The short and sweet: Due to the resistance difference of kanthal and nickel, the dna 40 device will need to be set lower than the wanted temp.
To achieve 410 F, with 32 (or 30) gauge nickel and kanthal, set temp to 340 F. Using 30 gauge Ni and 32 gauge Kanthal, set to 370 F (best match I found)
Now the ugly math part
Table 1, Used to calculate Ω's per inch. Data from Steam Engine | free vaping calculators
Table 2, Calculates the increased length(resistance is proportional) of wire when twisted (forms a helical)
Multiply the straight wire resistance by the correction factor.
Formula from Math Forum - Ask Dr. Math
Table 3, coil parameters that I typically wind, gives me a realistic wire length.
Data obtained from Steam Engine | free vaping calculators
Table 5, Data from http://www.specialmetals.com/documents/Nickel 200 & 201.pdf
Handy values for Nickel 200 at various temperatures
cmf is circular mil foot, circ mil = 0.001". Keeping cmf constant, the Ω cmf is the resistance change due to temperature. The ratio from the 70/200/400/600 data points forms the cardinal resistances in the table below for 32 AWG Single Ni. Interpolation fills the rest of that column. The 32 AWG Twisted Ni gets it's factor increase from table 2, at 15 turns per inch, 1.067872 times the single resistance. Yeah, I know the factor does change somewhat when mixing 32/30/28 gauge in the twist, but I don't think it's enough to make much of a change on the final results.
The Single K Ω comes from the single Ni length (table 3) times it's Ω per inch (table 1). Twisted K Ω from single times the same factor used for single Ni (1.067872). K (kanthal) resistance stays fairly constant in the 70-600 F range.
The ## Ni ## K Total Ω = ## Twisted Ni Ω times ## Twisted K Ω divided by sum of ## Twisted Ni and K (Parallel resistance formula).
Setting dna 40 device for left-most column temp, found under "Set device temp". Example: want temp of 410 F, set DNA 40 device to 340 F (for 32 AWG twisted Ni/K).
For 32 gauge Ni wire
For 30 gauge Ni wire
It's interesting to note that 30 gauge Nickel and 32 gauge Kanthal twisted, gets the smallest correction factor to the DNA 40 setting. Makes sense, as in parallel resistances, as the larger value gets further away from the smaller resistance, the less effect it has on the total resistance.
Well, there you have it. Most likely there are some mistakes here, I've tried my best. I did make some measurements on wire resistance, single and twisted and they did come out in the ballpark of instrument accuracy. Only thing I didn't have was a thermal gun to check actual generated temperatures.
That's it, thanks for your time.
To achieve 410 F, with 32 (or 30) gauge nickel and kanthal, set temp to 340 F. Using 30 gauge Ni and 32 gauge Kanthal, set to 370 F (best match I found)
Now the ugly math part
Table 1, Used to calculate Ω's per inch. Data from Steam Engine | free vaping calculators
AWG | Wire Dia | Inches K | Ohms K | Ω/" K | Inches Ni | Ohms Ni | Ω/" Ni |
28 | 0.01264 | 6.596 | 3 | 0.45482 | 6.642 | 0.2 | 0.03011 |
30 | 0.01003 | 6.914 | 5 | 0.72317 | 6.266 | 0.3 | 0.04788 |
32 | 0.00795 | 6.957 | 8 | 1.14992 | 6.567 | 0.5 | 0.07614 |
Table 2, Calculates the increased length(resistance is proportional) of wire when twisted (forms a helical)
Multiply the straight wire resistance by the correction factor.
Formula from Math Forum - Ask Dr. Math
Turns/" | 28 AWG | 30 AWG | 32 AWG |
10 | 1.075958 | 1.048470 | 1.030717 |
12 | 1.107731 | 1.069101 | 1.043947 |
15 | 1.163956 | 1.106074 | 1.067872 |
20 | 1.277006 | 1.182014 | 1.117816 |
24 | 1.381403 | 1.253756 | 1.165890 |
Table 3, coil parameters that I typically wind, gives me a realistic wire length.
