Electrical – PCB trace size for pulsed current

If F1 and K1 are through hole parts, you could put two tracks in parallel, one on each side of the board. Each track would be roughly 10 - 15 mm wide.

Another option, Don't draw the connection as a track but as a polygon or fill. Most of the current will still follow close to the shortest path, but the added area will help to dissipate heat.

Also, be aware that for such short distances, the current crowding to get to the individual pins of your components may dominate the overall resistance of the connection. Using larger holes (requiring components with larger leads) will help with this.

Edit

First, I'm not sure how this plays in, but this ampacity table claims a 0.25 inch trace in 2 oz copper is sufficient to carry 24.5 A with 30 C temperature rise. This is about 1/4 of the number you are coming up with (25 mm). Unfortunately the source is not clear about what assumptions went into their calculations.

Second, the math you added in your edit looks fine.

As you see, increasing the copper area allows you to dissipate more heat. There's no reason you should only increase the area by increasing the trace width. You can simply create a large copper area of whatever shape is convenient the closer to a simple square or circle, the better), so long as it connects your input and output, and the heat will spread readily to allow dissipation over the whole area (with, of course, some concentration in the region where the heat is actually being generated).

Third, no back of the envelope calculation is likely to be especially accurate for these kinds of thermal estimates. If you really want to get a good estimate, you should look into a thermal analysis tool like FloTherm or Ansys IcePak. These tools will both improve the ability to estimate convection effects accurately, and take into account "edge effects" that come into play because your "trace length" is so much shorter than your "trace width".

Ultimately this is a question of when the FR4 will reach maximum specified temperature of 135 degrees C given an etch dimension and current.

The only analytical equation (that I've seen) that addresses time of heat rise of conductor given a current is the Onderdonk equation. The equation is meant to cover heat rise to fusing temp (copper is 1083C). You can find a write up about it here on the ultracad site.

I = \$\frac{A \sqrt{\frac{\log \left(\frac{T_m-T_a}{T_a+234}+1\right)}{t}}}{\sqrt{33}}\$

or turned around:

\$t_{\text{fuse}}\$ = \$\frac{A^2 \log \left(\frac{T_m-T_a}{T_a+234}+1\right)}{33 \text{ I}^2 }\$

where A is circular mils, temperatures are in degrees C, and time is seconds.

Be aware that the Onderdonk eq was written to estimate the time to fusing wire in air for a given current, not etch on a PCB. Looking at its structure, it appears to consider only thermal conduction through the cross sectional area of the conductor (I don't see any surface area). It is probably not accurate for times longer than 5 or 6 seconds, indeed for a long enough time zero current will reach \$T_m\$.

Using the second form of the equation, 20Amps through a 50mil by 5.6mil etch would reach fusing temp in about 7 seconds and would reach \$T_m\$ of 135C in about 1.5 seconds. These times seem shorter than expected.

It's a difficult problem and the thermal paths can have widely differing boundary conditions, limiting analytical solution region of usefulness. You may get the best estimates by building some test boards and measuring.

Note: In my comment I mentioned a freeware tool at ultracad to calculate heat rise, but now see that it is no longer freeware.