Science of Cricket - Drift and Dip

This is the last of a series of posts on the science of cricket. Its not really related to the others, conventional swing, reverse swing and contrast swing except that it is science and cricket related. Reading the other posts first may also help you to understand the terminology used here. When a spinner bowls, a batsman can be 'beaten in flight' or comentators may refer to the drift of a ball or the dip. This is due to a phenomenon known as the Magnus Effect.

Consider first a non-spinning ball moving through a steady fluid flow as seen below. There are no variations in the flow field between the top and bottom sides

of the ball and so there is no irregular movement. As usual, I've

just mined the net for images that will be useful, this ones from google knowledge.

However, then consider if you add spin to the ball, speeding up the flow on the top and slowing down the flow on the bottom as the fluid from the boundary layer of the ball will follow its rotation (image from bound vortex)

This speed change changes the flow field, increasing presure on the top of the ball and decreasing it on the bottom. The flow field for a spinning ball is something like this below from the avalanche center.

Because the pressure is higher below the ball than above, there will be a force towards the top (in this picture). This can be considered, and is valid for any representation where a ball spinning in two dimensions is in a fluid flow. So a purely leg or off-spinning ball (with no topspin) can be considered only from a cut away view that is like an extension of a crease line. And with a purely sideways spinning ball, the relevant fluid flow is only the slow drop of the ball (presuming no crosswind for this case). This will produce little (effectively no) movement due to the magnus effect. But if there is a cross wind, then dip or lift may be produced by this wind. For the example shown above, an off spinning ball with a wind from the bowler's left will cause lift. A similar situation happens when a leggie has a wind from his right. For most situations, dip produced by a cross wind is small, at least compared with that produced by over or under spin.

If you consider a solely overspinning ball, then you can take a side-on slice (along where a straight seam for a seam bowler would be) of the view. This means that the above diagram needs to be flipped vertically, as the ball pictured has underspin. The ball will then have the oncoming velocity of the ball's flight to use and so can produce a large down force, significantly affecting the ball's flight. An underspinning ball (like a flipper) will have a lift force and so will lose more vertical energy in flight, rebounding off the pitch lower. Where it gets even more interesting is when there is a cross wind and overspin. A topspinning ball will also have a small component of force sideways, in a similar manner to a ball with sidespin only. But in this situation the ball will produce a slight forwards or backwards force.

For sideways drift, the ball either has to spin as seen in a top-down plane which can happen with a different delivery style, or the drift is simply drag. This would happen if there was a cross wind which would move the ball in that direction. A ball which is spun in the top-down plane will have minimal deviation, so if a drifting ball seems not to spin then this is the source.

The Magnus Effect is also a major influence on other sports, particularly baseball and soccer curveballs. However, despite what some sources may say, the swing of a fast bowlers ball is not (and realistically cannot) be due to the Magnus Effect. That would require a large spin to be imparted in the top-down plane, which would result in a spinning seam. Common knowledge shows that even a wobbling seam can destroy a bowlers swing (and my earlier posts show why) so a ball that spins like a top? Not a chance in hell.

External Links for Cricket Science:

The Science of Swing Bowling (I disagree with Mehta on some corollories of his theories, but well worth a read. Many other sites just rip off his ideas without the fluid dynamics fundamentals to assert anything different)

Cricket in Full Swing(PDF, not sure about the dimpled/furry theory of his)

Cricket Ball Swing on stadiumturf.com

Wikipedia page on swing bowling

Why a cricket ball swings (also contains a bit on the Magnus Effect)

The Magnus Effect (actually as much about swing as the Magnus Effect)

The Magnus Effect : Why Pitches Move (not actually about cricket pitches spinning their way around the world, but a post on baseball aerodynamics)

Analytic Functions, the Magnus Effect, and Wings (very equation heavy, only worth looking at if you have an idea of potential flow analysis already. Also not directly cricket related.)

Wikipedia page on Magnus Effect

Is there anything you disagree with, or that I've missed? Drop me a comment and we can get into some heated intellectual discussion.

Science of Cricket - Contrast Swing

This is the 3rd in a series of posts about swing in cricket. The terminology is introduced gradually, so it is recommneded that you read The Science of Conventional Swing and The Science of Reverse Swing first. This time, we will discuss contrast swing, which is often confused with proper reverse swing. Contrast swing is actually the most simple type of swing conceptually.

