The Giant Punching Problem

[ferg]

So this may be a very simple problem to answer or a very stupid problem to even ask, but it’s something that I thought about and can’t quite figure it out. So my made up scenario is this.

Say we have a normal sized man, and when he throws a punch it takes him one second to complete the act of extending his arm and hit his target.

Now say we double his size. I assume it would still take him one second to complete the act of throwing a punch and hitting his target.

If you increased his size enough, I would assume the time would remain the same, but you can come to a point where his hand is moving faster than the speed of light.

Im not seeing how the time would increase just because from his perspective everything is still the same relative size. But then exceeding the speed of light isn’t possible either.

So I figure im either wrong about the time amount changing or size and time have some kind of relative relationship?

Anyone want to set me straight on what’s happening in this scenario?

 

[anuttarasammyak]

When his swing length becomes about 300000000 m, the giant's punch speed would becomes light speed. I don't think we need adjustment of time as you say here. Instead a mechanism would explain why such a swing would be impossible.

 

[Frabjous]

Think in terms of energy. If the time stays constant, the energy of the punch (0.5mv^2) is going to scale as size^5, while the muscles are going to scale as size^3. This is not sustainable.

 

[Borek]

I assume it would still take him one second to complete the act of throwing a punch and hitting his target.

Rule number one: if the assumption produces nonsensical results, check if the assumption holds.

 

[ferg]

Rule number one: if the assumption produces nonsensical results, check if the assumption holds.

I agree completely, but I would like to understand why this is wrong.

 

[ferg]

Think in terms of energy. If the time stays constant, the energy of the punch (0.5mv^2) is going to scale as size^5, while the muscles are going to scale as size^3. This is not sustainable.

To clarify let’s assume everything scales in correctly. He doubles im size each time.

 

[PeroK]

To clarify let’s assume everything scales in correctly. He doubles im size each time.

There's a finite limit on humanoid height due to the limitations of bone etc. Large animals don't move proportionally faster than small animals. If a man got large enough, he would collapse into a planet under his own gravity!

Many US citizens are well on the way to that fate! You don't see 600lb men and women leaping out of bed at half the speed of light.

 

[anuttarasammyak]

What might interest you is physics about rotating disk. Tangential speed of radius r is
$$v=r \omega$$By increasing r like size of your giant, at r = $\omega$ /c , v=c light speed. Such a size of rotating disk is impossible to make. You can easily find why in textbooks.
[EDIT]r=c/$\omega$

 

[Vanadium 50]

t I would like to understand why this is wrong.

"Assume a giant throws a punch faster than light. OMG, its faster than light!" is problematic.

 

[ferg]

There's a finite limit on humanoid height due to the limitations of bone etc. Large animals don't move proportionally faster than small animals. If a man got large enough, he would collapse into a planet under his own gravity!

Many US citizens are well on the way to that fate! You don't see 600lb men and women leaping out of bed at half the speed of light.

The human limits ARE NOT in question here. It could be a robot, any mechanism. The concept of mathematically scaling past what would be the speed of light is what im wondering about. Or time/size relative relationships.

 

[pinball1970]

The human limits ARE NOT in question here. It could be a robot, any mechanism.

Issue with rigid body

 

[ferg]

There's a finite limit on humanoid height due to the limitations of bone etc. Large animals don't move proportionally faster than small animals. If a man got large enough, he would collapse into a planet under his own gravity!

Many US citizens are well on the way to that fate! You don't see 600lb men and women leaping out of bed at half the speed of light.

He wouldn’t collapse into any planet as his size will be enormous before reaching a fist moving at that speed. Just so everyone understands, im not wondering how that can happen. Let me save some time. We don’t have the capabilities to double a man infinitely. So that’s the bigger problem than 600lb people moving at the speed of light.

But what you said about small animals not moving proportionally to big animals is related to this.

Thinking about insects vs large creatures. It’s like they move in fast forward compared to the larger animals. Maybe not related at all. But it just seems like the larger things are the slower they move relatively. It makes me wonder if time for his lunch would appear to us to take a very long time while it’s still relatively a second to the now enormously sized man/robot.

 

[Borek]

Different things scale differently - when you get exactly twice larger (as in "every size doubled") you will weight 8 times more (2³) but your muscles will be 4 times stronger (more or less their strength is directly proportional to the muscle cross section, which scales as a square, so 2²). So in general when getting larger you are also getting relatively weaker, and the assumption about being able to move the same way makes no sense.

 

[Frabjous]

To clarify let’s assume everything scales in correctly. He doubles im size each time.

In your scenario, it requires increasing amounts of energy per unit of “muscle”

 

[ferg]

"Assume a giant throws a punch faster than light. OMG, its faster than light!" is problematic.

