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While most rocket motor design programs do a decent job, my preference is AeroIsp. It is a great learning tool, actually has instructions and graphics to define the terms it uses, and is a heck of a lot of fun to play with what-if’s. It also lets you enter coefficient and exponent for calculating Pc based on Kn. Most of the other programs back calculate these from burn rate data or use some other method, but I’ve found that experimental Pc and Kn data do not always agree with back calculated data. They are normally close, but I’ve had better luck using the AeroIsp methods while working at Estes over the years. Lest I forget, the built in curve fitting and graphing tool is neat and saves a lot of time in the analysis of experimental info. Ed Brown |
AeroIsp is
a solid rocket motor (SRM) internal ballistics computer program
that assumes the rate of combustion of the burning gases are in
dynamic equilibrium with the rate at which the exhaust gases are
expelled out the nozzle. This dynamic balance is defined by using
a linear variation known as St. Robert's Law between the
rate at which the propellant surface recedes (r) and the chamber
pressure (Pc) as a function of time.
AeroIsp Summary of
Features
(1) Determine Thrust (F), Chamber Pressure (Pc), Burn Rate (rb),
Burn Area (Ab), Burn Area Ratio (Kn = Ab/At), and Thrust Coefficient
(Cf) as a function of Burn Time.
(2) Instantly switch between each color function plot by clicking
the function option button to the left of the plot region.
(3) See results instantly without pressing a Solve button every
time input data is modified. Propellant properties may be modified
on-the-fly to see effects of small modifications.
(4) Modify the propellant data base by Adding (Add), Removing
(Remove) or Updating (Update) propellant properties
in the Propellant Properties section.
(5) Instantly analyze Standard Core grains, Moonburner grains,
Moonburner (Offset Port) grains, C Slot grains (Slot depth = Grain
Radius), C Slot grains (Slot Depth < Grain Radius), Pellet
grains and Cored End Burner grains,
(6) See analysis results in the following units: Inches-Pounds-Seconds,
Feet-Pounds-Seconds and Meters-Newtons-Seconds. Input data is
presently set in units of Inches-Pounds-seconds.
(7) Every Analysis session may be saved for future use by using
the Save Project As command in the File menu.
(8) All function-time curves can be saved in CSV format
by using the Save Data File As command in the File menu.
(9) All function-time curves can be printed by using the Print
Results command in the File menu.
(10) Screen results may be printed using the Print Screen
command in the File menu.
(11) All input and output variables have clearly marked units
labels.
(12) Instantly see the grain type being analyzed by checking the
Click to view or hide grain geometry check box.
(13) Perform star grain analyses for 0, 1 and 2 inhibited grain ends.
New!
(14) Experimental burn rate data
curve fit
analysis by the method of least squares to determine burn rate coefficients.
New!
(15) Insert new curve fit data into the Propellant Properties section on the
main screen.
New!
(16) Expanded Help section.
New!
AeroIsp Minimum System Requirements
(1) Minimum screen resolution: 800 X 600
(2) System: Windows 98, 2000, XP, Vista, NT
or Mac with emulation
(3) Processor Speed: Pentium 3 or 4
For more information about AeroIsp please contact John Cipolla at
aerocfd@aerorocket.com.
| MAIN
PAGE |
PRODUCTS | CONSULTING | MISSION | RESUME | Buy On-Line |
AEROISP OPERATING INSTRUCTIONS BACK
A) BACKGROUND THEORY - SOLID
ROCKET MOTOR INTERNAL BALLISTICS
PERFORMANCE PREDICTION
AeroIsp predicts chamber pressure
(Pc) as a function of time for solid rocket motors. From the chamber
pressure time history and dimensions of the grain configuration
the program goes on to compute thrust as a function of time, specific
impulse (Isp), total impulse (I), average thrust, total burn time
and other important metrics of the rocket motor. However, initially
the user is required to provide information about the propellant
burning rate (rb) and the other coefficients specified in the
Propellant Properties section. This information may be
derived from static testing or by strand burning tests that define the burn rate coefficient
(a), burn rate exponent (n), and pressure coefficient (B). Performance
prediction begins by specifying the propellant formulation and
grain geometry by using the pull-down menu on the main screen
of the analysis. The following grain geometries can be specified
using AeroIsp. Please reference the figure below to see the corresponding
geometry as defined in AeroIsp and access these grain types by
using the Grain pull-down menu.
