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In the landing and landing attempts I've seen from the Falcon 9 first stage boosters, the landing legs are always deployed just a split second before landing, right when they are about to touch down.
Any idea why this is? It would seem that deploying them earlier would provide a greater drag surface, reducing the fuel needed to slow down. If they can hold the whole rocket up, I'd imagine they should be able to deal with the stresses of opening in flight.
Stability is one big reason. Fins are typically placed near the bottom of rockets, which means they are in the opposite direction of movement. This is because that position tends to make the rocket more stable. If the legs were deployed, it would tend to make the rocket flip around, as the leg "fins" would tend to want to be furthest away from the direction of motion, or upside-down. The rocket is poorly balanced as it is, so adding such an instability would make things even more difficult.
Also, note that if the legs deployed earlier, they would be subject to more stress, which might cause them to fail.
At the start of the landing burn, the stage is still supersonic. If they deploy the legs earlier, they'd get lots of aerodynamic heating. Now the legs can withstand a fair amount of heat: the Orbcomm-2 landing video showed the legs were on fire just before the landing. But that's just a few seconds. A long heat soak may induce structural failure.
That said, SpaceX does plan to refine the design so they can open the legs earlier:
Using legs as air brakes to drop terminal velocity in half requires slight redesign & more data. Maybe flight 21.
