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Added trajectories and alternative GUI

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This commit is contained in:
Patrik M
2026-01-19 17:25:18 +01:00
committed by GitHub
parent 2f88c321d1
commit d8dd920d6b
2 changed files with 930 additions and 24 deletions
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src/app.R Normal file
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# Flight Trajectory Analysis - Shiny GUI Application
# This app allows interactive selection of flights and displays trajectory analysis
library(shiny)
library(dplyr)
library(lubridate)
library(openSkies)
library(dotenv)
library(httr)
library(jsonlite)
library(trajr)
# UI Definition
ui <- fluidPage(
titlePanel("Flight Trajectory Analysis - GUI"),
sidebarLayout(
sidebarPanel(
width = 3,
h4("OpenSky Credentials"),
textInput("client_id", "Client ID:", value = Sys.getenv('OPENSKY_CLIENT_ID')),
passwordInput("client_secret", "Client Secret:", value = Sys.getenv('OPENSKY_CLIENT_SECRET')),
hr(),
h4("Airport Selection"),
textInput("airport_code", "Airport ICAO Code:", value = "EDDF"),
sliderInput("hours_back", "Hours back from now:", min = 1, max = 12, value = 1),
actionButton("load_departures", "Load Departures", class = "btn-primary"),
hr(),
h4("Flight Selection"),
selectInput("selected_flight", "Select Flight:", choices = NULL),
actionButton("analyze_flight", "Analyze Selected Flight", class = "btn-success"),
hr(),
h4("Batch Analysis"),
numericInput("batch_size", "Number of flights to analyze:", value = 10, min = 2, max = 50),
actionButton("batch_analyze", "Run Batch Analysis", class = "btn-warning"),
hr(),
verbatimTextOutput("status_text")
),
mainPanel(
width = 9,
tabsetPanel(
id = "main_tabs",
tabPanel("Departures List",
h4("Available Departures"),
tableOutput("departures_table")
),
tabPanel("Single Flight Analysis",
fluidRow(
column(6, plotOutput("route_plot", height = "400px")),
column(6, plotOutput("altitude_plot", height = "400px"))
),
fluidRow(
column(6, plotOutput("trajectory_plot", height = "400px")),
column(6,
h4("Trajectory Characteristics"),
tableOutput("characteristics_table"))
)
),
tabPanel("Statistical Analysis",
h4("Multiple Trajectory Statistics"),
tableOutput("stats_summary_table"),
hr(),
fluidRow(
column(12, plotOutput("boxplots", height = "500px"))
),
fluidRow(
column(12, plotOutput("density_plots", height = "500px"))
),
fluidRow(
column(12, plotOutput("histograms", height = "500px"))
)
),
tabPanel("Interpretation",
h4("Analysis Interpretation"),
verbatimTextOutput("interpretation_text")
)
)
)
)
)
# Server Logic
server <- function(input, output, session) {
# Reactive values to store data
rv <- reactiveValues(
creds = NULL,
departures = NULL,
departures_df = NULL,
current_route = NULL,
current_trj = NULL,
current_icao = NULL,
trajectory_stats_df = NULL
)
# Status message
status <- reactiveVal("Ready. Enter credentials and load departures.")
output$status_text <- renderText({
status()
})
# Load departures
observeEvent(input$load_departures, {
req(input$client_id, input$client_secret, input$airport_code)
status("Loading departures...")
tryCatch({
rv$creds <- getCredentials(
client_id = input$client_id,
client_secret = input$client_secret
)
time_now <- Sys.time()
rv$departures <- getAirportDepartures(
airport = input$airport_code,
startTime = time_now - hours(input$hours_back),
endTime = time_now,
credentials = rv$creds
)
if (length(rv$departures) > 0) {
# Create departures dataframe for display
departures_list <- lapply(seq_along(rv$departures), function(i) {
dep <- rv$departures[[i]]
data.frame(
Index = i,
ICAO24 = dep[["ICAO24"]] %||% NA,
Callsign = dep[["callsign"]] %||% NA,
Origin = dep[["estDepartureAirport"]] %||% NA,
Destination = dep[["estArrivalAirport"]] %||% NA,
DepartureTime = as.POSIXct(dep[["departure_time"]] %||% NA, origin = "1970-01-01"),
stringsAsFactors = FALSE
)
})
rv$departures_df <- do.call(rbind, departures_list)
# Update flight selection dropdown
choices <- setNames(
seq_along(rv$departures),
paste(rv$departures_df$ICAO24, "-", rv$departures_df$Callsign,
"(", rv$departures_df$Destination, ")")
)
updateSelectInput(session, "selected_flight", choices = choices)
status(paste("Loaded", length(rv$departures), "departures from", input$airport_code))
} else {
status("No departures found for the selected time period.")