We will start with a diagram from Mehta again.

The first major difference you will notice is that the seam is pointed straight. This means that the only difference between the sides of the ball is the roughness. At conventional swing speeds only the boundary layer flow over the rough side will become turbulent, meaning that it will stay attached longer. This means that the pressure exerted on the smooth side will be greater and the ball will move towards the rough side, meaning the ball is moving 'reverse'.

At reverse swing speeds, both sides will transition to turbulence. If the rough side is exceedingly rough, this roughness may have a similar effect as the seam in reverse swing and weaken the boundary layer, causing earlier transition. I think however, that this type of swing would cause minimal ball deflection compared with slower contrast swing or either seamed swing types. Any movement that would occur would be towards the smooth side.

The seam is irrelevent to contrast swing and so this type of swing can be practised with a standard 1/2 taped tennis ball (not 1/2 a ball, 1/2 taped).

A note on speeds: For both slow contrast swing and conventional swing, there is not only an upper limit to the speed the ball is bowled at, but also a lower limit. Below a certain speed, neither side will transition to turbulence. So for you park bowlers out there, you may simply be bowling too slow to swing it. All these speeds mentioned will vary depending on atmospheric conditions, as explained in the post on reverse swing.

Next in the series is spin bowling 'drift'.

Science of Cricket - Genuine Reverse Swing

The Science of Cricket series continues with the second type of swing bowling, reverse swing. This series will gradually increase in complexity, so you can learn more and understand better by reading them in order. The first in the series is The Science of Cricket - Conventional Swing. Despite common misconceptions, reverse swing is not bowled with a straight seam. That form of swing bowling is contrast swing, to be discussed in the next post. True reverse swing is performed with a similar action to conventional swing but with the rough side at the front of the ball. The seam is still angled, but in this case away from where the bowler wants it to go.

Again, we will start with another diagram from Mehta, who is the media's go-to man when it comes to swing science (and I can't really be bothered drawing my own diagrams, when he has the basic flow ideas right).

So again, we have the ball flowing through a fluid (air). But on this occassion, the ball has the rough side oriented towards the flow. The ball is bowled at a combination of higher speed and/or more roughness at the front of the ball. This causes the boundary layers (layers of fluid near the surface of the ball) at the top and the bottom of the ball to transition to turbulence (irregular, chaotic flow) before the flow hits the seam. In this case, the seam cannot kick the flow into turbulence as it does in conventional swing bowling, as the flow is already turbulent. So the seam strips away the base of the boundary layer (visualise it as a thin stream of fluid flowing over the ball), leaving a thinner boundary layer. Now as discussed in the conventional swing article, any

asymmetry in flow will produce a difference in the separation point of the boundary layer. In this case, as the boundary layer over the top is thinner and has less energy holding it to the ball, it will separate more easily. From this point, the macroscopic consequences of this are a mirror image of conventional swing, with the fluid flowing over the top side of the ball exerting more pressure once the boundary layer has separated. This moves the ball towards the bottom, swinging the ball away from where the seam is directed.

Reverse swing appears to be later than conventional, but paradoxially, this is because it begins earlier. The only sideways (technically perpendicular to the direction of travel) forces which will act on the ball are those provided by swing, assuming there is no sideways spin on the ball, and any backspin is minimal (we'll get into the effects of that later, in the article on spin "drift" and dip). These forces keep working over time, and so the sideways speed keeps increasing all the way to the keeper. In most (elite level at least) cases of conventional swing bowling the ball is not travelling slow enough to generate any swing before it is close to, or even after bouncing. This means the ball can only generate side force during around the last 8 metres or so of its flight (number will vary rapidly betwen bowlers and conditions, but 8 is good for an example). This is why a conventionally swinging ball will often move rapidly after it has passed the batsman. But a reverse swinging ball can move from the moment it leaves the bowler's hand. This enables it to build up to a high sideways speed by the time it reaches the batsman (where it may sometimes have stopped accelerating sideways). For the same reason, all swinging balls will move faster later in their flight.

If the flow state is between reverse and conventional swing (ie the flow just before the seam (top of the diagrams used) is laminar and the flow over the bottom is turbulent then no swing will result, as both sides will have turbulent boundary layers of similar thickness.

