### Some euler laws, some pretty css

rorist 1 year ago
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fd69a5fe03
2 changed files with 95 additions and 18 deletions
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 @@ -0,0 +1,11 @@ +.rendered_html { + font-size: 40%; +} +.rendered { + font-size: 70%; +} +.rise-enabled .fa-times-circle:before, +.rise-enabled .fa-question:before, +.rise-enabled aside.controls { + opacity: 0.1; +}

#### + 84 - 18 slides.ipynb View File

 @@ -8,7 +8,7 @@  }  },  "source": [ - "# Aerodynamic" + "# Aerodynamics"  ]  },  { @@ -25,19 +25,80 @@  },  {  "cell_type": "markdown", - "metadata": {}, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + },  "source": [ - "## Newton laws\n", + "## Newton's laws of motion\n", + "\n",  "### Net force is zero\n",  "\\n", - "\\sum \\mathbf {F} =0\\;\\Leftrightarrow \\;{\\frac {\\mathrm {d} \\mathbf {v} }{\\mathrm {d} t}}=0\n", + "\\mathbf{\\sum {F}} = 0\n",  "\\n", + "\n",  "### Change of momentum\n",  "\\n", - "\\mathbf {F} =m\\,{\\frac {\\mathrm {d} \\mathbf {v} }{\\mathrm {d} t}}=m\\mathbf {a}\n", + "\\mathbf{\\vec{F}} = m\\vec{a}\n", + "\\n", + "\n", + "### For every action, there is an equal and opposite reaction\n", + "\\n", + "F_{A} = -F_{B}\n",  "\"  ]  }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "source": [ + "First law:\tIn an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.\n", + "\n", + "Second law:\tIn an inertial frame of reference, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma.\n", + "\n", + "Third law:\tWhen one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Euler's laws of motion\n", + "### Linear momentum\n", + "\\n", + "\\mathbf{p} = m{v} _{cm}\\\\\n", + "\\n", + "\n", + "\\begin{align}\n", + "\\textrm{with,}&\\\\\n", + "{p} &= \\textrm{Linear momentum}\\\\\n", + "m &= \\textrm{Mass of the object}\\\\\n", + "{v} _{\\rm {cm}} &= \\textrm{Velocity of its center of mass}\n", + "\\end{align}\n", + "\n", + "### Angular momentum\n", + "\n", + "\\n", + "\\mathbf{M} = {dL \\over dt}\n", + "\\n", + "\n", + "\\begin{align}\n", + "\\textrm{with,}&\\\\\n", + "L &= \\textrm{Angular momentum}\\\\\n", + "M &= \\textrm{Sum of external moment of Forces}\\\\\n", + "t &= \\textrm{Time}\\FIXME\n", + "\\end{align}" + ] + },  {  "cell_type": "markdown",  "metadata": { @@ -52,10 +113,10 @@  "\\n",  "\\begin{align}\n",  "\\textrm{with,}&\\\\\n", - "Cl &= \\textrm{lift coefficient}\\\\\n", - "r &= \\textrm{air density}\\\\\n", - "V &= \\textrm{velocity between object and air}\\\\\n", - "A &= \\textrm{wing area}\n", + "Cl &= \\textrm{Lift coefficient}\\\\\n", + "r &= \\textrm{Air density}\\\\\n", + "V &= \\textrm{Velocity between object and air}\\\\\n", + "A &= \\textrm{Wing area}\n",  "\\end{align}"  ]  }, @@ -77,12 +138,17 @@  "- flow speed (~angle of attack? type of airfoil?)\n",  "\n",  "- misconception\n", - " - bernoulli effect is debunked (faster = lower pressure)" + " - bernoulli effect is not THE explaination (faster = lower pressure)\n", + " - It's a combination of effects\n", + " - air compression at the tip of the wing\n", + " - accelerate the air on one side (kind of bernouilli)\n", + " - air is accelerated downward so the wing is pushed up\n", + " -> conservation of mass, momentum and energy"  ]  },  {  "cell_type": "code", - "execution_count": 33, + "execution_count": 3,  "metadata": {  "slideshow": {  "slide_type": "fragment" @@ -93,8 +159,8 @@  "name": "stdout",  "output_type": "stream",  "text": [ - "Cl=19.74\n", - "L=1088.12 [kN]\n" + "Cl = 19.74\n", + "L = 1088.12 [kN]\n"  ]  }  ], @@ -103,14 +169,14 @@  "\n",  "angle = 180 * pi/180\n",  "Cl = 2*pi*angle\n", - "r = 1.225 #kg/m3\n", - "V = 30 #m/s =~ 100km/h\n", - "A = 100 #m2\n", + "r = 1.225 # kg/m3\n", + "V = 30 # m/s =~ 100km/h\n", + "A = 100 # m2\n",  "\n",  "L = Cl*(r*V**2)*0.5*A\n",  "\n", - "print('Cl={:.2f}'.format(Cl))\n", - "print('L={:.2f} [kN]'.format(L/1000))" + "print('Cl = {:.2f}'.format(Cl))\n", + "print('L = {:.2f} [kN]'.format(L/1000))"  ]  },  {