Cooperman's 22x22 is probably pretty close. It's probably copied off of an Elizabethan original that survives. There a a couple of these drums surviving from the 17th century, and there are engravings of drummers playing through which the relative size of the drums can be guessed at. Hugh Barty-King's book is probably the best source for information and pictures from that period. heck, even the fifes were bigger, looking more like flutes. In fact, upon the re-recapturing of Manhattan from the Dutch in 1673, the English "Entered the town with their trumpets trumpeting, their fluters fluting, and drummers drumming". The Farmington Drum Irishbrit told us about some time ago was 24 1/2 wide by 19 1/2 deep.
 
As for the Rev War, contemporary engravings and paintings are really the best source for documenting drum size (and sling type, for that matter). Most are British, and most look to be around 16x16, if not a little smaller.
 
Continental "Revolutionary War" drums pose the problem of documentation. This was before academicians, historians and museum curators establish policies and practices for proving claims of origin. Most of the Rev War drums I've seen base their alleged origin on tenuous family claims. Often, it's the wording of the claim that's important. When selling it, the family may say "This belonged to our great-great-great-grandfather, who was a drummer during the Revolution. That may be true, but he may have obtained it in 1810.
 
Of the well-documented Continental drums I've seen, I haven't seen much in the way of standardization. One in the Smithsonian is 14" wide and 18" long. Some are 18x18. One claimed to have been carried under General Lincoln was 16x16, but its construction looked too 19th century to me. Plus, someone had "restored" it with dacron rope, huge leather ears and plastic heads, which made it hard to date it as well.
 
As for the early 19th century, here are the US Quarter Master / Purveyors specifications of February 1812 detailing the construction of US drums. I have an 1821 16x16 made by Abner Stevens, He sold drums made to these specifications to the US army:

Diameter of the Shell from 15 ¾ to 16 Inches made of white oak with 7 Inch Cap [sic],  79 brass nails, depth from 14 ½ to 15 Inches,  about 1/8 Inch thick

 

Brace hoops 1 ¾ Inches deep & 3/8 Inches thick made of hicory, rounded on the top, flesh hoops 1 7/8 Inches wide & full ¼ Inches thick, made of hicory.

Inside hoops ¼ Inchs wide full ¼ Inches thick

Batter head Calfskin, Snare head Sheep skin, Snares made of Sheeps gut well finished.

 

Cord 11 ¼ yards long well finished

 

10 Braces 6 ½ Inches long, 1 7/8 Inches wide

 

Drum Carriage 1 ¼ Yards white worsted web 1 ½ Inches wide finished with leather & button.

 

Drum Sticks 18 Inches long of heavy west India wood,

 

Osnabrig [osnaburglinen] Cases made to draw with a Small cord of hemp or flax.

So 16x16 was probably the most popular size for the typical drum maker, and surviving Mexican War US regimental drums show 16x16 was the government standard by then. But you also had big drums still out there, like Eli Brown types.

 

Drums started to shrink during the Civil War, when the width really started to exceed the length. This was taken to extremes after the war, when the so-called "piccolo drums", as short as 4 inches high, became popular. I think Sue once said that in the early 20th century, Moeller started making the Ancient New England drums really long again, as a reaction to the tiny picollo drums.

 

Unfortunately, those "stretch drums" were still the rage when people started reenacting the Revoultionary and Civil Wars, and that's what reenactors initially brought into the field. It's improved though in the last twenty years, as drum makers started catering to reenactors rather than ancients. I still remember the time I asked Patty Cooperman to make me sticks without the rings around them, and he said "Why would you want to do that?"

 

By the way, all these measurements I mention are the complete drum, not just the shell. I know many people today refer only to shell sizes.