This past week we had a team meeting with a sports psychologist. She had us share how we use our minds to help us as athletes. She also asked us how our mind hinders us, but that’s another story. My teammates seemed entertained by my answer, so I thought I’d share. I often use my physics knowledge to think about rugby scientifically, as I am a physics graduate student. The following are some of the ways I approach rugby as a physicist. Perhaps you will find them useful.

I. Stiff-Arming and Force: The effectiveness of a stiff-arm is a consequence of how much force you are able to exert on your opponent. Newton’s second law pretty much says that: force is mass multiplied with acceleration (F=ma). The mass of your arm is fixed, but acceleration is a variable. Therefore if we want to maximize the force of a stiff-arm, we must learn to maximize the acceleration of our arm. Acceleration is the change in velocity with respect to time. Thus, to maximize the amount of force you can wield with your arm during a given rugby game, you need to increase the velocity as quickly as possible into your target. The mistake I see lots of people making is extending the arm too early. If your arm is fully extended before you hit your target, the only acceleration comes from your running. If you extend your arm into your target as you are running towards the target, however, the sum creates a maximal acceleration, and thus a maximal force imposed via stiff-arm.

II. Work Rate and Thermodynamic: The second law of thermodynamics is that entropy will increase unless you put energy into the system. Entropy is chaos, or disorder. In rugby, you don’t want to be disorganized. Consider how difficult it is defend when your team is chaotic on defense. The disconnected defense is the entropy of the rugby system. Thermodynamics says that the disconnect is only going to get worse unless you put additional energy into the system. The energy of the system is the work rate of the players. Translation: in order to organize a disconnected defense, you must increase your work rate.

III. Contact and Conservation of Momentum: When considering an elastic collision of a two-body system, the momentum is conserved. This situation applies to the interaction between a ball carrier and potential tackler. Meaning, the total momentum before the collision must be the same as the total momentum after the collision. To clarify, this does not mean that each person involved in the collision will have the same momentum before and after the collision. In fact, it’s likely each person’s momentum will be changed after the collision. Momentum conservation does, however, mean that when you add the momentum of both people before the collision, it should equal the addition of each person’s momentum after the collision. When you work this out, the person with the most momentum should have the most success in the collision. (Mb) = mass of the ball carrier, (Md) = mass of the defender, (Vb)= velocity of the ball carrier before the collision, (Vd)= velocity of the defender before the collision. The total momentum is: (Mb)( Vb)+(Md)(Vd) Total momentum of the system will not change once the collision occurs, so you want to have the most amount of momentum at the time of impact. This means you should never hesitate or stop before contact, because then your velocity goes to zero, in which case you have no momentum, and then, obviously, you will lose the momentum battle. You’ve also got to consider body weight — collision match-ups are all about weighing ratios of mass and velocity. If you’re the ball carrier, you want: (Mb)(Vb)>(Md)(Vd) Thus, you take the ratios of the person with the larger mass to the person with the smaller mass and compare it to the ratio of the person with the higher velocity to the person with the smaller velocity. Whichever fraction is larger is the person who has the most momentum. (This is true because velocity and mass are proportional variables in momentum.) Examples of momentum mismatches: You have the same mass as your opponent, but can generate a much greater velocity. You can achieve the same velocity as your opponent, but have significantly more mass. Examples of momentum matches: You and your opponent have the same mass and velocity. You have a much greater velocity then your opponent but your mass is less then your opponent.

IV. Passing and Newtonian Mechanics: The first law of Newtonian mechanics states that an object maintains its velocity unless acted upon by an outside force. Velocity is a vector; this means it has both magnitude (speed) and direction. This idea of velocity directly relates to releasing the ball and follow-through. Whatever velocity you give the ball in the plane parallel to the earth’s surface will be maintained. When the ball is in your hand it has the same velocity as your hand, so your hand should follow the vector that points at your target. Meaning, when you release the ball your hand should follow through at your target. If your hand points elsewhere, you are giving the ball velocity in the wrong direction. The spiral of the rugby ball is also an important part of passing mechanics. To minimize air resistance, the axis of rotation should be the same as the axis of symmetry, lengthwise of the ball. The axis of rotation should point in the direction that the ball is thrown. If these don’t line up, there are conflicting forces on the trajectory of the rugby ball and the ball will wobble as it travels through the air. Some of the energy put into the pass is lost when the pass wobbles. Kinetic energy (T) of the pass is one half of the mass multiplied with the velocity squared (T= 1/2mv2 ). Less energy means the ball will take longer to get to your target.

V. Kicking and Angles: The angle between the follow-through of your foot and the surface of the earth relates to two key components: height and distance. The larger this angle is, the higher the kick will be. However, if you kick the ball very high, much of its initial velocity is lost in the vertical direction, and it cannot travel as far and it would at a smaller angle. If you are concerned with the ball traveling as far as possible, a smaller angle puts more of the ball’s velocity in the direction along the field. However, the ball will hit the ground sooner. It can be calculated that if you want to maximize both height and length of the kicked ball, your foot should follow through the ball at a 45-degree angle from the ground.

If I struggle with a concept in rugby, I’ll take a step back and think about the physics of the situation. Maybe now, you’ll consider doing the same!