8/11/2019 Definitions and Staging for Rockets
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SUMMARY: Single Stage Rockets
The total mass of the rocket stage can be considered to be the
sum of several parts:
ML: Mass of the payload
MP: Mass of the propellantMS: Structural mass
The structural mass includes all other mass but the payload and
the propellant. Thisincludes engine, guidance system and control
equipment and fuel tanks. ther te!ts use
different definitions to divide the rocket into various
fractions, but these groupings are
most common. The initial mass of the rocket is "ritten as the
sum of these components:
SPLo MMMM ++= #
$f the rocket consumes all its propellant during firing, the
burnout mass is:
PoSLb MMMMM =+= %
These variables may be arranged in several important ratios, as
summari&ed belo":
Symbol Ratio Description
'SL
o
b
o
MM
M
M
MR
+
==
Mass Ratio: initial mass ( mass at theend of the thrust period.
)ant this
ratio large.
*
SP
L
Lo
L
MM
M
MM
M
+
=
=
Payload Ratio: ratio of payload to
everything but payload. )ant this
large, but larger the payload, thelo"er ma!imum attainable
velocity.
+
Lo
Lb
SP
S
MM
MM
MM
M
=
+
=Structural Coefficient: ratio of the
structural "eight to everything butthe payload. )ant this
small.
Lo
P
SP
P
MM
M
MM
M
=
+
= Propellant Ratio: 'atio of propellantto everything but the
payload.
-
)e can also "rite the mass ratio as:
+
+
=
#R
/ote that the structural and payload ratios are related by:
=# 0
#
8/11/2019 Definitions and Staging for Rockets
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SUMMARY: Multistage Rockets
Some key points about rocket staging:
1 multistage rocket is a series of individual vehicles or stages
each "ith its o"nstructure, tanks and engines. The stages are
connected so that each operates in
series and accelerates the remaining stages and payload before
being detached anddiscarded.
The stages are numbered in the order of firing.
The payload for any particular stage is simply the mass of all
subsequent stages.
Moi: Total initial mass of the ithstage priorto firing,
including its effective payload
Mbi: Total mass of the ithstage afterburnout, including its
effective payload
ML: Payload of the last stage to fire
Msi: Structural mass of the ithstage alone, including the mass
of its engine, controls, and
instruments.
2y slightly modifying the ratios defined in equations #30, "e
can e!amine multistagerockets. 'emember, that the payload of any
stage is simply the mass of all subsequent
stages.
The payload ratio, i, of the ithstage is:
4#5
4#5
+
+
=
iooi
io
i
MM
M
6
The structural coefficient of the ithstage is:
4#5 +
=
iooi
si
i
MM
M
#7
4#5
4#5
+
+
=
iooi
iobi
i
MM
MM
#7.#
The last e!pression holds if the i thstage contains no
propellant at burnout. The mass ratio
of the ithstage can be "ritten as:
bi
oi
i
M
MR =
##
ii
i
iR
+
+
=
# ##.#
%