}
}, error = function(e) {
status(paste("Error loading departures:", e$message))
})
})
# Display departures table
output$departures_table <- renderTable({
req(rv$departures_df)
rv$departures_df
})
# Analyze selected flight
observeEvent(input$analyze_flight, {
req(rv$departures, input$selected_flight, rv$creds)
status("Analyzing selected flight...")
tryCatch({
idx <- as.integer(input$selected_flight)
dep <- rv$departures[[idx]]
icao24 <- dep[["ICAO24"]]
dep_time <- dep[["departure_time"]]
rv$current_icao <- icao24
# Get track data
query <- list(icao24 = icao24, time = as.numeric(dep_time))
response <- makeAuthenticatedRequest('tracks/all', query, rv$creds)
if (httr::status_code(response) != 200) {
status(paste("Track data not available for", icao24, "(HTTP", httr::status_code(response), ")"))
return()
}
track_data <- fromJSON(content(response, as = "text", encoding = "UTF-8"))
if (is.null(track_data$path) || length(track_data$path) < 2) {
status(paste("No path data available for", icao24))
return()
}
route_df <- as.data.frame(track_data$path)
colnames(route_df) <- c("time", "lat", "lon", "alt", "heading", "on_ground")
rv$current_route <- route_df
# Create trajectory object
lat_ref <- route_df$lat[1]
lon_ref <- route_df$lon[1]
meters_per_deg_lat <- 111320
meters_per_deg_lon <- 111320 * cos(lat_ref * pi / 180)
x_meters <- (route_df$lon - lon_ref) * meters_per_deg_lon
y_meters <- (route_df$lat - lat_ref) * meters_per_deg_lat
time_seconds <- route_df$time - route_df$time[1]
rv$current_trj <- TrajFromCoords(
data.frame(x = x_meters, y = y_meters, time = time_seconds),
xCol = "x", yCol = "y", timeCol = "time"
)
status(paste("Successfully analyzed", icao24, "with", nrow(route_df), "points"))
# Switch to analysis tab
updateTabsetPanel(session, "main_tabs", selected = "Single Flight Analysis")
}, error = function(e) {
status(paste("Error analyzing flight:", e$message))
})
})
# Route plot
output$route_plot <- renderPlot({
req(rv$current_route)
plot(rv$current_route$lon, rv$current_route$lat, type = "o", pch = 20, col = "blue",
main = paste("Geographic Route of", rv$current_icao),
xlab = "Longitude", ylab = "Latitude")
})
# Altitude plot
output$altitude_plot <- renderPlot({
req(rv$current_route)
plot(rv$current_route$time, rv$current_route$alt, type = "l", col = "red", lwd = 2,
main = paste("Altitude Profile of", rv$current_icao),
xlab = "Time (Unix)", ylab = "Altitude (m)")
})
# Trajectory plot
output$trajectory_plot <- renderPlot({
req(rv$current_trj)
plot(rv$current_trj, main = paste("Trajectory of", rv$current_icao))
})
# Characteristics table
output$characteristics_table <- renderTable({
req(rv$current_trj)
trj <- rv$current_trj
duration <- TrajDuration(trj)
path_length <- TrajLength(trj)
diffusion_distance <- TrajDistance(trj)
straightness <- TrajStraightness(trj)
mean_velocity <- path_length / duration
fractal_dim <- tryCatch({
min_step <- path_length / 100
max_step <- path_length / 2
if (min_step > 0 && max_step > min_step) {
step_sizes <- exp(seq(log(min_step), log(max_step), length.out = 10))
TrajFractalDimension(trj, stepSizes = step_sizes)
} else {
NA
}
}, error = function(e) NA)
data.frame(
Parameter = c(
"Duration (s)", "Duration (min)",
"Path Length (m)", "Path Length (km)",
"Diffusion Distance (m)", "Diffusion Distance (km)",
"Straightness Index",
"Mean Velocity (m/s)", "Mean Velocity (km/h)",
"Fractal Dimension"
),
Value = c(
round(duration, 2), round(duration / 60, 2),
round(path_length, 2), round(path_length / 1000, 2),
round(diffusion_distance, 2), round(diffusion_distance / 1000, 2),
round(straightness, 4),
round(mean_velocity, 2), round(mean_velocity * 3.6, 2),
round(fractal_dim, 4)
)
)
})
# Batch analysis
observeEvent(input$batch_analyze, {
req(rv$departures, rv$creds)
status("Running batch analysis...")
