Weight is the force
generated by the gravitational attraction of a planet on
the mass of a rocket.
Weight is related to the mass through the
weight equation and each
part
of a rocket has a unique weight and mass.
For some problems it
is important to know the distribution of weight.
But for rocket
trajectory
and
stability,
we only need to be concerned with the total weight and
the location of the center of gravity.
For
model rockets and
compressed air rockets
the weight remains fairly constant during the flight and we can easily
compute the weight of the rocket.
But for
water rockets and
full scale rockets
the weight changes during launch.
How do you determine the weight of a model rocket?
A model rocket is a combination of many
parts;
the nose cone, payload, recovery system, frame,
engine,
and fins.
Each part has a weight associated with it which you can
determine using a scale, or calculate, using Newton's general
weight equation:
w = m * g
where w is the weight, m is the mass, and
g is the gravitational constant which is 32.2 ft/square
sec in English units and 9.8 meters/square sec in metric units
on the surface of the
Earth.
On the
Moon and
Mars,
the gravitational constant and the resulting weight is less than
on Earth.
The mass of any individual component can be calculated if we know
the size of the component and its chemical composition.
Every material (aluminum, balsa wood, plastic, rocket fuel, etc.) has a unique
density. Density r is defined to be the
mass divided by the volume v:
r = m / v
If we can calculate the
volume
of the component, then:
m = r * v
The total weight W of the rocket is simply the sum of
the weight of all of the individual components.
W = w(nose) + w(recovery) + w(engines) + w(body) + w(fins)
To generalize, if we have a total of
"n" discrete components, the weight of the rocket is
the sum of the individual i component weights with
the index i going from 1 to n.
The Greek letter sigma is used by mathematicians to denote this
addition. (Sigma is a zigzag symbol with the index designation being
placed below the bottom bar, the total number of additions placed over
the top bar, and the variable to be summed placed to the right of the sigma
with each component designated by the index.)
W = SUM(i=1 to i=n) [wi]
This equation
says that the weight of the rocket is equal to the sum of the
weight of "n" discrete parts.
What if the parts are not discrete? What if we had a continuous
change of mass from front to back, as occurs with a solid balsa nose cone?
The continuous change can be
computed using integral calculus. The sigma designation is changed
to the integral "S" shaped symbol to denote a continuous variation.
W = S w(x) dx
The discrete weight is replaced with w(x) which indicates that the
weight is some
function
of distance x. If we are given the form of the
function, there are methods to solve the integration. If we don't
know the actual functional form, we can still numerically integrate
the equation using a spread sheet by dividing the distance up into a
number of small distance segments and determining the average value
of the weight over that small segment, then summing up the
value.
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