VR sword haptics, part 2

Another option for a VR haptics sword is to use jets mounted to the tip of the sword create reaction torques. In spacecraft design, these are called cold gas thrusters. They work on the same principle as any jet engine or rocket - mass ejected from a system causes an equal and opposite momentum change in the system - except there is no combustion. A minimum of three nozzles (or maybe just one plus a direction actuator) mounted equally spaced in a plane normal to the sword would be able to generate torques about any combination of two axes.

What kind of pressures and flow rates would be required to generate the required thrusts? For an ideal nozzle, the imparted thrust equals the mass flow rate of the jet times the velocity of the jet:

F = ṁv

For supersonic flow from a diverging nozzle, jet exit velocity and mass flow rate are dependent on the inlet pressure, the nozzle throat diameter, and the type of gas. Hot, low density gases have better performance, but compressed air at room temperature is certainly easiest to use for this application. For a 200psi (14atm) inlet pressure, a 4mm diameter nozzle throat will allow the flow rate required to produce about 20N of thrust, which at a 1m lever arm of course means about 20N*m felt at the handle.

What would a system designed to generate these flows and pressures look like? Ideally, very little mass would be attached to the sword, especially the tip, so that swinging it around doesn’t take too much effort, and so that the jets have less momentum to counter. A proportional control (throttleable) air valve rated to the required pressure and flow rate costs maybe a few hundred dollars and weighs maybe 0.5kg, if well designed. A few of these would be too heavy to place at the tip, but a pipe running from handle to tip would be able to conduct the air with minimal pressure drop and keep the jet response time on the order of 20ms.

A tank large enough to hold enough pressurized air for even a minute of gameplay would be too large and heavy to be mounted to the handle, so the sword would have to be connected to an external supply hose. For continuous operation, a large stationary compressor and tank would be required - think large 6ft (2m) tall machine shop setups.

So, like the gyroscope approach, a reaction jet haptic sword would probably be too expensive for the consumer market. However, a reaction jet haptic sword would be significantly simpler to design and prototype, though it has the disadvantages of being tethered and very loud.