pub const MARGIN_CONDITION_LIMIT: f64 = 3.162_277_660_168_379_5;Expand description
The largest ratio κ = Σ |C_Nα,i| / C_Nα at which a margin is given: √10.
The center of pressure is x_cp = Σ C_Nα,i x_i / C_Nα, over the parts the model adds up, with
each part’s station x_i on the rocket, in [0, L]. Since x_cp − x_j = Σ C_Nα,i (x_i − x_j) / C_Nα, it lies within κ L of every
station. An error ε C_Nα,j in one component’s slope moves it by
ε C_Nα,j (x_j − x_cp) / C_Nα, so by at most ε κ² L. A rocket whose slopes all push the same
way has κ = 1, and a 1% error in one slope moves its center of pressure by at most 1% of its
length. As the net slope goes to zero, κ runs away: the loads become a pure couple with no
line of action, and the quotient is noise (Loft published ±12 to 15 calibres so,
lesson L33). At κ = √10 a 1% error in one slope can move the center of pressure by a
tenth of the rocket’s length; past it hpr gives no margin, only the pitch-moment slope, which
stays finite. The limit is a chosen bound on that sensitivity, not a measurement. The bound
holds for parts that each carry a force at a station: a part that is a pure couple (a step and
a flare of equal slopes) has none, and κ doesn’t count it.