1) Standard Core grains
2) Moonburner (Tangent Port) grains
3) Moonburner (Offset Port) grains
4) C Slot grains (Slot depth = Grain Radius)
4) C Slot grains (Slot Depth < Grain Radius)
5) Pellet grains
6) Cored End Burner grains
7) Star Grains
NEW!
Then,
once the basic propellant formulation and grain geometry are specified
the user defines the grain geometry by defining each of the remaining
data entries with specific information about the grain and rocket
motor nozzle. Please refer to the grain geometry image that appears
by checking the Check to view or hide grain geometry check
box. Nozzle related data include the Expansion ratio which is
defined as the ratio of the nozzle exit area to the nozzle throat
area. Nozzle throat diameter is also nozzle related information.
The Local atmospheric pressure is important because unless the
rocket motor is expanding into a vacuum the thrust, thrust coefficient
(Cf), Specific Impulse (Isp) and total impulse (I) will be lower
then when operating at higher local atmospheric pressure. The
following list of input variables are required to define the selected
propellant grain of the solid rocket motor.
NOTE: Specifying End Burning Grains
Set the core diameter
to zero with Cored End Burner selected which automatically
reverts the analysis to a pure endburning configuration. The only
burning surface is one end of the grain because the core diameter
is zero. An easy way to do this with AeroIsp is to set the number
of inhibited ends to 1 and to use zero for the core diameter which
reverts the analysis to an endburning configuration.
INPUT VARIABLE DEFINITIONS
1) Expansion
ratio: Standard Core Grain, Moonburner grain, C Slot grain, Pellet
grain, Cored End Burner grain, Star grain.
Ratio of the exit area to the throat area of the nozzle portion
of the solid rocket motor.
2) Local atmospheric pressure: Standard Core grain, Moonburner
grain, C Slot grain, Pellet grain, Cored End Burner grain, Star grain.
Absolute pressure of the environment in psia outside of the exhaust
plume of the solid rocket motor.
3) Outside grain diameter: Standard Core grain, Moonburner
grain, C Slot grain, Pellet grain, Cored End Burner grain, Star grain.
Outside diameter of the propellant grain in inches.
4) Grain length: Standard Core grain, Moonburner grain, C Slot
grain, Pellet grain, Cored End burner grain, Star grain.
Total overall length of the propellant grains in inches.
5) Number of grain ends inhibited: Standard Core grain, Moonburner
grain, C Slot grain, Pellet grain, Cored End Burner grain, Star grain.
Inhibited ends prevent burning on selected surfaces of the propellant
so the initial burning area can be controlled and reduced. An
inhibitor is a layer of slow or non-burning material applied to
a surface of the propellant grain. The number of inhibited ends
can be either 0, 1 or 2 depending on the grain geometry selected.
If 0 is specified the grain
is burning on both end surfaces and on the core surface. The grain
gets shorter as it burns. If 1 is selected the grain is burning
on one end surface and on the core surface. The grain also gets
shorter as it burns. If 2 is selected the grain is only burning
on the core surface and the grain remains the same length while
the core burning surface area increases. In real life hobby rocket
motors the grains are normally not inhibited on either end. Therefore,
the number of inhibited ends is 0 for most hobby rocket motors.
Definition of Number of grain ends inhibited.
Red Indicates Burning Surfaces and Black Indicates Inhibited Ends.
6) Nozzle throat diameter: Standard Core grain, Moonburner
grain, C Slot grain, Pellet grain, Cored End Burner grain, Star grain.
Minimum diameter of a converging-diverging rocket nozzle, in inches.
7) Grain core diameter: Standard Core grain, Moonburner grain,
Pellet grain, Cored End Burner grain.
