When a ball spins to left, shouldn't it curve right?(hurricane vise)

[Skhandelwal]

Basically, what I mean to say is that let's say I am playing ping pong...I put a lot of sidespin on the ball.(from back to forward vise, not up to down...how hurricane spins, not how clock runs)

If the ball is rotating to the right, shouldn't it travel to the left b/c wind is the median. Similar to how the tire travels on the road.

Am I being clear?

 

[russ_watters]

If you look at the ball from the top down and it is rotating counter-clockwise, it will curve left.

http://library.thinkquest.org/11902/physics/curve2.html

 

[rcgldr]

This exact example can be seen in the 2nd sequence in this video clip, the ball curves "left" quite a bit. The players are Jan-Ove Waldner and Kong Linghui.

tt2.wmv

 

[Skhandelwal]

Russ,

First of all, the baseball curves b/c its surface is uneven.
I am talking about a table tennis ball.(high quality ones have internal seam so they are perfectly smooth)

Also, from the article, how come the air hitting the top of the wings of the airplane is faster?

 

[arildno]

Russ,

First of all, the baseball curves b/c its surface is uneven.
I am talking about a table tennis ball.(high quality ones have internal seam so they are perfectly smooth)

Also, from the article, how come the air hitting the top of the wings of the airplane is faster?

No, the pressure above the wing is less than below; that means the air will accelerate more strongly along the upper surface than along the lower surface, since the pressure difference between a location in front of the plane and a location above the wing is greater than between that frontal location and a similar location beneath the wing.

Thus, the net effect is that the air above the wing will get a higher velocity than air going along the underside.

 

[arildno]

Around the wing, the air spins (caused ultimately by the viscosity of the air). Thus, flight is more related to the Magnus effect (the plane "curves" upwards!), the Bernoulli effect is a mere amplifying side result of the circulation that goes around the wing.

The Bernoulli effect, often coupled with the fallacious "equal trasit time"-principle yields a totally wrong estimation of the circulation strength, and hence lift, for the plane.


To understand a little better why a plane maintains flight, it is sufficient with geometrical streamline arguments for an inviscid fluid:

Assume the simplest case, in which both the upper and lower wing surfaces have positive effective curvatures, i.e, the centres of their osculating circles lie BELOW the surface.

Now, if we go way up vertically from the upper surface, we get into the freestrem, where the pressure is p.
Similarly, if we go way down vertically from the lower surface, we also hit the free stream, with the same pressure p.

Now, consider the pressure situation along the upper surface:
In order to traverse that curve, you must have a downwards acting centripetal acceleration, which means that the pressure along the upper surface, pU, must be less than the free-stream pressure p.
That is, pU<p

Similarly, on the lower surface, you also need a downwards centripetal acceleration, and the pressure there, pL must therefore be GREATER than p, i.e, p<pL

Combining these inequalities yields the desired result: pU<pL, hence lift.

 

[russ_watters]

First of all, the baseball curves b/c its surface is uneven.
I am talking about a table tennis ball.(high quality ones have internal seam so they are perfectly smooth)

A high quality table tennis ball still has a certain amount of friction and since it weighs virtually nothing, it only requires a little bit of friction (and thus lift) to have a big effect on it's flight path. I also suspect that you can spin a ping pong ball faster than a pitcher can spin a curveball.

Also, from the article, how come the air hitting the top of the wings of the airplane is faster?

I'm not sure exactly what you mean, but air flowing over the top surface of a wing flows faster because it has a longer distance to traverse. I'm not sure I like the way they tried to draw that analogy. With lift, the rotation theory is generally treated separately from Bernoulli's, but essentially the idea for a wing is that the wing's shape makes the airflow rotate, similar to the way a rotating ball does.

 

[rcgldr]

Getting back on topic, spin on a table tennis ball can reach 150 revolutions per second, that's 9000 rpm. Link below.

about table tennis

Before 2001, when ball size was 38mm (instead of the current 40mm), there was more variety in the surfaces of table tennis balls. Smooth ones (like a Peace) curved more than rough ones (like a Barna), but I don't recall either ball being very popular. The balls made now have a "matte" finish, similar to the older versions by Nittaku and Halex. The roughness of the surface of a table tennis ball has similar effect as the dimples on a golf ball (reduces the amount of curve).

When a table tennis ball is spinning and moving laterally, a very thin layer of air remains somewhat "attached" at the surface of the ball, quickly diminishing with distance from the surface, but it's enough to create a resistance to lateral airflow. This resistance results in a difference in acceleration of air on the forwards and backwards spinning surfaces, which results in a pressure differential, which in turn cause the ball to curve away from the forwards spinning surface.