tryCatch({
all_trajectories <- list()
n_departures <- min(length(rv$departures), input$batch_size)
withProgress(message = 'Analyzing flights', value = 0, {
for (i in 1:n_departures) {
dep <- rv$departures[[i]]
icao24 <- dep[["ICAO24"]]
dep_time <- dep[["departure_time"]]
incProgress(1/n_departures, detail = paste("Processing", icao24))
if (is.null(dep_time)) next
params <- tryCatch({
query <- list(icao24 = icao24, time = as.numeric(dep_time))
response <- makeAuthenticatedRequest('tracks/all', query, rv$creds)
if (httr::status_code(response) != 200) return(NULL)
track_data <- fromJSON(content(response, as = "text", encoding = "UTF-8"))
if (is.null(track_data$path) || length(track_data$path) < 3) return(NULL)
route_df <- as.data.frame(track_data$path)
colnames(route_df) <- c("time", "lat", "lon", "alt", "heading", "on_ground")
lat_ref <- route_df$lat[1]
lon_ref <- route_df$lon[1]
meters_per_deg_lat <- 111320
meters_per_deg_lon <- 111320 * cos(lat_ref * pi / 180)
x_meters <- (route_df$lon - lon_ref) * meters_per_deg_lon
y_meters <- (route_df$lat - lat_ref) * meters_per_deg_lat
time_seconds <- route_df$time - route_df$time[1]
trj <- TrajFromCoords(
data.frame(x = x_meters, y = y_meters, time = time_seconds),
xCol = "x", yCol = "y", timeCol = "time"
)
duration <- TrajDuration(trj)
path_length <- TrajLength(trj)
diffusion_dist <- TrajDistance(trj)
straight <- TrajStraightness(trj)
mean_vel <- path_length / duration
fractal <- tryCatch({
min_step <- path_length / 100
max_step <- path_length / 2
if (min_step > 0 && max_step > min_step) {
step_sizes <- exp(seq(log(min_step), log(max_step), length.out = 10))
TrajFractalDimension(trj, stepSizes = step_sizes)
} else {
NA
}
}, error = function(e) NA)
data.frame(
icao24 = icao24,
diffusion_distance_km = diffusion_dist / 1000,
straightness = straight,
duration_min = duration / 60,
mean_velocity_kmh = mean_vel * 3.6,
fractal_dimension = fractal
)
}, error = function(e) NULL)
if (!is.null(params)) {
all_trajectories[[length(all_trajectories) + 1]] <- params
}
Sys.sleep(0.3)
}
})
if (length(all_trajectories) > 0) {
rv$trajectory_stats_df <- do.call(rbind, all_trajectories)
status(paste("Batch analysis complete:", nrow(rv$trajectory_stats_df), "trajectories analyzed"))
updateTabsetPanel(session, "main_tabs", selected = "Statistical Analysis")
} else {
status("No trajectory data collected in batch analysis")
}
}, error = function(e) {
status(paste("Error in batch analysis:", e$message))
})
})
# Statistics summary table
output$stats_summary_table <- renderTable({
req(rv$trajectory_stats_df)
params <- c("diffusion_distance_km", "straightness", "duration_min",
"mean_velocity_kmh", "fractal_dimension")
labels <- c("Diffusion Distance (km)", "Straightness", "Duration (min)",
"Mean Velocity (km/h)", "Fractal Dimension")
stats_list <- lapply(seq_along(params), function(i) {
x <- rv$trajectory_stats_df[[params[i]]]
x <- x[!is.na(x)]
if (length(x) < 2) return(NULL)
data.frame(
Parameter = labels[i],
N = length(x),
Mean = round(mean(x), 4),
Variance = round(var(x), 4),
Std_Dev = round(sd(x), 4),
Q1 = round(quantile(x, 0.25), 4),
Median = round(median(x), 4),
Q3 = round(quantile(x, 0.75), 4)
)
})
do.call(rbind, stats_list[!sapply(stats_list, is.null)])
})
# Boxplots
output$boxplots <- renderPlot({
req(rv$trajectory_stats_df)
params <- c("diffusion_distance_km", "straightness", "duration_min",
