Power / weight calculations

[Groucho]

I don't know the math but surely a 90kg person who is faster than a 100kg person would hit contact with an almost identical amount of force.

That's an interesting point. Of course, a player of any size travelling at light speed would have infinite mass. Now tackle that!

But more seriously, the kinetic energy of an object of mass m traveling at any non-relativistic speed v is mv^2/2.

A 90 kg Finger traveling at 10 meters per second (about 20 mph) = .5 x 90 x 100 = 4500 joules.

For a 100 kg Carter to generate 4500 joules of kinetic energy they would have to be travelling at 9.5 meters per second, per the following calculation:

.5 x 100 x v^2 = 4500
100 x v^2 = 4500/.5 = 9000
v^2 = 90
v = sqrt(90) = 9.48633

 

[Scarfman]

Interesting. I was thinking that momentum (= mass x velocity) would be the appropriate equation, but you've got me thinking.

Any opinions about which is the appropriate "ouch" measure for runners? Momentum or kinetic energy?

 

[Newb]

 

[DPK]

Groucho, could you convert that to Newtons?

(Edit) I believe 1 joule is equal to 1 N-m?

 

[Moses]

That's an interesting point. Of course, a player of any size travelling at light speed would have infinite mass. Now tackle that!

But more seriously, the kinetic energy of an object of mass m traveling at any non-relativistic speed v is mv^2/2.

A 90 kg Finger traveling at 10 meters per second (about 20 mph) = .5 x 90 x 100 = 4500 joules.

For a 100 kg Carter to generate 4500 joules of kinetic energy they would have to be travelling at 9.5 meters per second, per the following calculation:

.5 x 100 x v^2 = 4500
100 x v^2 = 4500/.5 = 9000
v^2 = 90
v = sqrt(90) = 9.48633

Should you add the weight of Carter's chariot to the calculations?

 

[liquor box]

That's an interesting point. Of course, a player of any size travelling at light speed would have infinite mass. Now tackle that!

But more seriously, the kinetic energy of an object of mass m traveling at any non-relativistic speed v is mv^2/2.

A 90 kg Finger traveling at 10 meters per second (about 20 mph) = .5 x 90 x 100 = 4500 joules.

For a 100 kg Carter to generate 4500 joules of kinetic energy they would have to be travelling at 9.5 meters per second, per the following calculation:

.5 x 100 x v^2 = 4500
100 x v^2 = 4500/.5 = 9000
v^2 = 90
v = sqrt(90) = 9.48633

I would love to see actual stats of players actual speed and weight and see who the biggest hitters actually are. Palu would have to be close to the top althought the energy produced if Matt Dunning fell over would be fairly big

 

[Gnostic]

Wow a discussion on mass moving in straight lines. Easy to counter just have to alter the direction of the force. See my earlier post regarding effective tackles. The whole issue is about selecting talented and inform 12's (or any other player/position).

Nathan Grey was a very good 12, he wasn't large (by the standards of what is being discussed here) but I would put him up with the biggest tacklers and hardest runners at 12 I have ever seen. What stopped him fro being a truly great 12 was his relative lack of ability to offload and set up support runners like the others I previously mentioned. He also occasionally made a glaring miss or ineffective tackle when going for one of his huge hits.

 

[westius]

This is correct - although there is also some interesting physics to do with momentum here, as stopping someone takes time (ie you might bring him to a stop, but if it takes you 10 seconds then he's probably moved forward a bit and scored)

I am probably getting my physics completely wrong, but...

momentum = mv
Change in momentum (Impulse) = Ft

If you want to bring someone to a stop, then your change in momentum is simply mv. So the force you need is mv/t.
If someone ups their mass, then to stop them in the same amount of time as you used to, you will need more force. That said, I dont imagine that people keep their speed when they get heavier, but the speed is just the speed at impact, not their 100m pace.

To have the same impact at the tackle, its actually better for Carter than above, as the energy equations do not look at time. We simply need their change in momentums to be the same, so if Finger is 90kg and hits at 10m/s, then Carter needs to hit at 9m/s - he can be a bit slower

 

[Ash]

Units of momentum are in (mass * distance/time unit) - or (mass * speed) assuming we are in a straight line, whereas if you use kentic energy, then your units are in energy, or joules.

I think that kinetic energy (or 0.5mv^2) is correct to use instead of momentum, as it shows the amount of force required to stop the person running.

http://en.wikipedia.org/wiki/Momentum#Relating_to_force_-_General_equations_of_motion
http://en.wikipedia.org/wiki/Momentum#Conservation_of_linear_momentum

 

[Scotty]

Great discussion, but there are too many other factors to talk about it such a theoretical way:

1. Angle of impact
2. Height of impact
3. Change in direction at impact
4. Leg drive during and after initial impact (maintaining momentum - see comparison between a Latham and a Sharpe)
5. Location of impact (does attacking player adjust slightly prior to hitting the line to drive between defenders rather than at them)

And about 100 more.

