Hybrid motors are specifically rocket motors that use a fuel and an oxidizer that are in two different states, in this case, a solid fuel (plastic, cellulose, paper, etc) and a liquid/gaseous oxidizer (primarily nitrous oxide).  Nitrous Oxide has the stable characteristic of becoming a good to better oxidizer, the hotter it gets.  This fact allows it to be handled safely at room temperature, and provide a controlled burning with an ignition source, continuous flame. 
This, minus some ignition systems makes a motor system that is completely safe and "explosive free".  The fuel used, usually plastic can provide the same specific impulse as Ammonium Perchlorate Composite Propellant (APCP) motors at, in most cases, one third to one half the cost.

There are three types of hybrid motors systems approved for hobby rocket use and are listed below:

Aerotech's PyroValve™ Hybrid
This system uses standard Aerotech motor cases (54 and 98) with a modified injector bell style forward closure and flight tank.  The pyrovalve is a small domed membrane that seals the tank closed allowing  the tank to be filled off site/off pad.  A small grain of propellant is used to ignite the motor and the pryovalve is broken with a small charge, causing the nitrous to flow into a burning chamber.  The heat and the cellulose combine to provide thrust.  The main advantage to this system is the ability to use some standard motor hardware and there's no need for a dedicated nitrous fill and fire system.

The U/C Floating Injector Hybrid
The floating injector system is a hybrid motor using a standard diameter aluminum motor tube of various lengths.  The floating injector hybrid, or more correctly, the U/C Injector Hybrid was originally developed by John Urbanski and Bill Colburn, hence the term U/C Hybrid. This system is used by manufacturers such as R.A.T.T., Polymer Propulsion and West Coast Hybrids,  among others and is made up of 4 basic parts.  They are, the motor case, the nozzle, the injector bushing and the forward pressure closure.  Snap rings, retaining washers, tubing and seals as well as an ignition system are also used to complete the hardware requirements.  The U/C Injector portion consists of the fill and metering fitting system.  This consists of a brass nut, sleeve and metering orifice with a Nylon fill tube system routed up to the injector face, through the nozzle.
The name "floating injector" comes from the principle of how the injector bushing is positioned in the motor tube.  Under nitrous pressure, the injector bushing presses tight against the fuel grain and sleeve.  This allows different length fuel grains to be used and not affect the sealing capacity of the motor, nitrous tank as the injector "floats".  Filling is done on the pad prior to launch through the U/C fitting nylon tubing. 
To launch, the motor is filled until liquid nitrous is seen coming from the tank vent tube.  Ignition is either by a small amount of APCP propellant, or on some systems, through the burning of a small piece of steel wool or an Oxygen enhanced spark gap system.  This provides a sufficient amount of heat to melt the fill tube and start the plastic fuel grain/nitrous combustion cycle.  The advantage of this system is the minimum amount of specialized parts needed for the motor, motors can be doubled by changing the length of the case only, and the minimum of ground support equipment, lowering total launch cost

The HyperTek Hybrid
The HyperTek system, developed by Korey Kline, uses three major parts, an integrated  thermoplastic fuel grain/nozzle component, an injector bell and a Nitrous oxide flight tank.  The fuel grain component is a "throw-away" that is either used once for most combinations, or may be used once in the smaller tank combinations.  The injector bell system contains the injector orifice and is the seal interface for the grain and the tank, and is essentially, the heart of the system.  Orifices may be replaced or changed, where appropriate to regulate the burn profile of the motor as required by the user.  The tank has an integral vent tube, vented either to the side or the nozzle face of the motor to indicate when liquid is venting (indicating a full tank).  Ignition of the Hypertek Hybrid currently requires a specialized launch system described as "Fill & Fire, Ground Support Equipment" (GSE).  The GSE system controls the fill of the nitrous as well as a dump valve system, for safety, the igniter system which is a 7500 volt transformer and an O2 squirt system.

The rocket is loaded onto the rail while encompassing a  motor specific length, coaxial fill stem.  This fill stem is prepared with a igniter wire (see below text).  The fill stem enters through the nozzle and is inserted into the injector body, with the upper (center nitrous tube) seated and sealed into the center of the injector body and open to the fill tank.  The fill stem is then tied, via "pull ties", to the motor to insure the pressure of the flight tank cannot eject the fill stem from the injector body.

The fill and fire sequence is as follows:
The nitrous flight tank is filled through the center tube with a venting of air and gaseous nitrous out of the tank vent tube.  Once liquid nitrous is sensed or seen at the vent, the fire sequence is started.  Pure oxygen is introduced into the fuel grain through the outer tube of the coaxial fill stem, at the forward end of the fuel grain.  A 7500 volt spark is then fired through a length of 24 gauge speaker wire and in the presence of the oxygen rich atmosphere, ignites the fuel grain.  The heat from this burning process escapes out the motor nozzle, subsequently melting the stem pull ties.  This either allows the rocket to rise off of the stem, as long as the pressure in the tank against the fill stem is greater than the total vehicle weight or, in the case of larger rockets, allows the stem to drop a maximum of 1 inch.  This releases the liquid nitrous to flow into the burning chamber, and the subsequent full thrust cycle is started.


Summary
Hybrid motors are a excellent way to expand the flight preparation experience and with the adjustable features of grain types and orifice adjustments, provides the maximum potential for performance tuning.  The benefits of lower cost fuel and the minimum or non use of APCP allows less regulatory pressure on the flyer.


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