Suzy B Software 2/Suzy B Software CD-ROM 2 (1994).iso/nasa/specimpl/specimpl.txt

Text File | 1995-05-02 | 16.6 KB | 313 lines

                               Specific Impulse:
                    What, Besides Thrust, Gets Us to Orbit?

This article introduces the concept of specific impulse, an important value in
determining the performance and capabilities of a space propulsion system.  It
is intended primarily for those people who do not have a firm technical
knowledge of space propulsion systems, but would like to gain a working
knowledge of some of the parameters used in the field.  I have compiled, into
one paper, notes and information from several sources, notably space-systems
and propulsion courses at the USAF Academy.  In some classes, the original
reference cited in the coursework is Dr. Glasstone's "Sourcebook on the Space
Sciences."  Although the original material is now four times removed, it may be
safely assumed that credit for everything correct that follows belongs to my
USAFA instructors, or, if traced back, to Dr. Glasstone.  Conversely, blame for
everything incorrect belongs to me.  I hope there's not too much of the latter,
but occasionally I had to rely on memory.  If you find something, please let me
know, and I'll correct it.

First, a note on units.  To ensure that units' expressions appear the same on
all computers, the following conventions are used:  all superscripts are
indicated by numbers following, e.g. sec2 is read as "seconds squared;"
kg-m/sec2 is "kilogram meters per second squared;" the dash between kg and m is
present as a separator, and does not indicate subtraction.  Similarly, the
following abbreviations are used:

N ---- Newtons (kg-m/sec2), units of force, the metric equivalent to what we
       normally think of as pounds.  Note that kilograms are NOT equivalent to
       what we normally think of as pounds.  A Newton is the force required to
       accelerate a mass of one kilogram at the rate of one meter per second
       per second.  Quantitatively, a Newton is approximately the same as a
       Big Mac.

lbf -- pounds-force, what we normally think of as pounds; the English
       qualitative equivalent of Newtons.  A lbf is the force required to
       accelerate a lbm at 32.174 ft/sec2.

lbm -- pounds-mass, the English qualitative equivalent of kilograms.  2.2 lbm
       really equals a kilogram.  1 lbm = 0.4545 kg.  We use lbm because it
       simplifies some equations, as we'll see later.  Besides, otherwise we'd
       be using slugs.

g ---- one Earth gravity, equal to 32.174 ft/sec2 or 9.78 m/sec2.  The "g" is
       used in converting from mass to weight.

In formulas, the qualitative unit we are working with (such as thrust, which is
usually denoted F), is followed by an example of corresponding units in
parenthesis.  For example, thrust:  F (N); mass:  m (kg).  Any word with a
suffix "dot" is the equivalent of writing the unit with a dot over it, and
represents the rate equivalent of the unit.  For example, mass:  mdot (kg/sec),
is the mass flow RATE (in kg/sec).  (That's "em-dot" phonetically.)  While this
may seem overly simplistic, I can recall fervently wishing, some years back, at
2 a.m., that the author of some textbook had maybe been a bit more simplistic,
and I'll bet I'm not the only one.  (I'd also like non-engineers to be able to
read and understand it.)  Finally, it may make following the equations simpler
if you print out a copy of the article -- 25 lines isn't much room, once you
start into math.  Off we go.

The performance of a rocket engine can be primarily judged by two factors:  its
THRUST, and its SPECIFIC IMPULSE.  For the sake of completeness, we'll examine
thrust first.

Thrust is understood commonly enough as the resultant of Newton's Third Law,
action-reaction.  Thrust is expressed in units of force: Newtons or
pounds-force (lbf).  More specifically, thrust is defined as a "change in
momentum."  The momentum of a body is the product of its mass and its velocity.
Momentum = m*v.  This definition of thrust makes sense qualitatively; we have a
vehicle of mass m; it is moving at velocity v; we apply thrust, and the
velocity changes.  Since m*v now equals some new value, momentum has changed.

The value of an engine's thrust depends primarily on the engine's mass flow
rate and its exhaust velocity.  Mass flow rate (mdot, expressed in kg/sec or
lbm/sec) is simply the rate at which propellant is consumed and expelled out
the nozzle.  It is also called propellant flow rate.  The exhaust velocity is
often referred to with the letter "c" (we'll stick to the metric m/sec, and
note that this is NOT the speed of light).  Thus, we have:

F (N) = mdot*c = (kg/sec)(m/sec) = (kg-m/sec2)

We see that the units check out -- we expect thrust, F,  to be a force (since a
force is defined as the change of momentum), and the units work out correctly
to Newtons (kg-m/sec2).  This quantity is referred to as "momentum thrust," as
it results from the change of momentum of the exhaust gas.

Atmospheric pressure can rob an engine of thrust, depending on what altitude
the engine was designed for.  This contribution to thrust is called "pressure
thrust," and is usually negative (i.e. it causes a decrease in overall thrust).
I don't like it; it's confusing, so we'll ignore it here except to say that an
engine's performance can always be designed highest for a vaccuum -- there is a
performance loss from operating in an atmosphere, or from designing to operate
in an atmosphere.