"mean_velocity_kmh", "fractal_dimension")
labels <- c("Diffusion Distance (km)", "Straightness", "Duration (min)",
"Mean Velocity (km/h)", "Fractal Dimension")
par(mfrow = c(2, 3))
for (i in seq_along(params)) {
data <- rv$trajectory_stats_df[[params[i]]][!is.na(rv$trajectory_stats_df[[params[i]]])]
if (length(data) >= 2) {
boxplot(data, main = labels[i], ylab = labels[i], col = "lightblue", border = "darkblue")
points(1, mean(data), pch = 18, col = "red", cex = 1.5)
}
}
par(mfrow = c(1, 1))
})
# Density plots
output$density_plots <- renderPlot({
req(rv$trajectory_stats_df)
params <- c("diffusion_distance_km", "straightness", "duration_min",
"mean_velocity_kmh", "fractal_dimension")
labels <- c("Diffusion Distance (km)", "Straightness", "Duration (min)",
"Mean Velocity (km/h)", "Fractal Dimension")
par(mfrow = c(2, 3))
for (i in seq_along(params)) {
data <- rv$trajectory_stats_df[[params[i]]][!is.na(rv$trajectory_stats_df[[params[i]]])]
if (length(data) >= 3) {
dens <- density(data)
plot(dens, main = paste("Density:", labels[i]), xlab = labels[i], col = "darkblue", lwd = 2)
polygon(dens, col = rgb(0, 0, 1, 0.3), border = "darkblue")
abline(v = mean(data), col = "red", lwd = 2, lty = 2)
abline(v = median(data), col = "green", lwd = 2, lty = 3)
}
}
par(mfrow = c(1, 1))
})
# Histograms
output$histograms <- renderPlot({
req(rv$trajectory_stats_df)
params <- c("diffusion_distance_km", "straightness", "duration_min",
"mean_velocity_kmh", "fractal_dimension")
labels <- c("Diffusion Distance (km)", "Straightness", "Duration (min)",
"Mean Velocity (km/h)", "Fractal Dimension")
par(mfrow = c(2, 3))
for (i in seq_along(params)) {
data <- rv$trajectory_stats_df[[params[i]]][!is.na(rv$trajectory_stats_df[[params[i]]])]
if (length(data) >= 3) {
hist(data, probability = TRUE, main = paste("Histogram:", labels[i]),
xlab = labels[i], col = "lightgray", border = "darkgray")
lines(density(data), col = "red", lwd = 2)
}
}
par(mfrow = c(1, 1))
})
# Interpretation text
output$interpretation_text <- renderText({
req(rv$trajectory_stats_df)
df <- rv$trajectory_stats_df
text <- "========== INTERPRETATION OF TRAJECTORY PARAMETERS ==========\n\n"
# Diffusion Distance
dd <- df$diffusion_distance_km[!is.na(df$diffusion_distance_km)]
if (length(dd) >= 2) {
text <- paste0(text, "1. DIFFUSION DISTANCE (Net Displacement):\n")
text <- paste0(text, " - Mean: ", round(mean(dd), 2), " km\n")
text <- paste0(text, " - Represents straight-line distance from origin to destination.\n")
text <- paste0(text, " - Variance: ", round(var(dd), 2), " (indicates diversity in flight distances)\n\n")
}
# Straightness
st <- df$straightness[!is.na(df$straightness)]
if (length(st) >= 2) {
text <- paste0(text, "2. STRAIGHTNESS INDEX:\n")
text <- paste0(text, " - Mean: ", round(mean(st), 4), " (range 0-1, where 1 = perfectly straight)\n")
text <- paste0(text, " - Values close to 1 indicate efficient, direct flight paths.\n")
text <- paste0(text, " - Lower values suggest deviations due to weather, airspace, or routing.\n\n")
}
# Duration
dur <- df$duration_min[!is.na(df$duration_min)]
if (length(dur) >= 2) {
text <- paste0(text, "3. DURATION OF TRAVEL:\n")
text <- paste0(text, " - Mean: ", round(mean(dur), 2), " minutes\n")
text <- paste0(text, " - Range: ", round(min(dur), 2), " - ", round(max(dur), 2), " minutes\n")
