Hi Pilot DAR. Thanks for your input.
"All other things being equal, the best rate of climb performance will get you the farthest away from earth in the least time."
Agreed 100%.
"To keep the noise footprint small, you want to get the plane away from the ground as soon as possible."
Well, yes and no. It's certainly true that the further "up" you are, the better. Small piston engined airplanes do indeed use Vy to reach the noise measurement point (constraint) that is 8200 ft from brake release. Jet aircraft, however, use an airspeed closer to Vx (typically V2+10 to V2+20) and reach the noise measurement point (constraint) at 21,325 ft from brake release. They're allowed one thrust cutback after a certain altitude but no configuration change (e.g., flaps) other than gear retraction. So in this case, Vy may not be appropriate since you might think of the noise measurement point as an "obstacle".
"Best rate of climb speed clears obstacles better....."
I'm sure you meant to write "Best
angle of climb speed clears obstacles better....."
Comments invited.
Cheers,
Tom