State border properties

When a micronation or every other country in the world declares itself independent from another country, it is likely it will have to defend its claimed territory to protect its sovereignty somewhere in the (near) future. Many conflicts in the past are an example of this urge to guard the homeland from trespassers. The following two chapters describe two very simple formulas to calculate two numbers that give a careful and theoretical idea of how easy it will be to defend a given territory.

Inaccessibility index

The first question one could ask, and therefor calculate is “how simple is it to cross nation X’s borders?”. More specifically this means: how accessible is country x for cars and other motorized vehicles? Cars and roads are important because it is by far the most efficient and fastest way to transport people, materials, etc… However, more access points to a country also means more personnel or even troops to control them thoroughly (unless you signed the Schengen treaty). It’s one of the reasons why bridges often got blown up during both World Wars. Only a handful stayed intact to supply one of the conflicting parties that was in charge of the area. To calculate the Inaccessibility index (I) you need two properties of a country: the border length and the number of border crossings.

I = State border length (km)/Number of border crossings

The border length for this calculation does not include: parts of ocean coastlines, sea coastlines and lakes if no bridge or another structure spans it. Thus, for island states this formula is useless. Invasions from overseas can be a real threat (eg: D-day) but are more difficult to quantify and therefore not mutually comparable.

Border crossings should include all primary and secondary roads suitable for cars, lorries, etc. Dead end roads and roads forming a loop crossing the state border should not be included, as with roads that act as the state border itself. Paths only qualified for pedestrians and cycles are invalid. Border crossings consisting of a bridge or viaduct over some sort of obstacle like a river, valley, mountain pass or ravine count as half because of strategical advantages.

The result of the calculation should be interpreted as following: the higher the result, the harder it is to cross a nation’s border and thus the more capable the country is to protect its borders. The number can be read as “country X has one border crossing for every Y km of state border”. Countries with an index below 1 should be considered as very easy accessible and therefore vulnerable. Less than 2 is average; less than 4 normal. An index higher than five can be interpreted as a country that is very difficult to access.

Country	State border length (km)	Number of border crossings	Inaccessibility index
Liechtenstein	77,9	10,5	7,42
Belcity	40,148	9	4,46
San Marino	39	30	1,30
Heist-op-den-Berg	63,017	59	1,07
Vatican City	3,2	3	1,07
Monaco	4,4	24	0,18
People's Republic of Duke	0.01 (Falcon Border Crossing)	128	3,58

(feel free to add your own micronation)

Surface efficiency

An equilateral triangle, the most efficient shape for a country.

The shape of a country can take many forms, the same can be said about the proportion between circumference and surface area. It is a binominal balancing act. A long state border usually contains a large area of land. During a war, these big countries have the capacity of feeding and maintaining larger groups of people for a longer period of time, but also need those people to protect the above average state border. This has a negative impact on other necessary functions of a nation.

A shorter state border requires less people for guarding it, neither will the country be able to support many citizens. Still, the core functions of these nations will run smoother because in accordance to larger countries a greater part of inhabitants will be able to take part in diverse activities.

As a final argument, one can assume that if a situation of threat arises, extremely wavy border lines will be more difficult to than straight ones. Also this property is quantified in the surface efficiency.

To resume these characteristics into one formula, the Surface efficiency (SE) is:

SE = Surface Area (km^2)/State border length (km)

The most ideal shape for a country of any size in terms of surface efficiency is an equilateral triangle. The SE reaches its maximum (SEm) in this geometrical figure at any given circumference or area.

When the vertice V is known, the SE is calculated as: SE = (√3 V)/12

When the surface area A is known, the SE will be: SE = (√3 A)/6

A country with an efficiency below 1 should be considered as having a low surface efficiency as long as its claimed area is larger than 11 km². Other countries, or countries smaller than 11 km² can be divided into three groups according to the SEm: average (<40% of SEm), normal (>40% but <75% of SEm) and high (>75% of SEm).

Graphical presentation of the surface efficiency ratings up to 350km², together with the data of the 10 smallest world countries.

Country	Surface area (km²)	State border length (km)	Surface efficiency	Rating
Andorra	468	118	3,97	NORMAL
Liechtenstein	160	77,9	2,05	NORMAL
Saint Kitts And Nevis	261	135	1,93	AVERAGE
San Marino	61	39	1,56	NORMAL
Belcity	0,0006	40,148	1,49	HIGH
Heist-op-den-Berg	91,36	63,017	1,45	NORMAL
Malta	316	196,8	1,25	AVERAGE
Tuvalu	26	24	1,08	NORMAL
Nauru	21	30	0,70	LOW
Marshall Islands	181	370,4	0,49	LOW
The Maldives	300	644	0,47	LOW
Monaco	2,02	8,5	0,24	NORMAL
Vatican City	0,44	3,2	0,14	NORMAL

(feel free to add your own micronation)