Derivation of Table for Estimated Ejection Charge
First we assume the entire mass of the ejection
charge is burned and converted to a gas. Next from basic chemistry we
use the ideal gas law equation:
PV = NRT
constants for 4F black powder are:
= 266 in-lbf/lbm
3307 degrees R (combustion temp)
pressure in psi
volume in cubic inches =
mass in pounds. (Note: 454 gm/lb)
A good rule-of-thumb is to generally design for
15 psi pressure. If this is used as the design goal,
then the ideal gas equation reduces to:
N = 0.006*D2L (grams)
where D is the diameter in inches and
L is the length in inches of the compartment in the rocket that is to
be pressurized. N is the size of the ejection charge in grams.
on large diameter rockets, 15 psi will probably generate too much force!
For example, a 7.5-inch diameter rocket has 44 square inches of area on the
end of it so 15 psi would produce over 15*44 = 660 pounds of force!!
The amount of force needed for a large rocket is
going to depend on a great many factors, but a reasonable limit is probably
some where around 300-350 pounds. This is the same amount of force
generated in a 5.5-inch rocket at 15 psi.
We can refine our equations for large rockets by
adding a limit on the force that is to be generated. The force F
(in pounds) is given by:
F = PA
where P is the pressure in psi and A
is the area in square inches. Since A =
we can combine this equation with the ideal gas law equation to get:
N = 0.00052*FL (grams)
This last equation tells us how many grams N
of ejection charge to use to generate a specified force F in pounds
for a given length L of pressurized compartment. What is
interesting about this equation is that the diameter D is not
present. It means that for large rockets the ejection charge
size does not need to increase with body tube diameter.
Using these equations I created a handy
reference table for various body tube diameters. That table is the one