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_posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation.Rmd

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+---
+title: "Air Propulsion Simulation"
+description: |
+  Simulating the performace of an air propulsion system as an alternative to solid rocket motors. 
+author:
+  - name: Anson Biggs
+    url: https://ansonbiggs.com
+repository_url: https://gitlab.com/lander-team/air-prop-simulation
+date: 04-01-2021
+fig_width: 6
+fig_align: "center"
+output:
+  distill::distill_article:
+    self_contained: false
+categories:
+  - Julia
+  - Capstone
+---
+
+Boilerplate intro about why all of this was done
+
+```{r setup, include=FALSE}
+library(ggplot2)
+knitr::opts_chunk$set(echo = TRUE, results = 'hide')
+library(JuliaCall)
+julia_setup(JULIA_HOME = "/opt/julia-1.6.0/bin/")
+```
+
+```{julia, code_folding=TRUE}
+using Plots
+plotly()
+theme(:ggplot2); # In true R spirit
+
+using Unitful
+using DataFrames
+using Measurements
+using Measurements: value, uncertainty
+```
+
+This code is just the setup the setup, using values scraped from various parts of the world wide web. 
+
+```{julia}
+# Tank https://www.amazon.com/Empire-Paintball-BASICS-Pressure-Compressed/dp/B07B6M48SR/
+V = (85 ± 5)u"inch^3"
+P0 = (4200.0 ± 300)u"psi"
+Wtank = (2.3 ± 0.2)u"lb"
+Pmax = (250 ± 50)u"psi" # Max Pressure that can come out the nozzle
+
+Wsolenoid = 1.5u"kg"
+
+# Params
+d_nozzle = ((1 // 18) ± 0.001)u"inch"
+a_nozzle = (pi / 4) * d_nozzle^2
+
+# Universal Stuff
+P_amb = (1 ± 0.2)u"atm"
+γ = 1.4 ± 0.05
+R = 287.05u"J/(kg * K)"
+T = (300 ± 20)u"K"
+```
+
+This is the actual simulation. Maybe throw some references in and explain some equations.
+
+The rocket equation is pretty sick:
+
+$$T = \dot{m} \cdot v_\text{Exit} + A_\text{Nozzle} \cdot (P - P_\text{Ambient}) $$
+And thats about all you need to get to the moon. 
+
+```{julia}
+let
+t = 0.0u"s"
+P = P0 |> u"Pa"
+M = V * (P / (R * T)) |> u"kg"
+ts = 1u"ms"
+global df = DataFrame(Thrust=(0 ± 0)u"N", Pressure=P0, Time=0.0u"s", Mass=M)
+  while M > 0.005u"kg"
+      # while t < 30u"s"
+      # Calculate what is leaving tank
+      P = minimum([P, Pmax])
+      ve = sqrt((2 * γ / (γ - 1)) * R * T * (1 - P_amb / P)^((γ - 1) / γ)) |> u"m/s"
+      ρ = P / (R * T) |> u"kg/m^3"
+      ṁ = ρ * a_nozzle * ve |> u"kg/s"
+  
+      Thrust = ṁ * ve + a_nozzle * (P - P_amb) |> u"N"
+  
+      # Calculate what is still in the tank
+      M = M - ṁ * ts |> u"kg"
+      P = (M * R * T) / V |> u"Pa"
+      t = t + ts
+  
+      df_step = DataFrame(Thrust=Thrust, Pressure=P, Time=t, Mass=M)
+      append!(df, df_step)
+  end
+end
+```
+
+Heres the results plotted. Notice the massive error once the tank starts running low.
+
+```{julia, echo=FALSE, results='show'}
+
+thrust_values = df.Thrust .|> ustrip .|> value;
+thrust_uncertainties = df.Thrust .|> ustrip .|> uncertainty;
+
+out = DataFrame(Thrust=thrust_values, Uncertainty=thrust_uncertainties, Time=df.Time .|> u"s" .|> ustrip);
+
+
+plot(df.Time .|> ustrip, thrust_values, 
+    title="Thrust Over Time", 
+    ribbon=(thrust_uncertainties, thrust_uncertainties), 
+    fillalpha=.2,label="Thrust",
+    xlabel="Time (s)", 
+    ylabel="Thrust (N)",
+    )
+```
+
+
+Big conclusion about things. 
+