Since the ball is a very thin shelled hollow sphere, it is affected a lot by aerodynamics. The 2001/2003 increase in size from 38mm to 40mm without an increase in weight caused the balls to lose more lateral and rotational energy to aerodynamic drag, they curve more, and slow down more, with less energy for the player returning the ball to deal with. The idea was to increase the length of the rallies.

Regarding the sub-topic aspect of wings, a flat plane will fly just fine, although with more drag, such as a box kite. All that is needed for lift is some air speed and an effective angle of attack. Air will be deflected from below and drawn towards the void above, with a net downwards acceleration (plus forwards acceleration, related to drag). Wings are shaped the way they are to reduce drag while increasing lift, designed for a range of air speed, and with the compromise of manufacturability, such as a flat bottomed wing (a fully cambered air foil would be more efficient). For those that think the hump has to be on top, I refer to this picture of a M2-F2 flying body glider (pre-shuttle prototype), which has a flat top and huge hump on the bottom, gliding next to a chase jet. Note the difference in angle of attack between the jet and the glider, and the fact that the upper surface of the glider is virtually horizontal.

flat top curved bottom glider.jpg

 

[Skhandelwal]

I am sorry guys...I feel really dumb. After all this explanation, I still don't get it. To begin w/...I need to know how a plane's wings look like?

Second, people still havn't answered WHY the table tennis ball curves.

 

[quetzalcoatl9]

the assumption here is laminar flow (i.e. the velocity of the wing is much less than the mean velocity of the gas, so that the gas "rearranges itself" around the wing nearly instantly). as the velocity of the wing approaches the mean velocity of the gas (which is related to the velocity of sound propagation through the gas) the gas can no longer "rearrange itself" ahead of the wing, and so the gas molecules are smashed out of the way by the wing. this is what we call supersonic flight, and the mechanism by which a supersonic wing stays aloft is completely different from a sub-sonic/laminar/Bernoulli wing..

 

[rcgldr]

Do I need to know how a plane's wings look like?

no.

Second, people still havn't answered WHY the table tennis ball curves.

I thought I did:

The drag part: While traveling laterally, a small amount of air is accelerated forwards, while most of the air is separated by the ball and flows around it. As the back of the ball passes through a volume of air, it leaves a low pressure moving void behind it, and the air accelerates towards this moving void. Since the air can't flow through the ball, there is a net forwards acceleration of air, and the reaction force of the air on the ball slows it down.

The curve part (again):

When a table tennis ball is spinning and moving laterally, a very thin layer of air remains somewhat "attached" at the surface of the ball, quickly diminishing with distance from the surface, but it's enough to create a resistance to lateral airflow. This resistance results in a difference in acceleration of air on the forwards and backwards spinning surfaces, which results in a pressure differential, which in turn cause the ball to curve away from the forwards spinning surface.

More explanation, the forwards spinning part of the ball accelerates air forwards (in the direction of ball travel) more than the backwards spinning part. This will create a pressure differential, higher for the forwards spinning part, lower for the backwards spinning part. The result of this pressure differential causes the air to accelerate "outwards" and the reaction force of the air causes the ball to curve "inwards", away from the forwards spinning part. So a left spin causes a right curve, a right spin causes a left curve, top spin causes a downwards curve, and enough back spin and speed will cause an upwards curve.

By definition, the reaction force in the direction that the ball moves, slowing it down, is called drag. The reaction force perpendicular to the direction the ball moves, causing it to curve, is called lift.

 

[arildno]

the assumption here is laminar flow (i.e. the velocity of the wing is much less than the mean velocity of the gas, so that the gas "rearranges itself" around the wing nearly instantly). as the velocity of the wing approaches the mean velocity of the gas (which is related to the velocity of sound propagation through the gas) the gas can no longer "rearrange itself" ahead of the wing, and so the gas molecules are smashed out of the way by the wing. this is what we call supersonic flight, and the mechanism by which a supersonic wing stays aloft is completely different from a sub-sonic/laminar/Bernoulli wing..

No, no, no!
Laminar is used in contrast to "turbulent".
ALL flows are turbulent, and turbulence concerns are crucial in any flight consideration.

The stationary inviscid fluid approximation (i.e, the reign within Bernoulii is applicable) is a limiting case of minimal turbulunce presence, a rough measure of which would be a very thin wake region behind the wing.


