Richard Nakka’s Experimental Rocketry Web Site
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Introduction
to Rocket Design
Appendix H
Sizing the Ejection Charge
Introduction
As mentioned in the Introduction to Rocket Design – Recovery System webpage, pyrotechnic material such as Crimson Powder or Black
Powder is used as part of a
rocket Recovery Deployment system. This material supplies the energy needed to
forcibly separate a rocket into two parts in order to destabilize a rocket,
allowing it to tumble after reaching apogee, or to deploy a drogue chute, or to
deploy a main parachute. This appendix provides details on sizing a pyrotechnic
ejection charge.
Overview
Figure 1 illustrates a pyrotechnic charge firing, pressurizing the
closed compartment in which the pyro device is contained. The pressure acts equally
on all sides of the enclosure…the walls (body tube), fixed bulkhead and the
AvBay base bulkhead. In this example the AvBay is held to the rocket body by a
set of nylon screws. As we want this particular joint to ‘fail’ in order to
separate the AvBay from the rest of the rocket, the magnitude of pressure
generated by the pyro must be sufficient such that the force acting on the
AvBay base bulkhead is greater than the combined shear strength of the nylon
screws.
Figure
1: Pyro charge firing
Sizing
the Charge
The ideal
gas law is employed to estimate
the pressure generated by a given mass of deployment charge material:
where:
P = pressure (N/m2 or psi)
V = volume of enclosure (m3 or in3)
m = mass of deployment charge (kg or lbm)
R = specific gas constant of combustion products
(J/kg-K or in-lbf/lbm-°R)
T = combustion temperature (K. or °R.)
Rearranging to solve for mass of deployment charge:
The specific heat
constant and the combustion temperature are both properties associated with the
deployment charge combusion products.
Volume of a cylindrical
enclosure is given by:
V = ¼ π D2 L
where:
D = inside diameter of enclosure (m. or in.)
L = length of enclosure (m. or in.)
The pressure that must be developed by combustion of the
deployment charge is that which will cause the nylon screw joint to fail. The force to fail the joint is given by:
Ffail = N Fshear
where N= number of screws and Fshear is the shear
strength of an individual nylon screw.
and as such, the
pressure is given by this force times the cross-sectional area of the
cylindrical enclosure:
The use of Crimson Powder and Black Powder as deployment charge material
are considered next.
Crimson Powder
Crimson Powder (CP) was
developed over 20 years ago by Peter Ericksson as a substitute for Black Powder
as a deployment charge. Crimson Powder has certain advantages over Black Powder
such as lower combustion temperature, higher potency and has an odourless
residue that cleans up easily with water. Crimson Powder is somewhat
hygroscopic and must be stored in a sealed container with desiccant (calcium
chloride is best). I have used CP exclusively
as a deployment charge over the past decade.
In order to obtain the
needed combustion parameters (R and T ), the combustion of Crimson Powder is analyzed using ProPep. Both R and T vary somewhat with pressure, but not significantly. As
such, the ProPep analysis is run at 100 psi. An
excerpt of the pertinent results is shown below.
Code WEIGHT D-H
DENS COMPOSITION
0 POTASSIUM NITRATE 6.200 -1169
0.07670 1 N 3 O
1 K
0 ASCORBIC ACID 4.500 -1581
0.05960 6 C 8 H
6 O
0
IRON OXIDE
0.500 -1230 0.18400
3 O 2 FE
THE
PROPELLANT DENSITY IS 0.07042 LB/CU-IN
OR 1.9491 GM/CC
THE
TOTAL PROPELLANT WEIGHT IS 11.2000
GRAMS
****************************CHAMBER
RESULTS FOLLOW
*****************************
T(K) T(F)
P(ATM) P(PSI) ENTHALPY ENTROPY
CP/CV GAS RT/V
1515 2268
6.80 100.00 -14.98
18.65 1.1387 0.259
26.255
SPECIFIC
HEAT (MOLAR) OF GAS AND TOTAL =
10.377 14.361
NUMBER
MOLS GAS AND CONDENSED = 0.259 0.035
The specific gas constant, R, is given by
the universal
gas constant , R¢, divided by the effective molecular mass of the
gaseous products, M.
R = R¢/M
And the effective molecular mass is given by the system mass
divided by the number of gas moles. Therefore, for Crimson Powder, using the
MKS system for convenience of calculation, and converted to US units:
M = 11.2/0.259 = 43.2 kg/kmole 95.2 lbm/kmole
R = 8314/43.2 = 192.3 J/kg-K 429 lbf-in/lbm-°R
The combustion temperature for a constant
pressure (isobaric) process, which ProPep assumes (as is
applicable to a rocket motor), is:
Tp = 1515 K.
