This is generally a well-known shape though not seen quite so much as it used to be. The traditional barrel was made of wood and was roughly cylindrical in shape except that it 'bulged' outwards in the middle. It was used to transport not only the obvious liquids (water, beer, wine etc.) but also other commodities such as fish and minerals.
It is a very good design for a container, being very strong and staying water-tight even with the most robust handling, yet surprisingly easy to move around.
If the dimensions are put in dm (decimetres) then the volume will be in litres (=cubic decimetres). If the dimensions are given in cm (centimetres) then the volume will have to be divided by 1000 to get it in litres.
Remember that if the outside dimensions are taken (and they are the easiest to get) due allowance must be made for the thickness of the wood before trying to work out the volume of the contents.
Limits on Proportion
The traditional barrel has a middle diameter (D) which is about 1.25 times its end diameter (d), and a height (h) of just less than 1.5 times d
In this calculator limits have been set which range a little beyond that.
D can equal d (a cylinder) but must be less than 3d
h can equal d but must be less than 6d or 2D
These limits have been chosen quite arbitrarily to allow room for experiment.
Appropriate messages will be given if these limits are exceeded.
Another very good reason for having such limits is that the formula used to find the volume, though very close, can only ever be an approximation since the exact shape of the curve is not defined, and the further away the proportions get from a 'real' barrel, then the more the volume will be in error.