Car Physics

This code has been declared by its author to be Public Domain code.

Car Physics by Vorderman

2001

2 part listing

part 1 - original listing from Marco Monster's code. Use as is and retrieve CAR position x,y to position car in-game.

part 2 - tidied up physics routine with variable front/rear/4 wheel drive option and thus the ability to maintain drifts / slides. Use part 1 and replace FUNC_do_physics() with the new one, then add the new GLOBAL variable shown at the top of part 2.

NOTE : FUNC_do_physics includes screen boundary checking and looping right at the bottom of the function. You'll need to change this for a 2D screen res other then 800,600 or remove if for 3d game.

1. FULL 2D SOURCE

Graphics 800,600
SetBuffer BackBuffer()

;physics variables
Global delta_t# = 0.01
Global M_PI# = 3.1415926
Global DRAG# = 5.0
Global RESISTANCE# = 30.0
Global CA_R# = -5.20
Global CA_F# = -5.0
Global MAX_GRIP# = 2.0    
Global MULT# = 57
Global MULT2# = 0.01745

Global CAR1_cartype = 1
Global CAR1_cartype_b# = 1.0
Global CAR1_cartype_c# = 1.0
Global CAR1_cartype_wheelbase# = CAR1_cartype_b# + CAR1_cartype_c#
Global CAR1_cartype_h# = 1.0
Global CAR1_cartype_mass# = 1500
Global CAR1_cartype_inertia# = 1500
Global CAR1_cartype_width# = 1.5
Global CAR1_cartype_length# = 3.0
Global CAR1_cartype_wheellength# = 0.7
Global CAR1_cartype_wheelwidth# = 0.3
Global CAR1_car_position_wc_x# = 400.0
Global CAR1_car_position_wc_y# = 300.0
Global CAR1_car_velocity_wc_x# = 0
Global CAR1_car_velocity_wc_y# = 0
Global CAR1_car_angle# = 0
Global CAR1_car_angularvelocity# = 0
Global CAR1_car_steerangle# = 0
Global CAR1_car_throttle# = 0
Global CAR1_car_brake# = 0

Global front_slip = 0
Global rear_slip = 0

Global velocity_x#
Global velocity_y#
Global yawspeed#
Global sn#, cs#
Global xpos#, ypos#
Global rot_angle#
Global sideslip#
Global slipanglefront#
Global slipanglerear#
Global flatf_x#, flatf_y#
Global flatr_x#, flatr_y#
Global weight#
Global ftraction_x#, ftraction_y# 
Global resistance_x#, resistance_y#
Global force_x#, force_y#
Global torque#
Global acceleration_x#, acceleration_y#, angular_acceleration# 
Global acceleration_wc_x#, acceleration_wc_y#


;main loop
While ( KeyHit(1)=0 )

    Cls

    FUNC_do_input()
    
    FUNC_do_physics()
        
    Flip
    
Wend

End




;input routine from joystick/pad/wheel
Function FUNC_do_input()

    If ( JoyYDir() = -1 ) CAR1_car_throttle# = 2000.0
    If ( JoyYDir() = 0 ) CAR1_car_throttle# = 0.0
    If ( JoyYDir() = 1 ) 
        CAR1_car_throttle# = 0.0
        CAR1_car_brake# = 100.0
    Else
        CAR1_car_brake# = 0.0
    EndIf

    CAR1_car_steerangle# = 0.0
    If ( JoyXDir() = 1 ) CAR1_car_steerangle# = (-M_PI# / 4.0) * 0.15;* MULT2#
    If ( JoyXDir() = -1 ) CAR1_car_steerangle# = (M_PI# / 4.0) * 0.15; MULT2#

    rear_slip = 0;
    If ( JoyDown(1) ) rear_slip = 1;
    
    ;temp display of vars
    Text 0,0,Str(CAR1_car_position_wc_x#)
    Text 0,12,Str(CAR1_car_position_wc_y#)
    Text 0,24,Str(CAR1_car_steerangle#)

    xpos# = CAR1_car_position_wc_x#
    ypos# = CAR1_car_position_wc_y#

    ;render a small moving car rep.
    renda1# =( -CAR1_car_angle# * MULT# ) - 60
    If (renda1#<0.0) Then renda1#=360.0+renda1#
    renda2# =( -CAR1_car_angle# * MULT# ) + 60
    If (renda2#>359.0) Then renda2#=renda2#-360.0
    renda3# =( -CAR1_car_angle# * MULT# ) - 120
    If (renda3#<0.0) Then renda3#=360.0+renda3#
    renda4# =( -CAR1_car_angle# * MULT# ) + 120
    If (renda4#>359.0) Then renda4#=renda4#-360.0

    rendx1#=25*Cos(renda1#) : rendy1#=25*Sin(renda1#)
    rendx2#=25*Cos(renda2#) : rendy2#=25*Sin(renda2#)
    rendx3#=25*Cos(renda3#) : rendy3#=25*Sin(renda3#)
    rendx4#=25*Cos(renda4#) : rendy4#=25*Sin(renda4#)

