diff options
| -rw-r--r-- | hw2/2-18.jl | 91 | ||||
| -rw-r--r-- | hw2/2-18a.svg | 49 | ||||
| -rw-r--r-- | hw2/2-18b.png | bin | 0 -> 26182 bytes | |||
| -rw-r--r-- | hw2/2-7.jl | 207 | ||||
| -rw-r--r-- | hw2/2-7a.svg | 51 | ||||
| -rw-r--r-- | hw2/2-7b.png | bin | 0 -> 45828 bytes | |||
| -rw-r--r-- | hw2/2-7c.svg | 47 | ||||
| -rw-r--r-- | hw2/2-7d.png | bin | 0 -> 45294 bytes | |||
| -rw-r--r-- | hw2/2-7e.svg | 49 | ||||
| -rw-r--r-- | hw2/2-7f.png | bin | 0 -> 45817 bytes | |||
| -rw-r--r-- | hw2/2-9.jl | 136 | ||||
| -rw-r--r-- | hw2/2-9a.svg | 55 | ||||
| -rw-r--r-- | hw2/hw2-writeup.pdf | bin | 0 -> 763541 bytes |
13 files changed, 685 insertions, 0 deletions
diff --git a/hw2/2-18.jl b/hw2/2-18.jl new file mode 100644 index 0000000..58bad47 --- /dev/null +++ b/hw2/2-18.jl @@ -0,0 +1,91 @@ +using Plots # for plotting trajectory + +# simulation parameters +Δt = 0.001 # time step +x_max = 60.0 # in feet +v_0 = 95.0 # mph +v_0 = v_0 * 5280 / 3600 # convert mph to feet/s +y_0 = 6.0 # in feet +ω = 0.0 # in rad/s +m = 149 # in grams +S_0_over_m = 4.1 * 10^(-4) # unitless +B_ref_over_m = 4.0 * 10^(-5) # in m-1, at 300K +g = 32.2 # in ft/s^2 + +function dynamics!( + x::Vector{Float64}, y::Vector{Float64}, + v_y::Vector{Float64}, v_x::Vector{Float64}, + t::Vector{Float64}) + while x[end] <= x_max + # decompose previous positions and velocities + x_i = x[end] + y_i = y[end] + v_x_i = v_x[end] + v_y_i = v_y[end] + + # calculate new positions + x_new = x_i + v_x_i * Δt + y_new = y_i + v_y_i * Δt + + # calculate drag force + v_i = sqrt(v_x_i^2 + v_y_i^2) + F_x = - B_ref_over_m * v_x_i * v_i + F_y = - g + S_0_over_m * v_x_i * ω + + # calculate new velocities + v_x_new = v_x_i + F_x * Δt + v_y_new = v_y_i + F_y * Δt + + # store new positions and velocities + push!(x, x_new) + push!(y, y_new) + push!(v_x, v_x_new) + push!(v_y, v_y_new) + push!(t, t[end] + Δt) + end +end + +# interpolate the last point that's past the x_max +function interpolate!(x::Vector{Float64}, y::Vector{Float64}) + if x[end] <= x_max + return + end + + x_i = x[end-1] + y_i = y[end-1] + + x_f = x[end] + y_f = y[end] + + m = (y_f - y_i) / (x_f - x_i) + b = y_i - m * x_i + + x_new = x_max + y_new = m * x_new + b + + x[end] = x_new + y[end] = y_new +end + +# run the simulation with ω = 0 +x = [0.0] +y = [y_0] +v_x = [v_0] # pitch only in x direction +v_y = [0.0] +t = [0.0] +dynamics!(x, y, v_y, v_x, t) +interpolate!(x, y) +plot(x, y, label="ω = 0", xlabel="x (feet)", ylabel="y (feet)", lw=2, title="Trajectory of a Fastball with Backspin") +println("y-value at x_max (60ft) for ω = 0:\t", y[end], " feet") + +# run the simulation with ω = 1000 rpm +ω = 1000 * 2 * π / 60 # convert rpm to rad/s +x = [0.0] +y = [y_0] +v_x = [v_0] # pitch only in x direction +v_y = [0.0] +t = [0.0] +dynamics!(x, y, v_y, v_x, t) +interpolate!(x, y) +println("y-value at x_max (60ft) for ω = 1000 rpm:\t", y[end], " feet") +plot!(x, y, label="ω = 1000 rpm", lw=2) diff --git a/hw2/2-18a.svg b/hw2/2-18a.svg new file mode 100644 index 0000000..26b2e7f --- /dev/null +++ b/hw2/2-18a.svg @@ -0,0 +1,49 @@ +<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="600" height="400" viewBox="0 0 2400 1600"> +<defs> + <clipPath id="clip840"> + <rect x="0" y="0" width="2400" height="1600"></rect> + </clipPath> +</defs> +<path clip-path="url(#clip840)" d="M0 1600 L2400 1600 L2400 8.88178e-14 L0 8.88178e-14 Z" fill="#ffffff" fill-rule="evenodd" fill-opacity="1"></path> +<defs> + <clipPath id="clip841"> + <rect x="480" y="0" width="1681" height="1600"></rect> + </clipPath> +</defs> +<path clip-path="url(#clip840)" d="M175.445 1423.18 L2352.76 1423.18 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\ No newline at end of file diff --git a/hw2/2-18b.png b/hw2/2-18b.png Binary files differnew file mode 100644 index 0000000..2a0c0b8 --- /dev/null +++ b/hw2/2-18b.png diff --git a/hw2/2-7.jl b/hw2/2-7.jl new file mode 100644 index 0000000..d936cfb --- /dev/null +++ b/hw2/2-7.jl @@ -0,0 +1,207 @@ +using Plots # for plotting trajectory + +# simulation parameters +Δt = 0.01 # time step +y_min = 0.0 +Δθ = 0.01 # in degrees +θ_start = 0.0 # in degrees +θ_end = 90.0 # in degrees +v_0 = 700.0 # in m/s + +# constants +B_ref_over_m = 4.0 * 10^(-5) # in m-1, at 300K +T_ref = 300.0 # in kelvin +T_0 = 300.0 # in kelvin +g = 9.8 # in m/s^2 + +# isothermic parameters +y_o = 10 * 10^4 # k_BT/mg in meter + +# adiabatic parameters +α = 2.5 # for air +a = 6.5 * 10^(-3) # in kelvin/meter + +function isothermic!