Cable that holds the elevator got disconnected

[Michael D. Sewell]

Originally posted by outandbeyond2004
we have overlooked the effect of terror ==> adrenaline ==> superhuman athletic feats.

For me to agree with you on this statement, you are going to have to modify it by changing the word "terror".

I can tell you that during years of skydiving and flying, I have seen many, many times, the "effect of terror" on human beings. The "effect of terror" is as follows: the terrorized person assumes the fetal position immediately, and stays in that position for several seconds, sometimes many seconds. Any attempts to communicate with the person during this time are futile. The terrorized person is in his or her own little world. If the terror passes; then, and only then, will the person begin to take steps to save his or her life.

In your elevator situation you would almost certainly be totally terrorized, and almost certainly found on the floor of the elevator, in the fetal position.

I don't want to hurt anyone's feelings here, but in my opinion, a discussion such as this should take place in a sandbox on a playground, not in the physics forums. Please close this thread.
-Mike

 

[outandbeyond2004]

I apologize if I have offended anyone by anything like a poor choice of words or by the tone of my writing. Besides, my attempts to produce witticisms and amuse people were perhaps misplaced.

 

[jdavel]

Integral said:

"If you can understand the analysis I did up stream a bit you will understand why your legs will NOT be flexed for the landing following a jump."

I think I understand your analysis, but I think you've made some mistakes. For example, you say:

"With respect to the elevator we have y= 2t -gt2 = .05"

I don't think this is correct. In this equation, t refers to the time interval that begins when my feet leave the floor and ends when they are .05m off the floor. But during that time the elevator and I are both in free fall, so my speed "with respect to the elevator" is not accelerating at g; it's a constant, namely 2(m/s). So the equation to find t is just:

y = 2t = .05m

Then you said this:

"According to my numbers you are .007s from hitting the floor traveling at over 8m/s, this equivalent to a free fall from about 12.5m."

I don't think this is correct either.

v(s) = sqrt(2gs)

It looks like you've dropped a factor of two somewhere; velocity should be more like 16(m/s).

I do agree with the 2(m/s) you used for a reasonable jumping speed. But that speed will come off your landing speed as long as you wait to jump until you're falling at a speed of at least 2(m/s). The problem is that 2(m/s) isn't very much, unless the fall is pretty short. Even from your 12.5m (about 40ft) you'd hit the ground at 16(m/s). A 2(m/s) jump cuts that to 14(m/s), better, but still pretty painful!

The reason this problem got so complicated is that we all mixed physics with physiology.

I think the pure physics is this. Two masses are in free fall with one just above the other. The total momentum transferred to the Earth when both masses have landed, has to be the same, no matter what happens on the way down. If at anytime during the fall, the top mass can increase the downward speed of the bottom mass by applying a downward force to it, then the bottom mass will transfer more momentum to the Earth than it would have, so the top mass will transfer less and land more gently than it would have. It doesn't even matter when the force is applied (again, as long as applying it doesn't cause the top mass to start moving away from the ground).

I think the physiology part is this: The best survival strategy is to give as much of your momentum as you can to the elevator and then bend your legs so that the impulse, integral(Fdt), that you apply to the Earth is spread over the maximum possible time, thus requiring the minimum possible force. But if the fall is from more than about 50 ft, even doing both of these won't prevent a pretty serious injury.

 

[outandbeyond2004]

I have been wondering if one should jump as soon as possible then try to use air resistance. Spread out your coat, e.g.; bump against walls. Maybe you can catch the edge of a floor that is a little past the floor's elevator doors. Yeah, that's what I'd try to do once I got to the top, try to land in a floor cavity behind some elevator doors. Even if you fall out, you can greatly slow your descent that way.

 

[Integral]

Integral said:

"If you can understand the analysis I did up stream a bit you will understand why your legs will NOT be flexed for the landing following a jump."

I think I understand your analysis, but I think you've made some mistakes. For example, you say:

"With respect to the elevator we have y= 2t -gt2 = .05"

I don't think this is correct. In this equation, t refers to the time interval that begins when my feet leave the floor and ends when they are .05m off the floor. But during that time the elevator and I are both in free fall, so my speed "with respect to the elevator" is not accelerating at g; it's a constant, namely 2(m/s). So the equation to find t is just:

y = 2t = .05m

Absolutely NOT. If the elevator is falling at a constant velocity you can jump up and down on it all day long and not know that it is moving, it will seem as if you are on a stationary floor.
My equations are correct and the time is correct

Then you said this:

"According to my numbers you are .007s from hitting the floor traveling at over 8m/s, this equivalent to a free fall from about 12.5m."