Another important measure of rocket performance, SPECIFIC IMPULSE, is related
to the thrust produced.  Specific impulse is written Isp. (Normally, the "sp"
would be a subscript.)  Two definitions have evolved for the term, and it's
important for engineers to know which they're using to solve problems.  First,
the technical definitions.  NASA's glossaries define specific impulse as the
thrust (force, in lbf or N) obtained from each unit mass of propellant (lbm or
kg of fuel and oxidizer), consumed in 1 second.  The rate at which the
propellant is consumed is exactly the same as the rate at which exhaust gas is
expelled, because the propellant material is converted into exhaust gas by the
operating rocket.  In English units, if F (lbf) is the rocket thrust and mdot
is the rate in lbm/sec at which exhaust gas is expelled (or propellant
consumed), then the specific impulse, Isp, can be represented by:

                     F(lbf)
           Isp = -------------- , or
                 mdot (lbm/sec)


                  F    (lbf sec)
           Isp = ---  -----------
                 mdot   (lbm)

Although this version of specific impulse should be given in units of
lbf/lbm/sec or lbf-sec/lbm, it is sometimes, erroneously, expressed in seconds.
The error arises when people equate lbf and lbm -- mass isn't force!
Consistent units are important.

We can see immediately that specific impulse is sort of an efficiency rating --
it tells how much thrust we get for a propellant consumption rate.  We'll
compare this English-units version to one with metric units shortly.

The second definition does give a result expressed appropriately in seconds.
It defines specific impulse as the force of thrust (N or lbf) produced for a
propellant consumption rate expressed in N/sec or lbf/sec).  Note the subtle
difference in units:  this definition gives "correct" values when the
propellants' WEIGHT flowrate is used.  Weight flowrate is calculated using a
gravity value of one earth's surface "g" (32.174 ft/sec2 or 9.78 m/sec2).  In
English units, the lbf is defined by "g", so, letting wdot represent weight
flow rate:

                F (lbf)
         Isp = -------------- = (sec)
               wdot (lbf/sec)

In metric units, to convert from mass (kg) to weight at 1g, we include 9.8
m/sec2 and call it g:

               F     mdot*c     c    (m/sec)
        Isp = ---- = ------- = --- = -------- = (sec)
              wdot   mdot*g     g    (m/sec2)

Now, let's return to the first definition, and use metric units:

                F (N)         (kg-m/sec2)
        Isp = ------------- = ----------- = m/sec
              mdot (kg/sec)    (kg/sec)

Now we have a third set of units for Isp!  Or do we?  Here's where it can get
complicated.  Notice the difference between the two metric-unit equations above
(sec and m/sec resultants).  If we calculate Isp using each of them, the second
one will give a value almost 10 times greater!  Specifically, it will be 9.8
times greater -- and that's because of "g" -- 9.8 m/sec2.

In English units, lbm and lbf are defined in such a way that "g" -- 32.2
ft/sec2 in English, is cancelled out -- 1 lbf is the force required to
accelerate 1 lbm at 32.2 ft/sec2.  (So a lbm is not the same as a slug.  A lbm
= 0.4545 kg, a slug = 14.5959 kg.)  In metric units, ironically, the units are
nice and neat -- a Newton is defined as one kg-ONE m/sec2.  As a consequence we
must include "g" explicitly, or we get results 9.8 times larger than expected.
In English units, to get around using slugs and to simplify our calculations,
we DEFINE our units of mass and force to incorporates "g."  (Actually, we
already have the lbf = slug ft/sec2.  But since this is a pretty useless mass,
we define lbm so that lbf = lbm 32.2 ft/sec2, which is a much more convenient
mass measure.)

All of which means?  Follow along:  we have an engine which produces 1 lbf
thrust per 1 lbm/sec mass flow rate.  Then, Isp = 1 lbf/lbm/sec.  Now, using
the same equation, break lbf into its subunits:  1 lbf = 32.2 lbm ft/sec2.  The
resultant = 32.2 ft/sec.  But we must now divide by "g" in the English system,
since we took it out when we broke up 1 lbf.  The result is Isp = 1 sec.

Now convert to metric -- 1 lbm = 0.4545 kg; 1 ft = 0.3048 m.  Then, 1 lbf =
4.45 N.  Isp = 4.45 N / 0.4545 kg/sec.  The result is 9.8 m/sec, until we
divide by the appropriate "g" -- 9.8 m/sec2.  Then we get Isp = 1 sec.  So,
whether we use English or metric units, the Isp, in seconds, is equivalent.
This makes sense, since seconds are the same in both systems.  Numerically, Isp
won't change either if we use lbf/lbm/sec.

The point is worth repeating:  Isp, in seconds or lbf/lbm/sec, is numerically
equivalent, regardless of the system used to calcuate it!

Now, what about that last equation, where we want to use metric units in NASA's
preferred definition--

                     F (N)      (kg-m/sec2)
            Isp = ----------- = ----------- = m/sec
                  mdot (kg/s)    (kg/sec)

Since "g" isn't built into the metric units, as it is into the lbf/lbm
relationship, the Isp will indeed be expressed in m/sec, and will be
approximately 10 times larger.  An Isp of 1 lbf/lbm/sec, numerically equivalent
to an Isp of 1 sec, is the same as an Isp of 9.8 m/sec (just call it about 10
m/sec).

