Wiring from garage panel to welder

NEC 630.11(A) may be of interest.

National Electric Code 2008

ARTICLE 630 Electric Welders

II. Arc Welders

630.11 Ampacity of Supply Conductors.

(A) Individual Welders. The ampacity of the supply conductors shall be not less than the I1eff value on the rating plate. Alternatively, if the I1eff is not given, the ampacity of the supply conductors shall not be less than the current value determined by multiplying the rated primary current in amperes given on the welder rating plate by the factor shown in Table 630.11(A) based on the duty cycle of the welder.

Also take a look at 630.12 Overcurrent Protection.

The Owners manual (PDF) seems to contain the answer.

Wiring from service panel to sub panel

If we look at 110.14(C) in 2008 NEC, it says:

National Electrical Code 2008

ARTICLE 110 Requirements for Electrical Installations

I. General

110.14 Electrical Connections.

(C) Temperature Limitations. The temperature rating associated with the ampacity of a conductor shall be selected and coordinated so as not to exceed the lowest temperature rating of any connected termination, conductor, or device. Conductors with temperature ratings higher than specified for terminations shall be permitted to be used for ampacity adjustment, correction, or both.

Which means we'll have to check the breakers temperature rating, and the subpanel terminals temperature rating. Then we'll have to look at table 310.16 (Table 310.15(B)(16) NEC 2011), so we can determine the wire size we should use.

In this example image you can see if we're using copper, we'll use 60°C. Once we look at the table, we'll see that for 50A @ 60°C we need 6 AWG copper wire. (50A @ 75°C = 8 AWG).

110.14(C)(1)(a) basically says that if the temperature is not listed, use 60°C for circuits less than 100A. 110.14(C)(1)(b) says if the temperature is not listed, use 75°C for circuits over 100A. However, in the real world 75°C is often used for both.

I believe that it would be against the NEC to have these two seperate circuits with a shared neutral and not have them on a double pole breaker (or at the very least a handle tie between a 15A and a 20A breaker).

Branch Circuit, Multiwire. A branch circuit that consists of two or more ungrounded conductors that have a voltage between them, and a grounded conductor that has equal voltage between it and each ungrounded conductor of the circuit and that is connected to the neutral or grounded conductor of the system

210.4 Multiwire Branch Circuits. (B) Disconnecting Means. Each multiwire branch circuit shall be provided with a means that will simultaneously disconnect all ungrounded conductors at the point where the branch circuit originates.

A double pole breaker will simultaneously disconnect both circuits and satisfy the code requirement.

20A breaker is required and 12 gauge copper 10 gauge aluminum is the minimum depending on how long the circuit run is.

Furthermore even if it is on a 20A circuit, you are not required to upgrade your 15A outlets to 20A outlets. This is only required if there exists a single receptacle on the circuit. One can only plug in 15A max devices into a 15A outlet, therefore the 20A load circuit load would not be achieved on a single device.

It might also be a code requirement now for a detached building to have its own grounded sub-panel as well but that I will have to look into.