text <- paste0(text, " - IQR: ", round(IQR(dur), 2), " minutes (middle 50% of flights)\n\n")
}
# Velocity
vel <- df$mean_velocity_kmh[!is.na(df$mean_velocity_kmh)]
if (length(vel) >= 2) {
text <- paste0(text, "4. MEAN TRAVEL VELOCITY:\n")
text <- paste0(text, " - Mean: ", round(mean(vel), 2), " km/h\n")
text <- paste0(text, " - Typical commercial aircraft cruise: 800-900 km/h\n")
text <- paste0(text, " - Lower values may include taxi, takeoff, and landing phases.\n\n")
}
# Fractal Dimension
fd <- df$fractal_dimension[!is.na(df$fractal_dimension)]
if (length(fd) >= 2) {
text <- paste0(text, "5. FRACTAL DIMENSION:\n")
text <- paste0(text, " - Mean: ", round(mean(fd), 4), "\n")
text <- paste0(text, " - Value of 1.0 = perfectly straight line\n")
text <- paste0(text, " - Values closer to 2.0 = more complex, space-filling paths\n")
text <- paste0(text, " - Aircraft typically show low fractal dimension (efficient paths).\n\n")
}
text <- paste0(text, "========== END OF ANALYSIS ==========")
text
})
}
# Run the application
shinyApp(ui = ui, server = server)

397
src/main.Rmd
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@@ -43,7 +43,6 @@ flights <- getFlights(icao,Sys.time(), creds)
# TODO map from all available flights to tracks
query <- list(icao24= icao, time=as.numeric(flights[[1]][["departure_time"]]))
# can get tracks for up to 30 days in the past
response <-makeAuthenticatedRequest('tracks/all',query, creds)
track_data <- fromJSON(content(response, as = "text", encoding = "UTF-8"))
if (!is.null(track_data$path) && length(track_data$path) > 0) {
@@ -66,29 +65,383 @@ if (!is.null(track_data$path) && length(track_data$path) > 0) {
}
```
# GUI selection
```{r gui}
icaos <- lapply(departures, function(x) x[["ICAO24"]])
options <- unlist(icaos) # tcltk needs a character vector
# Trajectory Characteristics Analysis
```{r trajectory-analysis}
if (exists("route_df") && nrow(route_df) > 1) {
# Create a GUI list selection
listSelect <- function(options){
selected_option <- NULL
tryCatch({
selected_option <- select.list(
title = "Select an aircraft",
choices = options,
preselect = NULL,
multiple = FALSE,
graphics = TRUE
# Convert lat/lon to approximate meters (using simple equirectangular projection)
# Reference point: first coordinate
lat_ref <- route_df$lat[1]
lon_ref <- route_df$lon[1]
# Convert to meters (approximate)
meters_per_deg_lat <- 111320
meters_per_deg_lon <- 111320 * cos(lat_ref * pi / 180)
x_meters <- (route_df$lon - lon_ref) * meters_per_deg_lon
y_meters <- (route_df$lat - lat_ref) * meters_per_deg_lat
time_seconds <- route_df$time - route_df$time[1]
# Create trajr trajectory object
trj <- TrajFromCoords(
data.frame(x = x_meters, y = y_meters, time = time_seconds),
xCol = "x", yCol = "y", timeCol = "time"
)
}, error = function(w) {
message('No GUI available')
}
# Calculate trajectory characteristics
# 1. Duration of travel (seconds)
duration <- TrajDuration(trj)
# 2. Total path length (meters)
path_length <- TrajLength(trj)
# 3. Diffusion distance (net displacement - straight line from start to end)
diffusion_distance <- TrajDistance(trj)
# 4. Straightness index (ratio of net displacement to path length, 0-1)
straightness <- TrajStraightness(trj)
# 5. Mean travel velocity (meters/second)
mean_velocity <- path_length / duration
# 6. Fractal dimension (using divider method)
# Note: requires sufficient points for accurate estimation
fractal_dim <- tryCatch({
