Flight Analysis

Flight Summary

Flight Statistics

Data normalized across several flight logs, spanning from NS45 to NS80, excepting NS54, NS55, and NS68 (NS54 is reserved for a flight still in development, and both NS55 and NS68 failed to record location data).

Due to a settings issue, before NS59, the cell tracker hardware stopped recording above 12.1 km (except for NS53). This limit is shown as a grey horizontal line in the figures depicting altitude.

require(ggplot2)

Loading required package: ggplot2

require(directlabels)

Loading required package: directlabels

require(scales)

Loading required package: scales

source("setup.R")
flight_times <- read_flight_times("flight_times.txt")
flight_data <- read_flight_data("flight_data/", calculate_difftime = TRUE)

1 Ascent Rate

1.1 Ascent Rate vs Time of Year

ggplot(flight_data,
       aes(
           x = as.Date(format(DateTime, format = "%m-%d"), format = "%m-%d"),
           y = Ascent_Rate_m_s,
           colour = Flight
       )) +
    geom_point() + geom_path() +
    geom_hline(yintercept = 0, alpha = 0.2) +
    scale_x_date(
        date_breaks = "1 month",
        labels = date_format("%b"),
        limits = as.Date(c("01-01", "12-31"), format = "%m-%d"),
        expand = c(0, 0)
    ) +
    geom_dl(aes(label = gsub("NS", "", Flight)),
            method = list(cex = 0.8, dl.trans(y = y + 0.2), "top.bumpup")) + guides(colour = FALSE) +
    labs(title = "Ascent Rate vs Time of Year", x = "Time of Year", y = "Ascent Rate (m/s)")

1.2 Ascent Rate After Burst

ggplot(flight_data,
       aes(x = burst_difftime / 60,
           y = Ascent_Rate_m_s,
           colour = Flight)) +
    geom_path() +
    xlim(-0.5, 3) +
    geom_dl(aes(label = gsub("NS", "", Flight)), method = list("smart.grid", "small.box.labels")) + guides(colour = FALSE) +
    labs(title = "Ascent Rate After Burst", x = "Time Since Burst (minutes)", y = "Ascent Rate (m/s)")

1.3 Ascent Rate vs Altitude

ggplot(flight_data,
       aes(x = Altitude_m / 1000,
           y = Ascent_Rate_m_s,
           colour = Flight)) +
    geom_path() +
    geom_dl(aes(label = gsub("NS", "", Flight)),
            method = list("far.from.others.borders", "small.box.labels")) + guides(colour = FALSE) +
    labs(title = "Ascent Rate vs Altitude", x = "Altitude (km)", y = "Ascent Rate (m/s)")

2 Ground Speed

2.1 Ground Speed vs Time of Year

ggplot(flight_data,
       aes(
           x = as.Date(format(DateTime, format = "%m-%d"), format = "%m-%d"),
           y = Ground_Speed_m_s,
           colour = Flight
       )) +
    geom_point() + geom_path() +
    scale_x_date(
        date_breaks = "1 month",
        labels = date_format("%b"),
        limits = as.Date(c("01-01", "12-31"), format = "%m-%d"),
        expand = c(0, 0)
    ) +
    geom_dl(aes(label = gsub("NS", "", Flight)),
            method = list(cex = 0.8, dl.trans(y = y + 0.2), "top.bumpup")) + guides(colour = FALSE) +
    labs(title = "Ground Speed vs Time of Year", x = "Time of Year", y = "Ground Speed (m/s)")

2.2 Ground Speed vs Altitude

ggplot(
    flight_data,
    aes(
        x = Altitude_m / 1000,
        y = Ground_Speed_m_s,
        colour = as.POSIXlt(DateTime)$yday
    )
) +
    geom_point() +
    scale_colour_gradient2(
        limits = c(0, 366),
        low = "green",
        mid = "red",
        midpoint = 366 / 2,
        high = "blue"
    ) +
    labs(
        title = "Ground Speed vs Altitude",
        x = "Altitude (km)",
        y = "Ground Speed (m/s)",
        colour = "Day of Year"
    ) +
    theme(
        legend.position = c(1, 1),
        legend.direction = "horizontal",
        legend.justification = "right"
    )

Green: late winter, Yellow: spring, Red: summer, Purple: autumn, Blue: early winter

3 Ascent and Descent Durations

For flights with definite burst and landing times, we can extract the times it took for the balloon to ascend and descend from max altitude.

flight_durations <- data.frame()
for (current_flight in flight_times$Flight)
{
    if (!is.na(flight_times$Launch_Time[flight_times$Flight == current_flight]) &&
        !is.na(flight_times$Burst_Time[flight_times$Flight == current_flight]) &&
        !is.na(flight_times$Landing_Time[flight_times$Flight == current_flight]))
    {
        current_ascent_duration <-
            as.numeric(with(
                flight_times,
                difftime(Launch_Time[Flight == current_flight], Burst_Time[Flight == current_flight], units = "mins")
            )) * -1
        current_descent_duration <-
            as.numeric(with(
                flight_times,
                difftime(Landing_Time[Flight == current_flight], Burst_Time[Flight == current_flight], units = "mins")
            ))
        
        flight_durations <- rbind(
            flight_durations,
            data.frame(
                Flight = current_flight,
                Date = flight_times$Date[flight_times$Flight == current_flight],
                Ascent_Duration_min = current_ascent_duration,
                Descent_Duration_min = current_descent_duration,
                Ratio = current_ascent_duration / current_descent_duration
            )
        )
    }
}
rm(current_flight,
   current_ascent_duration,
   current_descent_duration)
rmarkdown::paged_table(flight_durations)

On average, ascent takes 69 minutes, while descent takes 36 minutes, with a ratio of 2.

3.1 Ascent Duration vs Descent Duration

ggplot(
    flight_durations,
    aes(
        x = Descent_Duration_min,
        y = Ascent_Duration_min,
        colour = as.POSIXlt(Date)$yday
    )
) +
    geom_point(size = 0.1) + geom_abline(slope = 1:3) +
    scale_colour_gradient2(
        limits = c(0, 366),
        low = "green",
        mid = "red",
        midpoint = 366 / 2,
        high = "blue"
    ) +
    geom_dl(aes(label = gsub("NS", "", Flight)), method = list(cex = 0.8)) +
    labs(
        title = "Ascent Duration vs Descent Duration",
        x = "Descent Duration (minutes)",
        y = "Ascent Duration (minutes)",
        colour = "Day of Year"
    ) +
    coord_fixed(ratio = 1) +
    scale_x_continuous(breaks = seq(
        from = 0,
        to = max(flight_data$Downrange_Distance_m),
        by = 10
    )) +
    scale_y_continuous(breaks = seq(
        from = 0,
        to = max(flight_data$Altitude_m),
        by = 10
    )) +
    theme(
        legend.position = c(1, 0.96),
        legend.direction = "horizontal",
        legend.justification = "right"
    )

Green: late winter, Yellow: spring, Red: summer, Purple: autumn, Blue: early winter