( + x::Vector{Float64}, y::Vector{Float64}, + v_y::Vector{Float64}, v_x::Vector{Float64}, + t::Vector{Float64}) + while y[end] >= y_min + # decompose previous positions and velocities + x_i = x[end] + y_i = y[end] + v_x_i = v_x[end] + v_y_i = v_y[end] + + # calculate new positions + x_new = x_i + v_x_i * Δt + y_new = y_i + v_y_i * Δt + + # calculate drag force + v_i = sqrt(v_x_i^2 + v_y_i^2) + F_drag = - B_ref_over_m * (T_0 / T_ref)^α * # temperature variation + ℯ^(-y_i/y_o) # density/altitude variation + F_drag_x = F_drag * v_x_i * v_i + F_drag_y = F_drag * v_y_i * v_i + + # calculate new velocities + v_x_new = v_x_i + F_drag_x * Δt + v_y_new = v_y_i + F_drag_y * Δt - g * Δt + + # store new positions and velocities + push!(x, x_new) + push!(y, y_new) + push!(v_x, v_x_new) + push!(v_y, v_y_new) + push!(t, t[end] + Δt) + end +end + +function adiabatic!( + x::Vector{Float64}, y::Vector{Float64}, + v_y::Vector{Float64}, v_x::Vector{Float64}, + t::Vector{Float64}) + while y[end] >= y_min + # decompose previous positions and velocities + x_i = x[end] + y_i = y[end] + v_x_i = v_x[end] + v_y_i = v_y[end] + + # calculate new positions + x_new = x_i + v_x_i * Δt + y_new = y_i + v_y_i * Δt + + # calculate drag force + v_i = sqrt(v_x_i^2 + v_y_i^2) + F_drag = - B_ref_over_m * (T_0 / T_ref)^α * # temperature variation + (1 - ((a * y_i) / T_0))^α # density/altitude variation + F_drag_x = F_drag * v_x_i * v_i + F_drag_y = F_drag * v_y_i * v_i + + # calculate new velocities + v_x_new = v_x_i + F_drag_x * Δt + v_y_new = v_y_i + F_drag_y * Δt - g * Δt + + # store new positions and velocities + push!(x, x_new) + push!(y, y_new) + push!(v_x, v_x_new) + push!(v_y, v_y_new) + push!(t, t[end] + Δt) + end +end + +function nodensity!( + x::Vector{Float64}, y::Vector{Float64}, + v_y::Vector{Float64}, v_x::Vector{Float64}, + t::Vector{Float64}) + while y[end] >= y_min + # decompose previous positions and velocities + x_i = x[end] + y_i = y[end] + v_x_i = v_x[end] + v_y_i = v_y[end] + + # calculate new positions + x_new = x_i + v_x_i * Δt + y_new = y_i + v_y_i * Δt + + # calculate drag force + v_i = sqrt(v_x_i^2 + v_y_i^2) + F_drag = - B_ref_over_m # coefficient of drag alone + F_drag_x = F_drag * v_x_i * v_i + F_drag_y = F_drag * v_y_i * v_i + + # calculate new velocities + v_x_new = v_x_i + F_drag_x * Δt + v_y_new = v_y_i + F_drag_y * Δt - g * Δt + + # store new positions and velocities + push!(x, x_new) + push!(y, y_new) + push!(v_x, v_x_new) + push!(v_y, v_y_new) + push!(t, t[end] + Δt) + end +end + +# interpolate the last point that's underground +function interpolate!(x::Vector{Float64}, y::Vector{Float64}) + if y[end] == 0 + return # no nothing if y is perfectly on 0 + end + + # calculate x_l, the interpolated x value at y=0 + r = -y[end-1] / y[end] + x_l = (x[end-1] + r * x[end]) / (1 + r) + + # set final values in the array to interpolated point on ground (y=0 ) + x[end] = x_l + y[end] = 0.0 +end + +# arrays for holidng range and angle data +Θ_steps = Int64((θ_end - θ_start) / Δθ) +ranges_adi = zeros(Θ_steps + 1) +angles_adi = zeros(Θ_steps + 1) +ranges_iso = zeros(Θ_steps + 1) +angles_iso = zeros(Θ_steps + 1) +ranges_nod = zeros(Θ_steps + 1) +angles_nod = zeros(Θ_steps + 1) + +for i in 1:Θ_steps+1 + # arrays to store steps + θ = θ_start + (i-1) * Δθ + + local x_adi = [0.0] + local y_adi = [0.0] + local v_x_adi = [v_0 * cosd(θ)] + local v_y_adi = [v_0 * sind(θ)] + local t_adi = [0.0] + + local x_iso = [0.0] + local y_iso = [0.0] + local v_x_iso = [v_0 * cosd(θ)] + local v_y_iso = [v_0 * sind(θ)] + local t_iso = [0.0] + + local x_nod = [0.0] + local y_nod = [0.0] + local v_x_nod = [v_0 * cosd(θ)] + local v_y_nod = [v_0 * sind(θ)] + local t_nod = [0.0] + + # simulate the trajectory + adiabatic!(x_adi, y_adi, v_y_adi, v_x_adi, t_adi) + isothermic!(x_iso, y_iso, v_y_iso, v_x_iso, t_iso) + nodensity!(x_nod, y_nod, v_y_nod, v_x_nod, t_nod) + + # interpolate the last point that's underground + interpolate!(x_adi, y_adi) + interpolate!