Astronaut Hovering with Jet Pack: Calculating Fuel Mass Flow Rate and Maximum Hover Time
Calculating Fuel Mass Flow Rate
A small rocket motor is used to power a "jet pack" device to lift a single astronaut above the Earth's surface. The rocket motor produces a uniform exhaust jet with constant speed, Ve = 2940 m/s. The total initial mass of the astronaut and the jet pack is Mo = 130 kg. Of this, 40 kg is fuel for the rocket motor. To keep the jet pack and astronaut hovering in a fixed position above the ground, we need to develop an algebraic expression for the variable fuel mass flow rate required.
Formula for Fuel Mass Flow Rate
The formula for the fuel mass flow rate needed to keep the jet pack and astronaut hovering is m' = Mg/Ve, where m' is the mass flow rate, M is the total mass of the astronaut and jet pack, g is the acceleration due to gravity, and Ve is the exhaust velocity of the rocket motor.
Calculating Maximum Hover Time
The maximum hover time aloft before the fuel supply is expended can be determined by calculating the total mass of fuel and using the mass flow rate. The formula for calculating the maximum hover time is t = Mf / m', where t is the time, Mf is the total mass of fuel, and m' is the mass flow rate.
A small rocket motor is used to power a "jet pack" device to lift a single astronaut above the Earth's surface. What is the formula for the variable fuel mass flow rate required to keep the jet pack and astronaut hovering in a fixed position above the ground? To keep a jet pack hovering above the ground, the rate of mass flow from the rocket must counteract the force of gravity on the total mass of the astronaut and the jet pack. This requires utilizing the formula m' = Mg/Ve.