IntroductionLate in the summer of 1999, I set out to design and construct a rocket motor quite unlike any previous motor that I'd previously developed. All the motors that I had built previously were powered by the KN-Sucrose propellant. These were of relatively simple design, which provided a high thrust with a very short burn, a consequence of unrestricted-burning grains. The steel casings used for these motors were well suited to this purpose, providing the required strength at the high temperatures experienced during operation. This approach resulted in highly reliable motors that were capable of rapidly boosting my rockets aloft, which helped ensure stability of the rockets.
My goal then became one to design a motor that would be capable of boosting a rocket to a much higher altitude, targeted at 10 000 feet, or 3 km. This represented a nearly threefold increase in altitude with respect to any previous rocket I had launched. Preliminary analysis indicated that K-Class performance of about 2000 N-s impulse would be capable of achieving this goal with a sufficient margin to allow for a respectably sized rocket and payload. I opted to design the motor to operate interchangeably with either of the two contemporary, and easier to cast propellants: KN-Dextrose and KN-Sorbitol. Although I considered the use of KN-Sucrose as a third alternative, this option was later dropped, as it would have necessitated modifications to the nozzle due to the more rapid burn rate
Physically, the size of the proposed motor was such that the use of steel for a casing would have resulted in a significant weight penalty, since steel has a density of nearly three times that of aluminum alloy (for similar strength). The obvious reason for minimizing motor "dead" mass is to make the rocket lighter, providing improved mass ratio, or increased payload capacity. But another important motive is stability. A heavy motor drives the rocket c.g. aft, which is opposite to what is desired.
Another key departure from my earlier designs was the grain configuration. An unrestricted-burning grain with consequential high thrust and short burn time would impose undesired high g-loading to any sensitive payload. As well, due to the high terminal velocity, the aerodynamic drag penalty would be particularly great. It was felt that a better approach was to have the motor produce lower thrust, but with a longer burn time. As such, a BATES grain profile was chosen, with the grain consisting of four individual segments. Burning would occur at the central core as well as the segment ends. This necessitated developing an effective means of inhibiting the outer segment surfaces from burning (this would turn out to be the most formidable and frustrating challenge). Motor capacity allows for a grain mass of up to 1.5 kg (3.3 lb.). Empty weight of the assembled motor is 2.40 lbs. (1.09 kg.).
In order to design the motor, an Excel spreadsheet was created which used the propellants' characterization data to calculate predicted motor performance, such as chamber pressure and thrust as a function of time. From this, predicted total impulse and specific impulse could be derived for various motor and grain configurations. The starting point for all this, however, was the motor casing. Earlier that summer, I had come upon a quantity of 2 ½ inch thin-walled 6061 aluminum alloy tubing. This formed the basis for designing the Kappa motor. Since I wanted to minimize overall motor mass, and maximize operating efficiency, the structural limit of this casing material set the maximum operating pressure (MEOP) of the motor.
During the development phase, the Kappa motor was static test fired a total of four times, and was subsequently used to propel the Cirrus One rocket to an altitude of over 10,000 feet, in April 2001.
Altitude simulations using the SOAR program predict that the Kappa rocket motor will boost a 15 lb. (7 kg.) , 2.5 inch (6.35 cm) diameter rocket , with a constant Cd=0.4, to an altitude of over 11 000 feet (3.3 km.). Maximum mach number would be 0.90. A similar rocket designed for minimal drag and slightly reduced mass could achieve Mach 1.07 (initial Cd=0.25, Cd@M1.07=0.417).
The Pyrogen Igniter as installed in the Forward Bulkhead, is illustrated in Figure 8. The detail of the pyrogen canister is shown in Figure 9. The canister is machined from 6061-T6 aluminum alloy bar stock, and retained by six screws that are identical to those that retain the nozzle. This design allows for the pyrogen to be installed on site, for safety considerations.
RTV is employed to seal the canister against the bulkhead, and to seal the screw threads.
