I pondered this for far too long to be honest and this post is the result of my question to find out what a Hill of Beans is actually worth.
P.G. Wodehouse in his 1921 novel "Indiscretions of Archie" from 1921 wrote:
“Here have I been kicking because you weren’t a real burglar, when it doesn’t amount to a hill of beans whether you are or not”.
Perhaps the most famous us of the phrase comes from the 1941 film "Casablanca" in which Rick Blaine (played by Humphrey Bogart) says:
"Ilsa, I’m no good at being noble, but it doesn’t take much to see that the problems of three little people don’t amount to a hill of beans in this crazy world”.
The first question we need to address in finding out what a hill is worth, is to find out what constitutes a hill.
As discussed in the 1995 film "The Englishman Who Went Up a Hill But Came Down a Mountain", a mountain is a hill which is taller than 1000ft; by inference a hill is less than 1000ft.
Interestingly I can't seem to find a common law definition of what a hill is; not even the Ordnance Survey Act of 1841 defines a hill. The definition of a "top" though appears to be "all elevations with a drop of at least 100 feet (30.48m) on all sides and elevations of sufficient topographical merit"
Certainly if you were to create a pile of beans 100 feet tall, that would probably be "of sufficient topographical merit" and so this is the working definition I've chosen.
This was backed up by a comment which I'd recieved on the topic from a forum board:
"It would depend if you are including hillocks in your definition, in which case pretty much any height you like. Exclude hillocks and I'd suggest you're looking at ~100ft / ~33m.
However, the problem you'd face is getting your beans to form a hill shape without a suitable container. They'd naturally tend to form a lake, rather than a hill. So maybe the movie needs to be remade or at the very least re-dubbed with the phrase "lake of beans".
- Dave Brockman, 22nd Jun 11.
This last point was quite instructive I must say. Obviously it stands to reason that if you were to build a hill of beans, you'd want a self-supporting pile.
Experiments with tinned baked beans led me to believe that beans in tomato sauce do react differently depending on how hot the liquid sauce is. In general, the viscosity of a simple liquid decreases with increasing temperature, so it stands to reason that if you're cooking baked beans on a stovetop, they will have a greater propensity to form a lake. Likewise at colder temperatures, baked bean sauce will tend to coagulate.
Fortuneately, the Commission Internationale du Genie Rural or CIGR, has already conducted studies into the shape of a pile that beans take:
Of course you tend to ask "why" such a study needs to be made in the first place.
The answer has to do with bulk handling of cargoes. Bulk handlers of foodstuffs and minerals need to be aware of the shape of piles they build with their bulk cargo; it's also important when building things like silos, railway hoppers and conveyor belts.
The shape of of the cone made by a pile is described by something called the "Angle of Repose". This report from the CIGR indicates that the Angle of Repose for coffee is 35° and for Baked Beans in tomato sauce it's 25°. Always wanting to check my figures I emailed H.J. Heinz Company and SPC Ardmona and they both have confirmed the figure of 25°.
The next question is how much it would cost to build a 100ft pile of beans. Again Dave was rather helpful:
If you were intending to use them for construction rather than sustenance I would suggest that you use Tesco Value, which are 28p for 420g, according to mysupermarket.co.uk
28p/420g works out to be A$1.01348/kg
Interestingly I find this to be the cheapest source of baked banes in the world. Franklins No Frills baked beans which cost 77c for 425g comes to A$1.83333/kg and nowhere in the US, NZ or South Africa, came out as cheap.
The next section involves maths. If you want to skip this bit, then please just scroll down:
To find the radius of the cone requires simple trignometry. A cone can be described as solid formed by a rotating right triangle through 360°.
A/sin a° = B / sin b° = C / sin c°
A/sin 65° = 100 / sin 25°
A = 214.4506920 feet.
Volume of a Cone (the hill of beans) : V = 1/3πr²h
V = 1/3 x π x 100ft² x 214.4506920ft
V = 4,815,968 cubic feet
V = 136,373,027.625L
Beans however are not sold by volume but by weight.
If you assume that beans are not compressible, then if follows that they pack into a tin at the same rate as they would into a pile. After measuring several baked bean tins in the supermarket, I find that the standard baked bean tin is 75mm across and 110mmm tall.
Volume of a Cylinder (a bean tin) : V = πr²h
V = π x (75mm)² x 110mm
V = 154,687.5mm³
V = 0.1546875L for 420g
V = 0.368303514L/kg
This means to say that at 0.368303514L/kg in a volume of 136,373,027.625L there are 50,226,666kg of beans.
At the Franklins rate of $1.83333/kg a Hill of beans would cost:
If the hill was made of Tesco Value at A$1.01348/kg, the Hill of beans costs:
Going back to Rick Blaine's comment in Casablanca that "the problems of three little people don’t amount to a hill of beans in this crazy world" then this is probably true.
Gail Kelly the CEO of Westpac is reportedly on a salary of A$9.5m a year. It is estimated that she has a net worth of A$32.9m.
It probably follows that the problems of three "little" people, ie people of low net worth, don't amount to the value of a Hill of Beans. However if you were to take three people like Wayne Rooney, Michael Schumacher and Gail Kelly, then you might be exceeding the value of a hill of beans.
On reflection a hill of beans is actually worth a considerable amount of money. I wouldn't fancy climbing it though as you'd get Tomato Sauce in your socks.