Depends on why you need to catch a Concorde...
If it's just a "friendly-see-who-can-do-Mach 2-the-longest," there isn't anyone out there now I think that can do it. Fighters that are capable of Mach 2.0+ don't have the gas to do Mach 2+ for sustained periods of time... Don't know how fast a B-1 can do. But I don't think the Concorde can do Mach 2.0 at all altitudes, it only is able to reach Mach 2 at certain altitudes and depends on how much fuel is onboard... The Concorde carries a lot of unusable fuel, required to be onboard to keep CG within limits, but that's a totally different subject. And I think the Concorde uses afterburners to accelerate to Mach 2, but doesn't need afterburners to sustain.
If you're trying to stop the Concorde to keep it from doing something untoward, ... don't we (in the US Air Force anyways) have ABM (Air Battle Managers) whose job is to figure out where to put the fighters so the fighters aren't doing tail chases? e.g. positioning the fighters so that they have the best possible chance of intercept? We've already established that Mach 2.0+ fighters can't catch the Concorde from the paragraph above. If Lt-Awacs were here instead of over there (he sounded like an ABM to me) he could probably elaborate.
If you position the fighter in the right place you don't have to chase down the Concorde. You would probably use up a lot of fighters trying to guess where the Concorde is going to be... unless you have good I&W and intel. But position the fighters where ever they need to be to employ their weapons successfully.
Don't know the range of a Patriot battery, but if the Concorde is still over the North Atlantic, and the Navy were able to get an AEGIS ship into position, and it happened to have one of those shiny new SM-2 Block IV surface-to-air missiles (100+ mile range) as opposed to the old SM-2 Block IIs and Block IIIs (40 and 80 mile ranges), it could shoot down the Concorde. But same problems exists here as well, still need to position the Patriot battery or AEGIS ship in the right position to achieve a successful intercept.
But with a larger AAM/SAM missile envelope afforded by a longer missile range, it gives the ABM greater freedom on where to place the interceptor (whether aircraft, SAM battery, or ship) to still achieve a successful intercept.
This BTW I think are the same troubles that are troubling the guys that are working on developing the ballistic missile defense. Whether it be a Mach 2+ Concorde or an incoming ballistic missile you have similar problems although for different reasons.
Woodreau / KMVL
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