Of course, your concerns about the assumptions of sub-sonic flight is very relevant and to the point, but that is not to be confused with the distinction laminarity/turbulunce.
There exist good laminar approximations to some supersonic flows as well, not just for sub-sonic ones.

 

[quetzalcoatl9]

No, no, no!
Laminar is used in contrast to "turbulent".
ALL flows are turbulent, and turbulence concerns are crucial in any flight consideration.

The stationary inviscid fluid approximation (i.e, the reign within Bernoulii is applicable) is a limiting case of minimal turbulunce presence, a rough measure of which would be a very thin wake region behind the wing.

what's the difference? you are saying that the opposite of turbulence is laminar, which i agree with. then you are saying that the "stationary inviscid fluid approximation" is what you get in the limit of no turbulence...how is that not laminar? (pardon my ignorance, i am not an engineer but a chemist)

in other words i agree with the statement that "all flows are inherently turbulent" but it is a matter of degree, at what point can we refer to the ideal as if it were "real". in the end, i highly doubt that the navier-stokes is numerically solved each time we want to consider airflow.

am i misunderstanding something here?

 

[rcgldr]

Shouldn't we create yet another separate thread on how wings produce lift, and leave this thread to spinning balls?

 

[arildno]

what's the difference? you are saying that the opposite of turbulence is laminar, which i agree with. then you are saying that the "stationary inviscid fluid approximation" is what you get in the limit of no turbulence...how is that not laminar? (pardon my ignorance, i am not an engineer but a chemist)

in other words i agree with the statement that "all flows are inherently turbulent" but it is a matter of degree, at what point can we refer to the ideal as if it were "real". in the end, i highly doubt that the navier-stokes is numerically solved each time we want to consider airflow.

am i misunderstanding something here?

YOU used laminar flow in contrast to supersonic flow. That is incorrect.

Supersonic flow, as well as subsonic flow, can be either (practically) laminar or turbulent.

 

[quetzalcoatl9]

YOU used laminar flow in contrast to supersonic flow. That is incorrect.

Supersonic flow, as well as subsonic flow, can be either (practically) laminar or turbulent.

i see, that is news to me but then i don't (admittedly) know much of anything about this area.

can you explain to me how a supersonic object could possibly have laminar flow? my understanding is that you will always be stuck with a (albeit very complicated) shock wave propagating from the object. how could such a thing possibly be considered laminar? i believe you (in the sense that the fluid dynamics become difficult to intuitively predict) but it is hard to imagine any sort of stream-lined layer near the wing.

it was my understanding that supersonic flight occurs successfully because the shock waves propagate in such a way that there is upward momentum transferred to the object that is "riding" the wave (actually, the wave is continually hammering the object from below), a situation that i would hardly describe as being laminar.

 

[rcgldr]

A bit off-topic, but since this continues and the the OP got his answer already ...

wing approaches the mean velocity of the gas (which is related to the velocity of sound propagation through the gas) ... smashed ...

The velocity of air molecules, 502m/s, is much faster than the speed of sound, 343 m/s (at 20 degrees C). Also the molecules aren't "smashed". I'm not sure if the outer electron shells are "compressed" significantly more than they would be at sub-sonic speeds. At super-sonic speeds, effective angle of attack is going to be very small. Lift will still be the result of accelerating air downwards (and drag related to accelerating air forwards). The main issue is designing the airframe and engines to deal with the shock waves generated at the leading edges of the aircraft. For the SR-71, adjustable cones at the intake make use of the shock waves to slow the air down, and in addition, use large internal pipes to bypass a significant part of the compressor stage turning the engines into partial ram jet engines. In older aircraft, spikes at the nose were used to initiate shock wave generation. Note that scram jets operate just fine with super-sonic intake and output.

Regarding "laminar" air flow, it doesn't really exist. Even "laminar" air foils are named so only because they maintain laminar air flow for more of their chord length than other air foils. At low Reynolds numbers, such as model gliders, the laminar flow to turbulent flow transition is an issue so they use "turbulators" (tape or a rough leading edge) to prevent this. One of many links about this:

http://www.dreesecode.com/primer/airfoil5.html

 

[arildno]

Regarding "laminar" air flow, it doesn't really exist. Even "laminar" air foils are named so only because they maintain laminar air flow for more of their chord length than other air foils. At low Reynolds numbers, such as model gliders, the laminar flow to turbulent flow transition is an issue so they use "turbulators" (tape or a rough leading edge) to prevent this. One of many links about this:

http://www.dreesecode.com/primer/airfoil5.html

Sure turbulators are used in order to dissipate energy so that you get "streamline attachment" to the wing faster. This is a crucial feature in how lift is GENERATED, but once that is done, calculations based on inviscid flow are extremely accurate in predicting, say the pressure differential across the wing.

