I'll address a couple of your questions...
Yes, the part you're rebuilding with the wire coil is called the atomizer.
It should be wrapped around a wick. Are you replacing the wick when you are rewinding a new coil with the kanthal wire?
Is that what you're referring to when you say you're twisting it together like a rope is the wicking material? Or are you twisting the actual metal wire that you make the coil out of?
Answering that will help me out a bit...
And for a very quick layman lesson on how that resistance wire (Kanthal) is working...
33AWG is referring to the size of the wire. The numbers relate to the size of the wire in an inverse fashion, meaning that the higher the number, the smaller the wire. 33AWG (American Wire Gauge) is pretty tiny, 34 is about as small as you would want to go.
Wire gauge can be loosely related to a water pipe... A big huge pipe will allow water to flow very freely, this means it has very little resistance, which in electrical terms in measured in Ohms. A little tiny pipe will create a lot more back pressure to push the same amount of water through at the same rate of flow, this little tiny pipe has very high resistance. So, using that analogy, a wire with a lower gauge has a lower resistance than a wire with a higher gauge. Because 33AWG Is pretty small, it has pretty high resistance. Depending on how many times you are wrapping your coil, you could be ending up with a coil with an overall resistance somewhere around 4 Ohms. With 33AWG I probably wouldn't wrap more than 4 times, 5 at the most. Now this is a guess, but 5 should get you around 2.8-3.2 Ohms.
I don't know what type of device you are using, so I am going to assume you are using a device with fixed voltage. Most of these fixed voltage devices have a voltage of 3.7V
At this point, the relationship of voltage, resistance, current, and power all come together. These factors of electricity are all calculated using formulas based on Ohm's Law and Joule's Law. Joule's Law states that Power (Measured in Watts) is equal to voltage squared divided by resistance. I like using this formula over the standard Ohm's Law calculations because it makes it unnecessary for us to determine current. For the purpose of this conversation, we don't NEED to know how much current is being pushed.
What we DO want to know, is how much heat your device is going to create with your custom wrapped coils!
That's where power comes in. Power, or Watts, is directly related to how much heat you will create.
So, if we know the resistance of your coil, and we know how many volts your device is set to, we can easily determine how many watts your coil is burning at using Joule's Law.
A couple of quick examples, all using the assumption that your device is fixed at 3.7V: 3.7 x 3.7 = 13.69, so we will use 13.69 as our Voltage Squared variable.
First, with a custom coil of 4 Ohms: 13.69 / 4 = 3.4225 Watts
and second with a coil of 3 Ohms: 13.69 / 3 = 4.5633 Watts
Now, this is VERY general, but I have heard that most folks like to vape at somewhere between 6 and 9 watts...
What you can see above is that neither a 4 Ohm OR a 3 Ohm coil are going to get us into that range. Both are still going to burn relatively cold at 3.7V. So, in order to get into that 6-9W zone, we need to reduce the resistance of our coil. Using a variant of the formula we used above, we can find out a range of resistance values that will work for us. That formula is resistance = voltage squared divided by power.
So we still use 13.69 (Voltage Squared) and now we plug in our high and low range wattage values that we'd like to reach.
13.69 / 6 = 2.2817 Ohms
13.69 / 9 = 1.5211 Ohms
So, to achieve a burn of 6 watts, we need a resistance of ~2.3 Ohms, and for 9 watts we need a resistance of ~1.5 Ohms
So, if your 33AWG wire, which has a higher resistance, is burning too cool, we need to use a bigger wire. So step it up to 32AWG. 5 wraps of 32AWG kanthal will give you a resistance of ~2 Ohms. This is right in your range! 4 wraps will be a little it less resistance which will burn hotter, and 6 wraps will be a little more resistance which will run cooler.
Hopefully all that makes sense. I can certainly answer any questions you might have! I apologize for the lengthy pot, but I thought it would help you understand the correlations on exactly how Voltage, Power, and Resistance are all working together to achieve that vapor quality you're looking for
I hope it helped! LoL, probably made it worse!
