• dickalan@lemmy.world
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    4 days ago

    Achieving Ballistic Velocity (The Tsiolkovsky Cow Equation)

    The **Rocket Equation** is brutal:

    `Δv = Isp * g₀ * ln(m₀ / m_f)`

    Where:

    * `Δv` = Change in velocity needed (`11,186 m/s` for escape).

    * `Isp` = Specific impulse (`~360 s` for CH4/LOX).

    * `g₀` = Gravity (`9.81 m/s²`).

    * `m₀` = Initial mass (cow + engines + LOX + methane).

    * `m_f` = Final mass (just… cooked cow?).

    **Assumptions:**

    *   Engine mass: `300 kg` (mini-Raptor).

    *   LOX mass: **5x** methane mass (rocket ratio).

    *   Methane stored: `500 kg` (we’re pumping hard).

    *   `m₀ = 700 (cow) + 300 (engine) + 500 (CH₄) + 2,500 (LOX) = 4,000 kg`.

    *   `m_f = 700 kg` (cow, assuming engines/tanks detach).

    **Calculation:**

    `Δv = 360 * 9.81 * ln(4,000 / 700)`

    `= 3,531.6 * ln(5.71)`

    `= 3,531.6 * 1.74`

    `= ~6,150 m/s`.

    **Result:** **6,150 m/s < 11,186 m/s**.

    → **Verdict:** Suborbital cow. Maximum apogee: **~1,000 km** (a very high moo).

    → **Impact Velocity:** **~3-4 km/s** (kinetic energy = 0.5 * 700kg * (3,500m/s)^2 ≈ **4.3 gigajoules**).

    → **Effect:** Creates a **10m wide crater**, vaporizing the cow and any nearby farmers. A true “pasture bomb.”