Inside diameter of the internal burning surface of the propellant
grain.
8) Number of propellant grains: Standard Core grain, Moonburner
grain, Star grain.
Total number of propellant grains making up a stack of propellant
grains of total length, L.
9) Core center to grain side offset: Moonburner (Offset Port)
grain.
Distance from the outside diameter of the grain to the center
of an offset core for Moon Burner grains in inches.
10) Slot width: C Slot grain.
Circumferential width of a C Slot grain in inches.
11) Slot depth: C Slot grain.
Distance from the outside diameter of the grain to the internal
surface of a C Slot grain in inches.
12) Pellet
outside diameter: Pellet grain.
Outside diameter of each pellet in inches.
13) Pellet length: Pellet grain.
Overall length of each pellet in inches.
14) Number of pellets: Pellet grain.
Total number of pellets making up the total mass or volume of
propellant.
15) Radius of flat part of nozzle: Cored End Burner grain.
Internal radius of the nozzle near the exit end of the propellant
grain in inches.
16) Core depth: Cored End Burner grain.
Depth of the hole from the exit end of the grain to the inner
most part of the internal core in inches.
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17) Star Grain Geometry Specific Data a) Outside grain diameter (D), inches. b) Web grain thickness (W), inches. c) Tip radius of star (r1), inches. d) Internal radius of star (r2), inches. e) Separation angle (ETA), degrees. f) Secant fillet angle (Xi), degrees. g) Number of star points (Npts), 1 point to as many points allowed by the geometry. |
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EXAMPLE - STAR GRAIN INPUT DATA
Figure-1, AeroIsp Input Propellant Selection of the Trip Barber
BP Propellant - Star grain with 2 inhibited ends (ends not burning).
Figure-2, AeroIsp Input Propellant Selection of the Trip Barber
BP Propellant - Star grain with 0 inhibited ends (both ends burning).
STAR GRAIN VALIDATION
AEROISP 4-POINT STAR
VERSES NASA SP-8076 DERIVED RESULTS
Figure-3,
4-point star validation runs displaying Force verses time and star geometry
plots for both ends inhibited.
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INPUT
DATA FROM STRAND BURNER TESTS
BACK
The rocket motor
industry standard for determining linear burn rate, r is the so-called
Crawford bomb technique first proposed in 1947. Strands of propellant
3 mm to 6 mm in diameter and 10 mm to 150 mm long are coated with
an inhibitor to prevent side burning. RTV silicone rubber may
be used to totally inhibit burning on all sides of the propellant
strand except for the open end that will be exposed to burning.
The strand of propellant is supported in a holder and then inserted
in a vessel that will be pressurized by nitrogen gas. To start,
the vessel is pressurized to some initial pressure using a pressure
regulator. Then, the open end of the strand is ignited by a hot
wire or fuse and the burn time is measured by the time it takes
for the burning surface to reach the second fuse at the base of
the propellant strand. The pressure in the vessel is measured
at the beginning and end of the burn and the time it takes for
the strand to burn to the second fuse is recorded. The burn time
for the test is the time lapse between ignition of the open end
of the strand and the time it takes for the second fuse at the
base of the strand to ignite. The burn rate (r) for the test is
simply the initial length of the strand divided by the burn time.
The chamber pressure (Pc) for the test is the average of the initial
vessel pressure and the final vessel pressure at the end of the
test. Measuring the time lapse between igniter ignition and second
fuse ignition is more accurate than measuring burn time from the
pressure rise in the chamber, although this is a viable alternative
for burn time measurement. Usually, several measurements at increasing
initial pressure are required to generate a series of (r, Pc)
data points. For the strand test to be valid the burning surface
should remain planar and normal to the strand axis for all burns
so extra care applying the inhibitor should be taken.
 Figure-1, Definition of burn rate (r), where r = a * Pc^n. Burn rate is also called the surface recession rate. The red segment is the burning surface. |
 Figure-2, Strand Test Pressure Vessel Set-up. The red segment is the burning surface. |
SECTION 2: DETERMINE BURN RATE
COEFFICIENTS FROM EXPERIMENTAL DATA
PROCEDURE TO DETERMINE a,
n, B, 1/(1-n), RATIO OF SPECIFIC HEATS AND DENSITY
(1) Determine
the thermo-chemical properties of the combustion exhaust gases.
