3 gods rotted shots and the wife and I still came down with the plague! The other two daughters are on their own when they get married! 
good horse, look back a page or two and you will find a lot of the information you need. From there you will know enugh to be ignorant, and we can really get down to helping you out. 

How do I determine the width of the side draft firebox and the depth?

When you say fire box are you referring to the hearth or the actual hole the fire sits in?

yes home

 

Charles R. Stevens- how has your fire pot been holding up?

I am thinking of a similar design, but I only have anthracite available and a hairdryer as an air source. 

In your opinion would half inch mild steel last in the shape that you welded up your fire pot?

1/2" is probably going to be just fine. Regardless of the fuel, you're not going to be working the fire hotter with a side blast than you would with a bottom blast.

Have you read the Recommendations for Working with Anthracite article?

48 minutes ago, FrancoisVDH said:

a hairdryer as an air source

While the constant blast from a hairdryer is beneficial for an anthracite fire (which goes out without a steady supply of air), you do want to be able to adjust the volume of air. There are a couple of good methods mentioned in this comment.

Yes, did read both those articles. Especially the Anthracite one. Only coal available and because it doesn't smoke as much it works well for me.

The pot has held up fine to both andracite and charcoal. I would use a larger tuyere for the hair dryer necked down just before it enters the pot. The 5deg down slope pushes the center of the fire away from the tuyere. The wall gets hot otherwise. 
what hasn’t held up is the bricks, which melt them acasinaly 

Well, I spent the night modifying my bottom blast to a side blast, also changed my air control to pipe fittings with a valve etc.

Firstly, I love the side draft even without a water cooled tuyere. Works really well for the little time I spent forging tonight.

With the better air control I could forge significantly longer using a lot less coal than before. Thank you to everyone sharing their knowledge and experience, have been reading the forums for the past 3 years and it has been a tremendous help.

Bottom blast and side blast is where the air enters the forge, either from the bottom of the fire or the side of the fire.

 

Side draft is where the smoke enters the chimney, from the top and side of the fire.

So just an update from my side. The side blast has been working well even with my screwed up fabricating. Air hole came in at roughly 16-20mm, was supposed to be 1 inch but after breaking the drill bit I left it as is.
Depth of the fire pot is about 3 inches above the air inlet, and just shy of two inches below the air inlet.
Air source is a hair dryer, but tuned up or down with a ball valve and overflow dumped up the chimney.
So far I struggle to get to a neutral flame unless I go almost full bore on the air and mound up the coal quite high. 
Had a similar issue when the forge was bottom blast for those wondering.
What I can say is that my anthracite does tend to coke up a bit and becomes sticky when running on very high air, and with the side blast I can "stir" the whole fire pot and the clinker pools easier at the bottom.
Side note - I have to stir my anthracite fire every half hour or so otherwise it forms a dense "cake" at the bottom that eventually blocks off the airflow. No idea why this happens, but it is easier to break up on the side blast configuration for me.