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Death by van der Graff generator

01/19/2008 10:55 PM

Does anyone have documentation of a high school student actually dying using a school scale van der Graff generator? There are countless warnings about students with heart conditions, but I spent an evening searching the internet, as did a colleage, with no confirmation. Mythbusters did a show that subjected healthy adults with no bad after effects.

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#1

Re: Death by van der Graff generator

01/20/2008 10:16 AM

I don't think they generate nearly enough current. I once directed a CCTV physical science show and I had the lecturer stand on an insulating platform while touching the Van Der Graff to make his hair stand on end. Unfortunately, the boom mike wasn't picking him up very well over the noise of the motor, so I hooked him up with an around the neck lavalier mike - a GROUNDED lavalier! It didn't harm him and he couldn't run as fast as me.

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#3
In reply to #1

Re: Death by van der Graff generator

01/20/2008 10:59 PM

Dear TVP45, As you and the lecturer discover the key word is GROUNDED as long as there is no ground there is no curcuit.


I personal have been struck by lightning but because it passed by not through me I was not harmed.(Here comes the bad pun) But it was an electrifying experience.

Dragon

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#5
In reply to #3

Re: Death by van der Graff generator

01/21/2008 2:27 AM

Dragonsfarm, do you charge for puns such as that?

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#20
In reply to #5

Re: Death by van der Graff generator

01/21/2008 11:28 PM

To All: Have I not been "pun"-ished enough?

Dragon

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#10
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Re: Death by van der Graff generator

01/21/2008 7:17 AM

I am truly shocked that you would charge yourself to emit such a pun.

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#30
In reply to #3

Re: Death by van der Graff generator

01/23/2008 4:42 PM

Why do people find lightning so shocking?

Because it doesn't know how to conduct itself properly.

(I'm a fifth-grader at heart, slightly older in other areas.)

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#12
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Re: Death by van der Graff generator

01/21/2008 9:33 AM

Being a former Pittsburgher and having an interest in science all my life, I spent many hours at the old Buhl Planetarium on the North Side. They had there a small Van de Graff generator which was used for demonstrations. They also had a much larger VdG generator (built and donated by J&L Steel Company). The later unit was capabile of generating at least 1 million volts. [ I believe the unit may be still at Buhl or in the Science Center now.] To demonstrate the large unit, it was necessary to clear the entire main room of the center of the exhibit and observers were required to be ~50 feet away, suggesting that there was some danger. I believe that post #8 is accurate.

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#2

Re: Death by van der Graff generator

01/20/2008 2:08 PM

Unsafe, not that I am aware of (it really is only a big static generator). If you made it large enough than you could probably cause injury.

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#47
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Re: Death by van der Graff generator

11/28/2008 4:02 PM

where do i get info on building a VG gene.

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#48
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Re: Death by van der Graff generator

11/28/2008 11:23 PM

Easiest way is to try a google search. There is plenty of information and designs on the web.

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#4

Re: Death by van der Graff generator

01/20/2008 11:46 PM

we used to set those up on the Science room bench (Box Hill Tech - Olden days - Early '80's)

then we would get someone to stand on a chair so they could comfortably hold the top... their feet about 1-2 foot above the floor.

People didn't like the arc running from the chair leg, around the plastic seat and in thru their shoe.

I had the brain storm to use the smaller "discharge globe" to discharge the main hat, the kid I discharged could run pretty damn quick, punching was his problem.

his first few steps were a bit wonky too :P

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#6

Re: Death by van der Graff generator

01/21/2008 3:44 AM

I have participated in such an experiment before. When i was at high school (which was only 5 years ago) my science teacher setup this generator and almost all of the students in the school had taken part. They use to set it up on information day when year one students come to the school to take a tour and take part in a few different tasks set out by various teachers.

This was a regular occurance to see the Van Der Graff generator up and running as it use to amaze students wanting to join the school. Never in the history of the school did i hear of a fatal occurrance. I am sure that this would not go un-noticed as the british school legal system is pretty tough on health and safety.

But most deffinatly there was a rubber mat around an inch thick below the students who touched the generator at all times, also the generator was always started after the student was on the mat never before.

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#7
In reply to #6

Re: Death by van der Graff generator

01/21/2008 4:06 AM

I heard Don King stepped just a little off the mat when he was in school. Could be an inner-city-urban myth, though. ...the part about being in school, too.