# Calculate appropriate step sizes based on trajectory length
min_step <- TrajLength(trj) / 100
max_step <- TrajLength(trj) / 2
step_sizes <- exp(seq(log(min_step), log(max_step), length.out = 10))
TrajFractalDimension(trj, stepSizes = step_sizes)
}, error = function(e) {
message("Could not calculate fractal dimension: ", e$message)
NA
})
# Create summary data frame
trajectory_characteristics <- data.frame(
Parameter = c(
"Duration of Travel (s)",
"Duration of Travel (min)",
"Path Length (m)",
"Path Length (km)",
"Diffusion Distance (m)",
"Diffusion Distance (km)",
"Straightness Index",
"Mean Travel Velocity (m/s)",
"Mean Travel Velocity (km/h)",
"Fractal Dimension"
),
Value = c(
round(duration, 2),
round(duration / 60, 2),
round(path_length, 2),
round(path_length / 1000, 2),
round(diffusion_distance, 2),
round(diffusion_distance / 1000, 2),
round(straightness, 4),
round(mean_velocity, 2),
round(mean_velocity * 3.6, 2),
round(fractal_dim, 4)
)
if (nzchar(selected_option)){
return(selected_option)
}
return(options[1])
)
print(trajectory_characteristics)
# Visualize the trajectory using trajr
plot(trj, main = paste("Trajectory of", icao))
} else {
message("No valid trajectory data available for analysis")
}
```
# Statistical Analysis of Multiple Trajectories
```{r multi-trajectory-analysis}
# Function to calculate trajectory characteristics for a single flight
calculate_trajectory_params <- function(icao24, departure_time, creds) {
tryCatch({
query <- list(icao24 = icao24, time = as.numeric(departure_time))
response <- makeAuthenticatedRequest('tracks/all', query, creds)
# Check for HTTP errors
if (httr::status_code(response) != 200) {
return(NULL)
}
track_data <- fromJSON(content(response, as = "text", encoding = "UTF-8"))
if (is.null(track_data$path) || length(track_data$path) < 2) {
return(NULL)
}
route_df <- as.data.frame(track_data$path)
colnames(route_df) <- c("time", "lat", "lon", "alt", "heading", "on_ground")
if (nrow(route_df) < 3) return(NULL)
# Convert to meters
lat_ref <- route_df$lat[1]
lon_ref <- route_df$lon[1]
meters_per_deg_lat <- 111320
meters_per_deg_lon <- 111320 * cos(lat_ref * pi / 180)
x_meters <- (route_df$lon - lon_ref) * meters_per_deg_lon
y_meters <- (route_df$lat - lat_ref) * meters_per_deg_lat
time_seconds <- route_df$time - route_df$time[1]
trj <- TrajFromCoords(
data.frame(x = x_meters, y = y_meters, time = time_seconds),
xCol = "x", yCol = "y", timeCol = "time"
)
# Calculate parameters
duration <- TrajDuration(trj)
path_length <- TrajLength(trj)
diffusion_dist <- TrajDistance(trj)
straight <- TrajStraightness(trj)
mean_vel <- path_length / duration
# Fractal dimension
fractal <- tryCatch({
min_step <- path_length / 100
max_step <- path_length / 2
if (min_step > 0 && max_step > min_step) {
step_sizes <- exp(seq(log(min_step), log(max_step), length.out = 10))
TrajFractalDimension(trj, stepSizes = step_sizes)
} else {
NA
}
}, error = function(e) NA)
return(data.frame(
icao24 = icao24,
diffusion_distance_km = diffusion_dist / 1000,
straightness = straight,
duration_min = duration / 60,
mean_velocity_kmh = mean_vel * 3.6,
fractal_dimension = fractal
))
}, error = function(e) {
message("Error processing ", icao24, ": ", e$message)
return(NULL)
})
}
# Collect trajectory data from multiple departures
message("Collecting trajectory data from departures...")