Data obtained from Steam Engine | free vaping calculators
AWG | 30 | 32 |
T ohms | 0.2 | 0.3 |
Coil ID | 0.125 | 0.125 |
Leads | 0.197 | 0.197 |
T Length | 4.177 | 3.94 |
# Turns | 8.73 | 8.46 |
Table 5, Data from http://www.specialmetals.com/documents/Nickel 200 & 201.pdf
Handy values for Nickel 200 at various temperatures
Deg F | Ω cmf |
0 | 48 |
70 | 58 |
200 | 76 |
400 | 113 |
600 | 164 |
800 | 204 |
cmf is circular mil foot, circ mil = 0.001". Keeping cmf constant, the Ω cmf is the resistance change due to temperature. The ratio from the 70/200/400/600 data points forms the cardinal resistances in the table below for 32 AWG Single Ni. Interpolation fills the rest of that column. The 32 AWG Twisted Ni gets it's factor increase from table 2, at 15 turns per inch, 1.067872 times the single resistance. Yeah, I know the factor does change somewhat when mixing 32/30/28 gauge in the twist, but I don't think it's enough to make much of a change on the final results.
The Single K Ω comes from the single Ni length (table 3) times it's Ω per inch (table 1). Twisted K Ω from single times the same factor used for single Ni (1.067872). K (kanthal) resistance stays fairly constant in the 70-600 F range.
The ## Ni ## K Total Ω = ## Twisted Ni Ω times ## Twisted K Ω divided by sum of ## Twisted Ni and K (Parallel resistance formula).
Setting dna 40 device for left-most column temp, found under "Set device temp". Example: want temp of 410 F, set DNA 40 device to 340 F (for 32 AWG twisted Ni/K).
For 32 gauge Ni wire
32 AWG | 32 AWG | 28 AWG | 28 AWG | 30 AWG | 30 AWG | 32 AWG | 32 AWG | 32 Ni | Set | 32 Ni | Set | 32 Ni | Set | |
Deg F | Single Ni | Twisted Ni | Single K | Twisted K | Single K | Twisted K | Single K | Twisted K | 28 K | device | 30 K | device | 32 K | device |
Ω | Ω | Ω | Ω | Ω | Ω | Ω | Ω | Total Ω | temp | Total Ω | temp | Total Ω | temp | |
70 | 0.300 | 0.320 | 1.792 | 1.914 | 2.849 | 3.043 | 4.531 | 4.838 | 0.274 | 0.290 | 0.300 | |||
200 | 0.393 | 0.420 | 1.914 | 3.043 | 4.838 | 0.344 | 0.369 | 0.386 | ||||||
210 | 0.403 | 0.430 | 1.914 | 3.043 | 4.838 | 0.351 | 0.377 | 0.395 | ||||||
220 | 0.412 | 0.440 | 1.914 | 3.043 | 4.838 | 0.358 | 0.385 | 0.404 | ||||||
230 | 0.422 | 0.450 | 1.914 | 3.043 | 4.838 | 0.365 | 0.392 | 0.412 | ||||||
240 | 0.431 | 0.461 | 1.914 | 3.043 | 4.838 | 0.371 | 0.400 | 0.421 | ||||||
250 | 0.441 | 0.471 | 1.914 | 3.043 | 4.838 | 0.378 | 0.408 | 0.429 | ||||||
260 | 0.451 | 0.481 | 1.914 | 3.043 | 4.838 | 0.384 | 0.415 | 0.438 | ||||||