(x_iso, y_iso) + interpolate!(x_nod, y_nod) + + # store the range and angle + ranges_adi[i] = x_adi[end] + angles_adi[i] = θ + ranges_iso[i] = x_iso[end] + angles_iso[i] = θ + ranges_nod[i] = x_nod[end] + angles_nod[i] = θ +end + +max_i_adi = argmax(ranges_adi) +max_i_iso = argmax(ranges_iso) +max_i_nod = argmax(ranges_nod) + +# print the max range and angle +println("Max range (adiabatic): ", ranges_adi[max_i_adi], " at angle ", angles_adi[max_i_adi], " (T=", T_0, "K)") +println("Max range (isothermic): ", ranges_iso[max_i_iso], " at angle ", angles_iso[max_i_iso], " (T=", T_0, "K)") +println("Max range (no density model): ", ranges_nod[max_i_nod], " at angle ", angles_nod[max_i_nod], " (T=", T_0, "K)") + +# plot the range over angles +plot_title = "Range over angle (T=$T_0 K)" +plot(angles_adi, ranges_adi, xlabel="angle (degrees)", ylabel="range (m)", title=plot_title, label="adiabatic", lw=2, color=:blue) +plot!(angles_iso, ranges_iso, label="isothermic", lw=2, color=:red) +plot!(angles_nod, ranges_nod, label="no density model", lw=2, color=:green) + diff --git a/hw2/2-7a.svg b/hw2/2-7a.svg new file mode 100644 index 0000000..7217e7b --- /dev/null +++ b/hw2/2-7a.svg @@ 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\ No newline at end of file diff --git a/hw2/2-7f.png b/hw2/2-7f.png Binary files differnew file mode 100644 index 0000000..39139fc --- /dev/null +++ b/hw2/2-7f.png diff --git a/hw2/2-9.jl b/hw2/2-9.jl new file mode 100644 index 0000000..1190c4a --- /dev/null +++ b/hw2/2-9.jl @@ -0,0 +1,136 @@ +using Plots # for plotting trajectory + +# simulation parameters +Δt = 0.01 # time step +y_min = 0.0 +θ_to_use = [45, 35] # in degrees +v_0 = 700.0 # in m/s + +# constants +B_ref_over_m = 4.0 * 10^(-5) # in m-1, at 300K +T_ref = 300.0 # in kelvin +T_0 = 300.0 # in kelvin +g = 9.8 # in m/s^2 + +# isothermic parameters +y_o = 10 * 10^4 # k_BT/mg in meter + +# adiabatic parameters +α = 2.5 # for air +a = 6.5 * 10^(-3) # in kelvin/meter + +function adiabatic!( + x::Vector{Float64}, y::Vector{Float64}, + v_y::Vector{Float64}, v_x::Vector{Float64}, + t::Vector{Float64}) + while y[end] >= y_min + # decompose previous positions and velocities + x_i = x[end] + y_i = y[end] + v_x_i = v_x[end] + v_y_i = v_y[end] + + # calculate new positions + x_new = x_i + v_x_i * Δt + y_new = y_i + v_y_i * Δt + + # calculate drag force + v_i = sqrt(v_x_i^2 + v_y_i^2) + F_drag = - B_ref_over_m * (T_0 / T_ref)^α * # temperature variation + (1 - ((a * y_i) / T_0))^α # density/altitude variation + F_drag_x = F_drag * v_x_i * v_i + F_drag_y = F_drag * v_y_i * v_i + + # calculate new velocities + v_x_new = v_x_i + F_drag_x * Δt + v_y_new = v_y_i + F_drag_y * Δt - g * Δt + + # store new positions and velocities + push!(x, x_new) + push!(y, y_new) + push!(v_x, v_x_new) + push!(v_y, v_y_new) + push!(t, t[end] + Δt) + end +end + +function nodensity!( + x::Vector{Float64}, y::Vector{Float64}, + v_y::Vector{Float64}, v_x::Vector{Float64}, + t::Vector{Float64}) + while y[end] >= y_min + # decompose previous positions and velocities + x_i = x[end] + y_i = y[end] + v_x_i = v_x[end] + v_y_i = v_y[end] + + # calculate new positions + x_new = x_i + v_x_i * Δt + y_new = y_i + v_y_i * Δt + + # calculate drag force + v_i = sqrt(v_x_i^2 + v_y_i^2) + F_drag = - B_ref_over_m # coefficient of drag alone + F_drag_x = F_drag * v_x_i * v_i + F_drag_y = F_drag * v_y_i * v_i + + # calculate new velocities + v_x_new = v_x_i + F_drag_x * Δt + v_y_new = v_y_i + F_drag_y * Δt - g * Δt + + # store new positions and velocities + push!(x, x_new) + push!(y, y_new) + push!(v_x, v_x_new) + push!(v_y, v_y_new) + push!(t, t[end] + Δt) + end +end + +# interpolate the last point that's underground +function interpolate!(x::Vector{Float64}, y::Vector{Float64}) + if y[end] == 0 + return # no nothing if y is perfectly on 0 + end + + # calculate x_l, the interpolated x value at y=0 + r = -y[end-1] / y[end] + x_l = (x[end-1] + r * x[end]) / (1 + r) + + # set final values in the array to interpolated point on ground (y=0 ) + x[end] = x_l + y[end] = 0.0 +end + +# setup empty plot to add to +p = plot(xlabel="x (m)", ylabel="y (m)", title="Cannon Shell Trajectory", xlim=(0, 30000), xticks=0:5000:30000, legend=:topright, lw=2) +for θ in θ_to_use + # arrays to store the trajectory + x = [0.0] + y = [0.0] + v_x = [v_0 * cosd(θ)] + v_y = [v_0 * sind(θ)] + t = [0.0] + + # run the simulation + adiabatic!