I don't think this is correct either.

v(s) = sqrt(2gs)

It looks like you've dropped a factor of two somewhere; velocity should be more like 16(m/s).

You are correct here, it is not a missing factor it is reading the wrong numbers out of my spread sheet. actually is is only a fall of about 3.5m which is survivable.

I do agree with the 2(m/s) you used for a reasonable jumping speed. But that speed will come off your landing speed as long as you wait to jump until you're falling at a speed of at least 2(m/s). The problem is that 2(m/s) isn't very much, unless the fall is pretty short. Even from your 12.5m (about 40ft) you'd hit the ground at 16(m/s). A 2(m/s) jump cuts that to 14(m/s), better, but still pretty painful!

Read my post for the correct numbers. Rember the elevator is falling at 10m/s so the impact speed is 8m/s I still maintain that the jump will do more harm because of the poor postion of your body at impact.

The reason this problem got so complicated is that we all mixed physics with physiology.

I think the pure physics is this. Two masses are in free fall with one just above the other. The total momentum transferred to the Earth when both masses have landed, has to be the same, no matter what happens on the way down. If at anytime during the fall, the top mass can increase the downward speed of the bottom mass by applying a downward force to it, then the bottom mass will transfer more momentum to the Earth than it would have, so the top mass will transfer less and land more gently than it would have. It doesn't even matter when the force is applied (again, as long as applying it doesn't cause the top mass to start moving away from the ground).

Most of what you say here is nonsense. I do not think your jumping will have any significant effect on the motion of the elevator. Keep it simple, treat the problem as that of a falling body, because that is what it is.
I very carefully specified that the elevator is falling at a constant 10m/s NOT under free fall acceleration, simply because if you are in a free fall you will NOT be standing on the floor you will be floating somewhere inside the elevator, unless you have had some experience dealing with free fall it is not clear to me that you could orient yourself and push off in the right direction. This simply adds a lot of complexity, therefore I assumed that the elevator is at terminal velocity.

I think the physiology part is this: The best survival strategy is to give as much of your momentum as you can to the elevator and then bend your legs so that the impulse, integral(Fdt), that you apply to the Earth is spread over the maximum possible time, thus requiring the minimum possible force. But if the fall is from more than about 50 ft, even doing both of these won't prevent a pretty serious injury.

I do not disagree with this, what you say here is not the same as jumping, Though I have no clue what you mean by "give as much of your momentum to the elevator as you can" this is serious mumbo jumbo AFAIK.

 

[Michael D. Sewell]

I apologize if I have offended anyone by anything like a poor choice of words or by the tone of my writing. Besides, my attempts to produce witticisms and amuse people were perhaps misplaced.

outandbeyond2004,
Please don't apologize. I owe you an apology. My tone was too harsh and I was too sarcastic. I'm truly sorry.

The point I was trying to make is that many of us seemed to be more interested in argumentation than analysis. When discussing physics we all share an obligation to be realistic. We had people entertaining the idea of jumping upward at velocities that were not attainable. The discussion was getting foolish. This is physics forums, not a comic book.

We are not speculating on something that has never happened before. The statistics on accidents involving falls are available. The facts are known. Falls from 15 stories are not considered to be survivable-period.

Please accept my apology,
-Mike

 

[outandbeyond2004]

In response to Michael D. Sewell's apology and explanation of why he wrote as he did, I will accept his apology and let bygones be bygones. Now let me explain. I was not arguing for arguing's sake. Rather, I was simply exploring or trying out ideas or throwing them out. I don't deny I did not try hard to keep them realistic. However, when we are still trying to understand the problem thoroughly, it seems to me that we should allow our exploration to be somewhat unconstrainted. For one thing an idea may spark others. As our understanding matures, we can and should try to be more realistic, I agree. However, is it now time to be purely realistic? I am doubtful we really understand the problem now. It frequently happens that people overlook something that looks obvious only after the fact, you know, such as Integral's insight that the person's potentially-fatal kinetic energy must be dissipated slowly enough. Besides, we may find something interesting that has only a tenuous connection to the original question. Well, any thoughts about this post? Please don't be, shall we say, too nice.

