Curve balls and Bernoulli's principle

[Yuqing]

It has always been explained to me that balls curve because a thin layer of fluid adheres to its surface as a boundary layer. This boundary layer retards the flow on one side of the ball and speeds it on the other. And then Bernoulli's principle is applied to make the pressure difference happen.

But recently I have read that Bernoulli's principle plays little part in this effect because Bernoulli's principle cannot be applied to viscid flows which is essentially what is happening at the surface of the ball. The effect is instead explained with mass diversion which seems more logic. So if anyone is able to give a more thorough explanation of this effect and explain what part Bernoulli's principle actually plays, it would be greatly appreciated.

 

[rcgldr]

mass diversion

It's called Magnus Effect. Without getting into the complicated details, this Nasa article explains that the lift comes from diverted flow:

http://www.grc.nasa.gov/WWW/K-12/airplane/cyl.html

Most of the lift is due to the fact that the flow on a cylinder or sphere with 'backspin' remains attached a bit longer on the downwards moving surface on the back side of a cylinder or sphere, and this diverts the air downwards, resulting in a reactive lift force. Some of the lift is due to the forwards moving surface at the bottom of the cylinder or sphere accelerating the air more than the upper surface, creating a higher pressure zone below than above, but most articles state that dominant factor is the difference in detached flow on the backside of a cylinder or sphere. If it's topspin, the aerodynamic force is downwards. A table tennis ball is relative light for it's size, and the rackets use very sticky and elastic rubber to impart a lot of spin, so the ball curves a lot.

http://rcgldr.net/real/tt2.wmv

Generally when a solid moves through a gas or fluid, the direct interaction violates Bernoulli because work is done. Away from that direct interaction though, the interaction within the gas or fluid is Bernoulli like. Ignoring how pressure differentials are created in a gas or fluid, once those pressure differentials exist, then a gas or fluild will accelerate away from higher pressure zones to lower pressure zones. What Bernoulli principle notes is the somewhat obvious consequence that as a gas accelerates away from a higher pressure zone towards a lower pressure zone, it's speed increases as its pressure decreases. Bernoulli's equation approximates the relationship between speed and pressure of that accelerating gas or fluid (ignoring effects like turbulence).

In order to model the interaction between solids and a gas or fluid, the much more complicated Navier-Stoke equations are used.

http://en.wikipedia.org/wiki/Navier–Stokes_equations

Generally the exact equations can't be determined, so an airfoil program will use some simplified set of differential equations to mathematically model airfoils.

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

 

[Yuqing]

I realize that it is the magnus effect. I'm simply wondering what is causing the lift. Is it bernoulli's principle or something else?

 

[rcgldr]

Is it Bernoulli's principle or something else?

I was in the process of updating my previous post. Please read it again for more information. Bernoulli principle doesn't apply to the interaction between the ball's surface and the air that creates the pressure differential and therefore the lift, only to the the air's reaction once the pressure differential exists.

When a solid object produces lift (upwards) the interaction produces a lower pressure zone above, and/or a higher pressure zone below, and a downwards acceleration of air that would otherwise accelrate upwards if the pressure zones existed without the presence of that object that is diverting the flow. In a sense, the object forces the air to flow in the 'wrong' direction with respect to the pressure zones it creates since the air can't flow upwards thorugh the solid object (air flows around the object, but the net result is a downwards acceleration of air).

 

[Yuqing]

Thank you very much. Just to clear up my basic understanding.

The cause of the lift is from mass diversion which in process will create pressure differentials. These pressure differentials are what causes the acceleration of the air, not the other way around as it is typically explained.

 

[rcgldr]

The cause of the lift is from mass diversion which in process will create pressure differentials. These pressure differentials are what causes the acceleration of the air, not the other way around as it is typically explained.

It's difficult to assign cause and effect, since the pressure differentials coexist with accelerations into the surrounding ambient pressure air. The pressure differentials are related to accelerations and inertia of the affected air, so it's hard to call one the cause and the other the effect.

Perhaps a better way to word this is that the spinning ball creates the pressure differentials, but the magnitude of those pressure differentials are related to the reaction of the affected air.

For Magnus Effect, the primary root cause is the fact that the flow remains attached a bit longer on the top or bottom back side of the ball (the differential in forwards acceleration of air near the top and bottom of a ball are a secondary cause) resulting in a diverted flow of air. How much lift is produced from this process is related to the air's inertia, viscosity (which was ignored in that Nasa link), the speeds involved, ... and all of this translates to some amount of net force and acceleration of air and ball.

 

[arildno]

The Magnus effect is, essentially, for stationary flow, what maintains the lift of the airplane.

This has more to do with differential centripetal accelerations, rather than accelerations along the streamline (i.e bernoulli effects).

