Different Curves: Baseball v beach ball

Cecil's Columns/Staff Reports
21

I’m not denying that the Magnus effect happens; I’m trying to make sense of 1s&0s’ claim that a beach ball breaks opposite to a baseball - what could be overcoming the Magnus force? So I’m not trying to explain why a beachball would have an exaggerated curve (if I were, besides density, the drag caused by the shape of the plastic seam compared to the seam of a baseball, which causes less disturbance, would also enter into it). I’m still accepting what he claims to have witnessed.

OnesandZeros never said the beachball had an exaggerated curve - you’re answering a question you set up to be what you wanted.

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If I read this correctly, it’s not his beach ball that breaks “differently”. It is his memory of baseballs and soccer balls that break the “wrong” way that is “different”.

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As an aerospace engineer, I feel compelled to chime in. It’s true that Bernoulli’s Principle is not wholly responsible for lift, not even an appreciable portion.

“Circulation” is one way of describing the phenomenon, but it’s a cumbersome mathematical abstraction that many actual airfoil designers choose not to use. Aerodynamics has too many mathematical abstractions as it is. There are equivalent, and better, methods that approach the problem from another vantage point, and come closer to describing the behavior in a realistic way. These other theories, such as the Newtonian theory, do a better job at describing the physical processes behind the generation of lift. Then again, everything in in aerodynamics comes down to Newton when you get down to the nitty-gritty. Circulation is “really more of a method of calculating lift in an ideal flow field than an explanation of the physical origins of lift.”

Also, real airfoil design is not completely empirical; computational methods play a large role in the process. And not just recently, either. Numerical methods are as old as practical airfoils themselves. But they’re generally validated by experimental data.

But I really hope hat this argument does not diminish the importance of Bernoulli’s Principle in aerodynamics. What everyone is referring to here, the Incompressible Bernoulli Equation, is entirely accurate, and an essential underpinning of any understanding of incompressible, inviscid flows. In low speed, low Reynolds number flows, as well as any hydrostatic problem, Bernoulli is used extensively to describe almost every parameter of importance. Similar equations, like the Compressible Bernoulli Equation, that hold under compressible and/or viscous flow are equally important in their respective regimes.

In short, don’t let the above arguments convince you that Bernoulli is bunk. It’s just not entirely the reason airplanes fly.

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Welcome audilover. I am glad to have your insights, especially since I completely agree with the above quotes. :slight_smile:

I also agree Bernoulli is not bunk. Very likely, none of us will remotely challenge his accomplishments.

My questions is this: Does Bernoulli’s Formula and Principle actually predict more than 2.5% of the lift on a wing?

I am NOT an Aeronautical Engineer. I certainly will consider your and all of the doper’s comments. However, Gail Craig supports my understanding that Bernoulli’s Formula and Principle provide ~2.5% of the lift of a wing. Your comments did not give me any hard information to counter that assertion.

Enquiring minds want to know! :wink:

Newton discovered the laws of physical interactions. Bernoulli applied these laws to fluids.

I have observed fluids. Wind and Water are fluids. I have observed that the faster a fluid flows over a surface, the more that surface tends to lift. Bernoulli’s principle in action. However, I have also observed that a fluid flowing against and under and around a surface is so much more powerful.

Dopers: Blow over and under and into tissues and wings; spin and throw whatever balls you can find. What do you see? Can you see things that I/We don’t see?

Please consider this experiment: 1) Measure the different airspeeds over and under a wing in (simulated) flight. 2) Reproduce the airspeed over the (flattened) surface area of the upper wing. 3) Measure the lift. 4) Reproduce the airspeed over the (flattened) surface area of the lower wing. 5) Measure the lift. Subtract the “Under the Wing Bernoulli Lift” (5) from the “Over the Wing Bernoulli Lift” (3).

This difference in lift is the actual lift generated according to Bernoulli’s Formula and Principle. I will be interested in the result.

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I think I might need to restate my argument, because I read it again and realized that I didn’t explain my point clearly. I did not mean to imply that the pressures associated with Bernoulli’s Equations were incapable of producing sufficient lift. I meant to say that using these equations are inappropriate if you want to truly explain where lift comes from.

