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Is there a mathematical formula between wire size, current, temperature and wire type(Or resistance)?

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closed as off-topic by Olin Lathrop, Daniel Grillo, Leon Heller, Nick Alexeev, Andy aka Feb 17 '14 at 17:56

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Questions on the use of electronic devices are off-topic as this site is intended specifically for questions on electronics design." – Olin Lathrop, Daniel Grillo, Andy aka
If this question can be reworded to fit the rules in the help center, please edit the question.

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    \$\begingroup\$ Please show some effort. Finding some related information shouldn't be hard and it is not clear from your question what EXACTLY you want to achieve. Then come back and ask a specific question about what you have trouble with. \$\endgroup\$ – Rev1.0 Feb 17 '14 at 15:18
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    \$\begingroup\$ en.wikipedia.org/wiki/American_wire_gauge \$\endgroup\$ – Andy aka Feb 17 '14 at 15:23
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Your question is rather broad. Assuming ampacity is what you are interested in determining, normally it is not determined by one formula. A single strand of wire may have a certain allowable current at STP, depending on the insulation and conductor type. That can be derated based on the maximum ambient temperature, maximum altitude, and bundling with other wires. There may be other constraints that have to be satisfied (standards and regulations, voltage drop limits, fuse rating etc).

For example, one might refer to AC 43.13 for aircraft wiring. (Charts are from the FAA regulation)

enter image description here

This would give you a very optimistic ampacity of almost 20A for a normal high performance AWG20 aircraft wire (200°C rated).. That's based on a single wire (not a bundle) at sea level. A 90°C rated PVC wire that has to work at 60°C ambient would be capable of about half that. You might have to derate 25% or 30% for altitude in an aircraft (depending on the aircraft specifications). In a vacuum, a lot more than that.

Then the derating for bundle size:

enter image description here

After all that we might be down to an amp or two for the cheap wire.

In the case of very large wires or high frequencies you may have to take skin effect into account and derate for that.

Here is another reference ( non aircraft).

Note that all constraints must be satisfied for the particular application-- regulatory, voltage drop, mechanical robustness, fuse ratings, etc.

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    \$\begingroup\$ +1 More than the question deserves, but useful for others. \$\endgroup\$ – Russell McMahon Feb 17 '14 at 20:37
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Yes

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