<commit_before>- var subtitle = 'Astronautics';
- var home = '.';


doctype html
html(lang='en')
  include ../inc/head.jade
  body
    include ../inc/header.jade
    div#main-wrapper: main(role='main')
      include ../inc/latex-declarations.jade



      section
        h1#definitions Definitions
        table.c-quantity-table
          thead
            tr
              th Symbol
              th Quantity
              th Units
          tbody
            tr
              td: var g#[sub 0]
              td Gravitational acceleration (at sea level)
              td m s#[sup &minus;2]
            tr
              td: var I#[sub SP]
              td Specific impulse
              td s
            tr
              td: var M
              td Mass
              td kg
            tr
              td: var M#[sub 0]
              td Initial mass
              td kg
            tr
              td: var M#[sub b]
              td Burnout mass
              td kg
            tr
              td: var P#[sub a]
              td Ambient pressure
              td Pa (N m#[sup &minus;2])
            tr
              td: var P#[sub e]
              td Exit pressure
              td Pa (N m#[sup &minus;2])
            tr
              td: var V
              td Velocity
              td m s#[sup &minus;1]
            tr
              td: var V#[sub e]
              td Exit velocity
              td m s#[sup &minus;1]
            tr
              td: var V#[sub ex]
              td Exhaust velocity
              td m s#[sup &minus;1]



      section
        h1#rocket-equation The rocket equation
        p \[ \ddx{V}{t} = -V_{ex} \frac{1}{M} \ddx{M}{t} \]
        p \[ \Delta V = V_{ex} \ln{\left(\frac{M_0}{M_b}\right)} \]



      section
        h1#chemical-propulsion Chemical propulsion
        p The following equations apply to high-thrust propulsion systems such as chemical propulsion
        h2 Thrust equation
        p \[ T = \ddx{m}{t} V_e + (P_e - P_a) A_e = \ddx{m}{t} V_{ex} \]
        h2 Impulse
        p \[ I = \int_0^t{T\dx{t}} = \int_0^t{-\ddx{M}{t} V_{ex}\dx{t}} = -V_{ex}\int_{M_0}^{M_b}{\dx{M}} = V_{ex}(M_0-M_b) = V_{ex}M_e \]
        p \[ I = K \sqrt\frac{T}{M} \]
        p \[ \frac{\Delta V}{V_{ex}} = \ln{\left(\frac{1}{1-\frac{M_e}{M_0}}\right)} \]
        h2 Specific impulse
        p \[ I_{SP} = \frac{I}{M_e g_0} = \frac{V_{ex}}{g_0} \]
        p \[ T = g_0 I_{SP} \ddx{m}{t} \]
        p \[ \Delta V = I_{SP} g_0 \ln\frac{M_0}{M_b} \]
<commit_msg>Astronautics: reorganise propulsion content<commit_after>- var subtitle = 'Astronautics';
- var home = '.';


doctype html
html(lang='en')
  include ../inc/head.jade
  body
    include ../inc/header.jade
    div#main-wrapper: main(role='main')
      include ../inc/latex-declarations.jade



      section
        h1#definitions Definitions
        table.c-quantity-table
          thead
            tr
              th Symbol
              th Quantity
              th Units
          tbody
            tr
              td: var g#[sub 0]
              td Gravitational acceleration (at sea level)
              td m s#[sup &minus;2]
            tr
              td: var I#[sub SP]
              td Specific impulse
              td s
            tr
              td: var M
              td Mass
              td kg
            tr
              td: var M#[sub 0]
              td Initial mass
              td kg
            tr
              td: var M#[sub b]
              td Burnout mass
              td kg
            tr
              td: var P#[sub a]
              td Ambient pressure
              td Pa (N m#[sup &minus;2])
            tr
              td: var P#[sub e]
              td Exit pressure
              td Pa (N m#[sup &minus;2])
            tr
              td: var V
              td Velocity
              td m s#[sup &minus;1]
            tr
              td: var V#[sub e]
              td Exit velocity
              td m s#[sup &minus;1]
            tr
              td: var V#[sub ex]
              td Exhaust velocity
              td m s#[sup &minus;1]



      section
        h1#rocket-equation Tsiolkovsky rocket equation
        p \[ \ddx{V}{t} = -V_{ex} \frac{1}{M} \ddx{M}{t} \]
        p \[ \Delta V = V_{ex} \ln{\left(\frac{M_0}{M_b}\right)} \]



      section
        h1#propulsion Propulsion

        h2 Specific impulse
        p \[ I_{SP} = \frac{I}{M_e g_0} = \frac{V_{ex}}{g_0} \]
        p \[ T = g_0 I_{SP} \ddx{m}{t} \]
        p \[ \Delta V = I_{SP} g_0 \ln\frac{M_0}{M_b} \]



      section
        h1#chemical-propulsion Chemical propulsion
        p The following equations apply to high-thrust propulsion systems such as chemical propulsion.
        h2 Thrust equation
        p \[ T = \ddx{m}{t} V_e + (P_e - P_a) A_e = \ddx{m}{t} V_{ex} \]
        h2 Impulse
        p \[ I = \int_0^t{T\dx{t}} = \int_0^t{-\ddx{M}{t} V_{ex}\dx{t}} = -V_{ex}\int_{M_0}^{M_b}{\dx{M}} = V_{ex}(M_0-M_b) = V_{ex}M_e \]
        p \[ I = K \sqrt\frac{T}{M} \]
        p \[ \frac{\Delta V}{V_{ex}} = \ln{\left(\frac{1}{1-\frac{M_e}{M_0}}\right)} \]


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