To get a handle on that, I picked a county in the heart of the eastern corn-belt, Putnam County, Ohio. Putnam County is blessed with fertile (if somewhat clay-ey) soils and generous natural rainfall in most years. There are hundreds of other counties I could have picked but I threw a dart and this is the one it hit.
Here are a few overhead images
|The entire county
|A closer view from somewhere near the center of the county.
Maybe 5% of the land has been intentionally left in woodlots. Darned fine farming country.
One peak was at 1900. Growing industry in Findley and Toledo started pulling the younger people off the farm. Automation both made bigger farms possible and mandatory. That equipment had to be paid off.
In 1890, the ideal farm in Ohio might be 40 acres with 10% of it left in woods for heating and construction material. At one time, the rule-of-thumb for defining an acre was the amount of land that could be plowed by a team of oxen in a day. That means that 36 acres of land would take five weeks of good weather to plow which is way too long to put in a single crop.
Farmers worked around the constraint in several ways. One was to divide their 36 acres into four plots and use a Corn-Oats or Beans-Wheat-forage rotation. The forage was necessary to feed the draft animals and was plowed-down to provide nitrogen for the corn. Instead of having to plow 36 acres in a single go, they only had to plow 9 acres in three separate time-windows.
Another work-around was to use horses or teams of horses. Horses walk faster than oxen and larger teams can pull two plow-shares instead of a single. More animals demand that a larger portion of the farm be dedicated to growing food for the draft animals.
Using our very crude 40 acres-per-farm and six people per household, we come up with a population density =640(acres per square mile)/40 (acres per farm)*6 (people per farm) or 96 people per square mile.
Six people per household was chosen as that is a multi-generational farm, two children, two parents, two grandparents...or a modest sized family in 1900.
The current population density of Putnam County is 74 people per square mile.
One assumption that is buried in the back-of-envelop calculations is that loss of petroleum inputs in agriculture will make the work far more labor intensive and productive agriculture will require many, many times more "farmers" laboring in the fields.
Another piece of background information is that we know much more about nitrogen fixation and the role nitrogen plays in grain yield. If the "target yield" in 1930 was 40 bushels of corn per acre that same field can yield 200 bushels per acre in 2020. The cost of eliminating petroleum or natural gas derived fertilizer is that you could only grow corn one-year-in-four and expect that kind of yield.
Pencil whipping estimates
Let's cut ourselves some slack and estimate
150 bushels-per-acre corn * 9 acres = 1350 bu = $8800 at current prices
50 bushels-per-acre soybeans * 9 acres = 450 bu = $6300
60 bushels-per-acre wheat * 9 acres = 540 bu = $4880
Gross yearly revenue of about $20k.
Gross Calories of human-quality food of about 240M, of which some will be diverted to feeding draft animals (and chickens, pigs and dairy cows). Shipping grain off-farm to feed animals somewhere else interrupts the efficient, on-farm cycling of nutrients.
Obviously this picture is painted with very broad brush-strokes and you can argue the numbers I chose. But it does plant one stake in the ground.