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#8

Re: Death by van der Graff generator

01/21/2008 6:09 AM

I dont have any documentation of a death from a van der Graff, and a school demo model van der Graff by itself will probably not deliver enough energy to stop a heart. But connect it to a few Leyden jars or other capacitors and it becomes deadly.

30kV and a thousand pF (if my arithmetic is correct) delivers about a half a joule. I wouldn't want to take that across my chest. You could make such a capacitor with a few modest sheets of thick window glass (or polycarbonate) and some aluminium foil

Have you ever taken the discharge from a colour TV tube, nasty bite it gives. A bit more capacitance and it too is deadly

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#9
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Re: Death by van der Graff generator

01/21/2008 7:10 AM

Been hit with TV tube anode........not fun.....wasn't quite right for several hours after.

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#11
In reply to #8

Re: Death by van der Graff generator

01/21/2008 8:51 AM

When I was in high school, I was working for a TV repair shop after school. I was asked to move a picture tube that was sitting on the bench. I picked it up by the face with the neck pointing up between my arms. A spark jumped from the anode to my arm. An experience I shall never forget. Fortunately, I did not drop the tube. To this day I am very cautious when poking around a CRT.

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#13

Re: Death by van der Graff generator

01/21/2008 11:28 AM

As post #8 indicates, the high freq. currents that travel "over" your body due to eddy currents which cause the 'skin effect' (google the terms) without causing harm, collect as a lethal D.C. voltage (no longer the harmless H.F. static charge) in a Leyden jar or other capacitive storage device.

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#14
In reply to #13

Re: Death by van der Graff generator

01/21/2008 1:42 PM

AC, are you sure? I would have said that the natural capacitance of a standard Van de Graff generator was not sufficient to store enough DC 'charge' to be lethal that it generates, but when used to charge a larger capacitor (the Leyden jar) then perhaps a large enough 'charge' could be stored to give the required 90mA (or so) of DC current across the heart to cause it to stop.

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#16
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Re: Death by van der Graff generator

01/21/2008 6:09 PM

Not sure what you mean by AC, but I think we are saying the same thing; the Van de Graff generator does not store any charge but the Leydan jar does .....as a D.C. voltage. Perhaps my sentence structure is confusing (comes with age).

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#33
In reply to #14

Re: Death by van der Graff generator

01/24/2008 12:03 AM

I believe that the phrase, "...90mA (or so) of DC current across the heart to cause it to stop", should correctly read, "...90mA (or so) of AC current across the chest to cause the heart to stop." These days most people are electrocuted by AC (Alternating Current) applied somehow to the extremities of the body, resulting in a fatal current flow that is distributed over and through the chest region, only a small portion of which actually flows through the heart region.

Also, I have read that a mere 5 milliamperes flowing directly across the heart, which can be (accidentally) applied during open heart surgery is enough to trigger ventricular fibrillation. Which is why hospitals use "Hospital" grade wiring and "Hospital" grade receptacles, with very low leakage currents to ground.

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#15
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Re: Death by van der Graff generator

01/21/2008 5:48 PM

A van der Graff is a DC device, and the dome at the top is the capacitor where the charge accumulates. When discharged it is a DC current that runs through you to earth. Further capacitance can be added if the insulators of the capacitors are good enough. You could for example have the class stand on insulating mats, hold hands and get the first in line to touch the dome. The charge that accumulates will be to the total capacitance of the group of students and the dome. Their hair may stand on end. The charge stored will be much higher than just the dome and if the last student in line touches the water tap, the current that flows (and the shock that results) will be much greater than one student just touching the dome.

On the other hand High frequency surface currents are generated by such devices as a Tesla coil, a completely different type of spark demonstration device.

Whilst we see small models in lecture demonstrations, the van der Graff has in the past had serious applications in accelerating elecrons to make deeply penetrating Xrays for radio therapy, and also for accelerating ions for implantation.

I have seen a serious Tesla coil which threw sparks a metre long. It was dicharged against an enclosed cage, in which I was standing. It's purpose was to show how I was protected from electric shock by an enclosed cage. I do not know if there are any longer more serious applications of a Tesla coil.