(x, y, v_y, v_x, t) + interpolate!(x, y) + plot_label = "adiabatic, θ = $θ" + plot!(x, y, label=plot_label, lw=2) + + # reset arrays + x = [0.0] + y = [0.0] + v_x = [v_0 * cosd(θ)] + v_y = [v_0 * sind(θ)] + t = [0.0] + + nodensity!(x, y, v_y, v_x, t) + interpolate!(x, y) + plot_label = "nodensity, θ = $θ" + plot!(x, y, label=plot_label, lw=2, linestyle=:dash) +end + +# display the plot +display(p) diff --git a/hw2/2-9a.svg b/hw2/2-9a.svg new file mode 100644 index 0000000..7593221 --- /dev/null +++ b/hw2/2-9a.svg @@ -0,0 +1,55 @@ +<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="600" height="400" viewBox="0 0 2400 1600"> +<defs> + <clipPath id="clip880"> + <rect x="0" y="0" width="2400" height="1600"></rect> + </clipPath> +</defs> +<path clip-path="url(#clip880)" d="M0 1600 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1059.02,237.784 1059.22,237.722 1059.42,237.661 1059.62,237.6 1059.82,237.54 1060.02,237.479 1060.21,237.419 1060.41,237.358 1060.61,237.298 1060.81,237.238 1061.01,237.178 1061.2,237.119 1061.4,237.059 1061.6,237 1061.8,236.941 1062,236.882 1062.19,236.823 1062.39,236.764 1062.59,236.705 1062.79,236.647 1062.99,236.589 1063.18,236.531 1063.38,236.473 1063.58,236.415 1063.78,236.357 1063.97,236.3 1064.17,236.243 1064.37,236.186 1064.57,236.129 1064.77,236.072 1064.96,236.015 1065.16,235.959 1065.36,235.902 1065.56,235.846 1065.75,235.79 1065.95,235.734 1066.15,235.678 1066.35,235.623 1066.54,235.567 1066.74,235.512 1066.94,235.457 1067.14,235.402 1067.33,235.347 1067.53,235.293 1067.73,235.238 1067.93,235.184 1068.12,235.13 1068.32,235.076 1068.52,235.022 1068.71,234.968 1068.91,234.915 1069.11,234.862 1069.31,234.808 1069.5,234.755 1069.7,234.702 1069.9,234.65 1070.09,234.597 1070.29,234.545 1070.49,234.492 1070.69,234.44 1070.88,234.388 1071.08,234.337 1071.28,234.285 1071.47,234.233 1071.67,234.182 1071.87,234.131 1072.06,234.08 1072.26,234.029 1072.46,233.978 1072.65,233.928 1072.85,233.878 1073.05,233.827 1073.24,233.777 1073.44,233.727 1073.64,233.678 1073.83,233.628 1074.03,233.579 1074.23,233.529 1074.42,233.48 1074.62,233.431 1074.82,233.382 1075.01,233.334 1075.21,233.285 1075.41,233.237 1075.6,233.189 1075.8,233.141 1076,233.093 1076.19,233.045 1076.39,232.998 1076.58,232.95 1076.78,232.903 1076.98,232.856 1077.17,232.809 1077.37,232.762 1077.57,232.715 1077.76,232.669 1077.96,232.623 1078.15,232.577 1078.35,232.531 1078.55,232.485 1078.74,232.439 1078.94,232.394 1079.13,232.348 1079.33,232.303 1079.53,232.258 1079.72,232.213 1079.92,232.168 1080.11,232.124 1080.31,232.079 1080.51,232.035 1080.7,231.991 1080.9,231.947 1081.09,231.903 1081.29,231.859 1081.48,231.816 1081.68,231.773 1081.88,231.729 1082.07,231.686 1082.27,231.644 1082.46,231.601 1082.66,231.558 1082.85,231.516 1083.05,231.474 1083.25,231.431 1083.44,231.39 1083.64,231.348 1083.83,231.306 1084.03,231.265 1084.22,231.223 1084.42,231.182 1084.61,231.141 1084.81,231.1 1085,231.06 1085.2,231.019 1085.4,230.979 1085.59,230.939 1085.79,230.898 1085.98,230.859 1086.18,230.819 1086.37,230.779 1086.57,230.74 1086.76,230.7 1086.96,230.661 1087.15,230.622 1087.35,230.584 1087.54,230.545 1087.74,230.506 1087.93,230.468 1088.13,230.43 1088.32,230.392 1088.52,230.354 1088.71,230.316 1088.91,230.279 1089.1,230.241 1089.3,230.204 1089.49,230.167 1089.69,230.13 1089.88,230.093 1090.08,230.056 1090.27,230.02 1090.47,229.984 1090.66,229.947 1090.86,229.911 1091.05,229.875 1091.24,229.84 1091.44,229.804 1091.63,229.769 1091.83,229.734 1092.02,229.698 1092.22,229.663 1092.41,229.629 1092.61,229.594 1092.8,229.56 1093,229.525 1093.19,229.491 1093.38,229.457 1093.58,229.423 1093.77,229.39 1093.97,229.356 1094.16,229.323 1094.36,229.289 1094.55,229.256 1094.74,229.223 1094.94,229.191 1095.13,229.158 1095.33,229.125 1095.52,229.093 1095.72,229.061 1095.91,229.029 1096.1,228.997 1096.3,228.965 1096.49,228.934 1096.69,228.903 1096.88,228.871 1097.07,228.84 1097.27,228.809 1097.46,228.779 1097.66,228.748 1097.85,228.718 1098.04,228.687 1098.24,228.657 1098.43,228.627 1098.63,228.597 1098.82,228.568 