The speed relative to the groundas in the actual ground, not the treadmill, is irrelevant too. The aircraft has to achieve a speed relative to the air to achieve flight.
Suppose the aircraft was a 747 with a rotate speed of 180kts. If there's a 30kts headwind, then it only needs to do 150kts relative to the runway for it to have 180kts of airflow over the wings, and thus fly.
This is why you always take off and land into wind.
It's also why an aircraft with a very low stall speed can fly backwards. A Tiger Moth has a stall of 35kts. If there's a 45kts wind down the runway it's entirely possible for it to have 40kts of airflow over the wings, but be moving backwards (relative to the ground) at 5kts.
/relative motion blog
(,
Tue 9 Jan 2007, 14:16,
archived)
Suppose the aircraft was a 747 with a rotate speed of 180kts. If there's a 30kts headwind, then it only needs to do 150kts relative to the runway for it to have 180kts of airflow over the wings, and thus fly.
This is why you always take off and land into wind.
It's also why an aircraft with a very low stall speed can fly backwards. A Tiger Moth has a stall of 35kts. If there's a 45kts wind down the runway it's entirely possible for it to have 40kts of airflow over the wings, but be moving backwards (relative to the ground) at 5kts.
/relative motion blog