Unformatted scripts are dumped here, in sequence. They are intended to be run in sequence after the relevant packages are added to the environment.
The ninth script may in some cases error on the first attempt due to a world-age issue. If that happens, just repeat once more in the same session.
For future proof (issues may arise with future versions), the exact Manifest.toml file is also dumped here.
These raw scripts refers a web-page internal function for generating html plots. Define this dummy to avoid the error messages:
last_plot_with_data_to_html(fnam) = nothing
import MechanicalUnits: @import_expand, dimension # HIDE
@import_expand(mm, cm, m, km, ft, inch, s, °, kg) # HIDE
println( 1km .|> (m, ft, m²/ft ))
println([dimension(x) for x in (m, ft, m²/ft)])import MechanicalUnits: @import_expand, dimension # HIDE
@import_expand(mm, cm, m, km, ft, inch, s, °, kg) # HIDE
println( 1km .|> (m, ft, m²/ft ))
println([dimension(x) for x in (m, ft, m²/ft)])import MechanicalUnits: @import_expand, dimension # HIDE
@import_expand(mm, cm, m, km, ft, inch, s, °, kg) # HIDE
using MechGluecode # HIDE
using DifferentialEquations, Plots, ArrayTools # HIDE
plotly() # HIDE
Plots.PlotlyBackend() # HIDE
u´(u,p,t) = 1.01s⁻¹ * u
const uᵢ = 0.5m
prob = ODEProblem(u´, uᵢ, (0.0, 2)s)
sol = solve(prob)
default(width = 5, framestyle = :zerolines, legend=(0.15, 0.9),
foreground_color_legend = nothing, background_color_legend = nothing)
plot(sol, label = "Interpolation curve")
scatter!(sol.t, sol.u, marker=true, linewidth=0, label="Exact points")
last_plot_with_data_to_html("output/script02.html") # HIDE, defined in 'generate_results_functions.jl'
const targval = 1.0m
condition(u,t,integrator) = (u - targval) / m
affect!(integrator) = terminate!(integrator)
cb = ContinuousCallback(condition, affect!)
solstop = solve(prob,Tsit5(), callback=cb)
plot!(solstop, xlims = (0,2)s,
label = "Solve process stopped at $targval",
linewidth = 8, color=:black)
scatter!(solstop.t, solstop.u, marker=true, linewidth=0,
label="Exact points, stopped at $targval")
last_plot_with_data_to_html("output/script03.html") # HIDE, defined in 'generate_results_functions.jl'
u´(u,α,t) = α * u
function time_to_targval(p)
sol = solve(prob, Tsit5(); callback=cb, p = p)
sol.t[end]
end
@time plot(time_to_targval, xlims = (1.00000/s, 1.5/s), xguide ="Parameter α",
label = "Time to reach $targval")
last_plot_with_data_to_html("output/script04.html") # HIDE, defined in 'generate_results_functions.jl'
import MechanicalUnits: g, ∙ #HIDE
"Barrel elevation"
α₀() = 26°
"Muzzle velocity"
v₀() = 1050m/s
let
Δt = 2 * v₀() * sin(α₀()) / g
Δx = v₀() * cos(α₀()) * Δt
println("Time until impact, Δt = ", round(s, Δt))
println("Horizontal distance, Δx = ", round(km, Δx))
end
using Interpolations # HIDE
using MechanicalUnits: Velocity, Density # HIDE
# Constants we don't think we'll change
const x₀ = 0.0km
const y₀ = 0.0km
const ø = (1900//127)inch
# Calculated constants
const Aₚᵣ = π/4 * ø^2
# 'Constants' that we might want to modify later
mₚ() = 495kg
x´₀() = v₀() * cos(α₀())
y´₀() = v₀() * sin(α₀())
c() = 323.0m/s
ρ() = 1.225kg/m³
# Functions of current velocities
const ptsM = [0, 0.5, 0.75, 0.875, 1, 1.125, 1.25, 1.5, 2, 2.5, 3.0]
const ptsCd = [0.155, 0.16, 0.165, 0.17, 0.2575, 0.3875, 0.3775,
0.3425, 0.2875, 0.245, 0.215]
Cₛ(vₘₐ::Real) = LinearInterpolation(ptsM, ptsCd, extrapolation_bc=Flat() )(vₘₐ)
Cₛ(v::T, c::T) where T<:Velocity = Cₛ(v / c)
v(vx, vy) = √(vx^2 + vy^2)
R(v::T, c::T, ρ::Density) where T<:Velocity = 0.5∙ρ∙Cₛ(v, c)∙Aₚᵣ∙v^2
α(vx, vy) = atan(vy, vx)
Rx(vx, vy, c, ρ) = R(v(vx, vy), c, ρ) * cos(α(vx, vy))
Ry(vx, vy, c, ρ) = R(v(vx, vy), c, ρ) * sin(α(vx, vy))
plot(Cₛ, xlims = (0,3), label = :none,
yguide = "Shape coefficient, Cₛ []", xguide = "Mach number, vₘₐ []",
title = "Interpolation curve, Cₛ(vₘₐ)" )
last_plot_with_data_to_html("output/script06.html") # HIDE, defined in from generate_results_functions.jl
"""
Γ₁!(Γ´, Γ´, p, t)
Local tuple with derivatives. p and t are not used.
