The power levers to idle and maximum braking happen at the same time, there is nothing smooth about it. The automatic ground spoilers should beat you to the speed brakes, but you still need to back them up.
G450 takeoff performance is based on no reverse for a dry runway, one engine in reverse for a wet runway. You should have adequate directional control even with only one engine in reverse; if you don't, cancel the reverse, regain directional control, and reapply reverse as necessary.
B-747 nose bob technique. The purest sign of a smooth 747 pilot was one who could stop the airplane without bobbing the nose. But during a takeoff abort, the pilot's inner ear can be fooled into thinking the airplane is stopped when it really isn't. We preached: full braking until the nose bobs.
Everything here is from the references shown below, with a few comments in an alternate color.
[G450 AFM, §04-19-60]
After initiating the takeoff roll, if it becomes necessary to abort the takeoff for any reason, use the following procedure:
NOTE: Ground spoilers should extend automatically when the power levers are retarded to idle during an aborted takeoff. Extending the speed brakes ensures all spoilers are extended.
NOTE: Any takeoff abort should be a maximum stop effort, regardless of the speed at which it is initiated.
NOTE: During a rejected takeoff (RTO), reverse thrust can be used to bring the airplane to stop (zero ground speed), if deemed necessary. If reverse thrust is used below 60 KCAS, record the event and report the occurrence for maintenance action.
Gulfstream G450 Airplane Flight Manual, Revision 35, April 18, 2013
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