 

[Michael D. Sewell]

Your point is well taken, and again I apologize. I am new to the internet and sometimes I find it hard to cope with not being able to read facial expressions and body language when communicating. When I re-read my post now, it looks a lot more malicious to me than when I wrote it. I am truly sorry, and I hope you will forgive me.

That being said, falls from 15 stories are not considered to be survivable. Many of you have presented, how should I say this... creative solutions to the problem. However, Integral is right, your solutions will not work. Falls from 15 stories are not considered to be survivable. -Mike

 

[outandbeyond2004]

Two ideas that does not seem to be good. Perhaps you can see a flaw in my reasoning or find improvements.

Integral appears to think my idea of taking off one's shoes and flinging them to the floor so as to propel oneself to the ceiling of the elevator is not workable, generally speaking. He's probably right. I want to consider a case that is clearly borderline. I would guess the elevator is moving 7 m/s and still accelerating, OK? I guess each floor is 5-7 meters. Clearly, the elevator can easily fall several floors by the time you take your shoes off, if you could ever acutally have any chance of doing so. Maybe 3 more floors by the time you throw the shoes, and yet 3 more floors by the time you arrive at the ceiling . . .

The other idea is this: You want to go to the 10th floor and you are at the 6th floor when you realize the elevator is going to fall. I think then that you brace your hands against the upper door frame until you know the elevator is falling freely. (I assume of course that you know the safety devices all are going to fail.) Then you push off it to flex your legs against the floor. Then you can jump to the ceiling. I am afraid this is iffy or worse, because you would need to go through the ceiling to the elevator top quickly for the manuever to do you any good. Besides, it won't work for people too short to touch the upper door frame.

 

[Michael D. Sewell]

Imho the first thing one would probably do in this situation is this .

The next thing one would do is this [zz)] , for a long, long time.

The EMTs would do this .

And the rest of us would feel this for you .

-Mike

wow, now my posts look like they belong in a comic book too...

 

[jdavel]

Integral said: "I very carefully specified that the elevator is falling at a constant 10m/s NOT under free fall acceleration..."

Really? How could I have possibly thought we were both talking about an accelerating elevator? Oh...maybe because of these:

from your post: #17 "...given there are no safety mechanisms in place and that the elevator is in a free fall condition, the occupants would also be in a free fall condition..."

from your post: #19 "...I doubt that the elevator would have time to reach terminal velocity unless the shaft were nearly air tight..."

from your post #40 "If you could jump in a free fall (it is not clear to me how you would do this!)you will not change your final velocity."

from your post #55 "So applying a force to the floor and staying at rest wrt that same floor is nonsense"

and again from #55 "Now a good question is what is a fatal velocity, is a 20m drop fatal? Maybe not, but I would not want to try it. A bit of computation shows that v = sqrt(2gx) This gives a value of ~20m/s for a 20m fall..."

It's not until your post #75 (out of around 100 in this thread) that we finally get this: "edit: Forgot a bit. Now let us suppose that the elevator is falling at a constant velocity..." (This one's my favorite. When did you remember to go back and sneak that in?)

Your post #89 "So if the elevator, falling at say 10m/s..." (By the way, I think this is the quote you were referring to when you said, "I very carefully specified that the elevator is falling at a constant 10m/s NOT under free fall acceleration" So that's not really true is it?)

And now you respond to me in your post #95 with this: "Rember the elevator is falling at 10m/s...Most of what you say here is nonsense...Keep it simple, treat the problem as that of a falling body, because that is what it is...this is serious mumbo jumbo"

And you're a mentor?

 

[Integral]

No we are saying that if you were falling at 60mph and jumped so your speed was 0 your body would be every bit as crushed as if you had let the ground stop you.
edit:
Forgot a bit.


Now let us suppose that the elevator is falling at a constant velocity.(I am going back to metric, just because.) Also I am going to totally neglect any superhuman feats, So the elevator is falling at a dangerously fast constant velocity, say 20m/s. If at some random time during the fall you jump up wards with an initial velocity of 2m/s your equation of motion wrt to the elevator will be given by y= 2t- gt²/2. You velocity will be given by v= 2-gt. The max height of the jump will occur when the velocity is 0 or at t= 2/g (let g=10 for easy numbers) so t~.2s. Now at the peak of your jump your velocity wrt elevator =0 at that point you begin to fall back to the floor of the elevator your velocity is still described by v=2-gt but now we have gt>2 so your velocity is negative. That is you are moving down.