One could equally well say that "pure" objects don't really exist, since we disregard their wave-like nature as well.

It depends on the relevant scale of accuracy what bits and pieces of physics we need to take into account to make a realistic model.

For pipe flow, the laminar Hagen-Pousseille model is often sufficiently accurate.

 

[codec9]

ping pong ball

I think I can explain the ping pong ball using forces. The trick is to realize that air around the ball effects the ball and that the ball also effects the way the air moving.

So when a ball with no spin is flying through the air, say without gravity, there is just one force pushing against the ball straight on in the opposite direction the ball is moving.

When there is a perfect side-spin, say counter-clockwise, the air moves around the ball with the spin. So the air is moving counter clockwise, too. Imagine you are on the ceiling looking down at the ball below. Now let's consider three forces: at the forward tip or "nose" (very unofficial term) of the ball, on left side, and on the right.

At the tip there is still a force going right against the straight path the ball is moving in, so no change there. The only thing that can weaken this straight force is another straight force. The force won't weaken or anything due to a sideways force if there is one, that will just be added.

On the left the air is moving past the ball. So the straight forces not hitting the exact nose of the ball but between the nose and the very left side are basically being helped by the air spinning in the same direction.. you see? What's important is that they are working together on the left.

On the right the air is moving with the ball. It's going along the ball's path but that is also against the air which is sitting there and trying to be inert. So we have the force of the air due to the spin banging up against the air ahead which is sitting still, effectively pushing with a straight force against the top right corner of the between the nose and the very right side. So these forces are working against each other in opposite directions.. you see? That's important.

Now to where it gets a little weird, there is basically more pressure on the right. The air is more dense because the two types of air we are talking about--the moving air just around the ball and the normal air in the room which is staying still (or yes, pushing against the ball because the ball is moving)-- are smashing together on the right. The left on the other hand is smooth sailing. Nothing but free flowing air over there.

Now because it is less dense on the left compared to the right, the ball goes over there. Why? That is just how pressure works. I don't know why.

 

[codec9]

I didn't realize you were originally talking about top-spin (as opposed to back-spin), Skhandelwal. With top-spin the "easy" side where it is less dense is the BOTTOM and the "harder" side where the air is more dense because it is banging against each other is the TOP. So, the ball moves to the bottom.

When you do top-spin the ball arcs downward more than it would from just gravity. When you do back-spin/bottom-spin the ball could arc up or just float along because it is less dense on top.

 

[craghunath]

clarification please

Basically, what I mean to say is that let's say I am playing ping pong...I put a lot of sidespin on the ball.(from back to forward vise, not up to down...how hurricane spins, not how clock runs)

If the ball is rotating to the right, shouldn't it travel to the left b/c wind is the median. Similar to how the tire travels on the road.

Am I being clear?

Hi
I am raghunath, your thought is interesting..
Can you please be more explicit...

letz take the ping pong board as the refrence and when the ball spins specify the direction of angular momentum vector.
Please see the attachment.

 

[codec9]

I explained it spinning on the side, counterclockwise if you look from the top. So if you hit the ball I am talking about, and you are right handed, you would hit it on the right side most likely or else move the paddle from the left side of your body across to the right side and beyond.

 

[quetzalcoatl9]

A bit off-topic, but since this continues and the the OP got his answer already ...

The velocity of air molecules, 502m/s, is much faster than the speed of sound, 343 m/s (at 20 degrees C). Also the molecules aren't "smashed". I'm not sure if the outer electron shells are "compressed" significantly more than they would be at sub-sonic speeds. At super-sonic speeds, effective angle of attack is going to be very small. Lift will still be the result of accelerating air downwards (and drag related to accelerating air forwards). The main issue is designing the airframe and engines to deal with the shock waves generated at the leading edges of the aircraft. For the SR-71, adjustable cones at the intake make use of the shock waves to slow the air down, and in addition, use large internal pipes to bypass a significant part of the compressor stage turning the engines into partial ram jet engines. In older aircraft, spikes at the nose were used to initiate shock wave generation. Note that scram jets operate just fine with super-sonic intake and output.

i never said that the mean velocity of the gas was equal to the speed of sound propagation (only that they were RELATED - see McQuarrie's derivation in "Statistical Mechanics" for the exact relation, pg. 391 in my copy).