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#17
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Re: Death by van der Graff generator

01/21/2008 7:15 PM

Geez! Talk about misspeak. I REALLY have my machines mixed up. Can't imagine confusing a resonant transformer with an electrostatic device. Sorry folks, Mr MaHarg is absolutely correct. None-the-less, store the DC charge that collects on the device dome and one could certainly do some damage.

So, anybody wanna try and build my "Van de Tesla" widget ????

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#18
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Re: Death by van der Graff generator

01/21/2008 7:27 PM

Hahahahaa! Humility is such a refreshing human trait.

cr3

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#19
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Re: Death by van der Graff generator

01/21/2008 10:29 PM

"A van der Graff is a DC device, and the dome at the top is the capacitor where the charge accumulates."

Correct on the first part. A VdG is effectively an electron pump, pumping electrons either up or down, depending on the materials used for the pulleys and belt. Actually I believe the best description would be pulsating DC (essentially no external current until the spark jumps); certainly not AC.

A capacitor consists of two conductors separated by an insulator, so the dome is only half a capacitor. Commonly a nearby person is the second conductor, and once the air gap between the person becomes ionized, a very short duration spark discharges that capacitor. Since the dome and the person have very little parallel surface area and a rather large gap, the capacitance is very small, and the resulting current is very small. That tiny current combined with an extremely short duration make it very unlikely to cause any significant injury (beyond that caused by bumping into some sharp object while jerking back from the shock), much less lethal injury.

Over many years of teaching physics and science, I gave at least a couple thousand students the opportunity to experience the VdG. Many really liked it, and a few were really scared of it, but I'm not aware of any suffering any consequences that lasted for more than a minute or two.

Now the Leyden jar is another story: I never asked a student to discharge one with any body part; only with the wire arc with balls mounted on an insulting handle. I did accidentally discharge one a few times, never on purpose. Not pleasant, but then not as bad as a CRT (yes, I found a couple of those the hard way too). I'm still very much alive and still enjoy working with electricity!

Now a caveat! Clearly a person with a pacemaker or other similar device should never be allowed near any high voltage device. If indeed there was someone killed by a VdG (I haven't yet heard of any), I would expect it to be the result of damaging an electronic life support device, not directly of tissue damage.

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#25
In reply to #19

Re: Death by van der Graff generator

01/22/2008 5:46 AM

Without getting into semantics, the van der Graff might be better described as a mono polar electrostatic device. It however can sustain delivering small continous DC currents, as is apparent in its application as a particle or electron accelerator.

The belt can consist of lumps of conductor joined by flexible insulating material, in which case the dome will charge in increments, but in the demonstration models, the belt is a continuous rubber belt and the charge is continuously deposited inside the dome.

Whilst I agree that a capacitor usually consists of a pair of parallel flat conductors separated by an insulator, and there is not much area of a human body to form a capacitor, an isolated body does have capacitance. Having put an initial charge on an isolated body, it repels further charges of the same sign, viz the body has potential, and the ratio of the charge to the work done in getting the extra charge to the isolated body is its capacitance.

I have in mind that the isolated human body has about 30 pF of capacitance, more if near the earth. 30 kids in a class adds 900pF and if the electrostatic generator is 30 kV there is an extra 0.5 Joules of energy stored.

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#21
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Re: Death by van der Graff generator

01/21/2008 11:39 PM

Dear Lleros Mahrg, One of the most common uses today of a Tesla design is used to power an automobile: the spark coil that drives the spark plugs.

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#23
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Re: Death by van der Graff generator

01/22/2008 5:08 AM

Dear Dragonsfarm,

Thankyou for your comment on an application of Tesla Coils in automobiles.

I would not have called an ignition coil from an automobile a form of "Tesla Coil", but rather an "Induction Coil". Although the spark from such will have high frequency components, and there is a capacitor across the points (I thought for stopping the points from burning out) I was unaware that the primary and capacitor formed a resonant circuit, of the type one one would expect to see in a Tesla Coil.

Is there a distinction between Tesla Coils and Induction Coils or are they the same animal?

Early Xray generators used induction coils as a voltage source, for which they would need to have a DC component from the secondary!

Lleros

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#28
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Re: Death by van der Graff generator

01/22/2008 10:22 PM

Lleros, Yes the differences are the points and the condenser. Tesla's early versions ramped up the generation of electricity until the energy overran the air gap or the capacitors. Later he used step induction, one transformer fed into another.

