RWC Physics Blog II: Forward Passing the Buck

When physics and rugby appear in the same conversation, it usually goes like this:

A: “Did you see the winning try the other day?”
B. “Yeah it was super sweet.”
A. “No it wasn’t, the last pass was forward!”
B. “It wasn’t forward. Watch the ball as it leaves the passer’s hands, it travels backwards.”
A. “What are you talking about you egg, it was clearly forward, it started on one side of the 22 metre line and ended up on the other side.”
B. “Yeah but you have to account for the passer’s momentum.”
A. “You’re as bad as that blind touch judge.”
B. “You’re an idiot, it’s simple physics.”

etc.

To some readers this chat might sound odd, but let me assure you that similar conversations are not at all uncommon! You’ll hear them at the rugby club, on the bus, in the back row at a funeral, or in media commentaries.

What is happening here is that a player has been running towards the opponent’s goal line, and passed the ball to a team-mate. The forward pass (or not) decision can be crucial; if you asked a rugby-following New Zealander to name a forward pass from history, I’d wager that most of them would immediately name one particularly traumatic example from 2007.

The interpretation that has been adopted by official bodies (World Rugby, SANZAR etc.) is explained – or at least demonstrated – in this video.* Physics can help here, because we can say that the passer and the field are in different frames of reference. The passer’s frame of reference is moving relative to the field’s frame of reference. The laws of physics behave the same regardless of your frame of reference. You can bounce a tennis ball in the aisle of a fast-moving train, and it will appear to go vertically up and down, just as it would if you were stationary on the train platform. But if you are on the platform looking at someone bouncing the ball on the moving train, you would see the ball moving sideways as well as up and down.

FwdPass

As for the rugby, and the stationary spectator (in the field’s frame of reference) is like the observer on the train platform. They see the passer running with some velocity (blue arrow) and the ball going forwards (red arrow). We can switch to the passer’s frame of reference by subtracting a vector representing the velocity difference between the two frames: we turn around the blue arrow. The resulting green arrow goes backwards. The accepted interpretation (as in the video) is that the ball must go backwards in the passer’s frame of reference, which means it can travel forwards relative to the field.

To summarise, the advice to “watch the passer’s hands” is good, and the motion of the ball relative to lines on the field is irrelevant.

All’s well that ends well, right? Happily, I still have a fair few gripes:
  • “Momentum” is often used to describe the motion of the passer. Remember p = mv (momentum = mass times velocity)? Momentum involves the mass of the player, which is irrelevant to this discussion.** The velocity is what is important.
  • Many prominent rugby people (e.g. commentators on NZ television) are essentially person A in that conversation above.
  • Players can be tackled while they are passing, or they can accelerate so that the velocity difference between the frames of reference changes.
  • Finally, the law itself is ambiguous. “Forward” is defined as “towards the opposing team’s dead ball line”, without mentioning the frame of reference. If anything, this reference to the dead ball line suggests that we should be using the field’s frame of reference, which contradicts the interpretation in the video above. So, ambiguity does not arise from misunderstanding the physics, but (as usual) from rugby’s idiosyncratic laws, and the law-making process; hence the title of today’s rant blog.

Comments are welcome here or @GeoffWillmott

Update: nice to find that Matthew Collett, my colleague in the physics department, talked to the Herald about this topic in 2011

* It was a Youtube video much like this which enabled a consistent refereeing interpretation to develop. I believe the original video was made and posted by referees in Queensland. So a proper discussion is a product of the Youtube era, and I guess we have one thing for which to thank the Aussies.

** When “momentum” is used to describe the motion of a player tackled close to the tryline, with respect to whether they cross over the tryline without propelling themselves, this IS a good use of the word. The motion of the moving player depends on the forces acting on them, and therefore on their mass.
 

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