The following thermo-chemical properties are required: combustion
chamber temperature (Tc), molecular weight (M), ratio of specific
heats (g), and propellant density
(r). Please refer to Space
Propulsion Analysis and Design, Chapter 4 or use GuiPEP,
a thermo-chemical equilibrium computer program to determine Tc,
M, g and r.
(2) Determine exhaust gas characteristic velocity, Cstar from
isentropic analysis. Cstar
is used to compare the relative performance of different rocket
propulsion designs and propellants.The computation of Cstar is
illustrated in the step-by-step example
below. However, other formulations include: Cstar = Pc*At/M =
Isp*g0/CF = c/CF, where Pc is the chamber pressure, At is the
throat area and M is the mass flow rate of the rocket motor, Isp
is the specific impulse, CF is the thrust coefficient, c is the
effective exhaust velocity and g0 is the gravitational constant.
A more theoretical formula for Cstar is described in Rocket
Propulsion Elements on page 62, equation 3-32 and many more
basic rocket propulsion equations can be found on page 83 and
84 of that book.
(3) Measure at least four (4) burn rate and chamber pressure data
point combinations (r,Pc) to determine burn rate coefficient and
burn rate exponent using the strand burner pressure vessel. Determine
burn rate coefficient (a) and burn rate exponent (n) from curve-fit
programs such as CURVEFIT.exe or Excel. Select the
"power" form of the equation, y = a * x^n in
the curve-fit program to determine burn rate coefficient, a and
burn rate exponent, n. The chamber pressure (Pc) and burn rate
(r) measured in the Crawford bomb pressure vessel are presented
in Table-1. From the burn rate data in Table-1, CURVEFIT.exe determined
the burn rate coefficient (a) to be 0.0831 and the burn rate exponent
(n) to be 0.3858.
(4) Plot the resulting St. Robert's Law burn rate equation (r
= a * Pc^n) for r verses Pc on a log10 chart for the vertical
(r) and horizontal axes (Pc). To be correct, the plot should be
a linear relation where the slope of the log-log plot represents
the burn rate exponent (n) and the log(a) intercept determines
the burn rate coefficient (a). St. Robert's Law very accurately
represents the burn rate relationship for many composite propellants
including ammonium nitrate and ammonium perchlorate.
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Table-1, Strand Burner Measurement
Data and Curve-Fit Results.
(5) Graphical Method (Optional): For those without access
to a curve fit program, the burn rate coefficient (a) and burn
rate exponent (n) may be determined graphically. First, plot burn
rate data on log-log chart paper with the horizontal axis representing
chamber pressure (Pc) and the vertical axis representing burn
rate (r). Then, draw a straight line through the measurements
that best determine the average "spread" of the data
and continue the line to the r-axis.The origin of the chamber
pressure axis must be Pc =1.0 psig or Log(Pc) = 0.0. The slope
of the line is the burn rate exponent (n) and the burn rate coefficient
(a) is the intercept with the log(r) axis. The slope of the burn-rate
curve is determined by inserting any two points (r, Pc) on the
line into the equation, n = [ log(r2) - log(r1) ] / [ log(Pc2)
- log(Pc1) ] to determine the burn rate exponent (n). Finally,
the r-intercept represents log(a) of the burn rate coefficient,
where log(a) = log(r). The burn rate coefficient is determined
by the equation, a = 10^ log(a), where a is the inverse of log
(a).
Figure-3, Graphical Method to Determine
Burn Rate Coefficients, n and a in r = a * Pc^n.
(6) Determine the SRM burn-area ratio (Kn = Ab/At) which is the
ratio of the total burning area to the area of the throat at two
chamber pressures (Pc). Then, using these two values of Kn, determine
the pressure coefficient, B at the same two chamber pressures.