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#22
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Re: Death by van der Graff generator

01/22/2008 2:12 AM

you went to Science Works didn't you :P

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#31
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Re: Death by van der Graff generator

01/23/2008 6:04 PM

No, I haven't been to Science Works, but I was a Physics Teacher before I became a Physicist in Radiation Therapy.

I made the Spark Coil and the Tesla Coil from the book "The Boy Electrician" Still use the book for inspiration and formulae using old units like the Oersted and the StatVolt. The text is actually on the Internet (Just Google "The Boy Electrician" by Simms)

The ironical part is that when I was 6 I used to look at my toes in the shoe shop every day on the way home from school, and then at the age of 10 having made the Spark Coil could not understand why I could not buy an X-Ray tube so that I could do all the interesting experiments in that chapter. Now I am a Radiation Safety Officer!!!!

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#39
In reply to #31

Re: Death by van der Graff generator

01/24/2008 11:53 PM

Ahhh, but have you finished the experiments in that book yet?

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#40
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Re: Death by van der Graff generator

01/25/2008 12:24 AM

No,

I am not permitted to go into the X-Ray room with the machine running so that I can look at my fingers on a platinocyanide screen.

Have you looked up the book yet? Fascinating reading for something written in the 1920s

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#24

Re: Death by van der Graff generator

01/22/2008 5:30 AM

"Correct on the first part. A VdG is effectively an electron pump, pumping electrons either up or down, depending on the materials used for the pulleys and belt. Actually I believe the best description would be pulsating DC (essentially no external current until the spark jumps); certainly not AC."

Yes you are correct that a VdG is sort of an electron pump. But the electrons are "pumped up" and not down. As for it being pulsating DC? A VdG develops a static charge through the friction of the belt and wiper, which ramps up the electron charge from 0 potential until it reaches its critical charge. The electrons are collected and stored on the dome of the VdG where the surface area determines the charge. As you can only fit so many electrons in one area. Once the critical charge is reached, as further electrons are added an equal number are expelled to the air due the the repulsive action of the like charges in close proximity to each other. This is what causes the fly away hair effect of the person who is touching the VdG. (Humidity in the air also plays a roll. The higher the humidity, the lower the potential charge.)

A VdG is really not a capacitor either. Yes it holds a charge as long as there is a supply of electrons being fed to it but it will quickly lose the charge once it is turned off. It also lacks a source of an opposing charge. A capacitor works by holding and retaining the charge as a result of the attractive force of positive and negative charges separated by a dielectric. (Simply put without getting scientific.) The arc that is created is the electrons equalizing the difference in the negative charge potential between the dome and the person reaching to touch it. The larger the arc the higher the voltage. The voltage is the difference in potential.

Being this, the highest current flow is only seen at the initial onset of the electron movement. As the difference in potential (IE Voltage) is reduced so does the current flow as the high resistance of the air gap and the body does not change fast enough to really matter. The high current doesn't last long enough (picoseconds) to cause much harm, but can cause pain and muscular reactions.

If the person is directly grounded, they become a conductor. They will feel a slight bit more due to the potential difference equalizing at zero, but the belt of the VdG then becomes the high resistance in the circuit, being that it is a natural insulator, (usually made of rubber), and can not transfer enough electrons resulting in a very low if any voltage. This is exactly why VdG's can not be used to produce useful electricity.

I have not personally heard of anyone dying as a result of static produced by a VdG, but personally know that static can be deadly. Having hooked up loads to the bottom of a hovering helicopter in the military, I have personally seen arcs reaching several feet in length due to static build up. So if a VdG could be made big enough to create a huge potential difference, and or the circumstances were just right, it could be possible to be killed.

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#32
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Re: Death by van der Graff generator

01/23/2008 11:09 PM

"But the electrons are "pumped up" and not down."

Not necessarily! I made a VdG generator as a high school physics project (50 years ago this year - still have it!). I couldn't find a rubber belt that was sufficiently flexible, so I made one of velvet ribbon. An electroscope quickly showed that it produced a positive charge on the top ball (5" copper horse watering trough float).

You surely remember rubbing wool on a rubber rod to produce a negative charge, and silk on glass to produce a positive charge. Same thing can occur in VdG generators. It is true that every commercial VdG generator I've seen did use a rubber belt and so produced a negative charge on top.