Now let us superimpose the motion of the elevator on the motion of the jump. This is what an outside observer would see.

V_elevator + V_you = -20 + 2 -gt = -18-gt.

The first thing to notice that there is no value of t for which this is a positive number, so you are ALWAYS falling. For the time period (0,.2) your velocity will be less then 20m/s, at t=.2 your velocity will BE 20m/s (remember we have 0 velocity wrt to the elevator) for t > .2s you velocity will be GREATER then 20m/s as you will be accelerating in free fall motion until you reach the floor of the elevator. This would occur at t=.4s, at that time your velocity will be 22m/s.

OK, so there it is, during the period (0,.2s) you have succeeded in reducing your velocity wrt to the ground. Now, consider that you MUST be in the air when the collision occurs, the further into that initial .2s you are the faster you are falling, consider the condition of your legs at the instant you jump, they are fully extended, knees straight and perhaps locked, this looks like the way to MAXIMIZE injury, especially since you are still falling and will impact the ground before completion of the jump.


I still maintain that jumping will do no good.

Jdavel,.
Foolish me, perhaps I assumed you had read and UNDERSTOOD, this post which is the one where I developed my basic model.

YOU said that you understood this:

I think I understand your analysis, but I think you've made some mistakes. For example, you say:

Those are your words, so what you are now telling is that you DID NOT read and understand the analysis I did.

Please take some time to do that then perhaps we can get on the same stage.

I have assumed a constant velocity simply so you COULD jump. In a free fall situation of any significant distance, unless you are accustom to low or no gravity, there will be little you can do other then come to a sudden stop when the elevator hits bottom, If you think pushing off and suspending yourself in mid air will some how cushion the fall, well... RIP.

To me when I specify a specific velocity it precludes "freefall" which to my knowledge implies acceleration. If you have other ideas of what freefall means please share them.

It's not until your post #75 (out of around 100 in this thread) that we finally get this: "edit: Forgot a bit. Now let us suppose that the elevator is falling at a constant velocity..." (This one's my favorite. When did you remember to go back and sneak that in?)

Simply check the edit times. That addition was made within minutes of the original post. This bit that I forgot was the entire text after the edit statement.

I will stand by everyone of my quotes that you posted. In the context they were written they represent the state of the then current conversation.

I also carefully set up the conditions of my analysis. perhaps you need to read with fewer preconceived notions.

 

[Michael D. Sewell]

When Integral is faced with 10 different situations he has no choice but to respond with 10 different velocities.

The mentors on this site are here to help us all, out of the goodness of their hearts. Many of the mentors have full-time jobs; they often take the time (free of charge) to do research(read that Ft-Lbs or N-M) to help answer our questions.

I was sarcastic myself on this thread and others. I apologized here, and I reget saying some of the things that I said.

Please, let's chill out a little bit, and not abuse the mentors.

Thank you,
-Mike

 

[chroot]

Well, guys, it's really simple. If you fall ten stories in a small box, you, and the box itself, are going to gain a tremendous amount of kinetic energy. You're going to have to get rid of that energy somehow, or it's going to kill you. Unfortunately, while trapped inside that little box, there's nothing you can do. Even if you could jump forcefully enough to negate your downward velocity, you'll still have to contend with the ceiling of the box. Your kinetic energy is going to be dissipated somehow, whether by the floor or the roof of the box, and it's going to kill you no matter what you do. It's a closed system, and the only way to save your butt is to involve something outside the box -- no pun intended.

- Warren

 

[Michael D. Sewell]

Heck Fire!

 

[jdavel]

Michael D. Sewell said: "Please, let's chill out a little bit, and not abuse the mentors."

How about this? Please, let's chill out a little bit, and not abuse ANYONE.

In my post (#93) I tried to stay on topic, and didn't think I was being in anyway abusive. If anyone thinks I was, then I apologize. That was not my intent.

Integral responed (#95) by calling parts of my post "nonsense" and "serious mumbo jumbo".

I fired back in (#101) with some sarcasm. I don't think anything I said was more abusive than "nonsense" or "serious mumbo jumbo". If anyone thinks otherwise, again, I apologize.

