DRAFT: Launch Operations

Abstract

The lecture on Launch, Ascent, and Entry Operations provided a detailed examination of the phases of spacecraft launch and re-entry, the dynamics involved, and the critical technologies. Topics included launch site logistics, propulsion principles, multistage rockets, rendezvous techniques, interplanetary travel strategies, and atmospheric re-entry mechanisms. The key objective was to underscore the challenges and methodologies involved in achieving mission success from Earth’s surface to space and back.

General Concepts

Launch Site Logistics:

The selection of launch sites considers orbital inclinations, geographic constraints, and infrastructure capabilities.
Pre-launch operations involve ground support equipment (GSE) design, scheduling, and compliance with safety standards.

Spacecraft Propulsion:

The Tsiolkovsky rocket equation governs ΔV and mass ratios.
Efficiency is measured by the specific impulse (Isp)

Overview over the different Isps of different propellants
For a LEO Launch with 4.5km/s exhaust velocity the mass ratio is about 10 → 90% of the mass is propellant
Different types of Propulsion Systems were discussed:
- CH4 + LOX
- Nuclear rocket engine
- Electric/Ion Propulsion

Launch and ascent to orbit

Orbit insertion: Bringing the spacecraft to a stable orbit
On different planets with different Atmospheres need different launch angles

Inclination and launch latitude: The minimum inclination of a spacecraft is the latitude of the launchpad. If the rocket launches eastwards (prograde Orbit) the earth rotation velocity can also be used.

Multistage Rockets:
- Dividing the propulsion system into stages optimizes the payload-to-orbit ratio.
Rendezvous and Docking in Low Earth Orbit (LEO):
- Techniques like Hohmann transfer and phasing maneuvers are crucial.
Interplanetary Travel:
- The patched conics method simplifies trajectory planning, leveraging the sphere of influence (SOI) for celestial bodies.
Atmospheric Re-entry:
- Methods such as skip entry reduce thermal loads.
- Thermal protection systems (TPS) are essential for managing the heat generated during re-entry.

Facts to Memorize

ΔV Calculation: ΔV=veln(mi/mf), where ve is the exhaust velocity, mi and mf are initial and final masses.

ΔV=veln⁡(mi/mf)\Delta V = v_e \ln(m_i/m_f)

vev_e

mim_i

mfm_f
Specific Impulse: Isp≈450s for cryogenic engines (LH2/LOX).

Isp≈450sI_{sp} \approx 450s
Mass Ratios: For 10 km/s velocity, 90% of the rocket’s initial mass is propellant.
Launch Inclinations: Launch sites near the equator (e.g., Kourou) allow inclinations down to 0°.

Important Formulas

Tsiolkovsky Rocket Equation:

$Δ V = v_{e} ln (\frac{m _{i}}{m _{f}})$
- Relates the change in velocity to mass and engine exhaust velocity.
With drag force and the gravity loss the formula looks like this:

$Δ V = g I_{s p} lo g_{e} (\frac{m _{i}}{m _{f}}) - (\int_{t_{0}}^{t_{f}} g sin γ d t + \int_{t_{0}}^{t_{f}} \frac{D}{m} d t)$

with:

D: Drag force in Newton

$γ$ : flight path angle (angle from horizontal)
Mass of propellant for a given $Δ v$
$Δ V = g I_{s p} lo g_{e} (\frac{m _{i}}{m _{f}}) ⟹ ⎩ ⎨ ⎧ m_{p} = m_{i} [1 - exp (- \frac{Δ V}{g _{0} I _{s p}})] m_{p} = m_{f} [exp (\frac{Δ V}{g _{0} I _{s p}}) - 1]$
With

$m_{i} :$ initial mass

$m_{f} :$ final vehicle mass

$m_{p} = m_{i} - m_{f}$
$a_{Dr a g} = \frac{1}{2} ρ v^{2} \frac{C _{D} A _{n}}{m} = \frac{1}{2} ρ v^{2} \times \frac{1}{BC}$

with:

$ρ : De n s i t y (k g / m^{3}) V : V e l oc i t y (m / s) C_{D} : Dr a g coe ff i c i e n t A_{n} : R e f ere n ce a re a (m^{2}) BC : B a ll i s t i c coe ff i c i e n t (k g / m^{2})$
Specific Impulse:Isp=m˙g0F

Isp=Fm˙g0I_{sp} = \frac{F}{\dot{m}g_0}
- Describes engine efficiency, where F is thrust, m˙ is propellant mass flow rate, and g0 is standard gravity.
  
  FF
  
  m˙\dot{m}
  
  g0g_0
Orbital Velocity:v=μ(r2−a1)

v=μ(2r−1a)v = \sqrt{\mu \left(\frac{2}{r} - \frac{1}{a}\right)}

🧑‍🚀 Space Systems

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DRAFT Launch Operations