    Color 255,255,255
    Line rendx1#+xpos#,rendy1#+ypos#,rendx2#+xpos#,rendy2#+ypos#
    Line rendx2#+xpos#,rendy2#+ypos#,rendx4#+xpos#,rendy4#+ypos#
    Line rendx4#+xpos#,rendy4#+ypos#,rendx3#+xpos#,rendy3#+ypos#
    Line rendx3#+xpos#,rendy3#+ypos#,rendx1#+xpos#,rendy1#+ypos#

End Function






Function FUNC_do_physics()

    sn# = Sin(CAR1_car_angle# * MULT#); * MULT2#
    cs# = Cos(CAR1_car_angle# * MULT#) ;* MULT2#

    Text 400,0,"sn="+Str(sn#)+" cs="+Str(cs#)

    ; SAE convention: x is To the front of the car, y is To the Right, z is down
    ; transform velocity in world reference frame To velocity in car reference frame
    velocity_x# = cs# * CAR1_car_velocity_wc_y# + sn# * CAR1_car_velocity_wc_x#
    velocity_y# = -sn# * CAR1_car_velocity_wc_y# + cs# * CAR1_car_velocity_wc_x#

    ; Lateral force on wheels
    ; Resulting velocity of the wheels as result of the yaw rate of the car body
    ; v = yawrate * r where r is distance of wheel To CG (approx. half wheel base)
    ; yawrate (ang.velocity) must be in rad/s
    yawspeed# = CAR1_cartype_wheelbase# * 0.5 * CAR1_car_angularvelocity#

    If( velocity_x# = 0 )
        rot_angle# = 0
    Else 
;        rot_angle# = ATan2( (yawspeed# * MULT#) , (velocity_x# * MULT#) )
        rot_angle# = ATan2( (yawspeed# ) , (velocity_x#) ) * MULT2#
    EndIf

    ; Calculate the side slip angle of the car (a.k.a. beta)
    If( velocity_x# = 0 )
        sideslip# = 0.0
    Else
;        sideslip# = ATan2( (velocity_y# * MULT#) , (velocity_x# * MULT#) )        
        sideslip# = ATan2( (velocity_y# ) , (velocity_x#) )    * MULT2#    
    EndIf

    ; Calculate slip angles For front And rear wheels (a.k.a. alpha)
    slipanglefront# = sideslip# + rot_angle# - CAR1_car_steerangle#
    slipanglerear# = sideslip# - rot_angle#

    ; weight per axle = half car mass times 1G (=9.8m/s^2) 
    weight# = CAR1_cartype_mass# * 9.8 * 0.5
    
    ; lateral force on front wheels = (Ca * slip angle) capped To friction circle * load
    flatf_x# = 0.0
    flatf_y# = CA_F# * slipanglefront#

;    If ( flatf_y# > MAX_GRIP# ) flatf_y# = MAX_GRIP#
;    If ( flatf_y# < -MAX_GRIP# ) flatf_y# = -MAX_GRIP#

    flatf_y# = flatf_y# * weight#
    
    ; allow front wheels to slip
    If(front_slip=1) flatf_y# = flatf_y# * 0.5

    ; lateral force on rear wheels
    flatr_x# = 0.0
    flatr_y# = CA_R# * slipanglerear#

;    If ( flatr_y# > MAX_GRIP# ) flatr_y# = MAX_GRIP#
;    If ( flatr_y# < -MAX_GRIP# ) flatr_y# = -MAX_GRIP#

    flatr_y# = flatr_y# * weight#
    
    If(rear_slip = 1) flatr_y# = flatr_y# * 0.5

    ; longtitudinal force on rear wheels - very simple traction model
    ftraction_x# = 100.0 * (CAR1_car_throttle# - CAR1_car_brake# * Sgn(velocity_x#))
    ftraction_y# = 0.0

    If(rear_slip = 1) ftraction_x# = ftraction_x# * 0.5

    ; Forces And torque on body
    ; drag And rolling resistance
    resistance_x# = -( RESISTANCE# * velocity_x# + DRAG# * velocity_x# * Abs( velocity_x# ) )
    resistance_y# = -( RESISTANCE# * velocity_y# + DRAG# * velocity_y# * Abs( velocity_y# ) )

    ; sum forces
    force_x# = ftraction_x# + (Sin( CAR1_car_steerangle# * MULT# )) * flatf_x# + flatr_x# + resistance_x#
    force_y# = ftraction_y# + (Cos( CAR1_car_steerangle# * MULT# )) * flatf_y# + flatr_y# + resistance_y#    

