Wire, heat, and current

[Mokele]

Ok, I've been drafted into the crab-lab here to help with some experiments involving magnetism, and we've decided we need a very large Helmholtz coil system. Since the cheapest one at the size we need (2 meter diameter, possibly bigger) costs as much as a new Lexus, we're going to build one, and have found plenty of resources on how to do so.

 

However, I've hit a snag: wire temperature. We're going to have a *LOT* of wire in this thing (image 2 wheels 2 meters in diameter each with about 500 wire wraps around each), and field strength is proportionate to current strength.

 

Now, I know the equation for power (P=RI^2), and I found the right equation to covert that into heat generation in degrees C per second, but the numbers are *really* wonky. Stuff like saying 10 gauge copper with 10 amps wire will rise in temperature by 7 C per *second*. Now, I'm no electrician, but I *know* that ain't right.

 

And I know why it's wrong: that's the heat generated, not counting the heat *lost* to the air. But I don't have the thermodynamic wherewithal to actually calculate that.

 

I saw something on a wiring site about "rated to 90 Amps" (this was for 6 gauge), and I was wondering if there was any standard I could use to find out how high we can push the current for a given wire diameter without burning the lab down in the process.

 

If, for example, I find a wire that says "rated to 30 amps", make a huge coil of it (which, I figure, will reduce the heat dispersion per unit length since the coils overlap), and only put 15 amps through, will I be safe?

 

I've got a tradeoff: I can either increase amps and use less wire (fewer coils) and worry about heat from straight amperage or use more coils and less amps and worry about heat disipation because the wires are overlapping.

 

For those interested, I need a field of 81 Gauss.

 

Mokele

[Rocket Man]

10 amps is a lot. i'm not surprised at 7 degrees per second.

copper has a fairly standard resistance, ratings don't take heat dissapation into account.

 

the magnetic intensity determined by current * length yes? if you take a cable twice as long, you can halve the current. if you use a cable such that the entire loop occupies the same area, resistance must go up by 4. (double the length, halve the cross section area.) so the power demand remains constant (the same current density).

 

if you use a coil cross section with double the area, power will drop proportionaly.

 

are you using dc? if you are, you can pass copper plates through the coil to act as heatsinking fins.

enameled copper wire doesn't mind fluids either. you could potentially mount the coil inside a pipe and pump chilled freon.

[swansont]

http://www.powerstream.com/Wire_Size.htm lists both chassis and power transmission wiring, which they describe as basically air vs bundled. Bundled wire limits are about a factor of 4 lower than air at the intermediate gauges. They point out that these are conservative values, meaning there is a good safety margin involved (i.e. running 5.01 amps with a limit of 5 shouldn't melt the wire or insulation) But one has to consider things like what the ambient temperature is, what kind of insulation is on the wire and whether you are using forced cooling rather than convection.

 

I'm an exprimentalist, so I tend to the empirical testing method. Build a small coil with the bundling you'll use and test it at higher than the design current.

 

Remember that the fields add, so two sets of coils will work, too. The problem is that if your supply is power limited, adding length doesn't solve the problem. P=IV, and V goes up as fast as I goes down

[Externet]

Hi Mokele.

The magnetic field is given by Ampere x turns.

Amperes are Volts ÷ Ohms; then

The magnetic field is also given as Volts x turns ÷ ohms.

 

Increasing the tension or the turns, or both, while keeping resistance low is the ideal for maximum efficiency in your application.

 

10 Amperes in a 10 gauge wire is not of concern at all. Such current is under half of the carrying capacity for that copper wire with no appreciable heating.

Forced ventilation of the coil may give you piece of mind for long time operation.

A rated 30 Amperes wire running at 15 is of no concern either.

The 7º rise per second does not make sense.

 

Now, is the magnetic field to be pulsed or constant?

 

Miguel

[Mokele]

Thanks for all the responses so far!

 

Rocketman, I definitely think we'll use the heat fins idea, since we're using DC, and we're probably going to move towards lower current and more coils.

 

swansont, thanks for the info, we'll definitely use the power-transmission rating as a guide so we don't burn down the lab.

 

externet, it's going to be a constant magnetic field, so that makes things a bit simpler. Forced ventilation, especially with the fins, is definitely something we'll consider.

 

Of course, the real determining factor, before we can do any of this, is going to be how big of an arena we need for the crabs to behave properly.

 

Mokele

[Rocket Man]

what factors gave you 7 degrees? what value did you use for resistance per metre?

 

the uniform area is a cylinder 1/5 the coil diameter. 2m gives a 40cm test area.

 

double the coil cross section area, halve the power. if the coil gets too big, you'll loose uniformity in the feild.

length of wire itself will do nothing for the power if you go down in diameter. the current density for the coil will remain constant unless you increase the area of the cross section

[Externet]

Somewhere, there is a old MRI tunnel -magnetic resonance imager- behind spider webs waiting for a dumpster.

Finding it is the task.

Or, can you lure the crabs to the hospital?

Miguel

[Mokele]

what factors gave you 7 degrees? what value did you use for resistance per metre?

