PROGRAM long_ball IMPLICIT NONE ! This program will simulate the flight of a baseball after impact with a bat ! launch_v is the launch speed off the bat in m/s ! bat_v is the bat speed in mph ! pitch_v is the speed of the pitch in mph ! gravity is in m/s^2 ! delta_t is the time increment in seconds ! i_angle is the initial trajectory angle in degrees ! ball_radius is the radius of the ball in m ! mall_mass is the mass of the ball in kg ! i_rad is the intitial trajectory angle in radians ! max_distance is the maximum distance the baseball travels in feet ! zk is the distance from the knob of the bat in m ! cm is the center of mass of the bat in m ! rg is the radius of gyration ! roe is the atmospheric pressure in kg/m^3 ! bat_si is the bat speed in m/s ! pitch_si is the pitch speed in m/s ! Written 014-Feb-2007 ! height and distance are in m ! the x and y velocities are in m/s ! angle is the angle of the bat in reference to the ground in radians ! spin is the spin of the ball in rpm ! distance_ft is the distance the ball travels in feet ! height_ft is the height the ball travels in feet ! written 3/10/07 ! by Lance Wheeler !jc Good inclusion of definitions of units and variables, though it would !jc probably look nicer if it were separated from the rest of the header !jc comment. REAL :: launch_v, bat_v, pitch_v, gravity, delta_t = .01, i_angle, lift_const, drag_const REAL :: R, area, pi = 3.14159265, ball_radius = .0366, ball_mass = .145, bat_mass = .9, i_rad, max_distance REAL :: zk = .564, cm = .564, cor = .6, rg = .23, roe =1.21, drag_coef = .5, bat_si, pitch_si REAL,DIMENSION(10000) :: height, distance, velocity_x, velocity_y, angle, v_total, spin, S, lift_coef REAL,DIMENSION(10000) :: distance_ft, height_ft INTEGER :: i, j PRINT *, 'Welcome to Home Run Derby' PRINT *, 'Enter the speed of the pitch (20 to 105 mph)' READ (*,*) pitch_v ! 1st user input speed of the pitch pitch_si = pitch_v * (1609.344 / 3600.) ! converts input from mph to m/s PRINT *, 'Enter the bat speed (20 to 120 mph)' ! 2nd user input is bat speed READ (*,*) bat_v bat_si = bat_v * (1609.344 / 3600.) ! converts input from mph to m/s PRINT *, 'Enter the uppercut angle of the swing (10 to 70 degrees)' ! 3rd user input is trajectory READ (*,*) i_angle !jc So this is ball's initial angle? You probably should have called it !jc something else - it isn't really the angle of the swing of the bat !jc which is what this sounds like. i_rad = i_angle * (pi / 180.) ! converts input from degrees to radians area = pi * (ball_radius ** 2.) ! area of baseball R = (ball_mass/bat_mass) * ( 1.+((zk - (cm**2.)) / rg)) ! reynolds number !jc Where did this come from? References in code are nice. launch_v = (((cor - R) / (1. + R)) * pitch_si) + (((cor + 1.) / (1. + R)) * bat_si) ! speed of ball off bat lift_const = roe * area ! calculates the constants in the force of lift drag_const = roe * area * drag_coef ! calculates the constants in the force of drag gravity = -(ball_mass * 9.81) ! calculates the force of gravity velocity_x(1) = (launch_v*(COS(i_rad))) ! sets initial x component of velocity velocity_y(1) = launch_v*(SIN(i_rad)) ! sets initial y component of velocity v_total(1) = launch_v ! sets initial velocity angle(1) = i_rad ! sets initial trajectory angle distance(1) = 0 ! sets initial distance height(1) = 1.2192 ! height of bat from ground during swing spin(1) = 500 ! sets