Said another way, the Bernoulli Effect doesn’t provide only a tiny percentage of the lift on a regular airfoil. Rather, the Bernoulli Effect is a flawed way of describing the creation of the lift, and the whole notion is invalid.

Here’s a rough, back-of-the-envelope approximation to show you that Bernoulli pressures can generate sufficient lift:

(I’m going to keep this as simple and crude an explanation as possible…apologies in advance.) The incompressible, inviscid Bernoulli Equation basically says that the total pressure above and below an airfoil should be equal. Total pressure is composed of dynamic pressure and static pressure. (p + ½rV²) Whatever gets turned into dynamic pressure by increasing the speed is taken away from static pressure. That’s why faster air doesn’t push as hard on the surface it’s flowing over, but hits harder on the surface it runs head-on into. It is static pressure that creates the surface forces on the airfoil, so the difference in static pressure over the wing area is equal to lift.

After manipulating the Bernoulli Equation, doing what I just explained above mathematically, you get:

L = (pB - pT) A = ½r(VT² - VB²) A

Where B means bottom, T means top, and A is wing area. We’ll make some rough assumptions, and plug them in. A Cessna 182 has a cruising speed of about 200 km/h, or 55 m/s. The wing surface area is 16.2 m². Let’s assume standard sea level air (density = 1.225 kg/m³). Also, as a very rough estimate, we’ll say that the air over the top surface is accelerated to about 15% faster than the freestream air, or 63 m/s for simplicity. The maximum velocity for flows like this can be 25% above freestream or more, but 15% is a good average for the whole upper surface.

L = (0.5)(1.225)(63² - 55²)(16.3) = 9424.66 N

This lift will hold up an aircraft of 961.7 kg. The Cessna 182’s empty weight is 808 kg, the max gross weight is 1338 kg. The lift we calculated is between these weights…not bad. Given that we used some very ballpark assumptions, we still got a number for lift that allows the aircraft to fly.

But, again…the above really isn’t the right way to do it. As an engineer, I cringe for having approached the problem in such a crude and dirty manner. But I was just showing that the pressures the Bernoulli Equation predicts are of the right order of magnitude, and that it can be a rough approximation to reality.

However, Bernoulli is still an incomplete and flawed approach. You can’t predict lift coefficients with any accuracy, because it doesn’t take into account viscous and compressibility effects.

Here’s a good site that explains some of the error of using Bernoulli as a source of lift. It does it at a pretty basic level and includes a cool Java toy. This applet is also what I used to validate my 25%-speed-increase assumption, since I couldn’t find a good cite in any of my texts.

Finally, there is a paper I’d like to point to that explains the creation of lift quite well, including what’s wrong with Bernoulli, circulation, and other old explanations. Unfortunately, it’s a technical paper, so it’s written in a way that would make most non-aerodynamicists’ heads spin. It’s pretty abstract, but not especially mathematical. It’s not available online unless you’re an AIAA member, but a trip to a technical library would turn it up…proceed at your own risk:

Hoffren, J,. Quest for an Improved Explanation of Lift, AIAA Paper 2001-0872, 39th AIAA Aerospace Sciences Meeting, Reno, NV, January 8-11, 2001.

Like anyone’s really gonna read it anyway :stuck_out_tongue:

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That’s a possible explanation, of course. You say he didn’t really see it; I say he did. However, when I posit that it’s really behaving as a knuckler, your correction of my reasoning for how it got that way doesn’t logically flow. You can’t say a proof with different assumptions is flawed because you’re proving something with a different set of assumptions.

Anyway, you and I have both been overthinking this. 1s&0s did see a beachball break to the right. Kicking a ball with your right foot, fairly straight on, strikes it with your right foot moving across your body, slightly right to left. It put a clockwise spin on it.

The beachball breaks to the right because you put a clockwise spin on it, OnesAndZeros.

You could get a ball to break to the left, like on a corner kick in soccer, if you really kick it with the side of your foot, slightly forward of the center of the ball.

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I much prefer actual experimental data to “very rough estimates”. What if we make a “very rough estimate” of 1.8% faster?