But here's the thing. A forum like this works best when the substance of one post is debated with the substance of another post. Dismissing the substance of one post by characterizing it with insulting adjectives adds nothing to the forum. It only leads to the whole board being cluttered with insults.

In the future I'll debate substance with substance and put anyone who doesn't show me the same courtesy on ignore.

Now, about this elevator...

 

[AnthreX]

i think i shouldn't have posted this one

i am getting everyone into troubles, but i am still unclear of the conclusion
because of all these other conclusions, and ideas. i was thinking of Integral's idea
but someone came up with some idea that integrals idea is not so true
so i don't really know what to believe, i hope you guyz would get 1 or 2 possible conclusions for me, if that happends, i would like to say sorry for all the troubles that i have caused and thanx

 

[Integral]

I stand by my conclusions.

Up thread, Janus made a very significant post, concerning the ability of a super human to leap at high enough speeds to counter that of the falling elevator, he pointed out if the body could with stand the forces of the jump it could survive the fall, so why jump.

Likewise the normal human body can convert a given amount of energy to other forms, this same energy could be used to adsorb as much shock as the body can take simply by standing solidly on the floor in a good ergonomic position. Jumping will only increase the severity of injuries and not increase your bodys ability to survive.

Have you ever misjudged a step? That is when you thought a small drop was 10" but in reality it was only 3" (the numbers are example only, pick any others you wish) When your foot hits the ground sooner then your body and mind expect there is a solid shock which can result in twisted ankles or in severe cases even broken bones. Your body spends a life time learning to predict when your feet will hit the ground, there is a significant amount of physiology involved. If the body is not prepared for contact injuries occur. When you jump your body knows about how long it has to prepare for a landing. This is why skydivers (as mentioned up thread) require training for a safe landing, they need to learn to judge when they will contact the ground and prepare for the event.

If you jumped in an elevator which was about to crash into the ground there is no possible way your body could be ready for the impact. It would nearly guarantee that you will be in a bad position. Why not simply crouch and pray.

 

[UltraPi1]

Heres another possibility for dissipating the energy. This is still assuming you could jump with some very quick strong legs. Jump the equivalent of half the speed the elevator is dropping where you hit the ceiling at half the speed the elevator is dropping or thereabouts. At the time you hit the elevator ceiling the elevator hits ground. you then continue to drop at a rate something a little more than half the speed the elevator was dropping thereby spreading the energy out.

 

[Michael D. Sewell]

i think i shouldn't have posted this one

i am getting everyone into troubles, but i am still unclear of the conclusion
because of all these other conclusions, and ideas. i was thinking of Integral's idea
but someone came up with some idea that integrals idea is not so true
so i don't really know what to believe, i hope you guyz would get 1 or 2 possible conclusions for me, if that happends, i would like to say sorry for all the troubles that i have caused and thanx

AnthreX,
You have not caused any of the trouble here. There is no reason for you to apologize. You posed a legitimate question and you deserve an answer. You have no reason to feel guilty about anything that has happened here.
-Mike

The reason for my edit: AnthreX, I have reviewed your posts, you are one of the few people on this thread who is without sin. -Mike

 

[Michael D. Sewell]

All,
15 stories is over 150 ft.
The duration of the fall is about 3 seconds.
The final velocity of the elevator is over 60 mph.
If the energy is dissipated over a distance of 6 feet(your entire height) you would be subjecting your body to an average g-force of about 25gs.

I have not seen a single post that has been able to dispute these numbers.

If you could jump upwards at half of the velocity of the elevator, you would reach a height of over 30 ft. Are you claiming that you can jump 30 ft? If you are making this claim, I'd like to see a clip of it. If you are not making this claim then your argument is not a legitimate one.

Subjecting your body to 25 gs would smash your bones to pieces. No reasonable human being would suggest that this is a survivable fall. If you doubt me on this, contact the NTSB(National Transportation Safety Board), they have plenty of information on how much force the human body can take. The NTSB is the most respected authority on this subject on the planet.

If human beings could withstand such tremendous forces, and survive falls from such incredible heights, why is it that we bother to wear parachutes when we skydive? To make a fashion statement? Do you seriously think we would be better off without the extra 20 pounds on our backs?