why would you say that the molecules are not smashed? that's what causes the shock wave. i certainly would not say that the gas molecules are flowing smoothly. electronically, yes there will be electrostatic repulsion and Pauli exclusion taking place but that need not concern us if we make the reasonable approximation that the air molecules are inert van der Waals spheres - none of that really matters here. for me, "smashing" is the antithesis of "flowing" and denotes that the air is being pushed away from the wing at a supersonic velocity. the air is "exploding" from the leading edge of the wing.

what you are referring to are rather clever engineering techniques for taking a shock wave (travelling supersonically) and "guiding" it into being sub-sonic with a more streamlined flow. that doesn't address my main point (well, it somewhat supports it) which is that supersonic flight occurs by an entirely different mechanism than subsonic flight...this is why so many pilots died shortly upon breaking the sound barrier. it is easy to understand why this happened when you realize that a sub-sonic wing could hardly be worse for the mechanism that i am alluding to.

 

[quetzalcoatl9]

Sure turbulators are used in order to dissipate energy so that you get "streamline attachment" to the wing faster. This is a crucial feature in how lift is GENERATED, but once that is done, calculations based on inviscid flow are extremely accurate in predicting, say the pressure differential across the wing.

are these the little triangular things that one typically sees on the fuselage of supersonic aircraft?

 

[rcgldr]

Although ping pong balls don't travel near the speed of sound, I'll answer, but this part should be split off into a separate thread about supersonic flight.

super sonic

why would you say that the molecules are not smashed? that's what causes the shock wave.

The molecules aren't smashed, but the amount of jerk and acceleration are very high on any surface producing a shock wave on an aircraft. Wiki mentions that the air can't send "information" faster than the speed of sound, so air ahead of a super-sonic aircraft doesn't "respond" until contact by the aircraft's leading surfaces that produce shockwaves.

Still the principle of lift is the same, the net downwards acceleration of air results in a reactive upwards force causing lift (and the net forwards acceleration of air results in a drag force). Also with good design, the shock wave is used to do some of the forwards acceleration of air, so that a significant part of the leading edges of surfaces don't involve a transition of speed greater than the speed of sound, although this effect diminishes as mach number increases (shock wave angle gets very small).

I defer to these articles:

http://en.wikipedia.org/wiki/Supersonic

http://en.wikipedia.org/wiki/Shock_wave

In the second half of this short video, a F14 does a supersonic flyby, where the "crack" (as opposed to a boom) can be heard:

f14flyby.wmv

 

[quetzalcoatl9]

Wiki mentions that the air can't send "information" faster than the speed of sound, so air ahead of a super-sonic aircraft doesn't "respond" until contact by the aircraft's leading surfaces that produce shockwaves.

this is exactly what i have been saying all along! please see my post #10.

Still the principle of lift is the same, the net downwards acceleration of air results in a reactive upwards force causing lift (and the net forwards acceleration of air results in a drag force).

in one case you have flight taking place because a shock wave is being "surfed", and in the other you have flight taking place by a Bernoulli effect: how could you possible say that the two mechanism are "the same"! I'm afraid that the wing of a cessna and the wing of an F-16 (and fuselage for that matter) look drastically different, wouldn't you agree??!

I defer to these articles:

i have read the wiki articles and they all support what i am saying here!

 

[rcgldr]

In one case you have flight taking place because a shock wave is being "surfed", and in the other you have flight taking place by a Bernoulli effect: how could you possible say that the two mechanism are "the same".

Because the key elements are the same. Forward speed and effective angle of attack accelerate air downwards and forwards, and the air reacts with an upwards and backwards force corresponding to lift and drag.

I've never liked using Bernoulli effect to describe lift. Take the simple case of ground based observer on a no wind day, watching an aircraft fly by. From the ground based observer's point of view, and assuming lift to drag ratio is reasonably higher than 1, then most of the acceleration of air is downwards (lift) and with a much smaller forwards acceleration of air (drag). For this ground based observer, there's very little horizontal movment of air compared to the vertical movment, and most of the horizontal movement is from below the wings. Where's the Bernoulli effect in this case?

Look at that video of the F14 flyby again f14flyby.wmv, in the first half, you can see the shockwave, which is a very widely angled cone. The F14 is not "surfing" on the bottom half of this nearly vertically shaped cone.

I'm afraid that the wing of a Cessna and the wing of an F-16 (and fuselage for that matter) look drastically different, wouldn't you agree??!