1099.01,228.538 1099.21,228.509 1099.4,228.479 1099.59,228.45 1099.79,228.421 1099.98,228.393 1100.18,228.364 1100.37,228.336 1100.56,228.307 1100.76,228.279 1100.95,228.251 1101.14,228.223 1101.34,228.196 1101.53,228.168 1101.72,228.141 1101.92,228.114 1102.11,228.087 1102.3,228.06 1102.5,228.033 1102.69,228.006 1102.88,227.98 1103.08,227.954 1103.27,227.927 1103.46,227.901 1103.66,227.876 1103.85,227.85 1104.04,227.824 1104.24,227.799 1104.43,227.774 1104.62,227.749 1104.82,227.724 1105.01,227.699 1105.2,227.675 1105.4,227.65 1105.59,227.626 1105.78,227.602 1105.97,227.578 1106.17,227.554 1106.36,227.53 1106.55,227.507 1106.75,227.483 1106.94,227.46 1107.13,227.437 1107.33,227.414 1107.52,227.391 1107.71,227.369 1107.9,227.346 1108.1,227.324 1108.29,227.302 1108.48,227.28 1108.67,227.258 1108.87,227.236 1109.06,227.215 1109.25,227.194 1109.45,227.172 1109.64,227.151 1109.83,227.13 1110.02,227.11 1110.22,227.089 1110.41,227.069 1110.6,227.048 1110.79,227.028 1110.99,227.008 1111.18,226.988 1111.37,226.969 1111.56,226.949 1111.76,226.93 1111.95,226.91 1112.14,226.891 1112.33,226.872 1112.52,226.854 1112.72,226.835 1112.91,226.817 1113.1,226.798 1113.29,226.78 1113.49,226.762 1113.68,226.744 1113.87,226.727 1114.06,226.709 1114.25,226.692 1114.45,226.675 1114.64,226.657 1114.83,226.641 1115.02,226.624 1115.21,226.607 1115.41,226.591 1115.6,226.574 1115.79,226.558 1115.98,226.542 1116.17,226.526 1116.37,226.511 1116.56,226.495 1116.75,226.48 1116.94,226.464 1117.13,226.449 1117.32,226.434 1117.52,226.42 1117.71,226.405 1117.9,226.39 1118.09,226.376 1118.28,226.362 1118.48,226.348 1118.67,226.334 1118.86,226.32 1119.05,226.307 1119.24,226.293 1119.43,226.28 1119.62,226.267 1119.82,226.254 1120.01,226.241 1120.2,226.229 1120.39,226.216 1120.58,226.204 1120.77,226.192 1120.96,226.18 1121.16,226.168 1121.35,226.156 1121.54,226.144 1121.73,226.133 1121.92,226.122 1122.11,226.11 1122.3,226.099 1122.49,226.089 1122.69,226.078 1122.88,226.067 1123.07,226.057 1123.26,226.047 1123.45,226.037 1123.64,226.027 1123.83,226.017 1124.02,226.008 1124.21,225.998 1124.41,225.989 1124.6,225.98 1124.79,225.971 1124.98,225.962 1125.17,225.953 1125.36,225.945 1125.55,225.936 1125.74,225.928 1125.93,225.92 1126.12,225.912 1126.31,225.904 1126.5,225.897 1126.7,225.889 1126.89,225.882 1127.08,225.875 1127.27,225.868 1127.46,225.861 1127.65,225.854 1127.84,225.847 1128.03,225.841 1128.22,225.835 1128.41,225.829 1128.6,225.823 1128.79,225.817 1128.98,225.811 1129.17,225.806 1129.36,225.8 1129.55,225.795 1129.74,225.79 1129.93,225.785 1130.12,225.78 1130.31,225.776 1130.51,225.771 1130.7,225.767 1130.89,225.763 1131.08,225.759 1131.27,225.755 1131.46,225.752 1131.65,225.748 1131.84,225.745 1132.03,225.741 1132.22,225.738 1132.41,225.735 1132.6,225.733 1132.79,225.73 1132.98,225.727 1133.17,225.725 1133.36,225.723 1133.55,225.721 1133.74,225.719 1133.93,225.717 1134.12,225.716 1134.31,225.714 1134.5,225.713 1134.69,225.712 1134.88,225.711 1135.07,225.71 1135.26,225.71 1135.45,225.709 1135.64,225.709 1135.83,225.709 1136.02,225.709 1136.2,225.709 1136.39,225.709 1136.58,225.709 1136.77,225.71 1136.96,225.711 1137.15,225.711 1137.34,225.712 1137.53,225.714 1137.72,225.715 1137.91,225.716 1138.1,225.718 1138.29,225.72 1138.48,225.722 1138.67,225.724 1138.86,225.726 1139.05,225.728 1139.24,225.731 1139.43,225.733 1139.62,225.736 1139.8,225.739 1139.99,225.742 1140.18,225.746 1140.37,225.749 1140.56,225.753 1140.75,225.756 1140.94,225.76 1141.13,225.764 1141.32,225.768 1141.51,225.773 1141.7,225.777 1141.89,225.782 1142.07,225.786 1142.26,225.791 1142.45,225.796 1142.64,225.802 1142.83,225.807 1143.02,225.813 1143.21,225.818 1143.4,225.824 1143.59,225.83 1143.78,225.836 1143.96,225.843 1144.15,225.849 1144.34,225.856 1144.53,225.862 1144.72,225.869 1144.91,225.876 1145.1,225.883 1145.29,225.891 1145.47,225.898 1145.66,225.906 1145.85,225.914 1146.04,225.922 1146.23,225.93 1146.42,225.938 1146.61,225.946 1146.79,225.955 1146.98,225.963 1147.17,225.972 1147.36,225.981 1147.55,225.99 1147.74,226 1147.92,226.009 1148.11,226.019 1148.3,226.028 1148.49,226.038 1148.68,226.048 1148.87,226.059 1149.06,226.069 1149.24,226.079 1149.43,226.09 1149.62,226.101 1149.81,226.112 1150,226.123 1150.18,226.134 