edit: Jeff Alton beat me to this one :)

30mph tailwind means essentially a -30mph indicated wind speed at standstill on the runway.

If the plane moves down the runway at 30mph ground speed, the tailwind is essentially negated since the air moving over the wing is moving at 0mph.

Increasing ground speed by another 30mph to 60mph ground speed will also increase wind speed by an additional 30mph, meaning at 60mph ground speed the air moving the wings will hit 30mph and allow the plane to take off.

Right?

Spot on, mate!

Like I said, I have seen an aircraft with and indicated airspeed of 120kts going backward over the ground on a radar.......

The water analogy posted earlier was a good one also.

Should we delve into mach numbers/true airspeed/indicated airspeed/ground speed?? I will leave that one to Scott!!

Cheers

Or how about this. The other day we were flying at 38,000 and we had a terrible headwind- about 120kts. I sat there thinking about our outside temps and our weight and decided we should go up to 43,000ft. When we got there the guy in the right seat who is reletively new to the plane said "Oh man, look how much we slowed down." I asked him what he meant since our true airspeed stayed the same and the ground speed went up 30 kts. He replied, "ya, but look at our IAS. (indicated airspeed). It's dropped down 20 kts." After a long discussion about all the measurements of speed (mach, indicated, calibrated, true airspeed and ground speed) it finally hit home when I said if the passengers ask "how long" then thats groundspeed. If the pilot wants to know when will the plane stall, thats indicated. Remember the SR-71 can go many times past the speed of sound and still be 10 kts above stall speed. The plane reacts and flies based on what it feels, with no regard to how quickly the ground is going by.