"""
function Γ₁´!(Γ´, Γ, p, t)
(x, y), (x´, y´) = packout(Γ)
@debug "Γ" x y x´ y´ maxlog = 2
x´´ = -Rx(x´, y´, c(), ρ()) / mₚ()
y´´ = -1g -Ry(x´, y´, c(), ρ()) / mₚ()
@debug "Γ Acceleration" x´´|> g y´´|>g maxlog = 2
packin!(Γ´, x´, y´, x´´, y´´)
end
"Local tuple initial condition"
Γ₀() = ArrayPartition([x₀, y₀], [x´₀(), y´₀()])
packout(Γ) = Γ.x[1], Γ.x[2]
function packin!(Γ´, x´, y´, x´´, y´´)
Γ´.x[1][1] = x´; Γ´.x[1][2] = y´
Γ´.x[2][1] = x´´; Γ´.x[2][2] = y´´
return Γ´
end
using Logging: disable_logging, LogLevel, Debug, with_logger # HIDE
import Logging # HIDE
using Test: @inferred # HIDE
# Exit criterion - hit sea level
function terminate_condition(Γ, t, integrator)
(_, y), (_, _) = packout(Γ)
y / m
end
cb1 = ContinuousCallback(terminate_condition, affect!)
function solve_guarded(Γ´!; Γᵢₙ = Γ₀(), alg = Tsit5(), debug=false)
# Test the functions
@inferred packout(Γᵢₙ)
@inferred packout(0.01Γᵢₙ/s)
@inferred Γ´!(Γᵢₙ/s, Γᵢₙ, nothing, nothing)
# Define and solve
prob = ODEProblem(Γ´!, Γᵢₙ, (0.0s, 200s))
sol = if debug
with_logger(Logging.ConsoleLogger(stderr, Logging.Debug)) do
solve(prob, Tsit5(), callback = cb1)
end
else
solve(prob, Tsit5(), callback = cb1)
end
sol
end
sol₁ = @time solve_guarded(Γ₁´!, debug=true);
function time_distributed_motion_vals(;sol = sol₁, Γ´! = Γ₁´!)
ts = range(sol.t[1], sol.t[end], length = 300)
xs = map(t->sol(t).x[1][1], ts)
ys = map(t->sol(t).x[1][2], ts)
x´s = map(t->sol(t).x[2][1], ts)
y´s = map(t->sol(t).x[2][2], ts)
vs = map(hypot, x´s, y´s)
Γs = map(sol, ts)
dummyΓ´ = Γs[1] / (ts[2]- ts[1])
x´´s = [Γ´!(dummyΓ´, Γ, nothing, nothing).x[2][1] |> g for Γ in Γs]
y´´s = [Γ´!(dummyΓ´, Γ, nothing, nothing).x[2][2] |> g for Γ in Γs]
as = map(hypot, x´´s, y´´s)
ts, xs, ys, vs, as
end
function plotvals₁()
ts, xs, ys, vs, as = time_distributed_motion_vals()
Cₛs = map(v->Cₛ(v, c()), vs)
ρs = repeat([ρ()], length(Cₛs))
xlims = (0.0km, maximum(xs))
ts, xs, ys, vs, as, Cₛs, ρs, xlims
end
function bulletplots(f; trajectory_label = "Constant atmosphere α₀ = $(round(°, α₀()))",
p_y_x = plot(), p_v_x = plot(), p_v = plot(), p_Cρs= plot(), p_a= plot(),
kw...)