The Igniter Body (see Eng. Dwg. #18) is fabricated from a #10-32 steel machine screw with a hole drilled centrally through. The igniter leads are fed through the hole, and sealed and secured by filling the hole with epoxy. The igniter filament consists of a 3 mm length of #36 nichrome wire soldered to the leads (which are looped at the ends to facilitate soldering).
The pyrogen main charge consists of a grain of KN-Sucrose propellant, chosen for its rapid burn rate. The propellant is cast directly into the canister, with a 0.25 inch (6.4 mm) core centrally cast. Initiation of grain burning is accomplished by use of Ignition Powder. To ensure rapid response, a burst diaphragm is employed to seal the canister to allow for pressure buildup. The diaphragm consists of thin cardboard of 0.0165 inch (0.42 mm) thickness, RTV bonded to the canister end. To assist ignition of the motor top segment, the canister has 6 radial ports located around the side walls, to divert a portion of the gas flow. Initially, these ports are sealed with burst tape (masking tape).
A bench test of the Pyrogen assembly was conducted prior to its use in an actual motor static test. The performance was impressive, with nearly instantaneous ignition of the powder, followed by pyrogen grain ignition a split-second later. The flame was about 2 feet (0.6 m.) long, and burn duration was about 2 seconds. In actual operation, the burn duration would be shorter, due to the effect of confinement.
The drawback to using cardboard as an insulating material is that it tends to char quite severely. An advanced insulation material that will be considered for future use is ceramic paper such as Cotronics Rescor 300 or 3M Nextel. These high-temperature papers are fabricated from alumina based refractory fibres, and have a service temperature of 1300oC - 1650oC, which should provide for an ideal casing insulator.
Final segment weight is required to be 375 grams maximum, for a total grain mass of 1.500 kg (excluding inhibitor). Due to unavoidable waste during the casting operation (typically 20%), the batch size should be a minimum of 450 grams of mixture, per segment.
Note that KN/Dextrose propellant is fully hard once it has cooled. The mandrel is removed typically after 1.25 hours. The KN/Sorbitol propellant, on the other hand, must be allowed to harden (cure) for 20 hours (minimum) before mandrel removal.
Installation of the segments into the motor simply involves sliding the segments into place, each separated by a spacer ring (see Eng. Dwg.#20). A spacer ring is also placed between the first segment and the nozzle. The spacer rings are made from short lengths of 2.50 inch diameter tubing (same material as casing), with a slot cut-out, which allows the rings to be slightly compressed to the required diameter. This also produces a spring-like behaviour which holds the rings in place even after the segments have burned away.
The calculated Kn (ratio of propellant burning area to nozzle throat area) for the Kappa motor is shown in Figure 11. The BATES grain configuration provides, ideally, a nearly neutral Kn, with initial Kn=317, maximum Kn=378, and final Kn=360.
The thrust v.s. time data is given in Figure 12 for the Kappa-DX motor, showing both the design (predicted) curve, and the static test results (KDX-002). Similar data is provided for the Kappa-SB motor in Figure 13, where the actual curve is that of static test KSB-002.
The actual performance of the Kappa-DX motor is in good agreement with the design curve, delivering a total impulse of 2003 N-sec., compared to the target impulse of 2076 N-sec. Delivered specific impulse was 137 sec., compared to the target of 141 sec.
The actual performance of the Kappa-SB motor suffers in comparison to the design target. The reason for the odd thrust curve is speculated to be a result of negative erosive burning. As such, the delivered total impulse is less than the predicted value of 1987 N-sec., producing 1821 N-sec., with the delivered specific impulse being 125 sec. compared to the target value of 137 seconds.
The chamber pressure time history is given in Figure 14 for the Kappa-DX motor, showing both the design (predicted) curve, and the static test results (KDX-002). Similar data is provided for the Kappa-SB motor in Figure 15, where the actual curve is that of static tests KSB-001 combined with KSB-002.
Note that the shape of the pressure curves (both design and actual) closely parallel the thrust curves. This is to be expected, as the chamber pressure and thrust are directly related by the thrust coefficient (Cf), which may be considered to be the degree of amplification of thrust generated by the nozzle. The Cf for the Kappa-DX motor is shown in Figure 16.