This can lead to difficulties in certain applications of the specific impulse
concept, but all three definitions are currently used.  You can usually
determine which definition to use by checking the units, but the confusion is
pervasive. A good check is to be aware of the "normal" Isp values of the class
of engine you're working with.

An interesting highlight of the metric version of this equation is that the
resulting Isp is in terms of the exhaust velocity of the engine.  You can
easily see, therefore, that a higher exhaust velocity means a more efficient
engine -- which makes sense, since that means the engine is getting more
momentum change out of each particle of exhaust gas.

Other conditions (especially operating pressure) being equal, it can be shown
that the velocity of the exhaust gas is proportional to the square root of the
temperature of the gas (before ejection), divided by its molecular weight.
That is:

                          T
                c2 = k * ----
                         M.W.

where T is the temperature of the gas and M.W. is its molecular weight.  A high
exhaust velocity, and consequently, a high specific impulse, results from high
temperature and low molecular weight exhaust gases.  (Since the exhaust gas is
usually a mixture of different substances, the molecular weight is a weighted
average value.)  This equation explains the desirability of hydrogen as a fuel,
and the need for high combustion chamber temperatures.  It also highlights
another point:  the source of the high temperature is irrelevant.  In chemical
rockets, we get the gas hot by burning a fuel and oxidizer.  In a nuclear
rocket, a nuclear reactor heats the fuel (which can be pure hydrogen -- the
lowest molecular weight).  In some fusion rocket designs, the fusion reaction
generates microwaves which heat hydrogen fuel.  The point is to get the
"working fluid" as hot as possible, so it will exit out the nozzle as fast as
possible.

Another way of looking at the Isp equation is to solve for thrust:

F = mdot*Isp

Systems with higher specific impulse can produce more thrust for a given fuel
burn rate, mdot.  Alternatively, a particular thrust value can be obtained with
a lower propellant consumption rate.  From a mission perspective, specific
impulse determines required propellant loading.  The TOTAL impulse is defined
as the product of the thrust multiplied by the operating time, and a given
mission can be defined in terms of total impulse required.  If we take the
specific impulse equation and multiply numerator and denominator by the total
operating time:

                       F*t          Total impulse
                Isp = ------ = ------------------------
                      mdot*t   Propellant mass consumed

We see the origin of the term specific impulse -- it is the impulse per unit
mass of propellant consumed.  To perform a given mission, the required
propellant mass will be less with a higher Isp.  This, in turn, increases the
thrust-to-weight ratio.

The concept of total impulse points out that we can obtain the same mission
result two ways -- we can burn with very little thrust for a long time, or we
can burn with a lot of thrust for a short time.  It is the nature of most very
high Isp engines that the mass flow rate is very low, and hence so is the
thrust.  (And conversely, most high thrust engines have low Isp.)  But,
consider a design where a certain amount of thrust is needed -- for example, to
achieve a thrust-to-weight ratio greater than one, for liftoff from a planet's
surface.  We can raise the specific impulse, perhaps by increasing the engine's
operating temperature.  If we can do this, while maintaining the same mass flow
rate, mdot, then our thrust goes up.  At the same time, with a higher Isp, the
necessary propellant mass goes down.  Thus, we have gained improvement in the
thrust-to-weight ratio from two areas, instead of one.  Alternately, excess
thrust can be traded for more payload or more velocity.  This demonstrates
clearly why today's engine designs are being pushed to the limit.

The specific impulse is a characteristic property of the propellant used.
Exact figures for a specified propellant combination will vary depending on the
operating conditions and engine design.  The SSME's Isp varies from 363 seconds
at sea level to 455 seconds in vaccuum.  Some other values are given below:

    Oxidizer               Fuel                Isp (sec)
Oxygen                  Hydrogen                  390
                        RP-1                      300
                        UDMH                      310
                        Ethyl alcohol (75%)       280
                        Hydyne                    305

Flourine                Hydrogen                  410
                        RP-1                      320
                        UDMH                      340

Inhibited Red Fuming-   RP-1                      270
  Nitric Acid (IRFNA)   JP-X                      270
                        UDMH                      275
                        Hydyne                    270

Nitrogen tetroxide      UDMH                      285
                        Hydrazine                 290

(above are for 1000 psi chamber operating in 1 atm)

PBAN           Ammonium perchlorate-aluminum      240
 (STS Solid Rocket Boosters)

Hydrogen peroxide (monopropellant)                160
Hydrazine (monopropellant)                        185

Electrostatic ion thrusters (milli-Newtons)  1500-10000
Magnetoplasmadynamic thrusters (100 N)       3000-4000

Solid core nuclear thermal rocket                 950
Gas core nuclear thermal rocket                   1400
Fusion engine (various types)                     10000+
Antimatter engines (various types)           1000-100000

Note the increase in Isp for the LOX/Liquid hydrogen combination in the SSME,
which uses 3000 psi chamber pressure, over the 1000 psi baseline.

John McDonnell
73437,3202