“...From ignition that Dragon rises and clears the tower a lot faster than an Atlas 5.”
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It sure did. American rocket designers have learned a lot since “back in the day”.
I can’t find a thing on the Dragon but the speed time/altitude numbers for Saturn V are:
5 seconds, 32 feet, 12 mph
10 seconds, 126 feet, 25 mph
15 seconds, 269 feet, 39 mph
20 seconds,510 feet, 56 mph.