There is nothing to argue about here, half of the posts are complete bull, and the people who wrote them know it. This discussion was supposed to answer AntreX's question. He deserves a realistic answer, not gibberish. The fact is, AntreX's question has been answered long ago. THIS FALL CAN NOT BE CONSIDERED TO BE SURVIVABLE, PERIOD. -Mike

 

[UltraPi1]

All,
15 stories is over 150 ft.
The duration of the fall is about 3 seconds.
The final velocity of the elevator is over 60 mph.
If the energy is dissipated over a distance of 6 feet(your entire height) you would be subjecting your body to an average g-force of about 25gs.
I have not seen a single post that has been able to dispute these numbers.



You have given no consideration whatever to the air pressure beneath an elevator. A single elevator in a single elevator shaft will reach terminal velocity at some point, and slow toward the bottom, due to an overall increase in air pressure beneath the elevator. How much is dependent on a whole host of things. Falling in an elevator 15 stories is not the same as falling from a fifteen story window.

One could make calculations that would see an elevator that would never hit ground , to an elevator that fell in a vacumm. An elevator in the real world will fall somewhere in between that, and any calculation of a real world elevator fall would be quite complicated. lest you measure it's speed in an actual drop.

 

[Michael D. Sewell]

If you think I can't do the "complicated" mathematics to solve this problem, you try me. The empirical equations for terminal velocity, air flow in ducts, and air flow through a nozzle are child's play and I can do them standing on my head. Can you? You can make this as complicated as you want, you would still be dead in the given situation.

If your elevator were in an airtight shaft, how would you be able to raise it to the 15th story with cables and an electric motor? How do you intend to bring it down through all of this compressed air? Why don't you show me some of your "complicated" math here? Are you planning on using check valves? This elevator of yours is unlike any I have ever seen in the construction business, and I have seen a lot of them.

In AntreX's question, he in no way indicated that he wanted to know if a super-hero could survive a fall in an elevator from star trek. I am assuming that this situation is an average person in an normal elevator. Is this not the way to proceed? After all, if we can just make up super-human capabilities in the occupants of the elevator, and build the elevator with technology from the 43rd century then how does this answer AntreX's question?

AntreX's question, as I read it, assumes that the elevator is falling at a rate that is hazardous to his health. If you are claiming now that this is not the case, then how do we answer his question? Would the answer be that since he is superman, and that since the elevator is only falling at a rate of one centimeter per minute, that he has asked a stupid question in the first place because he doesn't even have a problem?

Do you have any idea what the terminal velocity of an elevator box is? Bear in mind that steel weighs 490 pounds per cubic foot. Show me your "complicated" math on that one... be prepared, I will show you mine.
-Mike

 

[LURCH]

Heres another possibility for dissipating the energy. This is still assuming you could jump with some very quick strong legs. Jump the equivalent of half the speed the elevator is dropping where you hit the ceiling at half the speed the elevator is dropping or thereabouts. At the time you hit the elevator ceiling the elevator hits ground. you then continue to drop at a rate something a little more than half the speed the elevator was dropping thereby spreading the energy out.

This would work if you could jump hard enough to take up half the decent volocity which, it has been correctly pointed out, nobody could. However, given a fall from a lesser height, this method would indeed spread out the impact, essentially making it two impacts, each with only half the force of landing at the bottom of the elevator shaft. Fifteen floors is far too much, but this trick could make the difference in a shorter fall, enabling survival when taking the direct impact would have been lethal.

 

[Michael D. Sewell]

When the elevator fell, your feet would leave the floor, or at least your legs would extend to the point where you could not use them to propel yourself. You could not jump in any way, shape, or form.

Half of the velocity of the elevator in the given case is unattainable.

A skilled skydiver can walk away from a hard landing that would have injured an average person. No amount of skill can save one from a "lethal" fall.

We lost a very skilled skydiver in a landing accident at Duanesburg, NY about two years ago. His velocity was much lower than the velocity in the given problem. This accident happened in broad daylight, on the drop zone, within a few hundred feet of several witnesses who were themselves very experienced skydivers. Terry used all of the skills that he was taught, and had over 200 jumps under his belt. The local ambulance crew was on the scene almost immediately. He did not survive.

I repeat, there is nothing to speculate about here. These types of accidents happen every day, the statistics are available and the facts are known.

 

[chroot]

I'm wondering if this merry-go-round of a thread should be left open?

- Warren

 

[Integral]

I'm wondering if this merry-go-round of a thread should be left open?

- Warren

Been my exact thoughts.

Your question is a signal of your thoughts.

Thread closed.