This is indicated by the less well known Crocco's theorem, that is the complement to Bernoulli, where the integration goes ACROSS streamlines, rather than along.

MAJOR NOTE:
Jeff Reid's "void effect", essentially that a "vacuum-like" region sucks fluid into it due to lower pressure, AND the Coanda effect, where viscosity glues the streamlines onto the surface are BOTH crucial micro-mechanisms in order to understand how lift/Magnus effect is generated in the first place.

However, in stationary flow (when the liquid has "settled down" in a flow pattern), inviscid flow accurately predicts the magnitude of lift in terms of the net non-zero circulation (see, for example, Kutta-Jakowski theorem).

The following thread looks upon the "centripetal acceleration argument" as a rough introduction.

(The thread degenerates quickly, due the cracpot's 4Newton's intrusion).
The first few posts are really enough, though:
https://www.physicsforums.com/showthread.php?t=57710&highlight=crocco's

 

[Yuqing]

From what I've read from the sources given to me in this thread, it seems that the theories regarding lift is varied and extremely complex. It is probably beyond my scope for now. My remaining question is this. It seems from what I've read that Bernoulli's principle plays little part in lift and is used as a simple method of calculating the pressure distribution on the surface of an object. Still, how is Bernoulli's principle able to be used at all? Work is being done on the flow which makes the principle inapplicable. Am I right in assuming that Bernoulli's principle can only be used in very ideal approximations and the truth deviates from it?

 

[rcgldr]

Bernoulli's principle plays little part in lift and is used as a simple method of calculating the pressure distribution on the surface of an object.

Calculating the pressure distribution can't be done using just Bernoulli, you'd have to be able to calculate the speed distribution as well, and Bernoulli principle doesn't provide a means to calculate how an airfoil diverts the air flow, and the resulting pressure and speed distributions. You'd have to somehow calculate either the speed or pressure distributions using a more complex mathematical model, and the process for doing this can determine both speed and pressure distributions without relying on Bernoulli equation as a final step to convert from one to the other. The speed and pressure distributions don't quite follow Bernoulli because of turblence, and within the boundary layer, pressure is related to the adjacent airflow, not the speed of the airflow within the boundary layer.

Note that a wing could be 'instrumented' by placing pressure or speed sensors on the wing surfaces, then Bernoulli's equation could be used to appoximate speed given sampled pressure readings, or vice versa.

How is Bernoulli's principle able to be used at all?

A much better example of Bernoulli principle is Venturi principle. A gas or fluid is force to flow through a narrowing cone, and the narrowing of the cone (the Bernoulli principle part), plus wall friction and viscosity reduce the pressure of that flow at the narrow end of the cone. One common use is a device to drain water from Aquariums:

http://andysworld.org.uk/aquablog/?postid=247

If you follow the Cadian patent, you eventually get to images of the internals of this device. Figure 4 shows it operating as a vacuum pump. The top is connected to a tap, the bottom is the flow exit, the side is connected to the drain hose, and the pressure in the chamber under the cone exit is lower than ambient, allowing it to suck up water via the side connector. In Figure 5, the flow exit is closed, to allow the same connections to be use to refill an Aquarium.

Python Syphon diagram

Another practical usage of Bernoulli is the pitot tube on an aircraft. The pitot tube faces forwards, and the acceleration of the air affected by the pitot tube results in a increase in pressure within the pitot tube, related to the dynamic pressure component of Bernoulli equation. The static port is used to measure the ambient pressure of the air and is oriented perpendicular to the flow, and located so it's 'hides' underneath a boundary layer in order to sense the ambient pressure of the air just outside the boundary layer. The relative speed of the air versus the pitot and static ports is the same, yet the pitot port senses ambient + dynamic pressure in a Bernoulli like reaction, while the static port only senses the static pressure component, avoiding the Bernoulli related connection between relative speed and pressure, by operating inside a boundary layer, where Bernoulli principle doesn't apply.

Am I right in assuming that Bernoulli's principle can only be used in very ideal approximations and the truth deviates from it?

Yes Bernoulli equations are an approximation of real world effect, and don't apply to interactions between solids and gas or fluids where significant work is done. If the amount of work done and tubulence factors are relatively small, then Bernoulli equation is a reasonable approximation. Normally Bernoulli principle applies best to situations where the flow is constrained by a pipe or tube, such as the Venturi based pump and pitot tube examples above. In an open environment such as a solid object flowing through a gas or fluid, the calculations of lift, drag, and pitching torque factors require something based on the more complex Navier Stokes equations.

 

[LURCH]

Just an interesting note (I mention this every time I see a question about the aerodynamics of a curveball); according to the http://www.space.com/scienceastronomy/mars_curveballs_030221.html" a curve ball thrown on Mars would curve in the opposite direction.

This, of course, has yet to be verified experimentally. I volunteer.