1150.37,226.145 1150.56,226.157 1150.75,226.169 1150.94,226.18 1151.12,226.192 1151.31,226.205 1151.5,226.217 1151.69,226.229 1151.88,226.242 1152.06,226.255 1152.25,226.267 1152.44,226.28 1152.63,226.294 1152.82,226.307 1153,226.32 1153.19,226.334 1153.38,226.348 1153.57,226.362 1153.76,226.376 1153.94,226.39 1154.13,226.404 1154.32,226.419 1154.51,226.434 1154.69,226.449 1154.88,226.463 1155.07,226.479 1155.26,226.494 1155.44,226.509 1155.63,226.525 1155.82,226.541 1156.01,226.556 1156.19,226.572 1156.38,226.589 1156.57,226.605 1156.76,226.621 1156.94,226.638 1157.13,226.655 1157.32,226.672 1157.51,226.689 1157.69,226.706 1157.88,226.723 1158.07,226.741 1158.26,226.759 1158.44,226.776 1158.63,226.794 1158.82,226.812 1159.01,226.831 1159.19,226.849 1159.38,226.868 1159.57,226.886 1159.75,226.905 1159.94,226.924 1160.13,226.943 1160.32,226.963 1160.5,226.982 1160.69,227.002 1160.88,227.022 1161.06,227.041 1161.25,227.061 1161.44,227.082 1161.62,227.102 1161.81,227.122 1162,227.143 1162.18,227.164 1162.37,227.185 1162.56,227.206 1162.75,227.227 1162.93,227.249 1163.12,227.27 1163.31,227.292 1163.49,227.314 1163.68,227.336 1163.87,227.358 1164.05,227.38 1164.24,227.402 1164.43,227.425 1164.61,227.448 1164.8,227.471 1164.99,227.494 1165.17,227.517 1165.36,227.54 1165.54,227.564 1165.73,227.587 1165.92,227.611 1166.1,227.635 1166.29,227.659 1166.48,227.683 1166.66,227.708 1166.85,227.732 1167.04,227.757 1167.22,227.782 1167.41,227.806 1167.6,227.832 1167.78,227.857 1167.97,227.882 1168.15,227.908 1168.34,227.933 1168.53,227.959 1168.71,227.985 1168.9,228.011 1169.08,228.038 1169.27,228.064 1169.46,228.091 1169.64,228.117 1169.83,228.144 1170.02,228.171 1170.2,228.199 1170.39,228.226 1170.57,228.253 1170.76,228.281 1170.95,228.309 1171.13,228.337 1171.32,228.365 1171.5,228.393 1171.69,228.421 1171.87,228.45 1172.06,228.479 1172.25,228.507 1172.43,228.536 1172.62,228.565 1172.8,228.595 1172.99,228.624 1173.17,228.654 1173.36,228.683 1173.55,228.713 1173.73,228.743 1173.92,228.773 1174.1,228.804 1174.29,228.834 1174.47,228.865 1174.66,228.895 1174.85,228.926 1175.03,228.957 1175.22,228.988 1175.4,229.02 1175.59,229.051 1175.77,229.083 1175.96,229.115 1176.14,229.146 1176.33,229.178 1176.51,229.211 1176.7,229.243 1176.88,229.276 1177.07,229.308 1177.25,229.341 1177.44,229.374 1177.63,229.407 1177.81,229.44 1178,229.474 1178.18,229.507 1178.37,229.541 1178.55,229.575 1178.74,229.609 1178.92,229.643 1179.11,229.677 1179.29,229.712 1179.48,229.746 1179.66,229.781 1179.85,229.816 1180.03,229.851 1180.22,229.886 1180.4,229.921 1180.59,229.957 1180.77,229.992 1180.96,230.028 1181.14,230.064 1181.33,230.1 1181.51,230.136 1181.7,230.172 1181.88,230.209 1182.06,230.245 1182.25,230.282 1182.43,230.319 1182.62,230.356 1182.8,230.393 1182.99,230.431 1183.17,230.468 1183.36,230.506 1183.54,230.544 1183.73,230.582 1183.91,230.62 1184.1,230.658 1184.28,230.697 1184.46,230.735 1184.65,230.774 1184.83,230.813 1185.02,230.852 1185.2,230.891 1185.39,230.93 1185.57,230.969 1185.76,231.009 1185.94,231.049 1186.12,231.089 1186.31,231.129 1186.49,231.169 1186.68,231.209 1186.86,231.249 1187.05,231.29 1187.23,231.331 1187.41,231.372 1187.6,231.413 1187.78,231.454 1187.97,231.495 1188.15,231.537 1188.33,231.578 1188.52,231.62 1188.7,231.662 1188.89,231.704 1189.07,231.746 1189.25,231.789 1189.44,231.831 1189.62,231.874 1189.81,231.917 1189.99,231.96 1190.17,232.003 1190.36,232.046 1190.54,232.089 1190.73,232.133 1190.91,232.176 1191.09,232.22 1191.28,232.264 1191.46,232.308 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1515.72,579.608 1515.87,579.91 1516.02,580.211 1516.17,580.513 1516.32,580.815 1516.47,581.117 1516.62,581.419 1516.76,581.722 1516.91,582.024 1517.06,582.327 1517.21,582.629 1517.36,582.932 1517.51,583.235 1517.66,583.538 1517.8,583.841 1517.95,584.144 1518.1,584.447 1518.25,584.751 1518.4,585.054 1518.55,585.358 1518.7,585.662 1518.84,585.966 1518.99,586.27 1519.14,586.574 1519.29,586.878 1519.44,587.183 1519.59,587.487 1519.73,587.792 1519.88,588.096 1520.03,588.401 1520.18,588.706 1520.33,589.011 1520.48,589.316 1520.62,589.622 1520.77,589.927 1520.92,590.233 1521.07,590.538 1521.22,590.844 1521.37,591.15 1521.51,591.456 1521.66,591.762 1521.81,592.068 1521.96,592.375 