My opinion follows:
On a beach with normal large silica grains and much percolating water, a coin should mix downward into the sand until either there is no more mixing forces or the density is approximately balanced to the surrounding matrix. That could be 14 inches or more, to the point it is beyond detection. In this scenario it doesn’t matter the coin age as the mixing action is rapid, a matter of hours, days, or perhaps seasons. If soil grains are small and/or the soil is not as wet as at the beach, or the soil matrix contains many buried pebbles/rocks, then the final depth of a sinking artifact would not be as great (less mixing and more resistance) and take longer (slower vertical movement).
In nearly any soil, in the wet season, coins should likewise mix downward, at least into the root zone by physical processes (that is, precipitation, foot or animal traffic, wind action, lawnmowers, ground vibrations). A coin should mix downward 1-3 inches after one or two rainy seasons assuming a supporting root system or humus base (offering some resistance). Depending on the soil density (compactness) and its porosity/permeability to vertical water transport and/or propensity to being disturbed, a coin dropped in a field will be displaced downward to a point by the pull of gravity and should go no further. There is evidence that coins are often found deeper than would be expected by mechanical processes alone - that another action is at work, perhaps at random, altering the soil matrix enough to allow gravity to work the coin deeper.
I’d submit that there is a more significant action going on unnoticed in almost all soil matrixes. In a word, relics descend deeper or in some cases are brought back toward the surface by a nifty biological action – namely, unseen critters in the soil.
It may be hard to believe their effectiveness, but earthworms, ants, and rodents work overtime to mix the soil, and in the process transport coins/artifacts down deeper into the soil. Burrowing animals displace large objects downward, and can carry smaller object upward to the surface. So, we have to consider not only mechanical but biomechanical soil turnover, as I suspect these are the prime redistributors of buried objects in the soil.
Bioturbation is a real and moderately rapid effect (over the span of years). Once an artifact hits the ground it is subject to downward transport as well as deposition of soil over it. A 1994 study with a single earthworm found that after two years mammal bones had been vertically displaced downward 9 inches and laterally by six inches by the worm. Large rodents like gophers work hard to redistribute soil matrixes and tend to move smaller objects (1-2” in diameter) through their burrowing efforts toward the surface. Rodent activity can also bury surface objects under excavation mounds which can raise the ground surface. Their tunneling work can mix artifacts into the soil down to a working depth of 2 feet or more.
Likewise, earthworms working in the soil will cause deposited coins to sink further than expected by density alone. The mechanics of breaking apart the soil and the biological action of mound building by rodents, ants, and earthworms can cause artifacts to be buried deeper without raising the level of the ground, though deposition of soil can raise the ground level. The artifact depth finally obtained through bioturbation depends upon the depth mixed by these soil critters, their relative abundance, and the time allowed. It is estimated that surface soil can be completely mixed downward by gopher-action within about seven years or less.
Through the soil movement of earthworms and ants alone it is estimated that the first six inches of soil is mixed and displaced every fifty years or more. Earthworms move dirt to the surface at the estimated rate of about 0.10 to 0.40 inches per year. Rodent activity has been measured to bury artifacts at a rate of as much as 2.2 inches per 100 years. One study found that within seven years, artifacts on the surface had become buried by zooturbation (critter action) to a depth of about one inch.
The net effect of this burial and mixing is to redistribute coins and other artifacts further down into the soil. Rodent tunneling can stratify objects based not on density but rather by activity zones, such that one study found a relic settling depth of 8 inches and another at about 20 inches, corresponding to two levels of gopher burrowing activity. Smaller artifacts tend to be moved toward the surface (smaller than the rodent tunnels) and larger artifacts tend to mix downward thus creating separate zones sorted by size.
Other phenomenon was observed in which objects are buried without mixing. A layer of lime was laid down on a grassy field followed six years later by a layer of coal cinders. Ten years later a trench dug into the soil found the lime 3 inches deep into the ground and the coal layer was 1 inch beneath the surface, all still with the layers stratified. Thus layers moved downward into the soil and were buried as a layer, without mixing. This is the process by which buried artifacts of older cultures can be found beneath younger cultures, though mixing does and can occur.
The upshot is, artifacts and coins will sink both due to gravity acting through a water leached soil medium and by mechanical mixing such as from farming, wind deposition, frost heaving (that is, water layer at some depth freezes and expands thus forcing soil above it upward and soil beneath it downward. The ice layer (called an ice lens) can grow larger with capillary movement of liquid water from below, the net displacement upward can be significant enough to break pavement and lift the soil into mounds), tree uprooting, soil creep (down slope), foot or vehicle traffic, and further by bioturbation from rodents, ants, earthworms and the like that bury surface objects but also force deeper into the soil root-level artifacts, notably by mixing larger objects downward and smaller objects toward the surface.
I'd estimate that it would then be correct to expect coins dropped 50 years ago to be deeper than a coin dropped 10 years ago - all things being equal. If critters are present, and they usually are, energy is being expended that will mix the coin deeper - unless otherwise impeded. The actual sinking depth is likely only to be consistent within similar soil matrixes and with similar critter mixing actions and at similar critter working depths. What constitutes the final relic depth is going to be localized to the area in the proximity of the find, where soil variables that hinder/enhance vertical movement are generally similar and critter activity is about the same. With so many variables working in a dynamic soil, it should not be surprising if younger coins are located deep in the ground and older coins are found near the surface, or both are found at the same level. Which was the predominate force: was it the action of earthworms and gophers or was it the internal soil consistency and available leaching action of water that caused the final coin depth. Likely it was a combination of influences that over time acted in conjunction with gravity on the coin - but you'd be hard pressed to determine the culprit that put that Barber dime only 2 inches beneath the surface and that clad coin at 7 inches. Varying soil conditions and critter workings combine in unique and differing ways that makes predicting the final resting place of coins and relics more complicated than one might first assume.
Jack