In this installment we will follow a rocket's flight into space. The Basic program Rocket49.bas is a good simulation of this process, and is available as freeware from me, Mark Goll.
Sitting on the launch pad a rocket has weight. Just weight. The dry weight of each stage and the weight of the propellants. Actually that's mass, weight is a force on the rocket caused by gravity attracting the mass towards the center of the planet, but we'll just call it weight. The thrust of the rocket engine is a force on the rocket pushing away from the center of the planet. The thrust of the first stage engines, and or the strap on boosters zero stage engines, must produce more thrust than the rocket weight, or it just sits there making a loud noise. The atmospheric back pressure on the first stage engines also reduces their efficiency requiring these engines to be even larger. As the vehicle rises into the sky, four things happen. 1. The engines consume propellants, reducing the mass of the vehicle and increasing it's acceleration. 2. The vehicle accumulates velocity. 3. The dense air of the lower atmosphere produces drag, another force on the vehicle. 4. As the air pressure decreases with altitude, the engines become more efficient, producing more thrust. The large engines needed to overcome gravity, their gain in thrust with altitude, and the rapidly reducing mass of the vehicle due to propellant consumption, combine to produce high levels of acceleration at the end of the first stage run time. This situation can be alleviated by reducing the engine thrust, although throttling the engine reduces its efficiency, or by reducing the booster mass ratio (propellant weight / total weight). Reducing the mass ratio is a better option because a heavier vehicle is generally a cheaper vehicle. The booster should function as a lowest cost thrust producer. "Stage early and often." Guided launch vehicles liftoff slowly, consuming tons of propellant to gain just a few more feet per second of final velocity. Free flight sounding rockets accelerate rapidly off their launch rails to achieve aerodynamic stability, but at the penalty of higher drag. The second stage can take advantage of more efficient engines because the engines always operate in a near vacuum. The engines can also be smaller, producing less thrust than the vehicle weights, because the vehicle already has accumulated velocity from the first stage. Because the cost of upper stages can be considered to include the costs of the lower stages, and because they are smaller, it makes economic sense to invest in lighter weight materials to achieve a higher mass ratio for these stages. The upper stages accelerate more slowly adding orbital velocity rather than altitude. As the vehicle approaches orbit, the thrust of the engines becomes irrelevant, engine efficiency and a high mass ratio become paramount. It can be seen that lower stages and upper stages operate in very different environments with different requirements. There is also no perfect flight path to orbit. The characteristics of each stage, their relationship to each other, and the mission requirements define the optimum path to orbit. Included with the basic program Rocket49.bas are several flight path options. America's first satellite, Explorer 1, had a very interesting flight path. The Redstone first stage lofted the upper stages at a high angle. The upper stages (high acceleration solids) coasted to a point high above the atmosphere before firing in sequence to accelerate the payload to orbital velocity. The space shuttle is also lofted high by the power of its boosters. It then dives back towards the top of the atmosphere to accelerate to orbital velocity.