That’s is very interesting! Thank you for the reference!

 

[ferg]

"Assume a giant throws a punch faster than light. OMG, its faster than light!" is problematic.

Ahhh that’s HOW. In my post I am eluding to that being the problem. Im wanting to understand how the situation works. Or if it will be something like the disc.

 

[ferg]

What might interest you is physics about rotating disk. Tangential speed of radius r is
$$v=r \omega$$By increasing r like size of your giant, at r = $\omega$ /c , v=c light speed. Such a size of rotating disk is impossible to make. You can easily find why in textbooks.

I accidentally replied to the wrong post. So…
Ahh that is interesting. Thank you for the post!

 

[ferg]

When his swing length becomes about 300000000 m, the giant's punch speed would becomes light speed. I don't think we need adjustment of time as you say here. Instead a mechanism would explain why such a swing would be impossible.

So maybe like the disc suggested below. Im going to learn more about that.

 

[PeroK]

Ahhh that’s HOW. In my post I am eluding to that being the problem. Im wanting to understand how the situation works. Or if it will be something like the disc.

The same thing applies to motor vehicles. A car can accelerate faster than a large truck, even though the truck has a much bigger engine. Even to achieve the same acceleration requires more energy. It's absurd to imagine that a truck can accelerate proportionally faster than a car just because it's longer.

A car could move its length from rest in a much shorter time than a 20m long truck could move its length.

Common observation indicates precisely the opposite of what you are assuming.

 

[ferg]

Different things scale differently - when you get exactly twice larger (as in "every size doubled") you will weight 8 times more (2³) but your muscles will be 4 times stronger (more or less their strength is directly proportional to the muscle cross section, which scales as a square, so 2²). So in general when getting larger you are also getting relatively weaker, and the assumption about being able to move the same way makes no sense.

I have no idea about muscle etc. so let’s say it’s a robot where everything is doubled. Are you saying the powering mechanism won’t scale the same?

I.e. nothing could be scaled up to this size in a relative scale?

 

[PeroK]

Look how much slower a giant crane moves relative to its size than a fork-lift truck.

 

[jbriggs444]

In addition to the linear-square-cube scaling problem (e.g. 4 times the muscle area attempting to accelerate 8 times the mass at 2 times the acceleration resulting in 16 times more force and 32 times the energy in the same time interval) we have the issue of how rapidly our gentle giant can think.

If his neurons all scale up with his linear dimensions by a factor of two and the nerve impulse speed remains constant then his thought processes will plausibly be two times slower.

Small animals have to react quickly just to keep from falling over. Large animals can afford to think ponderously.

 

[Borek]

I have no idea about muscle etc. so let’s say it’s a robot where everything is doubled. Are you saying the powering mechanism won’t scale the same?

Yes.

Scaling problems are very common in every branch of physics/engineering. Different properties scale with different powers of some common parameter, and changing size of a "thing" beyond some range is simply impossible.

 

[ferg]

Yes.

Scaling problems are very common in every branch of physics/engineering. Different properties scale with different powers of some common parameter, and changing size of a "thing" beyond some range is simply impossible.

Very interesting. Never looked into scaling. But you have certainly peaked my interest.

 

[PeroK]

Very interesting. Never looked into scaling. But you have certainly peaked my interest.

It's piqued my interest:

https://www.dictionary.com/e/slang/piqued-my-interest/

 

[yungman]

I think the assumption is wrong that anyone can complete a punch at the same time regardless of size( that if the person is 1000ft talk and still can complete the punch in 1sec).

When the arm, body get heavier, it takes more force to start and stop. I don't know the detail.

just look at boxing, the feather weight people move, punch is much much higher speed than heavy weight people. difference is the heavy weight have a lot more weight behind the punch so it hit harder even at slower speed.

In real life, you can have a small guy with lighting speed punching a big guy over and over, the big guy likely standing. but when the big guy land one punch on the small guy, the small guy goes flying.

 

[yungman]

Also, strength and speed do not scale up with body size. one example is if you look at small animals, they usually can push many times their body weight, but if you look at the big animal their strength do NOT increase proportion to their size and weight.

One funny thing if anyone watch the old "Gladiator" tv show. You see the contestants always got beat up by the gladiators because the gladiators are bigger, stronger. But the whole thing is really unfair.

One time I remember they made the gladiator ran the obstacle course as the contestants. The gladiator cannot even run up the inclined treadmill because they are too slow. The key is for the contestant to pass the basic obstacle course to qualify, they have to be small and light. But if all of them are small and light, they get beat up by the gladiator on the other challenges that involve strength. That's why you always see the gladiator beating up the contestants.

Bottom line, you cannot size up strength and speed with body size.