I do not have any actual measurements, but I see only a miniscule airflow acceleration over the the top surface. The difference between a 1.8% acceleration and a 15% acceleration is considerable.

The real bottom line is that all Fluid Dynamic Equations: Bernoulli, Kutta-Zhukovsky, Euler, Navier-Stokes, Circulation, Magnus, Coanda: all are mathematical representations of Newtonian Physics as they apply to fluids. “Then again, everything in in aerodynamics comes down to Newton when you get down to the nitty-gritty”.

When all is said and done, lift is 100% Newton.

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True, the upper surface path is only about 1.6% longer on that Cessna wing. But angle of attack helps make that path even longer. However, that’s still not the point…

So the relative lengths of the upper and lower surfaces are irrelevant, since the air spends less time over the top surface anyway.

I had a hard time coming up with experimental data for velocity over parts of an airfoil. Viscous effects make this a pain to get right, anyway. Abbott and von Doenhoff weren’t any help, and I really tought I could count on those guys. I thought about running a quick and dirty computational analysis at work, but my boss may wonder why I’m wasting CFD resources with 2-D, inviscid airfoil problems. So instead, I used that NASA applet to validate an estimate I already knew offhand. I was pretty close, possibly even underestimating.

One more bit of supporting evidence, although it’s in a different speed regime: A typical subsonic airfoil section (Like you’d find on a Cessna) has a critical Mach number of about 0.75. That it, air over the top starts going sonic when the freestream velocity is around Mach 0.75. We’ll be conservative and say Mach 0.8, to be safe. That still puts the upper-surface velocity at 125% of the freestream. According to Bertin and Smith¹, for subsonic, compressible flows, airfoils exhibit much of the same behaviors as at lower speeds. (Citing from recollection…read it this afternoon, but the book is at work).

So I think my 15% assumption is well within the realm of possibility, and possibly a little conservative. That being said…I still don’t assert that Bernoulli is why aircraft fly. I just think the the pressures predicted by the Principle are reasonable, as long as we agree with the crude, misleading assumption that the air on the upper surface is faster than on the lower surface.

But, I also recognize that a flat plate with an angle of attack will generate lift. Even though the air on top is massively separated, and therefor slower. That’s all Newtonian, baby. :cool:

¹ - Bertin, John J.; and Smith, Michael L.: Aerodynamics for Engineers, Second ed. Prentice-Hall , Inc. , 1989

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bup: I could find nothing in OnesNZeros posts that I could interpret as the beachball acting like a Knuckleball.

Again, whenever I spin a ball, even a beachball, it behaves like Master Cecil says it should. I’m thinking that the Laws of Physics probably also hold for OnesNZero’s balls. :slight_smile:

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audilover: My compliments on your posts. I thank you for the clarifications.

ronbo

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I should also add that your referenced website seems to verify my upper-surface velocity assumptions. This is down the page from his mathematical example:

So it would seem that whatever velocities Bernoulli says we would need do, in fact, exist. They are not the cause as much as the effect. But It still shows that my assumptions were valid despite being rough.

Also remember that equal transit time is a requirement of hump theory, not of Bernoulli’s Principle (BP). Bernoulli doesn’t care whether the upper-surface air meets up with it’s lower-surface counterpart. The two halves of the airstream can do whatever they want relative to each other, as far as BP is concerned.

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ronbo, thanks. For someone who isn’t an aeronautical engineer, you’ve displayed an admirable ability to latch on to some of the more arcane concepts. Just don’t let too many people know how easy it is, lest you take the mystique out of my job.

While not completely OT, this tangent has been a bit of a hijack. The Magnus effect has a lot of parallels to airfoil theory, and understanding one helps with the other. But, having exhausted airfoils for now (I’m exhausted, anyway), let’s steer this one back on course.

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I got out a couple beach balls (from the shed and kicked these suckers all around my backyard, fully prepared to record the experiments for uploding and public scrutiny.

And I was thunderstruck: Every single kick, throw, sling, fling, cast, chuck, pitch, toss…every @&%$# one broke in the direction of the spin as described by the Magnus Effect and all contributors to this thread except me.

