JonS, I have never said that density maps are useless, only that their information is conditioned by the total number of guns in Malta. You put too much faith in them. Just some examples:
JonS wrote:The density map tells you how many guns can engage a target (plane/raid/paradrop/whatever) at any given time and place (at 16k ft, blah blah blah. Assume other maps - or overlays - for different engagement altitudes). That - to me - is the critical measure. If you are only interested in the number of guns, then you need to add all the spares that are indicated in Tony R's post. But that would be silly, since it tell you nothing about how many can be bought to bear.
The density map tells you exactly what you say. Still, even disregarding the fact that you would need a whole sheet of maps telling the story at different heights, there are many things they do not tell. For example, taking the map you showed: how many guns included in the zone of 60-80 density are also included of 40-60 density? (or, in other words, if you are firing 80 guns to the 60-80 zone, how many guns are left to fire to the 40-60 zone? That's a function of the total number of guns... so, at the end, the density maps do not tell you how many guns you can actually be brought to bear in two or more zones at the same time, while the total number of guns tells you how many guns can actually be brought to bear over the whole island...
JonS wrote:Total number of guns also can't tell you if you've inadvertently left a key point - or approach route - undefended, under-defended, or if you've 'over' defended a certain area or route.
I agree with the "undenfended" point, but not with the other two. First, whether a point is under-defended or over-defended is not an absolute, but depends on the total number of "defense" features that you have... For example, defending a city with 112 guns will not be over-defending by Berlin-1944 standards, but it will definitively be for Malta in 1942, as it would mean using all the guns available in the island. As the density map is a tool to optimize your deployment, it is highly dependent on the total number of resources available. In other words, you start with the total number of guns and then deploy them in the best possible disposition, not the other way round.
Density maps also allow you to plan standing barrages at particular locations on certain approach routes and over certain targets, knowing that you'll be able to achieve a given shell density per m^3 at a given rate of fire from a known number of guns. Knowing the total number of guns tells you how many guns you have.
Yes, density maps allow you to plan, always in function of what you have... So the prime data is the total number of guns, and the density map is just a tool to deploy it in a "maximum benefit" configuration.
JonS wrote:Extracting max efficiency from the resources they had was a more practical and useful approach than whining to the War Office for another bty or regt of guns.
No matter how much you try, you are not going to obtain more than 100%... No matter how hard you try, if you have 100 guns you are going to fire 100 shells at a time (or less...). So yes, extracting maximum efficiency from the resources was more practical and useful, but not better.
After all this, I think that you still have not understand what I am trying to say. My original statement was that in the following statement...
Briadier Beckett, stated that in April 1942 there were [...] 112 heavy guns [...] and that "Investigation proved that there was no point over Malta itself at which less than eighty Heavy AA guns could fire at one time...
the relevant information was the total number of guns, as the data about anti-aircraft fire density was not correctly stated, and even contradicted the information of the map you presented (within the conditions stated by LWD)
Even the map you provided is fairly limited in the information it gives, as it is only valuable at a certain height. I find the data about the total number of guns more "absolute" in its usefullness... but at the end, to know the real state of Malta anti-aircraft defense, you will need the total number of guns, the type of the guns, the density maps, the location maps, the data about ammo reserves, etc... So I think we can try to provide more data, instead of arguing about what seems to be just a matter of taste...
Best whishes,
Gonzalo