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.
When determining the performance of a full scale rocket,
we must account for the change in weight during an
engine firing.
On the web page which describes the
major systems
of a rocket, we group the various parts according to
function. The major systems include the
structural systems, the
payload systems, the
guidance systems, and the
propulsion systems. On this page we
group the parts in a slightly different manner according to mass.
We assign a mass variable to three major parts; the mass of
the payload is noted by md, the total mass of
the propellants is noted by mp, and the mass of
all of the rest of the rocket, excluding the payload and the propellant,
is noted by the structural mass ms. The engine pumps and nozzle
are grouped with the propulsion system according to function, but kept
with the structure according to mass.
We are making the distinction according to mass because
the mass of some parts of the rocket are always the same
and some change with time.
During the launch the propellants are
burned
and exhausted out the
nozzle.
To evaluate the
performance
of a rocket during a burn, we must account for the
large change in weight in the equations of
motion.
Engineers have developed several dimensionless parameters
to characterize the weight of a full scale rocket. We
have listed some of these mass ratios on this page.
The empty mass, denoted by me, is the sum of the
payload and structural mass of the rocket:
me = ms + md
The empty mass is the mass of the vehicle at the end of a burn, assuming
all the propellant has been consumed.
The full mass, denoted by mf, is the mass at the beginning
of the burn and is equal to the sum of the mass of the payload, propellant,
and structure:
mf = ms + md + mp
mf = me + mp
The propellant mass ratio is denoted MR and is equal to the
ratio
of the full mass to the empty mass:
MR = mf / me
MR = 1 + mp / me
The ideal
rocket equation
indicates that the total change in velocity during a burn depends on the
natural log
of the mass ratio. So we want the ratio to be a large number to produce
a large change in velocity.
Another way to look at this parameter is that a large propellant mass ratio
implies that the empty weight to hold the propellant is very small.
The payload ratio is denoted by the Greek letter lambda and
is equal to the mass of the payload divided by mass of the propellant and
the structure:
lambda = md / (mp + ms)
lambda = md / (mf  md)
We want the payload ratio to be a large number. This indicates that a large
payload can be lofted with a small amount of propellant. The last mass
ratio is the structural coefficient, denoted by the Greek letter
epsilon, and equal to the mass of the structure divided by
the mass of the structure plus propellant.
epsilon = ms / (mp + ms)
This parameter is independent of the payload that is launches and is
a measure of the efficiency of the booster design.
A small value of this coefficient indicates a good design.
With a little algebra, you can show that:
MR = (1 + lambda) / (epsilon + lambda)
Again, we desire a large payload ratio, a small structural coefficient
and a large mass ratio.
Guided Tours

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