Building a customised 1/4 scale patriot rocket
HP-I280DM DMS Rocket Motor. Specs:
Motor Type: SU
Delays: 6,8,10,12,14
Diameter: 38 mm
Length: 356 mm
Total Weight: 616 g
Prop. Weight: 355 g
Avg. Thrust: 280.0 N
Initial Thrust: 311.2 N
Max. Thrust: 386.0 N
Total Impulse: 561.0 Ns
Burn Time: 1.9 s
Propellant: Dark Matter
First an understanding of the solid fuel combustion process is needed. The nozzle:
Directs and accelerate combustion gasses to high velocities. Provides Choked flow to prevent catastrophic erosive burning. (Going supersonic in the propellant core)
Goal is maximum thrust coefficient with minimum nozzle weight.
Nozzle throat area controls combustion chamber pressure and divergent angle controls thrust amplification through the coefficient of thrust.
A typical nozzle design:
The motor’s length, inner and outer diameters are summarised here.
The solid fuel motor has a hollow core, the interior area of which is th eburn area. The $K_n$ burning-area to throat-area ratio determines the combusiton chamber pressure.
The longer the motor, the greater the erosive effect, due to more combustiongases flowing.
HP-I280DM Variables used:
Dc
= 38mmLc
= 356mmDo
= 18mmdo
= 36mm (assumed casing thickness ~2mm)Lo
= Lc
= 356mm (assumed 1 segment.)N
= 1$^{note}$ Details on the propellant type was quite difficult to find, as we are using a COTS motor. Perhaps a custom sugar motor might be an option for future launches. Regardless, a datasheet from RCS on the Metalstorm propellant for 38mm diameter solid motors is included in this repository, see:
resource_files/motor/rcs_propellant_grain_msds_11014.pdf
This mentions an Ammonium Perchlorate base with a rubber binder, which is usually HTPB. This is a typical solid fuel formulation shown below.
Credit to Georgia Tech
The AeroTech rockets use the “moonburner” grain design, shown here:
The SRM sheet (see resource_files/motor/SRM_2023.xls
) is made for sugar motors, but I figured it would still
do an okay job of generating ballpark nozzle dimensions:
Experimental Composite Propellant by Terry McCreary, PROPEL20.xls