Yes they are different, but both a Cessna 182 and a F14 can fly at 140 knots. However the F14 has movable wings, so a comparason with a fixed wing F15 be better, which can also fly at 140knots.

In this picture, an M2-F2 flying body glider, is gliding along side a F104 chase jet (more like a missle with wings). Obviously the air foils are very different, but both are flying just fine and at the same speed, although the F104's visual angle of attack is higher than that of the M2-F2. Regarding Bernoulli effect explanation of lift, how would it apply to the M2-F2 with its big hump on the bottom and its flat top?

http://www1.dfrc.nasa.gov/gallery/photo/M2-F2/Medium/EC66-1567.jpg

http://en.wikipedia.org/wiki/Northrop_M2-F2

http://en.wikipedia.org/wiki/F-104_Starfighter

The powered succesor to the M2-F2, the M2-F3, was supersonic, with a fastest flight speed over Mach 1.6, using the same basic airfoil, but with a 3rd vertical fin added for stability. The F104 was faster with a top speed of Mach 2.2, but since it looks like a flying missle, it should have flown like one.

http://en.wikipedia.org/wiki/Northrop_M2-F3

More photos:

http://www.dfrc.nasa.gov/gallery/photo/M2-F2
http://www.dfrc.nasa.gov/gallery/photo/M2-F3

 

[Skhandelwal]

Hey Jeff...I still didn't get the concept back then...but I thought may be I should ask my physics professor but he seems to be harder to get hold of than I thought. And now, my assignment is due...so I am sorry for doing this...but could you explain more explicitly what you did earlier? I will phrase my doubts on those.

“When a table tennis ball is spinning and moving laterally, a very thin layer of air remains somewhat "attached" at the surface of the ball, quickly diminishing with distance from the surface, but it's enough to create a resistance to lateral airflow. This resistance results in a difference in acceleration of air on the forwards and backwards spinning surfaces, which results in a pressure differential, which in turn cause the ball to curve away from the forwards spinning surface.”

What do you mean by saying the air is attached? And how is it attached?? Why does diminish away? What the heck is lateral airflow? Now, once I can get these questions answered…then I can try reading what you wrote down further. Thanks a lot by the way for helping me out with such sincerity(that goes for the rest of you too.)

 

[Skhandelwal]

I tried reading further anyways….

“the forwards spinning part of the ball accelerates air forwards (in the direction of ball travel)”

Why and how?

I think…I understand the rest…thanks again the favor.

 

[rcgldr]

By lateral I meant in a straight line, as opposed to rotational.

If the ball is moving and not spinning, it's accelerating the air in the direction that the ball is moving, which reacts with an opposing force, drag.

If the ball has backspin, then the bottom surface of the ball is moving forwards faster, and the top surface of the ball is moving forwards slower (or backwards if rotational surface speed is faster than latera [forwards] speed), than the non spinning case. The bottom surface of the ball accelerates the air forwards a bit more than the non-spinning case, and top surface of the ball is accelerating air forwards less than the non-spinning case. This creates a differential in acceleration of air, more at the bottom, less at the top (in the case of backspin). The greater the acceleration, the higher the pressure because of the air's momentum and resistance to acceleration. So the differential in acceleration of air corresponds to a differential in reactive pressure, higher pressure below, and lower pressure above. Air can't flow through the ball, so there's a net downwards acceleration of the air because of the pressure differential, and the air reacts with an opposing upwards force on the ball, "lift".

Air "attaches" to the ball because of friction between the air and the ball. This boundary is not infinitly thin, because of "friction" within the air itself, called viscousity. The result is a small amount of air that spins in the same direction as the ball, diminishing with distance from the surface of the ball.

Wiki has an article on this:

http://en.wikipedia.org/wiki/Magnus_effect

Personally, I prefer Newton explanations for "lift" as opposed to Bernoulli explanations. With the Newton method, the focus is on acceleration of air and the corresponding reaction force. With the Bernoulli method, the focus is on relative velocities of air streams, which are meaningless unless the causes for these air stream velocities is known. Also with the Newton approach, it's clear that work is being done on the air, while in some cases work done on the air is ignored with Bernoulli approach.

Another issue with the Bernoulli approach is that its frame of reference is based on an object, not the air itself, similar to a stationary object inside a wind tunnel. An association is made between "faster" moving air and lower pressure. However change the frame of reference to the air itself, similar to a ground observer in a no-wind condition, or an observer hovering along with the wind in a balloon. From the air's frame of reference, the faster moving air is the result of acceleration and is associated with higher pressure, not less.

update - see next post.