all_trajectories <- list()
# Process available departures (limit to avoid API rate limits)
n_departures <- min(length(departures), 20)
for (i in 1:n_departures) {
dep <- departures[[i]]
icao24 <- dep[["ICAO24"]]
dep_time <- dep[["departure_time"]] # Use departure time directly from departures list
# Skip if no departure time available
if (is.null(dep_time)) {
message("Skipping ", icao24, ": no departure time")
next
}
params <- calculate_trajectory_params(icao24, dep_time, creds)
if (!is.null(params)) {
all_trajectories[[length(all_trajectories) + 1]] <- params
message("Successfully processed trajectory for ", icao24)
}
Sys.sleep(0.5) # Rate limiting
}
# Combine all trajectory data
if (length(all_trajectories) > 0) {
trajectory_stats_df <- do.call(rbind, all_trajectories)
message("Successfully collected ", nrow(trajectory_stats_df), " trajectories")
print(trajectory_stats_df)
} else {
message("No trajectory data collected")
}
```
# Basic Statistical Analysis of Trajectory Parameters
```{r statistical-analysis}
if (exists("trajectory_stats_df") && nrow(trajectory_stats_df) >= 2) {
# Parameters to analyze
params_to_analyze <- c("diffusion_distance_km", "straightness", "duration_min",
"mean_velocity_kmh", "fractal_dimension")
param_labels <- c("Diffusion Distance (km)", "Straightness Index",
"Duration (min)", "Mean Velocity (km/h)", "Fractal Dimension")
# Function to calculate comprehensive statistics
calc_stats <- function(x, param_name) {
x <- x[!is.na(x)]
if (length(x) < 2) return(NULL)
data.frame(
Parameter = param_name,
N = length(x),
Mean = round(mean(x), 4),
Variance = round(var(x), 4),
Std_Dev = round(sd(x), 4),
Min = round(min(x), 4),
Q1 = round(quantile(x, 0.25), 4),
Median = round(median(x), 4),
Q3 = round(quantile(x, 0.75), 4),
Max = round(max(x), 4),
IQR = round(IQR(x), 4)
)
}
# Calculate statistics for each parameter
stats_list <- list()
for (i in seq_along(params_to_analyze)) {
param <- params_to_analyze[i]
label <- param_labels[i]
stats_list[[i]] <- calc_stats(trajectory_stats_df[[param]], label)
}
# Combine into summary table
stats_summary <- do.call(rbind, stats_list[!sapply(stats_list, is.null)])
cat("\n========== STATISTICAL SUMMARY ==========\n\n")
print(stats_summary, row.names = FALSE)
# Boxplots for each parameter
par(mfrow = c(2, 3))
for (i in seq_along(params_to_analyze)) {
param <- params_to_analyze[i]
label <- param_labels[i]
data <- trajectory_stats_df[[param]][!is.na(trajectory_stats_df[[param]])]
if (length(data) >= 2) {
boxplot(data,
main = paste("Boxplot:", label),
ylab = label,
col = "lightblue",
border = "darkblue")
# Add mean point
points(1, mean(data), pch = 18, col = "red", cex = 1.5)
}
}
par(mfrow = c(1, 1))
# Density plots for each parameter
par(mfrow = c(2, 3))
for (i in seq_along(params_to_analyze)) {
param <- params_to_analyze[i]
label <- param_labels[i]
data <- trajectory_stats_df[[param]][!is.na(trajectory_stats_df[[param]])]
if (length(data) >= 3) {
dens <- density(data, na.rm = TRUE)
plot(dens,
main = paste("Density:", label),
xlab = label,
ylab = "Density",
col = "darkblue",
lwd = 2)
