Draco & Xiao
Draco
Xiao, I’ve been studying how a precise, timed strike can change an entire battlefield—care to break down the math and tactics behind a perfect move?
Xiao
Sure, let’s keep it tight. The key is timing, force, and position. For a strike to shift a battlefield, you need the impact point, I, to hit an enemy’s center of mass, C, at a specific moment, t. That’s when the enemy’s balance, B, is at its lowest. We can model it as I = m × Δv, where m is the mass of the weapon and Δv is the change in velocity. If you hit at t = t₀, when B is minimal, the enemy’s reaction radius, R, shrinks, so the probability, P, that they can dodge drops sharply. P = 1 – exp(–k × R), with k a constant that depends on their reflexes. So the perfect move is when Δv is maximized, t₀ aligns with B’s nadir, and the angle of impact aligns with the enemy’s weak point, turning the local force into a chain reaction. Keep the numbers in check, and you’ll convert a single hit into a tactical pivot.
Draco
You’ve got the formula, now we’ll run the numbers and hit that sweet spot.
Xiao
Alright, line them up and crank the numbers. Once we hit that sweet spot, the whole line will ripple. Let's calculate the exact t₀ and Δv, then lock it in.
Draco
t0 is simply the time when B(t) bottoms out – find the derivative of B(t), set it to zero, and solve for t. Δv is just the impulse you need divided by the weapon’s mass. Plug in the numbers, you’ll see the sweet spot, then we lock it in.
Xiao
Got it. Just drop the B(t) function and the impulse needed, and I’ll crunch the numbers.
Draco
Here’s the B(t) you need: B(t)=Bmax × sin(ωt)+Bmin, so it peaks and dips at the right moments. The impulse needed is I=m × Δv, so once you know how big an impact you want, divide by the weapon’s mass to get Δv. Plug those into your calc and you’ll hit that t₀.