In reverse swing, the smoothness of the "smooth side" is less important than the roughness of the rough side. If this smooth side is too rough, the boundary layer over this section after the seam will increase in thickness, negating the advantage gained by trimming the boundary layer with the seam. This will reduce the amount of movement, and combined with lessening seam protrusion as the ball wears is responsible for the ball stopping genuine reverse swing after a time.

The next post in this series will deal with Contrast Swing, aka "backyard reverse swing".

A "technical" aside, for those who want to know more: The flow will transition from laminar to turbulent at a certain "Reynolds number", smaller for a rougher surface. The Reynolds number is (ball speed*distance travelled along ball/kinematic viscosity) where kinematic viscosity is a property of the atmospheric environment. For example, the kinematic viscosity of the atmosphere is generally 8% higher at 1000m above sea level (lower than the Potchefstroom ground in South Africa) than at sea level, meaning a bowler must bowl 8% faster to get the saame reverse swing. But conventional swing can also be achieved at a speed of 8% faster at this altitude than at sea level. The kinematic viscosity varies all over the Earth too, and varies depending on weather conditions (if anyone reading this has links to measurements of kinematic viscosity, density or dynamic viscosity in sunny compared to overcast conditions, or England compared with Australia (to identify why swing bowling was so prevalent in the Ashes series of 2005 compared with 06/07) then I would appreciate the data) So to allow a ball to reverse swing, you can increase your speed, increase the surface roughness or increase your seam angle (although diverting this from the optimal will reduce the amount of movement, some movement is better than none). If you are trying to swing the ball conventionally then you need to keep the flow below transition over the bottom of the ball until separation (generally somewhere around 90 degrees around the ball). This means you may need to reduce your speed or change the atmospheric conditions, but changing the seam angle will not affect the transition speed. It will still affect the amount the ball swings.

Non-technical aside: Wow, that was a long post.

Science of Cricket - Conventional Swing

Over the next few posts, The Rushed Behind will enlighten you as to the science of cricket. How do the different types of swing work? What causes "drift" of a spinning ball? Why does the amount of swing differ depending on the atmospheric conditions? These, and possibly more (if I can think of more questions) will be answered over the coming posts. But first, why should you believe my explanations over those of cricketers who claim it is an unexplainable art form? Well, as you will probably be surprised to know, I actually have a degree in Aerospace Engineering. So despite my bowling being more like ex-PM John Howard than Andrew Flintoff I can explain what is going on. And hopefully, in a way that a layman can understand (which is the problem with most other sources of information on these subjects).

So, first off is conventional swing. The key to conventional swing (from here on, just swing) is the seam. Lets consider a cricket ball with an angled seam, like the one drawn by Mehta below.

The fluid (air) flow over the top of the ball (as seen in the picture above) is disturbed by the seam, causing the boundary layer (fluid near the surface of the ball) to become turbulent. At this point, you are probably wondering what turbulent means. Any flow can be either laminar, turbulent or in transition between the two states. Laminar flow is nice and steady while turbulent flow has vortices and rotation of fluid. However, turbulent flow can stay attached for longer (because of the irregularities in the flow, but you don't need to know that) so the flow over the top remains attached for longer. This means that there is separation of the boundary layer earlier on the bottom of the ball and so the fluid exerts more pressure on the ball here, without the effect of the boundary layer. So there is more pressure on the bottom than the top, and the ball is moved by this pressure, towards the top.

However, the point of separation will also depend on the speed the ball is travelling at, and the smoothness of the front side. If the speed is too high or the ball is too rough then the boundary layer on the smooth side will transition towards turbulence, negating the advantage of the seam kicking the top flow into turbulence. This will negate the conventional swing, causing a straight ball and the bowler to look silly if he planned on swinging it. This is what happens when the ball stops swinging after a while as it gets roughed up. The ball may not swing from the start, as the lacquer is often less smooth than the leather of the ball itself. This will decrease the transition speed of the bottom side and so the ball will not swing. This is what is happening with the Duke balls used in England in the Ashes at the moment, with the ball starting to swing once the lacquer comes off. The wear on the ball will also lessen the effect of the seam, reducing the protuberance and potentially keeping the flow laminar for longer, reducing swing.

There are situations where conventional swing may only happen after the ball has bounced, if the seam is still in a good position and the bounce of the ball has reduced the speed below the threshold speed, but the seam position is so critical that this is rare.

Next Post - Reverse Swing