R/ROSthetacalc.r

In cffdrs: Canadian Forest Fire Danger Rating System

.ROSthetacalc <- function(ROS, FROS, BROS, THETA){
  #############################################################################
  # Description:
  #   Computes the Rate of Spread at any point along the perimeter of an 
  #   elliptically shaped fire. Equations are from Wotton et. al. (2009).
  #
  #   Wotton, B.M., Alexander, M.E., Taylor, S.W. 2009. Updates and revisions to
  #   the 1992 Canadian forest fire behavior prediction system. Nat. Resour. 
  #   Can., Can. For. Serv., Great Lakes For. Cent., Sault Ste. Marie, Ontario, 
  #   Canada. Information Report GLC-X-10, 45p.
  #
  # Args:
  #   FUELTYPE: The Fire Behaviour Prediction FuelType
  #        ROS: Rate of Spread (m/min)
  #       FROS: Flank Fire Rate of Spread (m/min)
  #       BROS: Back Fire Rate of Spread (m/min)
  #      THETA: 
  # Returns:
  #   ROSTHETA: Rate of spread at point theta(m/min)
  #
  #############################################################################
  c1 <- cos(THETA)
	s1 <- sin(THETA)
  c1 <- ifelse(c1==0,cos(THETA+.001),c1)
  #Eq. 94 - Calculate the Rate of Spread at point THETA
  # large equation, view the paper to see a better representation
  ROStheta <- 
    ((ROS - BROS) / (2 * c1) + 
    (ROS + BROS)/(2*c1)) *
	  ((FROS * c1 * sqrt(FROS * FROS * c1 * c1 + (ROS * BROS) * s1 * s1) - 
	    ((ROS * ROS - BROS * BROS)/4) * s1 * s1) /
		 (FROS * FROS * c1 * c1 + ((ROS + BROS) / 2) * ((ROS + BROS) / 2) * s1 * s1)
	  )
	 return(ROStheta)
}