270 | 0.460 | 0.491 | 1.914 | 3.043 | 4.838 | 0.391 | 0.423 | 0.446 | ||||||
280 | 0.470 | 0.502 | 1.914 | 3.043 | 4.838 | 0.397 | 0.431 | 0.454 | ||||||
290 | 0.479 | 0.512 | 1.914 | 3.043 | 4.838 | 0.404 | 0.438 | 0.463 | ||||||
300 | 0.489 | 0.522 | 1.914 | 3.043 | 4.838 | 0.410 | 0.446 | 0.471 | ||||||
310 | 0.498 | 0.532 | 1.914 | 3.043 | 4.838 | 0.416 | 0.453 | 0.479 | ||||||
320 | 0.508 | 0.542 | 1.914 | 3.043 | 4.838 | 0.423 | 0.460 | 0.488 | ||||||
330 | 0.518 | 0.553 | 1.914 | 3.043 | 4.838 | 0.429 | 0.468 | 0.496 | ||||||
340 | 0.527 | 0.563 | 1.914 | 3.043 | 4.838 | 0.435 | 0.475 | 0.504 | ||||||
350 | 0.537 | 0.573 | 1.914 | 3.043 | 4.838 | 0.441 | 220 | 0.482 | 260 | 0.512 | 290 | |||
360 | 0.546 | 0.583 | 1.914 | 3.043 | 4.838 | 0.447 | 230 | 0.489 | 270 | 0.521 | 300 | |||
370 | 0.556 | 0.593 | 1.914 | 3.043 | 4.838 | 0.453 | 230 | 0.497 | 280 | 0.529 | 310 | |||
380 | 0.565 | 0.604 | 1.914 | 3.043 | 4.838 | 0.459 | 240 | 0.504 | 280 | 0.537 | 310 | |||
390 | 0.575 | 0.614 | 1.914 | 3.043 | 4.838 | 0.465 | 240 | 0.511 | 290 | 0.545 | 320 | |||
400 | 0.584 | 0.624 | 1.914 | 3.043 | 4.838 | 0.471 | 250 | 0.518 | 300 | 0.553 | 330 | |||
410 | 0.598 | 0.638 | 1.914 | 3.043 | 4.838 | 0.479 | 260 | 0.528 | 310 | 0.564 | 340 | |||
420 | 0.611 | 0.652 | 1.914 | 3.043 | 4.838 | 0.486 | 270 | 0.537 | 310 | 0.575 | 350 | |||
430 | 0.624 | 0.666 | 1.914 | 3.043 | 4.838 | 0.494 | 270 | 0.547 | 320 | 0.586 | 360 | |||
440 | 0.637 | 0.680 | 1.914 | 3.043 | 4.838 | 0.502 | 280 | 0.556 | 330 | 0.597 | 370 | |||
450 | 0.650 | 0.695 | 1.914 | 3.043 | 4.838 | 0.510 | 290 | 0.565 | 340 | 0.607 | 380 | |||
600 | 0.848 | 0.906 | 1.914 | 3.043 | 4.838 | 0.615 | 0.698 | 0.763 |
For 30 gauge Ni wire
30 AWG | 30 AWG | 32 AWG | 32 AWG | 30 AWG | 30 AWG | 28 AWG | 28 AWG | 30Ni/32K | 30Ni/30K | 30Ni/28K | ||||
Single Ni | Twisted Ni | Single K | Twisted K | Single K | Twisted K | Single K | Twisted K | Total Ω | Total Ω | Total Ω | ||||
70 | 0.194 | 0.217 | 4.659 | 5.208 | 2.930 | 3.276 | 1.843 | 2.060 | 0.208 | 0.203 | 0.196 | |||
200 | 0.254 | 0.284 | 4.659 | 5.208 | 3.276 | 2.060 | 0.269 | 0.261 | 0.250 | |||||
210 | 0.260 | 0.291 | 5.208 | 3.276 | 2.060 | 0.276 | 0.267 | 0.255 | ||||||
220 | 0.267 | 0.298 | 5.208 | 3.276 | 2.060 | 0.282 | 200 | 0.273 | 0.260 | |||||
230 | 0.273 | 0.305 | 5.208 | 3.276 | 2.060 | 0.288 | 200 | 0.279 | 0.266 | |||||
240 | 0.279 | 0.312 | 5.208 | 3.276 | 2.060 | 0.294 | 210 | 0.285 | 200 | 0.271 | ||||
250 | 0.285 | 0.319 | 5.208 | 3.276 | 2.060 | 0.300 | 220 | 0.290 | 210 | 0.276 | ||||