So there are two explanations for my memory of this. A) My synapses are deteriorating and I’m losing my mind. (I’m not kidding. My memory of this is clear enough that if it turns out to have been impossible I must be losing it.) Or, and I’ll be testing this and reporting back when able, B) the ball I kicked back then was not, after all, a beach ball, but one of those slick WalMart $1.99 balls, a bit heavier than a beach ball but not nearly as heavy as a soccer ball: More than one web page I saw commented on a “reverse Magnus effect” for very smooth spheres.

I’m not expecting expl. B to come to much though, which leaves me to grow old with a screwed up memory that couldn’t possible have happened but that my mind nevertheless remembers quite clearly.

Thanks for your patience and expertise folks, and apologies for the trouble,
1s&0s

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FWIW Ping Pong Balls are about as smooth as you can get. My Dad could put soo much english on those balls!!!

They always curved exactly like all other balls.

If you have the cites to the sites I would like to see them. There is a lot of crap on the web about Bernoulli.

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Here’s a few cited sites. (Hope I coded the links properly…)

Short paragraph right after the first graphic (Fig. 1)
http://www.geocities.com/k_achutarao/MAGNUS/magnus.html

http://www.space.com/scienceastronomy/mars_curveballs_030221.html

Second item down in the references section:
http://math.ucr.edu/home/baez/physics/General/golf.html

http://wings.avkids.com/Tennis/Project/windr-07.html

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Excellent experiment. Excellent documentation of the results of 60 years of of Bernoulli Brainwashing!!!

Amazing.

I have a different name for the “reverse Magnus effect”. I call it: “Bernoulli’s Principle”.

If you make a ball smooth enough that the spin does not deflect the airflow, then the surface with the greatest fluid speed exhibits the lowest pressure and the ball curves in that direction.

This is exactly what Bernoulli Principle and Formula predict and what I refered to earlier.

Reverse Magnus Effect. :smack:

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ronbo, I’m not understanding what you mean by that. Newton demands that anything that creates a side force on the ball would deflect the wake. It’s simple action-reaction. No wake deflection, no curve.

But the idea of the reverse Magnus effect is certainly possible. What it requires is the perfect combination of velocity, spin, and surface roughness. What it all comes down to is boundary layer physics. I’ll try not to get too technical for those that aren’t aerodynamicists in the crowd. But I will attempt to explain some background.

Consider air moving over a flat plate. The air right next to the surface (the first few molecules thick) must be stationary relative to it—the “no-slip” condition. Because of viscosity, the air in the next layer can only move a little bit faster. In the very next layer up, the air is moving just a little bit faster still. Finally, when you move out far enough, the air is unaffected by the presence of the plate, and is moving at full speed. This region where the air is slowed down is called the boundary layer. If you look at it the other way, with the object moving through still air, the boundary layer is the air that the object drags along with it.

What I just described is a laminar boundary layer. If the air is fast enough, and the Reynolds number exceeds a certain value, the BL will transition to a turbulent boundary layer. Turbulent BLs are thicker than their laminar counterparts and are characterized by swirling and mixing.

FYI, Reynolds number (Re) is a dimensionless number that is a function of fluid velocity, density, length of interest, and viscosity. Since Re is proportional to distance, the number keeps getting bigger the father along the surface the boundary layer travels. It will eventually exceed the transition value, and so any laminar BL can be expected to turn turbulent after enough distance. This turbulent transition can be aided by a rough surface, or delayed by a very smooth one.

Re is also directly proportional to velocity. So all else being equal, increasing the velocity over a surface will cause the boundary layer to go turbulent at some critical speed. In the case of the ball spinning through the air, the side spinning into the flow will still slow the air down relative to the freestream (the principle behind the Magnus effect). But the relative velocity of the freestream air to the ball’s surface is higher on that side, and that’s what’s important when considering BL transition.

So, with a very smooth surface, you have the possibility of a reverse Magnus effect. Here’s how it would happen: The overall speed of the ball is very close to the critical velocity for boundary layer transition. The spin of the ball produces a different relative velocity for the opposing sides of the ball. With the right speed and the right spin, the part of the ball spinning into the flow will cause the airspeed to exceed the transition velocity, while the opposite side moving with the flow keeps the relative velocity under the critical. So on one side of the ball, you have a turbulent boundary layer, but the other side has a laminar BL.