 

[Groucho]

Units of momentum are in (mass * distance/time unit) - or (mass * speed) assuming we are in a straight line, whereas if you use kentic energy, then your units are in energy, or joules.

I think that kinetic energy (or 0.5mv^2) is correct to use instead of momentum, as it shows the amount of force required to stop the person running.

http://en.wikipedia.org/wiki/Momentum#Relating_to_force_-_General_equations_of_motion
http://en.wikipedia.org/wiki/Momentum#Conservation_of_linear_momentum

I agree, Ash. In the the special case of objects colliding, a calculation based on momentum is equivalent to a calculation based on kinetic energy. But as Gnostic points out, the attacker has the opportunity to change direction and force the defender to defend in more complex ways than simply putting his body in the way. A calculation based on kinetic energy applies more generally, although if we're serious about this we'd have to factor the effects of players putting further energy into the system, such as from leg drive.

 

[Bruce Ross]

Scarfman said; "Interesting. I was thinking that momentum (= mass x velocity) would be the appropriate equation."

It's way out of my area of competence, but wouldn't the relevant variable be acceleration rather than velocity?

 

[Groucho]

Scarfman said; "Interesting. I was thinking that momentum (= mass x velocity) would be the appropriate equation."

It's way out of my area of competence, but wouldn't the relevant variable be acceleration rather than velocity?

If an object is accelerating at the point of impact, then its kinetic energy is increased by the energy that is added by the force causing the acceleration, expressed as a vector to its direction of movement.

 

[daz]

Christ, now I need a fucking science degree just to read these boards? How I pine for the days when rugby players just needed to be capable of mindlessly smashing someone into the ground. Now it seems they need to calculate the fucking velocity and how deep the fucking crater will be when they get off the bloke....

 

[Scarfman]

Bruce, in short, no, acceleration wouldn't make any difference.

I'm not yet convinced that kinestic energy is the best measure of the ouch value. I reckon momentum is the best measure. Which is why is hurts more when you tackle someone so that they stop dead; the momentum is higher (shorter amount of time in which the velocity is reduced to 0).

C'mon Groucho, talk us through it. I'll split the thread if I have to.

 

[Scarfman]

And daz - to put this discussion in layman's terms. Let's say Ant Fanger goes from 90kgs to 100kgs. But his running speed drops 10%. Is he better off, or the same, or worse?

We always want backs to bulk up - but how much speed can they afford to lose? Of course a lot depends on running height and other skills, but weight and speed are measurable, and it would be really interesting to compare the speed of these guys before and after the gym.

 

[magoo]

Weight vs tackling force? Two words come to mind - Trevor Gillmeister - sorry to talk league, but he was only about the same size as the smaller wallaby backs in the squad. I'd love to see one or two bigger players in the Aus backline (a fit Mortlock at 13 would be great, but a fit Chambers would do me), but more for attack. I think the ability to read the attack, some speed to cover the attackers, a decent tackling technique & most importantly the commitment to tackling are probably all more important than size in defence.

 

[Groucho]

Bruce, in short, no, acceleration wouldn't make any difference.

I'm not yet convinced that kinestic energy is the best measure of the ouch value. I reckon momentum is the best measure. Which is why is hurts more when you tackle someone so that they stop dead; the momentum is higher (shorter amount of time in which the velocity is reduced to 0).

C'mon Groucho, talk us through it. I'll split the thread if I have to.

Scarfy, it's an interesting question.

Momentum is the force required to stop an object in a given period of time in a direction (i.e. momentum points in the direction of an object's velocity). Kinetic energy is the force required to stop an object in a distance. If you want to model the complex behaviours of objects when they collide, then momentum is the best measurement to use. If you simply want to know how much force is required to stop an object, then kinetic energy is the best measurement to use.

Both are of interest here, actually. Since momentum is a vector, it changes as the players change direction. Once they collide, other factors can then come into play such as players grabbing onto each other, converting momentum into angular momentum. And there may in fact never be a classical collision: the tackle may be made entirely with the arms, resulting in a form of orbital capture. The result is a very complex equation, the kind of thing NASA uses supercomputers for.

Calculations made using kinetic energy simplify all that: provided no extra energy enters the system, then the minimum amount of energy required to stop the ball runner is a constant, no matter how much their individual momentum changes.

 

[DPK]

BTW, new thread?

Two, I think. One for the Groucho's Cat (Anyone? I'm here 'til Thursday) and one for Perfect Player Size.

 

[Bruce Ross]

Bruce, in short, no, acceleration wouldn't make any difference.

A logical extension of your statement, Scarfman, is that it would make no difference whether the moving player was trying to minimise the force of impact, i.e., the acceleration is negative, or tried to maximise the force of impact, i.e., positive acceleration.