260 | 0.291 | 0.326 | 5.208 | 3.276 | 2.060 | 0.306 | 230 | 0.296 | 220 | 0.281 | 200 | |||
270 | 0.298 | 0.333 | 5.208 | 3.276 | 2.060 | 0.313 | 240 | 0.302 | 230 | 0.286 | 200 | |||
280 | 0.304 | 0.339 | 5.208 | 3.276 | 2.060 | 0.319 | 250 | 0.308 | 230 | 0.291 | 210 | |||
290 | 0.310 | 0.346 | 5.208 | 3.276 | 2.060 | 0.325 | 260 | 0.313 | 240 | 0.297 | 220 | |||
300 | 0.316 | 0.353 | 5.208 | 3.276 | 2.060 | 0.331 | 270 | 0.319 | 250 | 0.302 | 220 | |||
310 | 0.322 | 0.360 | 5.208 | 3.276 | 2.060 | 0.337 | 280 | 0.325 | 260 | 0.307 | 230 | |||
320 | 0.328 | 0.367 | 5.208 | 3.276 | 2.060 | 0.343 | 290 | 0.330 | 270 | 0.312 | 240 | |||
330 | 0.335 | 0.374 | 5.208 | 3.276 | 2.060 | 0.349 | 290 | 0.336 | 280 | 0.317 | 250 | |||
340 | 0.341 | 0.381 | 5.208 | 3.276 | 2.060 | 0.355 | 300 | 0.341 | 280 | 0.322 | 250 | |||
350 | 0.347 | 0.388 | 5.208 | 3.276 | 2.060 | 0.361 | 310 | 0.347 | 290 | 0.326 | 260 | |||
360 | 0.353 | 0.395 | 5.208 | 3.276 | 2.060 | 0.367 | 320 | 0.352 | 300 | 0.331 | 270 | |||
370 | 0.359 | 0.402 | 5.208 | 3.276 | 2.060 | 0.373 | 330 | 0.358 | 310 | 0.336 | 270 | |||
380 | 0.366 | 0.409 | 5.208 | 3.276 | 2.060 | 0.379 | 340 | 0.363 | 310 | 0.341 | 280 | |||
390 | 0.372 | 0.416 | 5.208 | 3.276 | 2.060 | 0.385 | 350 | 0.369 | 320 | 0.346 | 290 | |||
400 | 0.378 | 0.422 | 5.208 | 3.276 | 2.060 | 0.391 | 350 | 0.374 | 330 | 0.351 | 300 | |||
410 | 0.386 | 0.432 | 5.208 | 3.276 | 2.060 | 0.399 | 370 | 0.382 | 340 | 0.357 | 310 | |||
420 | 0.395 | 0.442 | 5.208 | 3.276 | 2.060 | 0.407 | 380 | 0.389 | 350 | 0.364 | 310 | |||
430 | 0.404 | 0.451 | 5.208 | 3.276 | 2.060 | 0.415 | 390 | 0.396 | 360 | 0.370 | 320 | |||
440 | 0.412 | 0.461 | 5.208 | 3.276 | 2.060 | 0.423 | 400 | 0.404 | 370 | 0.376 | 330 | |||
450 | 0.421 | 0.470 | 5.208 | 3.276 | 2.060 | 0.431 | 410 | 0.411 | 380 | 0.383 | 340 | |||
600 | 0.549 | 0.613 | 5.208 | 3.276 | 2.060 | 0.549 | 0.516 | 0.473 |
It's interesting to note that 30 gauge Nickel and 32 gauge Kanthal twisted, gets the smallest correction factor to the DNA 40 setting. Makes sense, as in parallel resistances, as the larger value gets further away from the smaller resistance, the less effect it has on the total resistance.
Well, there you have it. Most likely there are some mistakes here, I've tried my best. I did make some measurements on wire resistance, single and twisted and they did come out in the ballpark of instrument accuracy. Only thing I didn't have was a thermal gun to check actual generated temperatures.
That's it, thanks for your time.