The Saturn V used to hold the record for the biggest rocket; I think it still does.
On the launch pad, fully loaded, fueled and ready to fly to the moon, the Saturn V weighs 6.6M lbs. Of this, 4.5M lbs is fuel for the first stage. The first stage has 5 engines that generate an aggregate 7.6M lbs of thrust. At lift off, this gives
7.6M - 6.6M = 1M lbsthrust net of gravity to get things moving.
Recalling that a slug weighs 32 lbs, we find that the rocket has a mass of
6.6M lbs / (32 lbs/slug) = 210K slugs.Finally, we use
a=F/mand find that the rocket comes off the launch pad with an initial acceleration of
1M lbs / 210K slugs = 4.8 feet/sec^2,also known as
4.8 ft/s^2 * (g/32 ft/s^2) = 0.15 gor
4.8 ft/s^2 * (mile/5280 ft) * (3600 s/hr) = 3.3 mph/secor
60 mph / 3.3 mph/sec = 18 sec0.15 g? 3.3 mph/sec?? 0 to 60 in 18 seconds??? I can beat that in a VW Rabbit. Any way you look at it, this is a lose.
Eventually, things get better. At the point of first stage burnout, the rocket weighs only 2.1M lbs, and we have
7.6M - 2.1M = 5.5M lbs net thrust 2.1M lbs / (32 lbs/slug) = 66K slugs 5.5M lbs / 66K slugs = 83 ft/sec^2or 2.6g, 57 mph/sec and 0 to 60 in 1.1 sec, which should pin your ears back nicely. Reality is probably even better, since by first stage burnout, the rocket is probably turning over on its side to accelerate into orbit, and gravity doesn't take as big a bite.
Still, it seems like there ought to be a better way. I mean, if I could put 7M lbs on a 747...well, the engines would tear the wings off the fuselage and go scuttling down the runway on their own. But aside from that, if I could really put 7M lbs on a 747, or even a good fraction of 7M lbs, I could...I could...I could fly it to orbit.
Yes and no. SpaceShipOne is the second stage of a two-stage vehicle. The first stage is an airplane, called White Knight. White Knight carries SpaceShipOne to an altitude of 15,000 meters. SpaceShipOne then separates and climbs to 100,000 meters. This is arguably better than simply standing a rocket on its tail and blasting directly from sea level to orbit. On the other hand, SpaceShipOne didn't get to orbit: it only got to space.
The potential energy of gravity is
E = mghso to lift something into space, you need
9.8 N/Kg * 100000 m = 1M N*m/Kg = 1M J/Kg
E = 0.5 mv^2so to accelerate something into orbit, you need
0.5 * (8 Km/s)^2 = 32M m^2 / s^2 = 32M J/Kgor more than 30 times the energy required to climb to space.
Now we need a first stage, and you aren't going to carry something the size of SpaceShip33 to 15,000 meters under the belly of White Knight, or any other twin-hulled, gossamer-winged sailplane wanna-be. No, we need a heavy lift vehicle. Maybe a couple of big solid-rocket boosters strapped to its belly would get it there. Yeah, that's the ticket...it would look something like this.