ts, xs, ys, vs, as, Cₛs, ρs, xlims = f()
plot!(p_y_x, xs, ys, xguide="x",
yguide ="y", label = trajectory_label; xlims, kw...)
plot!(p_v_x, xs, vs, xguide ="x",
yguide ="v"; xlims, label = trajectory_label, kw...)
plot!(p_v, ts, vs, yguide = "v"; label = trajectory_label, kw...)
plot!(p_Cρs, [ts ts], [Cₛs ρs], yguide = "Cₛ, ρ", color = ["Red" "Black"] ;
label = trajectory_label, kw...)
plot!(p_a, ts, as, yguide = "a", color = "Green", xguide = "Time",
label = trajectory_label; kw...)
return p_y_x, p_v_x, p_v, p_Cρs, p_a
end
# Subplots
p_y_x, p_v_x, p_v, p_Cρs, p_a = bulletplots(plotvals₁; linestyle=:dot)
# Assemble subplots
p_v_Cs_a = plot(layout = (3, 1), p_v, p_Cρs, p_a, legend=false)
last_plot_with_data_to_html("output/script10a.html") # HIDE, defined in from generate_results_functions.jl
p_y_x_v = plot(layout = (2, 1), p_y_x, p_v_x, legend=false)
last_plot_with_data_to_html("output/script10b.html") # HIDE, defined in from generate_results_functions.jl# Celsius temperature is affine, special treatment #HIDE
import MechanicalUnits: °C # HIDE
@import_expand(K, J, kPa) # HIDE
"Gas constant, dry air (other source)" # HIDE
const Rₛ = 287J∙kg⁻¹∙K⁻¹ # HIDE
"Base geopotential altitude" # HIDE
const yₐ₀ = -610m # HIDE
"Top of troposphere, geopotential altitude" # HIDE
const yₐ₁ = 11km # HIDE
"Base temperature" # HIDE
const T₀ = 19°C # HIDE
"Top of troposphere, temperature" # HIDE
const T₁ = -56.5°C # HIDE
"Base pressure" ps # HIDE
const p₀ = 108.9kPa # HIDE
"Adiabatic constant cp/cv, troposphere" # HIDE
const γ = 1.26 # HIDE
# HIDE
"Temperature in troposphere and tropopause" # HIDE
T(y) = y < yₐ₁ ? T₀ + (y-yₐ₀)∙(T₁-T₀) / (yₐ₁-yₐ₀) : K(T₁) # HIDE
# HIDE
println(lpad("At sea level, standard temperature = ", 52), # HIDE
round(°C, T(0m) , digits = 2)) # HIDE
# HIDE
"Density as a function of pressure and temperature" # HIDE
ρ(p, T) = p / (Rₛ∙(T |> K)) |> kg/m³ # HIDE
println(lpad("Air density ρ(p = 101kPa, T = 15.0°C) = ", 52), # HIDE
round(kg/m³, ρ(101kPa, 15.0°C), digits =3)) # HIDE
# HIDE
"Pressure derivative with respect to geopotential altitude" # HIDE
p´(p, notused, y) = -ρ(p, T(y))∙g |> kPa/km # HIDE
# HIDE
println(lpad("Pressure derivative with respect to altitude, 0m) = ", 52), # HIDE
round(kPa/km, p´(101kPa, nothing, 0m), digits= 2)) # HIDE
"Pressure solution with respect to geopotential altitude" # HIDE
psol = solve(ODEProblem(p´, p₀, (y₀, 25.0km)), Tsit5()) # HIDE
"Pressure as a function of altitude, with exact type warranty"
p(y) = kPa(psol(y))::typeof(1.0kPa)
println(lpad("Pressure at top of troposphere is p(y = 11km) = ", 52), # HIDE
round(kPa, p(11.0km), digits = 2)) # HIDE
println(lpad("Pressure at bottom of stratosphere is p(y = 20km) = ", 52), # HIDE
round(kPa, p(20.0km), digits = 2)) # HIDE
"Density as a function of altitude" # HIDE
ρ(y) = ρ(p(y), T(y)) # HIDE
println(lpad("Air density ρ(y = 11km) = ", 52), # HIDE
round(kg/m³, ρ(11km), digits = 4)) # HIDE
println(lpad("Air density ρ(y = 20km) = ", 52), # HIDE
