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2021-04-04 14:08:36 -07:00
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_posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation.Rmd
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@@ -38,6 +38,9 @@ using Measurements: value, uncertainty
using CSV
```
## The Simulation
An off the shelf paintball gun tank was used for the pressure vessel. This was chosen because they are very high pressure for their weight, and are designed to be bumped around.
```{julia}
@@ -66,14 +69,14 @@ 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 actual simulation is actually quite simple. The basic idea is that using the current pressure you can calculate $\dot{m}$, which allows calculating the Thrust, and then you can just subtract the current mass of air in the tank by $\dot{m}$ and recalculate pressure using the new mass then repeat the whole process.
The following equations also came from [@cengel_thermodynamics]
The rocket equation is pretty sick[@sutton_rocket_2001, eq: 2-14]:
The bulk of the equations in the simulation came from [@cengel_thermodynamics], while the Thrust and $v_e$ equations came from [@sutton_rocket_2001, eq: 2-14].
$$T = \dot{m} \cdot v_\text{Exit} + A_\text{Nozzle} \cdot (P - P_\text{Ambient}) $$
And thats about all you need to get to the Moon[@curtis_orbital].
$$ T = \dot{m} \cdot v_\text{Exit} + A_\text{Nozzle} \cdot (P - P_\text{Ambient}) $$
The initial pressure difference is `r julia_eval("P0 - P_amb |> u\"psi\"")` which is absolutely massive so the area of the nozzle greatly affects the simulation. The paintball tanks do come with pressure regulators, in our case 800 psi which is still a very large number compared to atmospheric pressure. While the total impulse of the system doesn't really change with different nozzle areas the peak thrust and _burn time_ vary greatly. One of the benefits of doing air propulsion, and the reason it was even considered so seriously, is that it should be possible to vary the nozzle diameter in flight which would make controlled landing much easier.
```{julia}
df = let
@@ -83,7 +86,6 @@ M = V * (P / (R * T)) |> u"kg"
ts = 1u"ms"
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"
@@ -104,17 +106,10 @@ df = DataFrame(Thrust=(0 ± 0)u"N", Pressure=P0, Time=0.0u"s", Mass=M)
end
```
breakdown of the data
```{julia, layout="l-body", echo=FALSE, results='asis'}
b = IOBuffer();
t = TextDisplay(b);
display(t, "text/html", describe(df));
table = String(take!(b)); # https://stackoverflow.com/a/60443621/8774114
```
## Analysis
Heres the results plotted. Notice the massive error once the tank starts running low.
Heres the results plotted. Notice the massive error once the tank starts running low. This is because the calculation for pressure has a lot of variables that are very uncertain. This is mostly due to air being a compressible fluid which is what makes this simulation so difficult to do accurately. The thrust being below 0 N might not make intuitive sense, but its technically possible for the pressure to compress which would leave the inside of the rocket nozzle with a pressure thats actually below atmospheric pressure. The effect would likely last a fraction of a second but the point stands that this simulation is very inaccurate and only meant to get an idea of what an air propulsion system is capable of.
```{julia, code_folding=TRUE, results='show',layout="l-body-outset", fig.cap = "Air Proplsion Simulation"}
@@ -135,7 +130,7 @@ plot(df.Time .|> ustrip, thrust_values,
```
Here the air prop is plotted along with rocket motors that are being
In Figure 2, the air propulsion simulation is compared to commercially available rocket motors. This early in the project we have no idea whether short burns or longer burns are ideal for a propulsive landing so the air propulsion system was compared to a variety of different motors.
```{julia, code_folding=TRUE, results='show',layout="l-body-outset",fig.cap= "Rocket Motor Data: [@thrustcurve]"}