    ; torque on body from lateral forces
    torque# = CAR1_cartype_b# * flatf_y# - CAR1_cartype_c# * flatr_y#

    ; Acceleration
    ; Newton F = m.a, therefore a = F/m
    acceleration_x# = force_x# / CAR1_cartype_mass#
    acceleration_y# = force_y# / CAR1_cartype_mass#
    
    angular_acceleration# = torque# / CAR1_cartype_inertia#

    ; Velocity And position
    ; transform acceleration from car reference frame To world reference frame
    acceleration_wc_x# = cs# * acceleration_y# + sn# * acceleration_x#
    acceleration_wc_y# = -sn# * acceleration_y# + cs# * acceleration_x#

    ; velocity is integrated acceleration
    CAR1_car_velocity_wc_x# = CAR1_car_velocity_wc_x# + (delta_t# * acceleration_wc_x#)
    CAR1_car_velocity_wc_y# = CAR1_car_velocity_wc_y# + (delta_t# * acceleration_wc_y#)

    ; position is integrated velocity
    CAR1_car_position_wc_x# = CAR1_car_position_wc_x# + (delta_t# * CAR1_car_velocity_wc_x#)
    CAR1_car_position_wc_y# = CAR1_car_position_wc_y# + (delta_t# * CAR1_car_velocity_wc_y#)

    ; Angular velocity And heading
    ; integrate angular acceleration To get angular velocity
    CAR1_car_angularvelocity# = CAR1_car_angularvelocity# + (delta_t# * angular_acceleration#)

    ; integrate angular velocity To get angular orientation
    CAR1_car_angle# = CAR1_car_angle# + (delta_t# * CAR1_car_angularvelocity#)

    If ( CAR1_car_position_wc_x# < 0.0 ) CAR1_car_position_wc_x# = 800.0
    If ( CAR1_car_position_wc_x# > 800.0 ) CAR1_car_position_wc_x# = 0.0
    If ( CAR1_car_position_wc_y# < 0.0 ) CAR1_car_position_wc_y# = 600.0
    If ( CAR1_car_position_wc_y# > 600.0 ) CAR1_car_position_wc_y# = 0.0
    
End Function




2. ADDITIONS / CHANGES for rear/front/4 wheel drive

;type of car - 1=rear 2=front 3=four
Global CAR1_car_drivetype = 3




Function FUNC_do_physics()

    ; SAE convention: x is To the front of the car, y is To the Right, z is down



    ;--------------------------
    ; TRANSFORM VELOCITY
    ;--------------------------
        ; transform velocity in world reference frame To velocity in car reference frame
        sn# = Sin(CAR1_car_angle# * MULT#); * MULT2#
        cs# = Cos(CAR1_car_angle# * MULT#) ;* MULT2#
        velocity_x# = cs# * CAR1_car_velocity_wc_y# + sn# * CAR1_car_velocity_wc_x#
        velocity_y# = -sn# * CAR1_car_velocity_wc_y# + cs# * CAR1_car_velocity_wc_x#


    ;--------------------------
    ; LATERAL FORCES ON WHEELS
    ;--------------------------
        ; Resulting velocity of the wheels as result of the yaw rate of the car body
        ; v = yawrate * r where r is distance of wheel To CG (approx. half wheel base)
        ; yawrate (ang.velocity) must be in rad/s

        ; 0.5 in this line becomes front/rear pos of COG - alter this later
        yawspeed# = CAR1_cartype_wheelbase# * 0.5 * CAR1_car_angularvelocity#
        If( velocity_x# = 0 )
            rot_angle# = 0
        Else 
            rot_angle# = ATan2( (yawspeed# ) , (velocity_x#) ) * MULT2#
        EndIf


    ;-------------------------
    ; SIDESLIP ANGLE
    ;-------------------------
        ; Calculate the side slip angle of the car (a.k.a. beta)
        If( velocity_x# = 0 )
            sideslip# = 0.0
        Else
            sideslip# = ATan2( (velocity_y# ) , (velocity_x#) )    * MULT2#    
        EndIf


    ;-------------------------
    ; SLIP ANGLES FRONT/REAR
    ;-------------------------
        ; Calculate slip angles For front And rear wheels (a.k.a. alpha)
        slipanglefront# = sideslip# + rot_angle# - CAR1_car_steerangle#
        slipanglerear# = (sideslip# - rot_angle#) 


    ;-------------------------
    ; WEIGHT PER AXLE
    ;-------------------------
        ; weight per axle = half car mass times 1G (=9.8m/s^2) 
        ; need to split this into front and rear masses - according to position of COG
        weight# = CAR1_cartype_mass# * 9.8 * 0.5


    ;--------------------------
    ; LATERAL FORCES ON WHEELS 
    ;--------------------------
        ; (Ca * slip angle) capped To friction circle * load
        flatf_x# = 0.0
        flatr_x# = 0.0

