Newton’s laws of motion describe the motion of an object in an inertial (non-accelerating) frame of reference. When Newton’s laws are transformed to a rotating frame of reference (such as the earth’s surface), the Coriolis force and centrifugal force appear. These forces are important in oceans and atmospheres. As water or air moves away from the equator toward the poles, its rotation rate about the earth’s rotation axis increases to conserve angular momentum as the distance to the axis of rotation decreases. Rather than flowing directly from areas of high pressure to low pressure, as they would in a non-rotating system, winds and currents tend to flow to the right of this direction north of the equator and to the left of this direction south of it. This effect is responsible for the rotation of large cyclones and the generation of warm currents that travel north and south from equatorial waters in the western Pacific Ocean. As described in IOP on 31 March 2017, reproduced here, these forces can also have a significant impact on sports.
The inertial forces generated by the Earth as it rotates can have an impact on sports as varied as cricket, bowls, rowing, swimming and horse racing, Australian researchers have shown.
Dr Garry Robinson, from the University of New South Wales, Canberra, and his brother Dr Ian Robinson, from Victoria University, Melbourne, looked at how the Coriolis force – which produces a sideways movement – and the centrifugal force, both resulting from the earth’s rotation, affect everything from a bowled cricket ball to a rowing scull.
They published their results today in the journal Physica Scripta. Ian Robinson said: “We wanted to explore what effect these forces would have on sports like cricket, where the ball is thrown or bowled; on golf – where the ball travels a longer distance; on lawn bowls, where accuracy is paramount; and on rowing and running, where large distances are covered.”
“Newton’s laws of motion apply in an inertial system, but our rotating Earth is not an inertial system. Two additional forces are present – the Coriolis force, and the centrifugal force. Generally, these two inertial forces produce noticeable effects only on the large scale, when either the time of travel and/or the path lengths are large – for example the Coriolis effect is extremely important for navigation.”
The researchers added both the forces to the equations of motion, and also included a ground friction-type force to simulate a ball rolling over a surface, or a body moving through something resistive like water.
Their expectation was that the effect for small-scale ball games – golf, and cricket – would be fairly small. This proved to be the case, with sideways movement for a cricketer’s throw from the boundary being less than one centimetre and less than 10 centimetres for a long drive in golf.
Garry Robinson said: “However, there were some sports where the effect was more than sufficient to make a difference to the outcome. In lawn bowls, for example, the sideways movement can be up to 2.8 centimetres, which is enough to affect the outcome of the game.
“Even more significantly, in a two kilometre rowing race the sideways movement can be up to 40 metres, if it is not compensated for, while an athlete running a four-minute mile will be subjected to a sideways movement of nearly 20 metres, again if not compensated for.
“It’s possible the participants in these sports aren’t even aware of the potential sideways effect, and could be compensating for it without knowing. Even if they are, we calculated that in the case of the rower, they will need to apply up to 7.5 per cent of their forward propulsion force to counteract it.”
Another example is found in horse racing. The Coriolis force can ‘push’ a horse towards the inner rail running in one direction, and towards the outer rail running in the opposite direction, with a potential sideways movement of up to 4 metres in a 1,200 metre sprint.
This is automatically (unknowingly) compensated for, and normally is likely to be totally masked by other effects. Nevertheless, the effects of the Coriolis force may sometimes be significant, as in some areas of the world horses run in a clockwise direction in one state, and in a counter-clockwise direction in a neighbouring state, with horses regularly moving between locations.
The researchers also noted that the matter is further complicated because the size of the effect is latitude dependent; it reverses in right/left direction in going from one hemisphere to the other; and, for a fixed hemisphere, it reverses from, for example, an east to west or north to south direction if the direction of the velocity reverses.
Ian Robinson said: “It is possible therefore, that there are subtle effects not noticed by athletes that may inhibit their performance, particularly if there is a change of venue or hemisphere.”