1522.11,592.681 1522.25,592.988 1522.4,593.294 1522.55,593.601 1522.7,593.908 1522.85,594.215 1522.99,594.522 1523.14,594.83 1523.29,595.137 1523.44,595.444 1523.59,595.752 1523.73,596.06 1523.88,596.368 1524.03,596.676 1524.18,596.984 1524.33,597.292 1524.47,597.6 1524.62,597.908 1524.77,598.217 1524.92,598.526 1525.06,598.834 1525.21,599.143 1525.36,599.452 1525.51,599.761 1525.66,600.071 1525.8,600.38 1525.95,600.689 1526.1,600.999 1526.25,601.309 1526.39,601.618 1526.54,601.928 1526.69,602.238 1526.84,602.548 1526.98,602.859 1527.13,603.169 1527.28,603.48 1527.43,603.79 1527.57,604.101 1527.72,604.412 1527.87,604.723 1528.02,605.034 1528.16,605.345 1528.31,605.656 1528.46,605.968 1528.61,606.279 1528.75,606.591 1528.9,606.902 1529.05,607.214 1529.19,607.526 1529.34,607.838 1529.49,608.151 1529.64,608.463 1529.78,608.775 1529.93,609.088 1530.08,609.4 1530.23,609.713 1530.37,610.026 1530.52,610.339 1530.67,610.652 1530.81,610.966 1530.96,611.279 1531.11,611.592 1531.25,611.906 1531.4,612.22 1531.55,612.533 1531.7,612.847 1531.84,613.161 1531.99,613.475 1532.14,613.79 1532.28,614.104 1532.43,614.419 1532.58,614.733 1532.72,615.048 1532.87,615.363 1533.02,615.678 1533.16,615.993 1533.31,616.308 1533.46,616.623 1533.6,616.939 1533.75,617.254 1533.9,617.57 1534.04,617.885 1534.19,618.201 1534.34,618.517 1534.48,618.833 1534.63,619.15 1534.78,619.466 1534.92,619.782 1535.07,620.099 1535.22,620.416 1535.36,620.732 1535.51,621.049 1535.66,621.366 1535.8,621.683 1535.95,622.001 1536.1,622.318 1536.24,622.635 1536.39,622.953 1536.54,623.271 1536.68,623.588 1536.83,623.906 1536.98,624.224 1537.12,624.542 1537.27,624.861 1537.41,625.179 1537.56,625.497 1537.71,625.816 1537.85,626.135 1538,626.454 1538.15,626.772 1538.29,627.092 1538.44,627.411 1538.58,627.73 1538.73,628.049 1538.88,628.369 1539.02,628.688 1539.17,629.008 1539.31,629.328 1539.46,629.648 1539.61,629.968 1539.75,630.288 1539.9,630.608 1540.04,630.929 1540.19,631.249 1540.34,631.57 1540.48,631.891 1540.63,632.212 1540.77,632.533 1540.92,632.854 1541.07,633.175 1541.21,633.496 1541.36,633.818 1541.5,634.139 1541.65,634.461 1541.8,634.782 1541.94,635.104 1542.09,635.426 1542.23,635.748 1542.38,636.071 1542.52,636.393 1542.67,636.715 1542.82,637.038 1542.96,637.361 1543.11,637.683 1543.25,638.006 1543.4,638.329 1543.54,638.652 1543.69,638.976 1543.83,639.299 1543.98,639.622 1544.13,639.946 1544.27,640.27 1544.42,640.593 1544.56,640.917 1544.71,641.241 1544.85,641.565 1545,641.89 1545.14,642.214 1545.29,642.539 1545.43,642.863 1545.58,643.188 1545.73,643.513 1545.87,643.838 1546.02,644.163 1546.16,644.488 1546.31,644.813 1546.45,645.138 1546.6,645.464 1546.74,645.789 1546.89,646.115 1547.03,646.441 1547.18,646.767 1547.32,647.093 1547.47,647.419 1547.61,647.745 1547.76,648.072 1547.9,648.398 1548.05,648.725 1548.19,649.051 1548.34,649.378 1548.48,649.705 1548.63,650.032 1548.77,650.359 1548.92,650.687 1549.06,651.014 1549.21,651.342 1549.35,651.669 1549.5,651.997 1549.64,652.325 1549.79,652.653 1549.93,652.981 1550.08,653.309 1550.22,653.637 1550.37,653.966 1550.51,654.294 1550.66,654.623 1550.8,654.951 1550.95,655.28 1551.09,655.609 1551.23,655.938 1551.38,656.268 1551.52,656.597 1551.67,656.926 1551.81,657.256 1551.96,657.585 1552.1,657.915 1552.25,658.245 1552.39,658.575 1552.54,658.905 1552.68,659.235 1552.82,659.565 1552.97,659.896 1553.11,660.226 1553.26,660.557 1553.4,660.888 1553.55,661.219 1553.69,661.55 1553.84,661.881 1553.98,662.212 1554.12,662.543 1554.27,662.875 1554.41,663.206 1554.56,663.538 1554.7,663.869 1554.85,664.201 1554.99,664.533 1555.13,664.865 1555.28,665.198 1555.42,665.53 1555.57,665.862 1555.71,666.195 1555.85,666.527 1556,666.86 1556.14,667.193 1556.29,667.526 1556.43,667.859 1556.57,668.192 1556.72,668.526 1556.86,668.859 1557.01,669.193 1557.15,669.526 1557.29,669.86 1557.44,670.194 1557.58,670.528 1557.73,670.862 1557.87,671.196 1558.01,671.53 1558.16,671.865 1558.3,672.199 1558.45,672.534 1558.59,672.869 1558.73,673.204 1558.88,673.538 1559.02,673.874 1559.16,674.209 1559.31,674.544 1559.45,674.879 1559.6,675.215 1559.74,675.551 1559.88,675.886 1560.03,676.222 1560.17,676.558 1560.31,676.894 1560.46,677.23 1560.6,677.567 1560.74,677.903 1560.89,678.24 1561.03,678.576 