Dick

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#35
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Re: Death by van der Graff generator

01/24/2008 7:22 AM

Yes sir, you are correct that electron flow would be reversed through the use of other materials such as velvet, and would produce a positive charge on the dome. I have never seen a VdG work in such a manner. Although I would not think that you would get the same visual effect, IE hair standing on end, as you do with a negatively charged dome being that the source of electrons would flow from the subject touching it. It would be interesting to find out.

It would be an interesting experiment to see what would happen if a machine of each type is placed in close proximity to each other:)

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#36
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Re: Death by van der Graff generator

01/24/2008 10:57 AM

"Although I would not think that you would get the same visual effect, IE hair standing on end..."

like charges repel each other, not just electrons, so the positive-top machine does still make hair stand on end. Without some charge-indicating device like the electroscope, it appears to work exactly like a negative-top machine. There is no obvious difference between the sparks that jump.

At the time I made it, the 5" copper horse watering-trough float was the biggest conductive ball I could find. As you may know, the curvature of the ball limits the maximum voltage attainable, and the belt/wheel combinations used (together with belt speed) limit current. I haven't run it in many years, but as I recall the biggest spark I could get from it was around an inch long, while in good conditions I could get around 3 inches or more from the commercial VdG we had with about a 10" ball. I do believe the velvet belt was much more dependent on low humidity to work well than is the case with rubber belts.

I did at least once try using the two (positive and negative) VdGs together, but nothing spectacular happened. The larger one had so much more voltage and current than the small one that the small one simply acted as an electrode to which sparks could jump from the large one. If there was an increase in the intensity or frequency of the sparks with the small one running, above the intensity and frequency of the sparks made with the small one turned off and a hand touching the opposite side of the small one's ball, it was not obvious.

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#26

Re: Death by van der Graff generator

01/22/2008 7:36 AM

I just have to say that although the premise of this thread was to find out if death was ever caused by a Van Der Graph machine, I have found the commentary quite fascinating and have learned some new information.

Thanks to all for the information, I wish i had thought to ask the question

I am also very surprised not to have heard from Sparkstation on this one. Or did we and I just over looked it?

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#27

Re: Death by van der Graff generator

01/22/2008 7:37 AM

I know of only one instance where a student was actually harmed using a VDG. It was a case where all the students were linked up by holding hands to make everyone's hair stand up. Then the last student in the line did not understand the instructions and stepprd off the mat. I died...

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#29

Re: Death by van der Graff generator

01/23/2008 1:32 AM

Its basically the quantum of energy the charge carries that is capable to do harm a person. Surge of static electricity is a normal phenomena where a person coming in contact may not harm except little burn at the point of contact and sensation acknowledged by reflex of body.

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#34

Re: Death by van der Graff generator

01/24/2008 12:31 AM

Topsy would not have been amused by talk of death in electrical experiments. This may only be DC, but it's electrickery all the same.

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#38
In reply to #34

Re: Death by van der Graff generator

01/24/2008 10:17 PM

Edison should have had the sandals placed on his feet. Yes, he was an effective inventor, even though most of the devices he took the credit for were invented by other people, he would have had society using DC for power. This would have meant a generating plant on every street corner.

Yes he was a good business man, all that means is that money was more important than humanity.

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#41
In reply to #38

Re: Death by van der Graff generator

01/25/2008 4:26 AM

Totally agree with you Dragonsfarm. He was 'inventive' in more ways than one. Science history is littered with plagiarists/idea thiefs. Even Crick and Watsons famous DNA spiral was not exactly theirs (pinched off a woman who's name I forget - It's in the WoW Blog I think). I wonder if Edison was always a ruthless sod, or he just became one with increasing fame.

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#37

Re: Death by van der Graff generator

01/24/2008 3:40 PM

The short answer is no, I have never heard of it, however as we all know, it is impossible to prove a negative. However, my 2 cents worth is that amperage cooks you, and voltage drives the aperage, and frequency screws up the circuitry. You need a potential difference between, say, one side of your body and the other. Sure, cooking your heart will stop it..as countless people in Sing Sing would testify to if they were alive, however, the voltage required to override the complex triggering system in your heart is not very much, and and the frequency is what does you in there! By accident, it seems that most people's hearts are VERY sensitive to 50 or 60 cycles per second, the most common household frequency used in the world.

