e_pilot_density_altitude: Compute Koch Chart density altitude, takeoff roll, and climb...

In erikerhardt/erikmisc: Erik Erhardt's miscellaneous functions for solving complex data analysis workflows

Compute Koch Chart density altitude, takeoff roll, and climb rate

Description

Approximation for Koch Chart density altitude for an increase in takeoff roll and decrease in climb rate based on pressure altitude and temperature.

Usage

e_pilot_density_altitude(
  pres_alt = 0,
  temp_C = 15,
  dist_takeoff_sea_level = 1000,
  climb_rate_sea_level = 500,
  sw_propeller = c("fixed_pitch", "constant_speed")[2]
)

Arguments

pres_alt	pressure altitude, inches of Mg
temp_C	temperature, degrees celsius
dist_takeoff_sea_level	POH distance for takeoff at standard temperature and pressure (STP)
climb_rate_sea_level	POH distance for climb at standard temperature and pressure (STP)
sw_propeller	Select propeller to be "fixed_pitch" or "constant_speed"

Details

dens_alt = (145426 * (1 - (((288.16 - pres_alt * 0.001981) / 288.16)^5.2563 / ((273.16 + temp_C) / 288.16))^0.235))

Equations and approximations from "Axioms of Flight",
James Embree, Flight Information Publications,
St. Louis MO, 1984. ISBN 0-9601062-7-8

Approximation (good to 8000 feet density altitude):

• Takeoff distance:

  • For fixed pitch prop, increase sea level standard day takeoff distance 15% for each 1000 foot increase in density altitude.

  • For constant speed prop, increase by 13%.

• Climb rate

  • For fixed pitch prop, decrease sea level standard day climb rate 7.5% for each 1000 foot increase in density altitude.

  • For constant speed prop, decrease by 7%.

Example takeoff for fixed pitch prop:

• dist_takeoff_dens_alt = dist_takeoff_sealevel * (1 + ((dens_alt / 1000) * 0.15))

(https://groups.google.com/g/rec.aviation.piloting/c/SDlMioBVqaA)

Value

out named list including density_altitude, dist_takeoff_dens_alt, climb_rate_dens_alt, and all the input parameters.

Examples

e_pilot_density_altitude(
    pres_alt               = 0
  , temp_C                 = 15
  , dist_takeoff_sea_level = 1000
  , climb_rate_sea_level   = 500
  , sw_propeller = c("fixed_pitch", "constant_speed")[1]
  )
e_pilot_density_altitude(
    pres_alt               = 7170
  , temp_C                 = 30
  , dist_takeoff_sea_level = 770
  , climb_rate_sea_level   = 900
  , sw_propeller = c("fixed_pitch", "constant_speed")[1]
  )
e_pilot_density_altitude(
    pres_alt               = 7170
  , temp_C                 = 30
  , dist_takeoff_sea_level = 770
  , climb_rate_sea_level   = 900
  , sw_propeller = c("fixed_pitch", "constant_speed")[2]
  )


## Tables
# 1972 Piper Arrow II
dist_takeoff_sea_level <- 770
climb_rate_sea_level   <- 900
sw_propeller           <- c("fixed_pitch", "constant_speed")[2]

list_out <- list()
i_list <- 0

for (i_pres_alt in seq(0, 10000, by = 2000)) {
  ## i_pres_alt = 0
  for (i_temp_C in c(0, seq(15, 40, by = 5))) {
    ## i_temp_C = 0

    i_list <- i_list + 1

    list_out[[ i_list ]] <-
      e_pilot_density_altitude(
        pres_alt               = i_pres_alt
      , temp_C                 = i_temp_C
      , dist_takeoff_sea_level = dist_takeoff_sea_level
      , climb_rate_sea_level   = climb_rate_sea_level
      , sw_propeller           = sw_propeller
      )
  }
}

dat_out <-
  list_out |>
  dplyr::bind_rows()
dat_out |> print(n = 10)

# Note: pres_alt = pressure altitude at 29.92 inches Mg

# density altitude
dat_density_altitude <-
  dat_out |>
  dplyr::select(
    density_altitude
  , pres_alt
  , temp_C
  ) |>
  tidyr::pivot_wider(
    id_cols     = temp_C
  , names_from  = pres_alt
  , values_from = density_altitude
  )

# takeoff roll
dat_takeoff_roll <-
  dat_out |>
  dplyr::select(
    dist_takeoff_dens_alt
  , pres_alt
  , temp_C
  ) |>
  tidyr::pivot_wider(
    id_cols     = temp_C
  , names_from  = pres_alt
  , values_from = dist_takeoff_dens_alt
  )

# climb rate
dat_climbrate <-
  dat_out |>
  dplyr::select(
    climb_rate_dens_alt
  , pres_alt
  , temp_C
  ) |>
  tidyr::pivot_wider(
    id_cols     = temp_C
  , names_from  = pres_alt
  , values_from = climb_rate_dens_alt
  )

dat_density_altitude
dat_takeoff_roll
dat_climbrate

erikerhardt/erikmisc documentation built on April 17, 2025, 10:48 a.m.