However, combustion of our deployment charge takes place in a
condition of constant volume (isochoric). The combustion temperature will be higher, as
no pressure-volume work is done by the expanding gases. The ratio of specific
heats (CP/CV) is used to factor up
the temperature to that of a constant volume process:
Tv = 1.1387 (1515) = 1725 Kelvin 3105° Rankine
As an example, consider 0.600 grams of Crimson Powder combusted in
a cylindrical enclosure of the following dimensions:
D = 3.48 cm.
L = 22.0 cm
Calculate the pressure that will be developed.
V = ¼
π (3.48)2 22.0 = 209 cm3 = 0.000209 m3
Or, in US units, 139 psi.
This is the theoretical
pressure obtained by the combustion of 0.600 grams of Crimson Powder. How does
this compare to the actual pressure
developed in such a closed vessel? Bearing in mind that the deployment charge
is a flight
critical component, I felt it was prudent to do some testing. As such I performed combustion testing, using
three samples of Crimson Powder (0.600, 1.224 and 1.699 gram specimens). The results, in comparison to theoretical, are shown below.
The measured pressures are indeed comparable to the theoretical. I
speculate that the lower pressures measured at the two higher levels are a
result of heat transfer to the vessel, which increases with pressure. As such,
using the ideal gas law with the aforementioned parameters for the combustion
of Crimson Powder is justified, when used in combination with a suitable design
factor.
Black Powder
Black Powder (BP) is the
earliest known explosive powder, originating in China in the 9th
century A.D. As a general rule, BP is comprised of a mixture of potassium
nitrate, charcoal and sulphur.
There have been
countless recipes developed over the centuries with great variation in the
percentages of each of the constituents. The modern, or standard,
formulation is considered to be the following:
Potassium nitrate 75%
Charcoal 15%
Sulphur 10%
(fun facts: certain
versions have little or no sulphur; one recipe uses 33% charcoal!)
There are various mil-specs for BP such as MIL-P-223 which states
the following formulation:
Potassium nitrate 74%
± 1%
Charcoal 15.6%
± 1%
Sulphur 10.4%
± 1%
Even though commercial BP has a consistent formulation, the fly
in the ointment, when it comes to
predicting performance as a deployment charge, is the charcoal
component. Charcoal, which is manufactured by the destructive distillation of
wood, has no standard chemical formula. It generally conforms to a composition
of about 75-80% carbon, with the remainder consisting of volatile content.
Exact formulation is dependant upon the type of wood and processing method (in
particular distillation temperature). As shown in the table below, not only
specific chemical composition, but also enthalpy
of formation (DfH°) varies greatly depending upon tree species.
The enthalpy of formation is a key parameter used in combustion temperature
calculation.
Ref. Journal of
Pyrotechnics, Iss.No.9, 1999
Even the Mil-spec is
vague with regard to specifying charcoal:
Charcoal
shall be prepared by the destructive distillation of willow, alder or suitable
hardwoods in such a manner as to yield charcoal of the best composition and
cleanliness of burning.
Different manufacturers use their own charcoal blend and
associated processes. For example, Schuetzen black powder is made with a blend of Alder,
Hazelnut, and Maple charcoals using a strict quality-control process to ensure
consistent and optimum performance.
There are several
on-line BP ejection charge calculators (example). They all seem to use the same T and R values, but
unfortunately I have been unable to find a reference for these particular
values:
R = 22.16 ft-lbf/lbm-°R.
T = 3307 °R.
A ProPep
analysis of BP using three different tree species (Oak, Maple & Pine) of charcoal was run at a pressure of 100 psi
to determine T and R.
Black Powder has been
used as an igniter pyrolant for solid propellant rocket motors. NASA
SP-8051 (Solid Rocket
Motor Igniters) conveniently gives the impetus
for BP:
where impetus (l), also refered to as effective
force, is given by:
An excerpt of the
pertinent ProPep results, together with the values for the on-line calculators (converted
to MKS units) and SP-8051, is shown in the table below. An example calculation
for pressure is done for 1 gram of BP assuming an arbitrary volume of 209 cm3
.
where Tv = flame
temperature at constant volume condition.
A comparison of the
impetus for the five suggests that the on-line calculator value is on the low
side. On one hand, this is conservative with regard to sizing the deployment
charge. On the other hand, an overly powerful ejection charge may be problematic,
depending on the type of recovery deployment system utilized.
As an example, consider 0.600 grams of Black Powder made with
maple charcoal combusted in a cylindrical enclosure of the following
dimensions:
D = 3.48 cm.
L = 22.0 cm
V = 209 cm3 = 0.000209 m3
Calculate the pressure
that will be developed.
Or, in US units, 125 psi.
Example 1 - Sizing the deployment
charges for Xi Rocket
Last updated December
6, 2024
Originally posted December
6, 2024