Sidestep and swerve

Change in direction.
The track athlete either runs straight or around a fixed curve of relatively large radius (indoor sprints on a curved track are now rare). The rugby player frequently changes direction with a large radius curve when outflanking the defence using pace, medium radius in a swerve to beat a player or with a very small radius in a sidestep to wrong foot a defender.
To achieve any change of direction it is necessary to apply a force that is not parallel to the motion of the runner. If the change in direction is to be achieved without change in speed the net force will be at right angles to the direction of motion and acts toward the inside of the curve or toward the centre of curvature. This type of force is called a centripetal force (centri – centre, petal – seeking).
This force produces an acceleration with no change in speed since an acceleration is the rate of change of velocity and velocity is a vector quantity which includes both speed and direction.
To find the acceleration and thus calculate the force we calculate the vector change in velocity:
using vector diagrams or using the formula for circular motion at a constant speed: mv^2/r
Note that the faster (greater v) the runner goes the much greater the force needed to change direction and the sharper the direction change (smaller r) the greater the force needed.
For example, a runner in the inside lane of the track must run a bend of radius about 35m and is sprinting at about 10m/s at the apex of the curve. For an 80kg runner, therefore, the force required across the direction of motion is 228N.
In accelerating at the start of the race a sprinter the average rate is about 4.0ms-2 indicating a force of about 320N. Taking this as the force that an athlete can exert through ground contact while running, the net force available for running tangentially is about225N so that the maximum speed that can be maintained on the bend is substantially less than that at the same stage of a straight run.
If the athlete is in the outside lane, however, the radius of the bend is increased to about 40m. The force now needed is 200N and the available tangential component is 250N or approximately 10% more than in the inside lane.
The centripetal force is provided by a transverse reaction or frictional force from the track. To provide this force while continuing to support the runner’s body, the leg must attack the ground at a sufficient angle. As the angle from the vertical increases to increase the transverse force, the total force increases disproportionately. E.g. doubling the centripetal force at a low level might increase the total force by 12% while a further doubling raise the total by a further 40%. Continuing to increase the force in this way will eventually exceed the ability of the leg to cope while continuing to run. (nature jan 2006 greyhounds). This discussion has been based on average forces but the leg is not in continuous ground contact and is thus giving a more impulsive change in momentum resulting in much greater peak forces and thus likelihood of damage. To limit this, the runner increases the time of contact of the foot to reduce the force for the same impulse. The recovery phase is not altered as the limit to speed is the rate at which leg recovery occurs and is at its shortest at top speed. The increased time for each stride without change in stride length means that the cadence is decreased and the athlete slows.
In the photograph of young athletes running a 200m race the lean is measured as about 10deg, with the angle decreasing from inside lane to outside lane.
Taking the weight of a young athlete as about 600N we get a transverse component of force from Wtanq= F
or 600tan10 = 106N
Taking the speed of these athletes as 8m/s the transverse (centripetal) force should be: 96N
This is in excellent agreement with the calculated value.
This analysis assumes that the centripetal force is continuous, but in reality it must be a series if impulses which occur only when a foot is in contact with the track. During a straight sprint this can be as little as 40% of the time, but in a driving phase, as in accelerating around a bend, it may be nearer to 70% of the time. Accordingly when the foot is in contact with the ground it will exert a greater force than the average centripetal force calculated above. The calculated transverse force from the angle of lean is indeed larger than the centripetal force.
Attempting to increase the lateral force other than by lean will be unsuccessful as the transverse reaction force will also exert a torque about the centre of mass of the athlete tending to make the upper body rotate outwards. To balance this, the athlete now leans towards the centre of the bend so that the normal or vertical reaction force now exerts a counterbalancing torque about the centre of mass. The greater the centripetal force the more the athlete will have to lean to give the required moment arm for his weight.
Transferring these principles to rugby we see that the looping run which increases the distance from the defence has such a large radius of curvature that the centripetal force has little limiting effect on the speed at which the player is running and allows the fast player who has sufficient room to move to out pace a slower opposition by making them run farther to the tackle position.
The swerve is usually carried out with a small radius curve requiring a substantial inward lean with the upper body much closer to the opposition than the lower body. This will make it difficult to maintain a high speed since the driving phase will have only a limited forward component during the manoeuvre. The running action when several strides are taken during the swerve is not as efficient as straight line motion. The lean does, however make it difficult to tackle the ball carrier low and leaves the tackler vulnerable to a fend if the attempt is higher. The fend will of course give the attacker additional support and enable the swerve to be completed more easily.
The sidestep is designed to carry the ball carrier away from the defender suddenly so that the tackler cannot adjust before the attacker is out of reach. It is normally achieved by a single very forceful thrust of the outside leg which gives a large impulse to change the direction sharply. To maximise the impulse the runner maintains contact for as long as possible preventing excess strain on the propping leg. Since the leg is often placed forward and to the outside to give the required impulse, the speed of the ball carrier is often reduced substantially and the side step must be followed immediately by forceful acceleration in the forward direction. It is noticeable that players who attempt to sidestep repeatedly in one run end up almost stationary. For its efficacy, the sidestep relies on the inertia of the defender carrying him out of reach of the attacker or preventing him from matching the change in direction of the attacker. For this reason the attacker will tend to step back against the motion of the defensive line using the defender’s own motion to create the gap through which the attacker can now accelerate. In this situation the loss of momentum is less crucial since the attacker is accelerating from a position out of reach of the defender, who must first stop and reverse his motion before commencing pursuit. Defensive lines are set up to counter this change of direction by ensuring that the tackler approaches the attacker from the inside and that remaining defenders move across the field to prevent the attacker cutting back.
To create the situation where the defender is wrong footed by a sudden change in direction the attacker will perform an in-out manoeuvre in which he initially steps or swerves toward the centre of the field causing the defender to check or reverse his movement across the field, whereupon the attacker steps out again into the gap produced by the initial change in direction. when this is performed in close contact, the initial inward step is merely to give a stronger prop for the outward evasive step. Even if contact is not avoided it puts the attacker into the defender’s weaker zone some distance from the core.
The sidestep is a much more violent manoeuvre than curve running since the change of direction which may be around 45deg occurs within a single stride.
Typically a runner travelling at 8m/s changes direction by45deg and slows to 6m/s in executing a sidestep. Video of the driving phase shows that the propping foot maintains contact with the ground for about 0.24s (6 frames at 25 frames/s). Finding the vector change in velocity and dividing by the time gives an acceleration of about 20m/s/s at 132deg to the original line of travel. That is to say, a force of approximately twice the weight of the runner. Initial trials on a three axis force plate by an amateur player showed peak forces of twice the weight and average forces exceeded the weight by 50% while in a simple run through the peak force equalling the weight and averaging less than half the weight. The time of contact in the sidestep was approximately 0.25s while the running step lasted only 0.15s, the impulse needed to maintain running being much less than that required to perform the sidestep.