Iskandria: Vector error

Iskandria

Vector error

Random errors in 3-d vectors are fundamental to the wargame Iskandria. The approach taken here is that, in most circumstances, vectors are most naturally aimed in spherical coordinates: (ρ,θ,ϕ) where the entries, in order, are:

ρ: the magnitude of the vector
θ: the rotation of the vector relative to an "obvious" "horizontal" plane, and
ϕ: how far the vector is from "straight up" relative to the above "obvious" "horizontal" plane. [This does make sense in "stratosphere math" -- I'm choosing the system to be "positively oriented".]

Recall that vector addition is component-wise: (a,b,c)+(x,y,z)=(a+x,b+y,c+z).

When a vector is "generated" (for instance: is X aimed correctly), the question is "how close is the actual vector to the one I think I'm using?"

"actual" = "target"+"error"

When a vector is "measured" (for instance, is X aiming at me too closely), the question is "how close is the vector I see to the vector that is actually there?"

"measured" = "actual"+"error"

In both cases, the abstract method is to add an "error" vector to the "target" or the "actual" vector. The method of generating the "error" vector depends on the exact circumstance. This "error" vector is a random error, and has nothing to do with operator error (another important factor).

In all cases, the actual vectors are used to resolve all events. The knowledge of the combatants, however, is restricted to target vectors (what the combatant intended) and measured vectors (what the combatant observes).

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