Tuesday, January 31, 2017

Function to Simulate Simple Parabolic Shooting.

This function simulates a parabolic shot from the origin and does not take into account the friction of the air.

# Script to calculate the most important info about the parabolic
# shot without friction and in International System of Units

# if you want to use another system of units only change the value
# of g and the units in the prints and legends

# Inputs of the function are:
# a) initial velocity vo
# b) shot angle alfa

# Parameter
# c) gravity acceleration g = 9.81 m/s^2

# The outputs of the function are:
# T_1: ascending time
# T_2: descending time
#   H: maximum height
#  Tt: total time
#   L: maximum horizontal range

parabolic <- function(vo, alfa){
  g <- 9.81
 an <- round((2*pi*alfa)/360,2)
T_1 <- round(vo*sin(an)/g,2)
  H <- round((vo^2)*(sin(an)^2)/(2*g),2)
T_2 <- round(vo*sin(an)/g,2)
T_t <- round(2*vo*sin(an)/g,2)
  L <- round(vo^2*sin(2*an)/g,2)
  print("Ascending time");print(paste(T_1,"s"))
  print("Maximum height");print(paste(H,"m"))
  print("Descending time");print(paste(T_2, "s"))
  print("Total time");print(paste(T_t,"s"))
  print("Max. horizontal range");print(paste(L,"m"))
  y <- vector()
  p <- seq(0.0, round(L), round(L)/100)
  y <- (tan(an)*p)-((g/((2*vo^2)*cos(an)^2))*(p^2))
  plot(p, y, xlab="X", ylab="Y", type = "o", col = "red", axes=F)
  axis(1, at = seq(0,L,L/10),labels=seq(0,L,L/10),
  axis(2, at = seq(0,H,H/100),labels=seq(0,H,H/100),
  legend(L/4, H/3, legend = c(paste("vo =", vo, "m/s"),
                paste("alfa =", alfa,"degrees"),
                paste("Ascending time", paste(T_1,"s")),
                paste("Maximum height", paste(H,"m")),
                paste("Descending time", paste(T_2, "s")),
                paste("Total time", paste(T_t,"s")),
                paste("Max. horizontal range", paste(L,"m"))),
         cex=0.7, bg = par("bg"))
  title(main = "Parabolic Shot", sub = "From Origin & Frictionless")


We test the function with a shot of 100 m / s of initial velocity and 45 degrees:


In a following post we will do the simulation but with the effect of the air friction.

If you want to use the function in another system of units, you only have to change the value of the acceleration of gravity g.

We eliminate some for loop to generate the trajectory -y- for been useless and for the kind recommendation of Andrej-Nikolai Spiess.

Get the script in: