Running at high speeds

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This topic was inspired by the RiskBreaker mod's thread in the Throne of Bhaal forum. I thought it would have been off-topic to continue it there. Hopefully, I've chosen the correct forum for it.

Goli Ironhead:

It's not a too exact question Running is an ability of creatures (at least in our context), which is a practical thing, so I'll start with that.

Obviously there is a biological (physical) limit of speed for each creature able to run. This is determined by several things -- and not just by the creature. It depends on the type of the ground you're running, and on all other forces affect you. (Try to run against the wind and you will feel what minimal speed means! )

You asked theory as well. First of all, it's required to understand what happens when you run on a surface. Your legs exert force on the ground, and according to the Third Law of Newton, the ground exerts the same force on you (in the opposite direction). This is what causes you to move. Yeah, it's the ground what causes you to move when you run! (Note: non-zero friction is required for this. Without friction, all objects such as your chairs, tables etc. and you too would be "slippering" due to the smallest impulse.)

The acceleration of a body is determined by the forces that affect it (see the Second Law of Newton; it's the fundamental law of dynamics. Dynamics give an answer to why a body is moving). As long as the resultant of forces that affect you is not zero, you are accelerating ( = your speed is increasing). That is, a body accelerated by a force in the vacuum would increase its velocity forever*. If there was no friction on the ground (and of course air resistance etc.), a moving object would keep moving forever on the surface, at a constant speed (First Law) -- without any forces (assuming it had a starting speed at the first moment, of course.)

*Of course not forever. At very high speeds, relativistic phenomenons appear. To descibe the cause of a body's movement at relativistic speeds, relativistic dynamics is used.

So theoretically, if we remain in the classical range of speeds (that is, where relativistic effects are completely negligible), you could reach a very high speed e.g. by running in a surface with friction ( => increasing speed), in vacuum. Another surface would be at the end of this one, connecting to it, with zero friction. You would be moving forever on this surface with the speed you reached at the end of the first surface. Of course not on your legs any longer, but rather like a sack full of potatoes: you would probably lose your balance when arriving to the new surface due to torque (turning moment) in your body. Of course we've assumed (e.g. usual) gravity in this theoretical example.

OTG:

I'm not an expert at all, but I don't think any of these statements are true. For example, the consequence of Heisenberg's Principle is completely negligible for macroscopical objects. Also, according to the generally accepted theory, the highest possible speed is c, the speed of light. (There are other theories.) As a consequence of special relativity, a particle with non-zero mass always travels at speeds less than c.

[ February 12, 2007, 23:10: Message edited by: Baronius ]

 

Being a sprinter the maximum speed a human can run depends upon the amount of power in their legs in relation to body size and weight.

Certainly when we're talking about running in vacumes and such the point is moot because things that run more often than not require air to breathe and an outside pressure on their bodies to keep everything on the inside from bursting out.

Running is basically your legs pushing your body away from the ground. If the ground can absorb some of the force from your legs (such as sand) then you'll run slower provided you're applying the same amount of force.

The art of running fast isn't about the number of steps you can take in 5 seconds but rather the distance traveled per step. So if you've watched Star Wars: Episode One seeing a young Obi and his master (name slips my mind at the moment) using their 'force speed' Lucas gets it wrong. They wouldn't turn into blurry men moving their legs really fast. They would simply take greater leaps and bounds when running, moving their legs at the same speed but perhaps covering twice or three times as much ground per stride. This is why the subject's weight is so important, the lighter you are the further you can throw your body.

 

Just to make sure our posts remain consistent when people are reading them:

The movement in horizontal direction is exclusively due to the force that is parallel with the ground. It's the static friction that allows the whole thing to happen. (If the maximum of the static friction force is exceeded, you slip. This maximum is determined by your weight and a constant that belongs to the material of the surface. This is why you fall so easily on slippery, icy ground.) When you run, you also lift your body (this is what I ignored and your post reminded me; it seems I talked about physical basics of walking instead of running). The vertical direction ("lifting the body", same with jumping) is caused by a force which comes from the elastic potential energy (~spring energy) stored in the muscles. This force works against gravity when lifting the body.

While this was good to introduce to certain physical basics (the fundemantal reasons of vertical and horizontal movement e.g. during jumps or runnings), it didn't descibe the much more complex human movement at all. Here is something about it in the wikipedia.

Force can't be "absorbed", but if the surface is not static (like your sand example), additional force is needed because the deformations/changes on the surface require additional work from the runner (and the collisions are also more complex than in case of a usual stone surface, but of course all these things can be easily handled with the correct energy and impulse formulas). So this is why you need greater force to keep the same speed.

What about a special superlight "spacesuit" to solve those biophysical problems? Yeah my example was quite theoretical. I dealt with biological/practical aspect of the question only in that short paragraph (ending in the wind example). You've offered much more practical examples.

 

Well, the spacesuit would work but if you're running with gravity the excess weight would slow them down... without gravity the person could only move as fast as their legs could move (although I personally would opt to use my hands then since I would have more control over my direction).

I'm offering more pratical examples because life isn't all about numbers and formulae, reality requires a bit more than just adding this, subtracting that and dividing by the coefficent of something.

 

Why would it? If you mean that the person is hindered in his or her movement by the suit's structure/weight, then yes he/she can accelerate at a smaller rate only, but the terminal speed is identical to the case of higher acceleration, just more time is needed to reach it -- and we've time... As for the second surface, its friction is 0 so the (perpendicular) gravity has no effect on the vertical movement at all.

It's nice, especially because Goli Ironhead is probably more interested in that than in my occasionally too technical approach.

