Update SIM_balloon README. #1210

trick_sims/SIM_balloon/README.md

@@ -4,11 +4,38 @@ A hot-air balloon is a lighter than air air-craft consisting of 1) an envelope (
 As the air inside the envelope is heated it becomes less dense than the cooler outside air, making the balloon more buoyant. This is how we will control the balloon, by changing the temperature of the air in the balloon’s envelope.
 
 
-
 ![Balloon Parts](Images/Picture1.png)
 
 The characteristics of the outside-air will be determined using a static atmospheric model called the US Standard Atmosphere.
 
+## U.S. Standard Atmosphere Model
+
+The US Standard Atmosphere is a static model of pressure, temperature, density, gravitational acceleration, and viscosity as functions of altitude. 
+
+In this simulation, the following four C-language functions are implemented using
+data found at [www.engineeringtoolbox.com](https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html). 
+
+
+```double US_STD_density( double alt_m);```
+
+Returns atmospheric density (kg/m3) at the given altitude (m).
+
+```double US_STD_gravity( double alt_m);```
+
+Returns acceleration of gravity (m/s2) at the given altitude (m).
+
+```double US_STD_temperature( double alt_m);```
+
+Returns atmospheric temperature (℃) at the given altitude (m).
+
+```double US_STD_pressure( double alt_m);```
+
+Returns atmospheric pressure (pascals) at the given altitude (m).
+
+
+
+## Dynamics Model
+
 The forces acting on our balloon will be those of gravity, buoyancy and aerodynamic drag.
 
 ![Balloon Forces](Images/Picture2.png)
@@ -21,20 +48,23 @@ To help us calculate these forces we’ll use a static atmosphere model called T
 
 To find the state of the balloon, we integrate acceleration over time to get velocity. We then integrate velocity over time to get position.
 
-## Force of Gravity
+---
+
+### Force of Gravity
+
 Applying the acceleration of gravity to Newton’s 2nd Law:
 
 ![Equation 1](Images/Equation2.png)
 
-At sea-level, **g** is around 9.81 m/s2. But as altitude increases **g** decreases. To determine **g** for a given altitude we’ll use the ```US_STD_gravity()``` function from the provided function library.
+At sea-level, **g** is around 9.81 m/s2. But as altitude increases **g** decreases. To determine **g** for a given altitude we’ll use the ```US_STD_gravity(altitude)``` function from the atmosphere model library.
 
-### Balloon Mass
+#### Balloon Mass
 
 The total balloon mass is the sum of the fixed mass and the mass of the heated air inside the balloon envelope.
 
 ![Equation 1](Images/Equation3.png)
 
-#### Balloon Fixed Mass
+##### Balloon Fixed Mass
 The fixed mass is simply the sum of the balloon component masses:
 
 | Balloon Component    | mass     |
@@ -48,13 +78,13 @@ The fixed mass is simply the sum of the balloon component masses:
 
 
 
-### Mass of Air in the Balloon
+#### Mass of Air in the Balloon
 
 The mass of the air in the balloon envelope is the product of the volume of the balloon envelope and the density of the heated air within the envelope.
 
 ![Equation 1](Images/Equation4.png)
 
-### Balloon Volume
+#### Balloon Volume
 
 To calculate the volume the the balloon, we separate the balloon into two parts: 1) a spherical dome and 2) a cone.
 
@@ -70,15 +100,17 @@ The volume of the cone is:
 The total volume of the envelope is the sum of the two component volumes.
 ![Equation 1](Images/Equation7.png)
 
-### Air Density
+#### Air Density
 To calculate air density (𝝆) we use the following form of the Ideal Gas Law.
 ![Equation 1](Images/Equation8.png)
 
 * p is just the standard pressure (in pascals) at the balloon's current altitude. Use ```US_STD_pressure(altitude)```.
-* R-{air} is the specific gas constant for dry air. R-{air} = 287.055 J/kg K
+* R<sub>air</sub> is the specific gas constant for dry air. R<sub>air</sub> = 287.055 J/kg K.
 * T is the temperature of the gas in kelvin. The conversion from Celsius to kelvin is T-kelvin = T-celcius + 273.15.
 
-## Force of Buoyancy
+---
+
+### Force of Buoyancy
 
 Buoyancy is a force on an object, that opposes gravity, by a fluid within which it’s immersed. This force is equal to the mass of the displaced fluid times the acceleration of gravity.
 
@@ -87,8 +119,9 @@ Buoyancy is a force on an object, that opposes gravity, by a fluid within which
 Here, we can do that same calculation for air mass as before, using
 Eq#4, but this time with 𝝆 = US_STD_density(altitude), which assumes U.S Standard temperature at the given altitude.
 
+---
 
-## Force of Drag
+### Force of Drag
 
 As the balloon moves upward, or downward, it will be subjected to an atmospheric drag force. Drag is a function of the balloon’s shape [
 presented by the coefficient of drag (Cd)], the density of the air (𝝆), and the cross-sectional area (A) perpendicular to the velocity (v). The drag force points in the opposite direction as the velocity.
@@ -101,3 +134,23 @@ Since the balloon will be moving through our “standard atmosphere” 𝝆 = ``
 We’ll calculate the cross-sectional area (A) from the radius of the spherical portion of our balloon.
 
 ![Equation 1](Images/Equation11.png)
+
+## Graphics
+
+Before running the simulation, the graphics client needs to be compiled. ```cd``` into ```models/graphics```, and run ```make```.
+
+![](Images/BalloonGraphicsClient.png)
+
+When the simulation is run, the client will automatically be launched.
+
+## References
+
+* [https://www.engineeringtoolbox.com/molecular-mass-air-d_679.html](https://www.engineeringtoolbox.com/molecular-mass-air-d_679.html)
+* [https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html]
+(https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html)
+* [https://en.wikipedia.org/wiki/Ideal_gas_law]
+(https://en.wikipedia.org/wiki/Ideal_gas_law)
+* [https://en.wikipedia.org/wiki/Hot-air_balloon]
+(https://en.wikipedia.org/wiki/Hot-air_balloon)
+* [https://www.balloon-rides.com/atics-facts.htm]
+(https://www.balloon-rides.com/atics-facts.htm)