The study of rockets is an excellent way for students
to learn the basics of forces and
the response of an object to external forces.
All rockets use the
thrust
generated by a propulsion system to overcome the
weight
of the rocket. For
stomp rockets,
bottle rockets, and
model rockets, the
aerodynamic drag and lift
are also important forces acting on the rocket.
For air-to-air and ground-to-air missiles, the aerodynamic
forces are significant, but for satellite
launchers,
the aerodynamic forces are not as important because of the
flight trajectory to orbit.
On this slide we show the major invents in the flight of
a two stage launcher to orbit.
Throughout the flight, the weight of the rocket is constantly
changing because of the
burning
of the propellants.
At launch,
the thrust produced by the
engine
is greater than the weight of the
rocket and the net force accelerates the rocket away from the pad.
Unlike model rockets, full scale launchers rely on
a sophisticated guidance system to balance and steer the
rocket during its flight. The thrust of the rocket is
gimbaled, or rotated, during
the flight to produce maneuvers.
Leaving the pad, the rocket begins a
powered vertical ascent.
The vehicle accelerates because of the high thrust and decreasing
weight and rather quickly moves out of the thick atmosphere near
the surface of the earth. Although the rocket is traveling
supersonically, the drag on the
vehicle is small because of the
shape of the rocket and the lower air
density at altitude.
As the rocket ascends, it also begins to
pitch
over and
its flight path becomes more inclined to the vertical.
Several minutes into the ascent, most launchers
discard some of the weight of the rocket. This process
is called
staging
and often includes the ignition of a second engine, or upper stage,
of the launcher. The discarded first stage continues on a
ballistic flight
back to earth. The first stage may be retrieved, as with the Space Shuttle
solid rocket engines, or it may be completely discarded, as was done
on the Apollo moon rockets. The lighter,
upper stage continues to accelerate under the power of its
engine and to pitch over to the horizontal.
At a carefully determined altitude and speed the upper stage
engine is cut off and the stage and
payload
are in orbit. The exact speed needed to orbit the earth depends on
the altitude, according to a formula that was developed by Johannes Kepler
in the early 1600's:
V = sqrt ( g0 * Re^2 / (Re + h) )
where V is the velocity for a circular orbit, g0 is
the surface gravitational constant of the Earth (32.2 ft/sec^2),
Re is the mean Earth radius (3963 miles), and h is the
height of the orbit in miles. If the rocket was launched from the
Moon or
Mars, the rocket would require a different orbital
velocity because of the different planetary radius and gravitational
constant.
For a 100 mile high orbit around the Earth, the orbital velocity
is 17,478 mph.
Let's investigate the circular orbit equation by using a Java
calculator.
The circular orbit velocity depends on the altitude at which you orbit, and
the planet that you are orbiting. You can select the planet by using the choice
button. Click on the menu and drag to the selected planet (Earth, Moon, or Mars).
The corresponding gravitational constant and planet radius is displayed
below the choice buttons. Type in the desired altitude of your orbit and
push the "Compute" button. This sends the information to the program
and calculates the value of the orbital velocity.
You may optionally enter the velocity and the program will solve for the
altitude of the orbit.
Calculations and input can be entered in either
English or Metric units by using the "Units" choice button.
You can download your own copy of this calculator for use off line. The program
is provided as Corbit.zip. You must save this file on your hard drive
and "Extract" the necessary files from Corbit.zip. Click on "Corbit.html"
to launch your browser and load the program.
Notice that orbital flight is a combination of altitude and
horizontal velocity. The recent Space Ship 1 flight acquired the
necessary altitude to "go into space", but lacked the horizontal
velocity needed to "go into orbit".
While they can not fly all the way to orbit, there are
two stage model rocket kits available.
You can study the flight characteristics of a two stage model rocket by
using the
RocketModeler II
simulation program.
