**Derivation of Table for Estimated Ejection Charge
Size**

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**

The
constants for 4F black powder are:

**R**
= 266 in-lbf/lbm

**T** =
3307 degrees R (combustion temp)

**P** =
pressure in psi

**V** =
volume in cubic inches =
pi*(**D**/2)^{2}**L**

**N** =
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*D**^{2}L (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.

**
However**,
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** =
pi*(**D**/2)^{2 }
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
listed above.