initial spin in rpm !jc Why rpm ? lift_coef(1) = 0 ! sets intial amount of lift force DO i = 2, 10000 ! loop to calculate position of the baseball in flight spin(i) = spin(i-1) - ((1./5.) * delta_t * spin(i-1)) ! determines the decay of spin during flight S(i) = (ball_radius * spin(i)) / velocity_y(1) ! variable used to determine value of lift coefficient !jc What does this do? Why the variate in lift_coef ? IF (S(i) <= .1) THEN ! statement gives appropriate values to lift coeffient lift_coef(i) = 1.5 * S(i) ELSE lift_coef(i) = .09 + .6 * S(i) END IF velocity_x(i)=(velocity_x(i-1) + (delta_t*(((-lift_const*lift_coef(i)*(v_total(i-1)**2.))*SIN(angle(i-1))) & +((-drag_const*(v_total(i-1)**2.))*COS(angle(i-1)))) / (2.*ball_mass))) ! x velocity component velocity_y(i)=(velocity_y(i-1)+(delta_t*((((lift_const*lift_coef(i)*(v_total(i-1)**2.))/2.)*COS(angle(i-1))) & +(((-drag_const*(v_total(i-1)**2.))/2.)*SIN(angle(i-1)))+gravity) / (ball_mass))) ! y velocity component v_total(i) = SQRT((velocity_x(i)**2.) + (velocity_y(i)**2.)) ! velocity change after launch angle(i) = ATAN((velocity_y(i)) / (velocity_x(i))) ! changing angle after launch distance(i) = velocity_x(i)*delta_t + distance(i-1) ! x position of baseball distance_ft(i) = distance(i) * (1. / .305) ! x position converted from meters to feet height(i) = velocity_y(i)*delta_t + height(i-1) ! y position of baseball height_ft(i) = height(i) * (1. / .305) ! y position converted from meters to feet IF (height(i) <= 0) THEN ! stops loop when ball hits the ground max_distance = distance_ft(i-1) ! determines max distance when ball hits ground EXIT END IF END DO WRITE(*,'(A20, x ,F4.0, x, A4)') 'You hit the baseball', max_distance,'feet' ! prints max distance of baseball CALL flight_plot(distance_ft, height_ft, i) ! calls flight_plot subroutine END PROGRAM long_ball SUBROUTINE flight_plot(distance_ft, height_ft, i) ! subroutine to plot the flight of a baseball IMPLICIT NONE INTEGER,INTENT(IN) :: i REAL,DIMENSION(1000),INTENT(IN) :: distance_ft, height_ft INTEGER :: j, ier, pgbeg REAL,DIMENSION(11) :: fence_y = (/ (j, j=2, 12) /) REAL,DIMENSION(11) :: fence_x = 385 ier = pgbeg(0, '/xserve',1,1) ! Initializes plot CALL pgsci(7) ! sets color to yellow CALL pgenv(0., 550., 0., 400., 0, 1) ! Sets scale for plot CALL pglab('distance(feet)','height(feet)','Home Run Derby') ! labels axes and title of the plot CALL pgsci(2) ! changes color to red CALL pgpt(i, REAL(distance_ft(1:i)), REAL(height_ft(1:i)), 1) ! Plot the points CALL pgtext(-40., 10., 'Batter') ! labels where the batter stands CALL pgsci(10) ! changes color to green CALL pgtext(353., -10., 'Fence') ! labels the fence CALL Pgpt(11, fence_x, fence_y, 6) ! plots the fence CALL pgline(11, fence_x, fence_y) ! makes line for points on fence IF (distance_ft(i) > 385.) THEN ! determines if ball went home run distance CALL pgsci(1) ! changes color to white CALL pgsch (5.) ! enlarges font by 5x CALL pgtext(100., 300., 'HOME RUN!') ! prints if ball went 385 feet ELSE CALL pgsci(1) ! changes color to white CALL pgsch (5.) ! enlarges font by 5x CALL pgtext(200., 300., 'OUT!') ! prints if ball did not go home run distance END IF CALL pgend ! closes the plot !jc Fancy plot END SUBROUTINE flight_plot !jc Nice program. There are some places where the comments should be more !jc descriptive, so it is a little more clear where things are coming from.