I am speaking just from experiences with random objects as well as coins. Certainly the density of an object in comparison to the density of the substance it is suspended in has a large determination factor as to how far it will sink and how fast. However, other factors such as displacement mass against the substance is also a factor. The reason an aircraft carrier floats is because it weighs less than the same amount of water it is displacing. It achieves this by massive displacement at the surface supporting the great weight above that initial or contact displacement.
Soil is nothing more than an atmosphere just as water is an atmosphere. If a coin falls and lays flat depending on the desity and displacement area of the coin it will sink in accordance with those factors placed against the soil atmosphere or density. Weather a coin sinks on edge or flat would be determined by the its placement upon impact as well as the input of the numerous obstructions it may hit on the way down ( rocks, roots, twigs, leaves, density changes, etc, etc.) In simple terms a coin falling flat may sink on edge if it hit the right obstructions and a coin which falls and land on edge may level and flatten due to the same forces. The possibilities are to great to calculate and there is no constant to use because each coin that falls lands in different soil with different specific placement, obstructions, density as well as outside factors such as rain soaking, frost upheaval etc.
In water which is not obstructed by rocks, twigs, roots, leaves etc., a sink factor can be determined using the constant of the unobstructed water density. Soil has too many interactive factors of obstruction and a coins density and mass determining it must sink is played against these factors. It may be a silver dollar with a large mass but if its weight is saying it must sink the angle of least resistance in an inconsistent or consistent atmosphere will ask it to edge itself and drop or slide at an angle. Example.. when a ship sinks in open water does it simply stay flat and sink or does it turn on end or roll over.... here in lies part of your answer.
So, the simplest reply to your question is that each case is different and it is more likely a coin will sink on edge or at an angle than it would be to sink flat, honestly you will never know as no lab test could take into account all the factors of all the soil conditions which in most cases are idiosyncratic... (specific to that one spot of soil) Just like a ship in water, once a coin hits its specific density equal or better it will stop sinking and at that point with time it may level out or flatten but again there are many factors unseen and unknowable....
Experiment... Take a 5 gal bucket filled with water and place a jar cover on the water. Fill the jar lid with water until it sinks and watch what it does. Do the same with a coin. Place it flat on the water surface, let go and watch it sink. Both jar cover and coins should flip and flop on their way down as would a coin in soil only with many, many more obstruction factors.
Don