round(kg/m³, ρ(20km), digits = 4)) # HIDE
"Speed of sound" # HIDE
c(y) = sqrt(γ∙Rₛ∙T(y)) |> m/s # HIDE
let # For plot # HIDE
ys = range(0, 25, length = 50)km # HIDE
ρs = map(ρ, ys) # HIDE
cs = map(c, ys) # HIDE
plot([ρs cs], [ys ys], yguide = "Altitude, y [km]", # HIDE
layout = (1, 2), label = :none) # HIDE
# Recipe don't work well with subplots # HIDE
plot!(xguide = ["Density [kg/m³]" "Speed of sound [m/s]"]) # HIDE
end # HIDE
last_plot_with_data_to_html("output/script11.html") # HIDE, defined in from generate_results.jl
function Γ₂´!(Γ´, Γ, p, t)
(x, y), (x´, y´) = packout(Γ)
@debug "Γ" x y x´ y´ maxlog = 2
x´´ = -Rx(x´, y´, c(y), ρ(y)) / mₚ()
y´´ = -1g -Ry(x´, y´, c(y), ρ(y)) / mₚ()
@debug "Γ Acceleration" x´´|> g y´´|>g maxlog = 2
packin!(Γ´, x´, y´, x´´, y´´)
end
sol₂ = solve_guarded(Γ₂´!);
function plotvals₂(;sol = sol₂, Γ´! = Γ₂´!)
ts, xs, ys, vs, as = time_distributed_motion_vals(;sol, Γ´!)
Cₛs = map(zip(vs, ys)) do (v, y)
Cₛ(v, c(y))
end
ρs = map(ρ, ys)
xlims = (0.0km, maximum(xs))
ts, xs, ys, vs, as, Cₛs, ρs, xlims
end
# # Subplots, solid lines, overlaid on the previous, dashed
bulletplots(plotvals₂;
trajectory_label = "α₀ = $(round(°, α₀()))",
p_y_x, p_v_x, p_v, p_Cρs, p_a)
# Assemble subplots
p_v_Cs_a₂ = plot(layout = (3, 1), p_v, p_Cρs, p_a, legend=false)
last_plot_with_data_to_html("output/script12a.html") # HIDE, defined in from generate_results_functions.jl
p_y_x_v₂ = plot(layout = (2, 1), p_y_x, p_v_x, legend=false)
last_plot_with_data_to_html("output/script12b.html") # HIDE, defined in from generate_results_functions.jl
const αᵢₙ₃ = (26:60)°
const Γᵢₙ₃ = [ArrayPartition([x₀, y₀], [v₀() * cos(α), v₀() * sin(α)])
for α in αᵢₙ₃]
const sols₃ = [solve_guarded(Γ₂´!; Γᵢₙ) for Γᵢₙ in Γᵢₙ₃]
p_y_x, p_v_x, p_v, p_Cρs, p_a = plot(), plot(),plot(),plot(),plot()
for (α₀, sol) in zip(αᵢₙ₃, sols₃)
foo = () -> plotvals₂(;sol)
bulletplots(foo;
trajectory_label = "α₀ = $(round(°, α₀))",
p_y_x, p_v_x, p_v, p_Cρs, p_a, legend=true)
end
# Assemble subplots
p_v_Cs_a₂ = plot(layout = (3, 1), p_v, p_Cρs, p_a, legend=false, linewidth = 1)
last_plot_with_data_to_html("output/script13a.html") # HIDE, defined in from generate_results_functions.jl
p_y_x_v₂ = plot(layout = (2, 1), p_y_x, p_v_x, legend=false, linewidth = 1,
xlims = (0,55))
last_plot_with_data_to_html("output/script13b.html") # HIDE, defined in from generate_results_functions.jl
# This file is machine-generated - editing it directly is not advised
[[ANSIColoredPrinters]]
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version = "0.1.6+4"
[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"
[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "fa14ac25af7a4b8a7f61b287a124df7aab601bcd"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.6+6"
[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2020.7.14+2"
[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.0.0+3"
[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"