Design of a Sorbitol-Based I-Class Solid Rocket Motor
The goal is to design, manufacture and static fire a Solid Rocket Motor with "Sugar Rocket Propellant" with a total impulse of around 450 Newton Seconds.
The requirement for this motor is to have a total impulse of around 450 Newton Seconds and to fit into a 38mm motor tube so through an iterative design process a 6 grain layout was chosen along with the inner grain diameter and the throat diameter in order to get the total impulse to the desired target while maintaining the MEOP below 3.8 MPa and the port-to-throat ratio higher than or equal to 2 in order to reduce the chances of erosive burning.
| Average Thrust: | 430 N. |
|---|---|
| Total Impulse: | 486 N-sec. |
| Thrust Duration: | 1.13 sec. |
| Diameter: | 38 mm |
| Specific Impulse | 125.6 sec. |
| Diameter: | 38 mm |
|---|---|
| Overall Length: | TBD mm |
| Propellant Mass: | 395 g. |
| Total Mass: | TBD g. |
| Port-to-Throat ratio: | 2 |
|---|---|
| Motor length/diameter: | 11 |
| Volumetric Loading Fraction: | 69% |
This motor uses Potassium Nitrate/Sorbitol (KNSB) propellant because of its ease of casting and safety when compared to other "sugar" based rocket propellants such as Potassium Nitrate/Sucrose (KNSU) that hardens quickly and needs higher temperatures to fully melt.
| Ingredients: | Percentage |
|---|---|
| Potassium Nitrate | 65% |
| Sorbitol | 35% |
To the above, 0.2% of Sodium laureth sulfate (SLES) surfactant is added to reduce the viscosity of the mixture to make the grain casting process much easier.
The Potassium nitrate is ground to a fine powder (100 um majority particle size) with an electric coffee grinder. Then the mixture is weighed with a precision scale and thoroughly mixed with an electric tumbler.
The grains are to be coated with an ignition primer so that ignition
happens instantly throughout the motor to have a steeper pressure
increase thus having a more flat thrust curve instead of a "spike" that
can be seen in many KNSB motors.
Ignition primer consists of:
| Ingredients: | Percentage |
|---|---|
| Potassium Nitrate | 80% |
| Carbon Powder | 20% |
To this mixture, isopropyl alcohol is added until the mixture gets to a thin, paint-like consistency and then it is brushed onto all exposed grain surfaces and is left to dry for at least 24 hours.
| Outer Diameter: | 32 mm |
|---|---|
| Core Diameter: | 15 mm |
| Length: | 60 mm |
The grain length was chosen to be 60mm to get a neutral thrust-time curve and to follow the average grain length/diameter for 38mm solid rocket motors (around 2).
After the propellant has been mixed it is poured into a non-stick milk pot with a spout that is heated to 125°C. Then it is mixed with a silicone spatula until fully melted. When fully melted the SLES must be added and stirred to reduce the viscosity of the mixture to facilitate easier casting. When all of this is done, the propellant is poured into the casting tubes that have the inhibitor and core rod already placed in them. The coring rod must be lined with rice paper to make it easier to demould the grain. After pouring the molten propellant, the pressure ring must be added to cure the grain under pressure to avoid air pockets and voids inside the grains.
The grains are left to cure and harden for 5 days in an air-tight box with desiccant bags. After the grains have fully cured they should be density checked for voids and air. The target density ratio is >0.95
This design uses rubber O-Rings for spacers, specifically 28mm ID, 3mm thickness O-Rings.
The inhibitor is a two-ply poster-board glued to create a hollow cylinder.
The thermal liner is again a two-ply poster-board but this time a thin layer of lacquer is applied in the inner surface to eliminate charring.
The material for the motor casing was chosen to be 6063-T6 Aluminum
mainly because of its high tensile strength and for its relative
availability.
The outer diameter is 38 mm to fit with readily available motor tubes
for rockets. With a thickness of 2 mm the inner diameter comes out to 34
mm.
Using Barlow’s formula
We can calculate that the bursting point of the casing comes to 26.3 MPa
so by knowing the MEOP of the system to be 3.67 MPa we can calculate
that the safety factor comes out to 7.2.
The bulkhead will also be machined from aluminum 6063-T6 and will be
"free floating" inside the motor held by a retaining ring.
Sealing will be achieved with two O-Rings.
The Bulkhead will be held inside the motor with an internal retaining
ring.
A Thing to consider about retaining rings when designing cases is that
-most of the times- if you push them to their limits the groove will
fail before the retaining ring itself does.
We can calculate the failing point of the retaining ring itself with the
formula given below:
R**s = D ⋅ T ⋅ S**s ⋅ π Where R**s is the maximum allowable load for the retaining ring (N), D is the housing diameter (mm) and S**s is the shear strength of the material of the retaining ring (MPa)
Using this formula we can calculate that the retaining ring will fail at
157 kN of force. If we calculate for pressure (dividing the force by the
area of the bulkhead) we can see that the motor has to reach a pressure
of 172.94 MPa for the retaining ring of the bulkhead to fail. This
result raises the problem that if the motor over-pressurizes that the
casing will fail before the bulkhead thus becoming a pipe bomb which
would be quite dangerous. But as was stated above, the groove that the
retaining ring sits into will fail with a lot less force than what is
needed to break the retaining ring itself.
We can calculate the force needed for the groove to fail with the
formula given below:
Where n is the edge margin of the groove and d is the depth of the groove as shown below:
We can now calculate that the load needed for the bulkhead retaining ring groove to fail is 12.11 kN, to reach that, the chamber pressure has to be 13.3 MPa, which produces a safety factor of 3.63. This pressure is well below the 26.31 MPa that the casing needs in order to break, helping us ensure that in case of over-pressurization the bulkhead will fail before the casing.
The nozzle will be made from mild steel with 15 degree convergent
half-angle and 40 degree divergent half-angle and a throat diameter of
10.6 mm.
The optimal expansion ratio for the nozzle was calculated to be 7 with
the equation below:
The loss of performance due to the straight-cut region in the nozzle was calculated and deemed to be insignificant for the design of this motor (1 sec. of specific impulse lost for 3 mm throat length)
Sealing will be achieved with two O-Rings.
Utilizing the same formulas used for the bulkhead we can calculate that the groove of the nozzle’s retaining ring needs a load of 17.55 k**N in order to fail, calculating for pressure, the chamber has to reach 14.9 MPa in order for the retaining ring groove to give in and break. We can observe that the groove of the nozzle needs 1.6 MPa more pressure in order to fail, that is favorable because the nozzle is harder to machine than the bulkhead.
For the ignition a simple blackpowder pyrolant will be used placed inside a drinking straw with a 10 mm section of nichrome (nickel-chromium) wire. The blackpowder will be packed tightly inside the straw and then silicone will be used to seal the whole igniter.
Calculations for the amount of blackpowder used are TBD. The goal is
when the ignition occurs that the ingiter and ignition primer gasses do
not exceed the MEOP of the motor (3.67 MPa)
I am now calculating the mass per area that the ignition primer can coat
so i can calculate the pressure rise due to the primer to then calculate
how much pressure there is left over for the igniter to finally
calculate the igniter mass.
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