Finally, plug the resulting values of a, n, B, 1/(1-n), g
and r into AeroISP to perform an SRM analysis based on
the new propellant data. Please see the example
analysis for a detailed explanation of the procedure to define
a new propellant in AeroIsp using experimentally derived data.
NOTE: Determination of the equation of the r-intercept, log(a)
= log(r), is derived from the equation, r = a * Pc^n. The log
of both sides of this equation is, log(r) = log(a * Pc^n). Then,
the basic log relations, log(x * y) = log(x) + log(y) and log(x^n)
= n * log(x) result in the equation, log(a) = log(r) - n * log(Pc).
Finally, if Pc is 1.0, the final result is, log(a) = log(r), which
represents the r-intercept of the burn-rate curve with the vertical
axis of the log-log plot.
(7) AeroIsp's Built-In Curve Fit Analysis: AeroIsp has a
built-in methodology for the determination of burn rate coefficient (a) and burn
rate exponent (n) that uses the Method of Least Squares for the "power" form of
the equation, y = a * x^n. The Method of Least Squares analysis
determines the values of log(a) and n by fitting a straight line to the set of
ordered pairs { log(Pc), log(r) }. For a complete display of the curve fit
equations please click Help and then References and Theory. Also
displayed in References and Theory is the equation that determines the
standard error (Se) of the curve fit estimate. The number of ordered pairs of
experimental data may vary from a minimum of 3 to a maximum of 25 ordered pairs
of Pc and r for the power function fit. In addition, the Maximum Plot
Pressure may be defined to be 10, 100, 1000, 10000, or 100000 psi and the Minimum Plot
Pressure may be defined to be 1, 10, 100 or 1000 psi by simply selecting each value from a
separate pull-down menu. An interesting feature of the built-in curve fit
analysis is its ability to determine the effect of each additional data point on
the "quality of fit" by changing the Number of Data Pairs to
instantaneously see the resulting curve fit line and its changing slope.
In addition, Pressure Coefficient (B), Characteristic velocity (ft/sec), and
Pressure exponent [ 1/(1-n) ] may be determined by the following thermo-chemical
input values. Flame temperature, (Tc) in degrees Rankin, Ratio of specific
heats, Propellant weight density [ lbf/in^3 ] and Propellant gas molecular
weight (M). The thermo-chemical properties must be determined by a separate
program such as
GuiPEP to determine Tc,
M, g and r. When complete, click, INSERT to install the propellant
properties on the main screen.
Figure-4, Burn rate data curve fit analysis by method of least squares.
See Section 2 of this report for similar methods.
TESTING SMALL SOLID
ROCKET MOTORS (SRMs)
Optionally, the burn rate
coefficients may be determined by static testing small solid rocket
motors (SRMs). Some manufactures prefer to test small SRMs with
simple grain configurations, no restrictors and with different
throat sizes to obtain burn rate data at different chamber pressures.
Similar to strand burner tests, the small SRM test results are
plotted in the form of log (r) verses log (Pc) to determine burn
rate coefficient (a) and burn rate exponent (n) using curve-fit
programs like CURVEFIT.exe and Excel or by graphical
means.
MATHCAD
EXAMPLE SRM CUSTOM PROPERTIES ANALYSIS
Figure-5, Burn Rate Coefficients MathCAD Analysis.
AEROISP NOTES
1) AeroIsp must be installed in the following default directory: C:/Program
Files/AeroIsp/. Program installation into any other directory will cause the
following message to be displayed: "Error Reading PROPCHAR File". The user does
not need to take any action for program installation to occur into the default
directory. After installation the AeroIsp executable (AeroIsp.exe) may be
relocated anywhere but the PROPCHAR.DAT data file needs to be in the
AeroIsp directory to use the propellant data base during program execution.
REFERENCES
Star Grain Analysis: NASA SP-8076, Solid
Propellant Grain Design and Internal Ballistics
Space Propulsion Analysis and Design, By Hubble, Henry and Larson
Rocket Propulsion Elements,
By George P. Sutton
Aerospace Design Engineers Guide, By the AIAA
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