 

10 gauge wire, 20 amps. IIRC, i used 1.72 * 10^-8 Ohm/meter

 

the uniform area is a cylinder 1/5 the coil diameter. 2m gives a 40cm test area.

 

Yep, but right now, we only have one test arena, and it's 4 feet across. We'll need to do behavioral trials to see what the crabs will do in smaller arenas, since, after all, a spiffy Helmholtz coil is wasted if the animals refuse to behave for us due to a small test arena.

 

double the coil cross section area, halve the power. if the coil gets too big, you'll loose uniformity in the feild.

 

Yeah, we're probably just gonna have an assload of coils at low amperage. Makes me glad it's not my thesis - poor Mike will have to spend all that time wrapping wire.

 

Somewhere, there is a old MRI tunnel -magnetic resonance imager- behind spider webs waiting for a dumpster.

Finding it is the task.

Or, can you lure the crabs to the hospital?

 

Unfortunately, MRIs aren't big enough. The experiment deals with path navigation in crabs, so the test arena has to be big enough for them to move around appeciably in order for us to get good results. Plus if it's too small, they just hide in the sand. Plus we want to be able to control the field strength.

 

Mokele

[swansont]

Yeah, we're probably just gonna have an assload of coils at low amperage. Makes me glad it's not my thesis - poor Mike will have to spend all that time wrapping wire.

 

 

Mike gets no sympathy from me. Sounds like standard physics gruntwork. Look at the coils. There are four octagonal ones that fit inside the framework that may not be obvious, since you can't see the wire. Does Mike want to align all those optics, and assemble the vacuum system? (And that's the job I did after I finished my thesis and did two postdocs)

[Rocket Man]

if it's navigaion all you need to do is get a compass to deflect 90 degrees or so in a roughly uniform fashion.

 

did you think of magnetising long strips of ferrous metal to place underneath the arena? it would be easier to bury steel rods at the beach than to construct a Helmholtz coil.

[swansont]

if it's navigaion all you need to do is get a compass to deflect 90 degrees or so in a roughly uniform fashion.

 

did you think of magnetising long strips of ferrous metal to place underneath the arena? it would be easier to bury steel rods at the beach than to construct a Helmholtz coil.

 

For 81 gauss I think magnets would be expensive and not give the uniform field you want. Grad student labor is often viewed as free in terms of lab expenditures. You save your budget for things you can't build yourself, so the cost of Helmholtz coils is only the cost of the wire and the form to hold them (I've seen old bicycle rims used for some sets) and power supplies can usually be found on the cheap.

[Mokele]

if it's navigaion all you need to do is get a compass to deflect 90 degrees or so in a roughly uniform fashion.

 

It's actually vertical orientation that's the issue.

 

Long-ass backstory: Crabs can do some neat stuff for an animal with a lump of ganglia that barely count as a brain. One of these tricks is path integration. As the crab moves about on the beach, it keeps adding up the distance vectors, so that if you disturb it, it can make a straight-line run to it's burrow, even if the burrow isn't visible. They detect their orientation by means of polarized light.

 

However, we don't know how they deal with vertical distances. We're pretty sure they can do path integration vertically too; if they climb over an object one way and then it's removed, they'll likely return to the burrow at the correct distance. What's not clear is how. It's likely they detect slope using an organ called a statocyst, which is basically a hollow ball of sensory cells with a grain of sand inside, so wherever the sand is, that's 'down'. The sand gets in when they molt, which gives us a unique opportunity: if they molt while on iron filings, they'll get *those* in their statocysts, and we can use a magnet to influence what they think is up and down.

 

As swansont correctly noted, powerful enough magnets are expensive and non-uniform, and the field needs to simulate a slope over an extensive area to make the results detectable (since there will always be error due to the fact they are astonishingly stupid creatures). Non-uniformities over a distance of a few cm are also a problem because the crabs have two statocysts, and we don't know what will happen if they get contradictory 'gravity vectors' from left and right organs.

 

So the idea is to use Helmholtz coils to generate a large, mostly-uniform field that'll make them think they're going up or down an incline as they forage, then turning it off and scaring them to see how they run back to their burrow. If the statocysts are used to find the horizontal components of a 3-D path, they'll screw up and either overshoot or undershoot (depending on the situation). If they don't use the statocysts, they'll just go home as per usual. If they do use them, though, we may be able to find out the exact neural control mechanism, how they add things up in their tiny little brains, by using this setup to decouple actual surface moved over from perceived surface moved over.

 

81 gauss is actually the number got testing how much is needed for filings to jump up, and thus the field strength that will exert 1g or so (remember, in biology there's a lot more slop, so +- even 10% is pretty tolerable for this sort of experiment due to all the usual variation). So if we've got a field of 1g running parallel to the ground, and gravity as usual, then the vectors add up and the crabs will see a 45 degree slope (we're reasonably sure the crabs just detect the direction of 'down', not the magnitude of the force, so the greater magnitude shouldn't be an issue).

 

Mokele