polygon(dens, col = rgb(0, 0, 1, 0.3), border = "darkblue")
# Add vertical lines for mean and median
abline(v = mean(data), col = "red", lwd = 2, lty = 2)
abline(v = median(data), col = "green", lwd = 2, lty = 3)
legend("topright", legend = c("Mean", "Median"),
col = c("red", "green"), lty = c(2, 3), lwd = 2, cex = 0.7)
}
}
par(mfrow = c(1, 1))
# Histogram with density overlay
par(mfrow = c(2, 3))
for (i in seq_along(params_to_analyze)) {
param <- params_to_analyze[i]
label <- param_labels[i]
data <- trajectory_stats_df[[param]][!is.na(trajectory_stats_df[[param]])]
if (length(data) >= 3) {
hist(data,
probability = TRUE,
main = paste("Histogram:", label),
xlab = label,
col = "lightgray",
border = "darkgray")
# Overlay density curve
lines(density(data), col = "red", lwd = 2)
}
}
par(mfrow = c(1, 1))
} else {
message("Insufficient trajectory data for statistical analysis (need at least 2 trajectories)")
}
```
# Interpretation of Results
```{r interpretation}
if (exists("trajectory_stats_df") && nrow(trajectory_stats_df) >= 2) {
cat("\n========== INTERPRETATION OF TRAJECTORY PARAMETERS ==========\n\n")
# Diffusion Distance
dd <- trajectory_stats_df$diffusion_distance_km[!is.na(trajectory_stats_df$diffusion_distance_km)]
if (length(dd) >= 2) {
cat("1. DIFFUSION DISTANCE (Net Displacement):\n")
cat(" - Mean:", round(mean(dd), 2), "km\n")
cat(" - This represents the straight-line distance from origin to destination.\n")
cat(" - High variance (", round(var(dd), 2), ") indicates diverse flight distances.\n\n")
}
# Straightness
st <- trajectory_stats_df$straightness[!is.na(trajectory_stats_df$straightness)]
if (length(st) >= 2) {
cat("2. STRAIGHTNESS INDEX:\n")
cat(" - Mean:", round(mean(st), 4), "(range 0-1, where 1 = perfectly straight)\n")
cat(" - Values close to 1 indicate efficient, direct flight paths.\n")
cat(" - Lower values suggest deviations due to weather, airspace, or routing.\n\n")
}
# Duration
dur <- trajectory_stats_df$duration_min[!is.na(trajectory_stats_df$duration_min)]
if (length(dur) >= 2) {
cat("3. DURATION OF TRAVEL:\n")
cat(" - Mean:", round(mean(dur), 2), "minutes\n")
cat(" - Range:", round(min(dur), 2), "-", round(max(dur), 2), "minutes\n")
cat(" - IQR:", round(IQR(dur), 2), "minutes (middle 50% of flights)\n\n")
}
# Velocity
vel <- trajectory_stats_df$mean_velocity_kmh[!is.na(trajectory_stats_df$mean_velocity_kmh)]
if (length(vel) >= 2) {
cat("4. MEAN TRAVEL VELOCITY:\n")
cat(" - Mean:", round(mean(vel), 2), "km/h\n")
cat(" - Typical commercial aircraft cruise: 800-900 km/h\n")
cat(" - Lower values may include taxi, takeoff, and landing phases.\n\n")
}
# Fractal Dimension
fd <- trajectory_stats_df$fractal_dimension[!is.na(trajectory_stats_df$fractal_dimension)]
if (length(fd) >= 2) {
cat("5. FRACTAL DIMENSION:\n")
cat(" - Mean:", round(mean(fd), 4), "\n")
cat(" - Value of 1.0 = perfectly straight line\n")
cat(" - Values closer to 2.0 = more complex, space-filling paths\n")
cat(" - Aircraft typically show low fractal dimension (efficient paths).\n\n")
}
cat("========== END OF ANALYSIS ==========\n")
}
```