Calculating Time on Target Salvoes

[NihilRex (OP)]

I am currently running into situations where it is possible (in fact it already happened by accident,) for slow moving long range torpedoes to enter the targets defense zone at the same time as shorter ranged, faster moving missiles that were fired later.

The problem I am having is figuring out how to do this on purpose.  Google isn't much help, mostly telling me about y=mx+b.

So, how do I figure out intercept time given my bearing\speed, enemy speed, bearing to target, missile speed\speeds.  Assume a constant intercept plot by enemy target.

[sublight]

Assuming you and the target are either flying directly towards each other or directly away from each other then:

D = Distance
VT = Target Velocity (speed)
VY = Your Velocity
VSm = Slow Missile Velocity
VFm = Fast Missile Velocity
T = Time
FD = Fire Delay

D + VT * T = VSm * T = VFm * (T - FD) + VY * FD

Solving the right left equation for Time T:
T = D / (VSm - VT)

Now we solve the right equation for Fire_Delay FD:
VSm * T = VFm * T - VFm * FD + VY * FD
T * (VSm - VFm) = FD (VY -  VFm)
FD = [ D / (VS - VT) ] * [(VSm - VFm) / (VY - VFm)]

And there you have it. 
If your ship and the target aren't heading directly toward/away each other then a few trig terms appear, but same idea.

[NihilRex (OP)]

Thank you very much!

I have that in  Excel now, and the pesky PD blanket will no longer require so many missiles to penetrate!

My previous solution to the ToT problem that worked marginally well, was to draw a line between TF and target, and place a WP on it, then stack several torpedo launches on the WP.  When the target entered the torpedoes' active seeking range, they swarmed en masse and took out several engines and (probably) turrets, allowing the next flight of Thunderbolt missiles to start slaughtering contacts.

[niflheimr]

Take in mind that if you or the target make course or velocity changes it gets complicated fast . Still , ToT missions are the best solution I found for penetrating heavy PD/interceptor umbrellas . A salvo of massive , armored warheads ( if they are MIRV the better) followed at 5s by a few dozen salvoes of ECMed MIRVs will go through most defenses easily - if you can afford the missile cost.