Other frequencies, like the 400 cps used in airplanes seem to be much safer, even though the voltage and of course, resultant amperage are the same. And of course, static electricity has only one half of one cycle per second and then only when it discharges, and this seems to be all it takes to trigger muscles all over the body. (Thats your CRT discharge....I had one throw me the length of an aircraft aisle!) But the heart seems to be quite resistant to this sudden sort of surge, causing it to "reboot" if it does anything at all!

I can testify to the fact that a good solid jolt of electricity to the chest will start your heart...it worked on me when I needed it. grin! I also note that as a measure of safety, they always told me to work with my left hand in my pocket when mucking about with high voltages. Don't really know if that was really important, but perhaps the natural shielding around the heart worked better if you sort of bypassed the current path.

The concept of "grounding" is a funny one....if your capacitor was not grounded, then grounding yourself would do nothing. Rather than saying "grounded" I would say "return path". It may be a "ground return", which is of course, a return through ground. The earth is not necessary grounded......I once disconnected an aircraft prepatory to launch, the pilot did his walk around, then changed his mind, and waited until the storm couds went away. When I re-hooked the grounding cable, a spark about 3 inches long occured. I researched this, and determined that the earth takes on a charge opposite to that of the storm cloud overhead, and in fact, can shift by several hundred volts positive or negative in relation to a theoretical medium point which we assume is "ground". When the cloud went away, the earth returned to normal, but my airplane on its rubber tires stayed at the voltage the whole area was only a few minutes before. This is the reason we also electrically bond the fuel truck to the airplane when we refuel it, and why I now "touch" my headset to the frame of the airplane before I plug it in to talk to the pilot....the plane flies in a world of changing electrical fields, and often is still highly charged when it rolls into its parking spot.

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#42
In reply to #37

Re: Death by van der Graff generator

01/25/2008 4:30 AM

Good post Yusef ! I've added a vote accordingly.

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#43
In reply to #42

Re: Death by van der Graff generator

01/25/2008 1:16 PM

Thank you. The proper person to talk with of course would be a cardioloist, rather than an electrician like me....and I could have gone into more detail, but I think that covered it well enough for the safety angle anyway.

. Electricity is pretty neat stuff. High voltage DC and static charges are often mis-understood, even by people who deal with it a lot, and the massive underutilization of an energy source which is normally considered a pest is hard to understand. It is fun to read about the early days of electrics and see how people like Edison and Tesla explored the electrical world.

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#44
In reply to #43

Re: Death by van der Graff generator

01/26/2008 6:49 AM

You're welcome Yusef, it's deserved.

There's a lot of good discussion around CR4 on Shock in general. Static has cropped up in the Challenge questions several times. Bill Bryson's book 'A Short History of Nearly Everything' gives a nice summary of the whole Tesla/Edison & AC/DC thing (It's a great general read)

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#45

Re: Death by van der Graff generator

01/28/2008 11:02 PM

The danger comes not from the voltage, but the amount of current. Any kind of shock can cause knee jerk reactions and physical hurt. High voltage with very low current generallly will not harm a healthy person, but can damage hearing aids or other types of electrical/electronic equipment. As an EE I do not think shocking any one is funny or good practice. There are plenty of ways to demo equipment without hurting someone. Of all people, a teacher should have the well being of the students kept in mind.

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#46
In reply to #45

Re: Death by van der Graff generator

01/29/2008 12:40 PM

Electricity is a natural phenomonon. Like gravity. You could fall and hurt yourself, similarly, you could get shocked and bang your head. Like gravity, it should be respected but not feared. The only way to know something is to experience it. A two year old will fall and "hurt" himself a dozen times. I am sure there are two year olds who have died from the experience, the remainder learn to walk.

I cannot agree with you enough about the need to find ways to demo equipment in a safe manner. The standard science show with the fellow whose hair flies up when they put their hands on a highly charged ball is an example of just the sort of things which need to be done, regularly, in order to demonstrate the effects of a phonomon which you can neither see, hear, smell, tase, but must be described only in mathematical terms.

The fact that every day somewhere in the world, there are people dying from stealing copper from power stations shows that more training must be done to de-mystify the subject. (though in the case of the power station idiots, it just may be Darwin in action.) But we also have people putting new plugs onto lamp cords, mowing grass around hydro towers, and trimming trees who get "zapped" on a regular basis. Like the guy in the pic below....kudos for wearing safety glasses.

Oh, and "guest", why not sign up?

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