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.