reusable first stage rockets - colorado college · 2020. 2. 10. · the rocket formula figure 1....

By Tamman Montanaro Reusable First Stage Rockets The Rocket Formula Figure 1. Robbert Goddard’s design of the first ever rocket to fly in 1926. Source: George Edward Pendray. Divide by dt Divide by m Figure 2: Flight path for the Falcon 9; After separation, the first stage orientates itself and prepares itself for landing. Source: SpaceX Thrust @vac = 7.543 MN Total Mass = 5.135 x 10 5 kg First Stage Mass = 3.975 x 10 5 kg Propellant Mass = 3.728 x 10 5 kg I sp @vac = 312 seconds H first stage = 40.9 m Burn Time = 102 seconds V cutoff = 1666 m/s H cutoff = 75.5 km Orbit = 620 km x 660 km x 47 o Merlin 1D mass (first stage) = 4230 kg Flight Specifications Launch Source: SpaceX (web, launch video, flight logs) Flip Maneuver How much time does it take for the first stage to descend? We assume this is the time it takes for the first stage to reorientate itself. How much mass is lost? What is the mass loss? What is the center of mass? Let us think of the first stage in two parts: a uniform hollow and solid cylinder stacked on one another. Assume cold gas thrusters that provide the force to flip are at a height of 35.8 meters and that the height of separation is 10.23 meters. What is the moment of inertia? What is the force required from the cold gas thrusters if we assume constancy. y 1 = 15.338 m m 1 = 2.047 x 10 4 kg y 2 = 5.115 m m 2 = 1.613 x 10 5 kg The moment of inertia of a solid disk: r per Now lets stack a bunch of these solid disk on each other: Length = l Figure 3: Falcon 9 first stage after landing on drone barge. Source: SpaceX If we do the same for the hollow cylinder, we get a moment of inertia of: Specific impulse for a rocket: On December 22 nd 2015, the Falcon 9 Orbcomm-2 first stage lands successfully. This is the first ever orbital- class rocket landing. From the video and flight logs, we can gather specifications about the first stage. What is the constant force required for its journey halfway (assuming that the force required to flip it 90 o is the equal and opposite to stabilize the flip). What is the moment of inertia about the center of mass for these two objects? Assuming constant alpha: With t = 62 sec, = 90 0 , and r = 29.53 m

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By Tamman Montanaro

Reusable First Stage Rockets

The Rocket Formula

Figure 1. Robbert Goddard’s design of the first ever rocket to fly in 1926. Source: George Edward Pendray.

Divide by dt

Divide by m

Figure 2: Flight path for the Falcon 9; After separation, the first stage orientates itself and prepares itself for landing. Source: SpaceX

Thrust @vac = 7.543 MNTotal Mass = 5.135 x 105 kgFirst Stage Mass = 3.975 x 105 kgPropellant Mass = 3.728 x 105 kgIsp @vac = 312 seconds

Hfirst stage = 40.9 mBurn Time = 102 secondsVcutoff = 1666 m/sHcutoff = 75.5 kmOrbit = 620 km x 660 km x 47o

Merlin 1D mass(first stage) = 4230 kg

Flight Specifications

Launch

Source: SpaceX (web, launch video, flight logs)

Flip ManeuverHow much time does it take for the first stage to descend? We assume this is the time it takes for the first stage to reorientate itself.

How much mass is lost? What is the mass loss?

What is the center of mass? Let us think of the first stage in two parts: a uniform hollow and solid cylinder stacked on one another. Assume cold gas thrusters that provide the force to flip are at a height of 35.8 meters and that the height of separation is 10.23 meters.

What is the moment of inertia? What is the force required from the cold gas thrusters if we assume constancy.

y1 = 15.338 m m1 = 2.047 x 104 kg

y2 = 5.115 m m2 = 1.613 x 105 kg

The moment of inertia of a solid disk:rper

Now lets stack a bunch of these solid disk on each other:

Length = l

Figure 3: Falcon 9 first stage after landing on drone barge. Source: SpaceX

If we do the same for the hollow cylinder, we get a moment of inertia of:

Specific impulse for a rocket:

On December 22nd 2015, the Falcon 9 Orbcomm-2 first stage lands successfully. This is the first ever orbital-class rocket landing. From the video and flight logs, we can gather specifications about the first stage.

What is the constant force required for its journey halfway (assuming that the force required to flip it 90o is the equal and opposite to stabilize the flip).

What is the moment of inertia about the center of mass for these two objects?

𝑟

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Assuming constant alpha:

With t = 62 sec, 𝜽 = 900, and r = 29.53 m

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