On the other hand, you wouldn't believe how the "reality" you enjoy is based on numbers, formulas, substracting, dividing and coefficients. The 99,9% of practical things that makes your life more comfortable and easier, are based on engineering, physics or other sciences...* (Of course, the most important things which we humans need can't be bought for any price, this is true.) Let me tell though that engineering and its paradigms have nothing to do with formulas or numbers.

*If you believe you have x computers in your home, multiply it with 3-4 and you will get the actual value. But you are right in a certain respect, no doubt.

[ February 13, 2007, 04:55: Message edited by: Baronius ]

 

Oh I understand and appreciate the influence all science has upon our daily lives, it's just that in the particular scenario you're talking about there are aspects that need to be considered and taken into the equation.

We're talking about something running, that requires a surface, legs and all the action between. There are things that formulae alone can't account for, and after some thought I've realised that if you're running without gravity on a surface every time you apply pressure you'll have to push yourself away from the surface. Eventually you won't be able to reach the surface and you'll remain at a constant speed rather than accelerating.

 

Hmmh... Intresting. But what would then happen if we remove the limitations of a body? I mean, if there were, say, some kind of a super-being that could run at any speed without tiring for unlimited time? Is there any kind of an universal limit here, as there is in freefall (not due same reasons, that much is clear)?

Oh, and let us assume that the gravity is earth level, and there is no wind at the time.

 

As I said, in freefall the limit is determined by drag. This is not "universal" by any means, since it varies depending on things like the shape and mass of the object, air density, and so on. Similarly, the actual gravitational acceleration is only constant insofar as our everyday experiences go.
Running, you experience the same increase in drag as you accelerate, but if you dictate that there's no bound on the force applied by your legs, then you can go as fast as you like. However, consider that the power required to overcome drag increases at a much quicker rate than your actual velocity.

 

Given those restrictions, no. Also, as Sim correctly points out, it's not like freefall represents a constant number for all objects. Your freefall speed is much faster than the freefall speed of a feather or leaf.

But regardless about what object you are talking about, it's "maximum" freefall speed is assuming it has no means of excelerating itself further. Skydivers can acheive a maximum speed of about 120 mph. However, to use a completely hypothetical example, say the skydiver had a rocket on his back. If he pointed down and activated the rocket, he could acheive a speed greater than 120 mph.

 

I've never said it should be done without gravity -- I even added it. If you've said it just to share it with others, just ignore my comment -- though you probably know that removing gravity from this theoretical example just makes it even less "practical". But such examples doesn't have to be completely realistic to introduce the point. I tried to explain the very basics which are required to understand anything -- practical or theoretical -- that is told about it. ("pushing your body away from the ground" doesn't explain why you can run or walk on a surface at all. Now I see though what Goli Ironhead was interested exactly -- a not fully theoretical problem, but several elements of realism -- biology -- are ignored, and the object in question is a creature able to run.)

The medium is air, just like in case of free fall (in our examples). No need for wind to feel how you can be hindered at high speeds...

...Just put out your hand (palm) in the car window while driving, e.g. at speeds 60 kmph, 90 kmph and 130 kmph. Then imagine that you're not in the car, you're running outside at the same speed! (You're the "super-runner"!)

As SimDing0 mentioned, the air resistance force increases at a quicker rate than your speed (non-linearly). There is a quadratic relation, so if you move at twice of your current speed, the resistance will be four times greater; if you travel at triple speed, the resistance will be nine times greater! This is why the momentary fuel consumption of your car is also determined by speed you're driving at! The force to keep the speed of your car at 100 kmph is four times greater than at 50 kmph -- consequently, fuel consumption increases at a higher rate than speed when you accelerate.

As I've said earlier, in vacuum there is no (classical) speed limit for an accelerating object.

 

From references to classical Newtonian physics and relativistic physics, I am sure that Baronius (amongst others) is well aware of this, but since it hadn't been explicitly stated I've decided to say it.

At high speeds (generally starting at about 0.1c), classical physics breaks down and relativistic physics is applied. The speed of light is someties called the 'universal speed limit', because as your speed approaches c (the speed of light), your mass rapidly increases.

I can't see how to replicate the formula in a post here, but as your speed approaches c, the lower half of the equation tends toward 0. Your relativistic mass is equal to your rest mass (what we observe at newtonian speeds) divided by this lower half. As dividing by 0 results in infinity, you end up with an infinite mass. To move this infinite mass, you require an infinite force. Naturally, infinite forces are rather hard to create.

To put it simply: the speed of light is the theoretical maximum possible speed to attain.

 

At least until we figure out a way to get around it.

I've watched way too much science fiction to believe in the speed of light being the speed limit. Engage the warp engines, full speed ahead......

 

Well, if the question is actually about running, then the real maximum speed becomes a factor of how quickly you can actually move your body parts. Remember, force is mass times acceleration (or a function of velocity in this case), so the force you exert by running is the mass of your body (the thing being moved) times the rate of chance of position of your leg. SO, the faster you can extend your leg, the more force you can exert, and the faster you can retract your leg, the faster you can get it into position of the next hop.

If we're talking about a theoretical man who can do this at any velocity, it becomes a function of wind resistance, but one dependent on how much force the person is actually exerting. I'd say it comes down to wind resistance (body position and current velocity), surface structure (the ground doesn't collapse as you push on it), and static friction (you don't slip when you push on the ground). All in all, I'd say this is far below the speed of light (due to static friction), but probably above the speed of sound. Human aerodynamics aren't great, but I imagine hard rubber shoes on metal grating could produce and withstand enough force to beat the wind resistance of Mach 1.