1561.17,678.913 1561.32,679.25 1561.46,679.587 1561.61,679.924 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1570.75,701.726 1570.89,702.07 1571.03,702.414 1571.18,702.759 1571.32,703.103 1571.46,703.448 1571.6,703.793 1571.74,704.138 1571.89,704.483 1572.03,704.828 1572.17,705.173 1572.31,705.518 1572.45,705.864 1572.6,706.209 1572.74,706.555 1572.88,706.901 1573.02,707.247 1573.17,707.593 1573.31,707.939 1573.45,708.285 1573.59,708.631 1573.73,708.978 1573.87,709.324 1574.02,709.671 1574.16,710.017 1574.3,710.364 1574.44,710.711 1574.58,711.058 1574.73,711.405 1574.87,711.753 1575.01,712.1 1575.15,712.448 1575.29,712.795 1575.44,713.143 1575.58,713.491 1575.72,713.839 1575.86,714.187 1576,714.535 1576.14,714.883 1576.29,715.231 1576.43,715.58 1576.57,715.929 1576.71,716.277 1576.85,716.626 1576.99,716.975 1577.13,717.324 1577.28,717.673 1577.42,718.022 1577.56,718.372 1577.7,718.721 1577.84,719.071 1577.98,719.42 1578.13,719.77 1578.27,720.12 1578.41,720.47 1578.55,720.82 1578.69,721.17 1578.83,721.521 1578.97,721.871 1579.11,722.222 1579.26,722.572 1579.4,722.923 1579.54,723.274 1579.68,723.625 1579.82,723.976 1579.96,724.327 1580.1,724.678 1580.24,725.03 1580.39,725.381 1580.53,725.733 1580.67,726.085 1580.81,726.437 1580.95,726.788 1581.09,727.141 1581.23,727.493 1581.37,727.845 1581.51,728.197 1581.66,728.55 1581.8,728.902 1581.94,729.255 1582.08,729.608 1582.22,729.961 1582.36,730.314 1582.5,730.667 1582.64,731.02 1582.78,731.374 1582.92,731.727 1583.06,732.081 1583.2,732.434 1583.35,732.788 1583.49,733.142 1583.63,733.496 1583.77,733.85 1583.91,734.204 1584.05,734.559 1584.19,734.913 1584.33,735.268 1584.47,735.622 1584.61,735.977 1584.75,736.332 1584.89,736.687 1585.03,737.042 1585.17,737.397 1585.31,737.752 1585.46,738.108 1585.6,738.463 1585.74,738.819 1585.88,739.174 1586.02,739.53 1586.16,739.886 1586.3,740.242 1586.44,740.598 1586.58,740.955 1586.72,741.311 1586.86,741.668 1587,742.024 1587.14,742.381 1587.28,742.738 1587.42,743.094 1587.56,743.451 1587.7,743.809 1587.84,744.166 1587.98,744.523 1588.12,744.881 1588.26,745.238 1588.4,745.596 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1066.13,563.26 1066.39,563.182 1066.65,563.104 1066.91,563.026 1067.16,562.948 1067.42,562.871 1067.68,562.794 1067.94,562.717 1068.2,562.64 1068.46,562.563 1068.72,562.486 1068.98,562.41 1069.24,562.333 1069.5,562.257 1069.76,562.181 1070.01,562.105 1070.27,562.03 1070.53,561.954 1070.79,561.879 1071.05,561.804 1071.31,561.728 1071.57,561.654 1071.83,561.579 1072.08,561.504 1072.34,561.43 1072.6,561.356 1072.86,561.281 1073.12,561.208 1073.38,561.134 1073.64,561.06 1073.89,560.987 1074.15,560.913 1074.41,560.84 1074.67,560.767 1074.93,560.694 1075.19,560.622 1075.44,560.549 1075.7,560.477 1075.96,560.405 1076.22,560.333 1076.48,560.261 1076.73,560.189 1076.99,560.118 1077.25,560.046 1077.51,559.975 1077.77,559.904 1078.02,559.833 1078.28,559.762 1078.54,559.692 1078.8,559.621 1079.06,559.551 1079.31,559.481 1079.57,559.411 1079.83,559.341 1080.09,559.271 1080.35,559.202 1080.6,559.132 1080.86,559.063 1081.12,558.994 1081.38,558.925 1081.63,558.857 1081.89,558.788 1082.15,558.72 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1797.31,1094.82 1797.49,1095.18 1797.67,1095.55 1797.85,1095.92 1798.03,1096.29 1798.21,1096.65 1798.39,1097.02 1798.58,1097.39 1798.76,1097.76 1798.94,1098.12 1799.12,1098.49 1799.3,1098.86 1799.48,1099.23 1799.66,1099.6 1799.84,1099.97 1800.02,1100.34 1800.2,1100.7 1800.39,1101.07 1800.57,1101.44 1800.75,1101.81 1800.93,1102.18 1801.11,1102.55 1801.29,1102.92 1801.47,1103.29 1801.65,1103.66 1801.83,1104.03 1802.01,1104.4 1802.19,1104.77 1802.37,1105.14 1802.55,1105.51 1802.73,1105.88 1802.91,1106.25 1803.1,1106.62 1803.28,1106.99 1803.46,1107.36 1803.64,1107.73 1803.82,1108.1 1804,1108.47 1804.18,1108.84 1804.36,1109.21 1804.54,1109.59 1804.72,1109.96 1804.9,1110.33 1805.08,1110.7 1805.26,1111.07 1805.44,1111.44 1805.62,1111.82 1805.8,1112.19 1805.98,1112.56 1806.16,1112.93 1806.34,1113.3 1806.52,1113.68 1806.7,1114.05 1806.88,1114.42 1807.06,1114.79 1807.24,1115.17 1807.42,1115.54 1807.6,1115.91 1807.78,1116.29 1807.96,1116.66 1808.14,1117.03 1808.32,1117.41 1808.5,1117.78 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