Rocket Science for Earthlings
a continuing series for the gravitationally
impaired.
Rocket Science for Earthlings 2
Chapter 2 Into Space
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.