The different types of flow will create an asymmetrical wake. The wake from the turbulent half will expand faster and fill in the region behind the ball. The wake from the laminar half will not. Since the turbulent wake essentially overpowers the laminar half, the wake is deflected towards the laminar half of the ball. Because of Newton, this creates a side force that pushes the ball away from the direction of the spin, or towards the side spinning into the flow. This is the opposite of the direction predicted by the Magnus effect alone.

The regular Magnus effect is overwhelmed by the effect of the difference in laminar and turbulent boundary layers. The side moving into the flow still slows the air down and creates more static pressure, but that action also makes the flow turbulent, and changes the wake characteristics enough to make the ball move in the opposite direction from normal.

The reason you need a smooth ball for this is because it only works for a rougher surface at exceedingly low speeds…the kinds of speeds for which the ball isn’t really going to move through the air very far.

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audilover: My apologies for the ambiguous if not misleading statement. BTW, good job explaining reverse Magnus in an understandable way. At least I think I understand what you are saying.

Short response: It sounds to me as though a “reverse Magnus effect” relies on unique spin/surface/flow characteristics involving specific and complicated turbulence outcomes.

The Bernoulli effect on the other hand is simple, easy to understand, intuitive and universal.

I’m wondering whether the “reverse Magnus effect” is another example of Bernoulli Believers gone Bad. The Magnus effect completely overpowers Bernoulli (similar to an airplane flying upside down). People trying to explain Magnus (or lift) with Bernoulli are missing the concept.

This might be a better statement:

The Bernoulli effect: “If a spinning ball is sufficiently smooth that it does not cause the surrounding air to rotate, the surface rotating into the air stream will experience a lowered pressure due to Bernoulli’s Principle. The ball will curve in the direction of the leeward rotation.”

Predictions of this effect:

  1. A specific combination of velocity, spin, and surface roughness must be exceeded for the Bernoulli effect to overpower the much stronger and opposing Magnus effect.
  2. The rougher the surface, the slower the rotation must be to prevent fluid rotation, therefore, the less Bernoulli effect will be observed.

(Further Comments)

Yes, Bernoulli is a Newtonian force and will leave a Newtonian wake.
Ronbo’s Principles of Fluid Dynamics: :slight_smile:

Newton:

  1. When a surface meets a fluid, energy accumulates on the windward surface and is carried by streamlines to the leeward side where it is released.
  2. Any deflection in the streamline indicates an equal and opposite deflection of the surface.

Magnus:
3) If the surface of an object is rotating beyond a certain velocity, additional streamlines are carried with the rotation (at the expense of the contra-lateral streamlines) according to the properties of that surface.
4) These enhanced streamlines are likewise carried to the leeward side where they are separated from the surface in the direction of rotation.
5) As these streamlines carry more force than the opposing streamlines, a net vector
from the trailing streamlines is in the direction of the leeward surface rotation. The object reacts in an equal and opposite direction, being deflected in the direction of the windward surface rotation.

Bernoulli:
6) The surface of an object moving (rotating) into a fluid flow experiences lower pressure than the surface moving (rotating) with the fluid flow (Bernoulli’s principle).
7) The net Bernoulli force on a rotating object is in the direction of the leeward surface rotation.
8) The streamline reacts with a deflection in an equal and opposite force and direction.

Result:
9) The object is deflected in the direction of the stronger of these opposing forces.

Disclaimer:
10) Turbulence will affect the net conditions.

Summary:
On any given spinning surface meeting a fluid: A spinning surface will tend to be deflected in the direction of the windward surface rotation. As the spin of the surface decreases, the rotating boundary layers will slow to a critical level, below which the Bernoulli Effect will predominate and the opposite deflection will occur.

Why do I feel like I’m defending Bernoulli?

Further questions:

  1. Does my understanding differ from what Magnus or Bernoulli actually states?
  2. If reverse Magnus is not Bernoulli, but applies only to specific, restrictive conditions, isn’t reverse Magnus just a footnote to Bernoulli?"
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You betcha. What am I looking at right now?

40

Sorry, my ESP sometimes fails me.

Tell us.