747) and get that huge object up around seven miles above the ground traveling at 500 miles per hour! And not just once, but thousands of times every day!
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, and it 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.
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. The batter swings where he expects the ball to be, and it is not always there! (If the wind is nearly calm, knuckleballs have the greatest effect. On windy days, they seem to have very little effect.)
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 serves are popular in high-level volleyball, too. If you have watched Olympic play, they rarely wail on the ball any more, but serve what appears to be an easy and simple serve. 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. (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.
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, 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 pattern of the blower output, the distribution of air velocity across the actual airflow. Make an accurate graph of that!
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 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 here???
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 fly 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 NOT 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 airspeed you will need to provide, which should provide sufficient Bernoulli Lift to raise that particular item up off the table. So you have 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 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 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) In the case of standard airliner wings (NACA 4415 shape), they can have a negative angle-of-attack of more than 3 degrees and still be creating upward lift. (The limit for that particular 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) 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 of Theory of Wing Sections for the chart of the data.
(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 the effect a little! That is done by aircraft designers because all aircraft (except gliders) are now expected to carry the heaviest loads 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.
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 pressures 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! 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 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%, which would have been quite significant. When I later examined and studied the videotape 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 where a physical process only ever showed 0.5% performance when everything went as 100 years of Aeronautical Engineering had desired. But having seen that brief (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!
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 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. Physicist friends of mine 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 shoot out 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 what was about to kill them.
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, 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 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 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 personal experience regarding how spectactularly Bernoulli Lift can 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 which will never be confirmed, supported or defended!
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). Id 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, 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.
For an airplane flying at 500 mph (730 ft/sec), in the less dense air at 30,000 feet altitude, the stagnation pressure is 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 pressing against your hand, and it also has greater leverage, so it tends to want to both tilt and raise your hand even more. 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 will quickly upset that temporary stability.
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 that meets the front edge of a wing must get past it, to meet up again after the wing has gone by. 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.
Bernoulli Lift does not require the massive power that is necessary for Reaction Lift. 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 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.
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! Some science teacher must 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 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 15 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" 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.
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.
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 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, 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 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 gamma, or rho), this can be written:
V12/2g + p1/gamma + z1 = V22/2g + p2/gamma + 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. 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 * rho * V2, where rho 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 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!
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 and 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 that 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 comes by and separates them, but once it has completely gone by, they would again be right next to each other. (Anything else causes net acceleration of the air in moving it from one place to another, which would also give that air a new velocity where it would continue. The wing unintentionally creates turbulence, which greatly complicates everything by causing such accelerations of the air, which is called drag, but we will here look at the situation called laminar flow where no turbulence and extremely little drag is created.
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 pass through. (we are simplifying by assuming no drag here which would have DRAGGED the top molecule FORWARD with the wing). 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 (straight line) path followed by the bottom molecule. They both 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!
Bernoulli says that the total energy in the (molecules of) air above and below the wing must be the same. The air that went over the top had to go farther, in the same time, so its velocity was a little higher. 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 the most common shape of wing used on airliners, 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 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.
The density of air 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 Brernoulli) Punder - P over = 1/2 * rho * Vunder2 - 1/2 * rho * Vover2 or 1/2 * rho * (Vunder2 - Vover2). 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.
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 * rho * 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 20°. 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, or 5,500 * 0.342 or about 1880 square feet. Each of those square feet experiences that stagnation pressure of 260 pounds/sq.ft., IN ALL DIRECTIONS including upward. Therefore the total upward force on the wings would be 260 * 1880 or about 489,000 pounds. This represents the Reaction Lift.
The entire amount of lift acting on our Boeing 747 is the total of these two independent lift components, or 103,000 + 489,000 or 592,000 pounds of lift. If the Boeing 747 had used up some of its fuel already, its total gross weight could be 592,000 pounds, so this situation would permit stable horizontal flight at constant speed, as long as the engines provided thrust to overcome air resistance (drag). 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.
Should an aircraft try to increase its angle of attack to a far larger angle, at some point, Bernoulli lift virtually instantly disappears, due to turbulence (called separation). This rather sudden and substantial change causes the aircraft to become very unstable almost immediately. (because now, only Reaction Lift would exist, and that is very unstable). In early aviation, this was the cause of many serious crashes. Since a pilot's natural reaction to suddenly losing the Bernoulli lift was to try to increase the angle of attack even more, and the unstable characteristic of Reaction Lift naturally did the same, the nose of the aircraft would generally point way up. The wings essentially stopped creating much lift at all, and the nearly vertical wings acted to very quickly slow the aircraft's forward speed due to massively increased air friction drag. This very noticeable immediate slowing of the aircraft just prior to crashing gave it the name of a stall. 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.
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 (rho) changes greatly with altitude, being only around 1/3 as much at 33,000 feet as at sea level.
( http://mb-soft.com/public/index.html )
C Johnson, Physicist, Physics Degree from Univ of Chicago