        ;check for front / rear / 4 wheel drive
        If ( CAR1_car_drivetype = 1 )

            ;rear wheel drive
            flatr_y# = CA_R# * slipanglerear# / ((CAR1_car_throttle# / 5000.0)+1)
            flatf_y# = CA_F# * slipanglefront#

        Else If ( CAR1_car_drivetype = 2 )

            ;front wheel drive
            flatr_y# = CA_R# * slipanglerear#
            flatf_y# = CA_F# * slipanglefront# / ((CAR1_car_throttle# / 5000.0)+1)

        Else If ( CAR1_car_drivetype = 3 )
    
            ;4 wheel drive
            flatr_y# = CA_R# * slipanglerear# / ((CAR1_car_throttle# / 5000.0)+1)
            flatf_y# = CA_F# * slipanglefront# / ((CAR1_car_throttle# / 5000.0)+1)
        
        EndIf
            
        flatf_y# = flatf_y# * weight#
        flatr_y# = flatr_y# * weight#

        ; allow for handbrake / reduced grip levels - use this for different surfaces later    
        If(front_slip=1) flatf_y# = flatf_y# * 0.5
        If(rear_slip = 1) flatr_y# = flatr_y# * 0.5


    ;-----------------------------
    ; LONGITUDINAL FORCES
    ;-----------------------------
        ; longtitudinal force on rear wheels - very simple traction model
        ftraction_x# = 100.0 * (CAR1_car_throttle# - CAR1_car_brake# * Sgn(velocity_x#))
        ftraction_y# = 0.0

        ; allow for handbrake
        If(rear_slip = 1) ftraction_x# = ftraction_x# * 0.5



    ;-------------------------------
    ; SUM FORCES AND TORQUE ON BODY
    ;-------------------------------
        ; drag And rolling resistance
        resistance_x# = -( RESISTANCE# * velocity_x# + DRAG# * velocity_x# * Abs( velocity_x# ) )
        resistance_y# = -( RESISTANCE# * velocity_y# + DRAG# * velocity_y# * Abs( velocity_y# ) )

        ; sum forces
        force_x# = ftraction_x# + (Sin( CAR1_car_steerangle# * MULT# )) * flatf_x# + flatr_x# + resistance_x#
        force_y# = ftraction_y# + (Cos( CAR1_car_steerangle# * MULT# )) * flatf_y# + flatr_y# + resistance_y#    

        
        ; torque on body from lateral forces
        torque# = CAR1_cartype_b# * flatf_y# - CAR1_cartype_c# * flatr_y#

        ; Acceleration - Newton F = m.a, therefore a = F/m
        acceleration_x# = force_x# / CAR1_cartype_mass#
        acceleration_y# = force_y# / CAR1_cartype_mass#
    
        ; angular acceleration around COG
        angular_acceleration# = torque# / CAR1_cartype_inertia#

        ; Velocity And position
        ; transform acceleration from car reference frame To world reference frame
        acceleration_wc_x# = cs# * acceleration_y# + sn# * acceleration_x#
        acceleration_wc_y# = -sn# * acceleration_y# + cs# * acceleration_x#

        ; velocity is integrated acceleration
        CAR1_car_velocity_wc_x# = CAR1_car_velocity_wc_x# + (delta_t# * acceleration_wc_x#)
        CAR1_car_velocity_wc_y# = CAR1_car_velocity_wc_y# + (delta_t# * acceleration_wc_y#)

        ; position is integrated velocity
        CAR1_car_position_wc_x# = CAR1_car_position_wc_x# + (delta_t# * CAR1_car_velocity_wc_x#)
        CAR1_car_position_wc_y# = CAR1_car_position_wc_y# + (delta_t# * CAR1_car_velocity_wc_y#)

        ; Angular velocity And heading
        ; integrate angular acceleration To get angular velocity
        CAR1_car_angularvelocity# = CAR1_car_angularvelocity# + (delta_t# * angular_acceleration#)

        ; move COG left / right according to body's angular rotation
        CAR1_car_COGx# = (CAR1_car_angularvelocity# * 10.0)
        CAR1_car_COGy# = CAR1_car_throttle# / 100.0
        
        ; integrate angular velocity To get angular orientation
        CAR1_car_angle# = CAR1_car_angle# + (delta_t# * CAR1_car_angularvelocity#)





    ;TEMP - SCREEN LIMITS
    If ( CAR1_car_position_wc_x# < 0.0 ) CAR1_car_position_wc_x# = 800.0
    If ( CAR1_car_position_wc_x# > 800.0 ) CAR1_car_position_wc_x# = 0.0
    If ( CAR1_car_position_wc_y# < 0.0 ) CAR1_car_position_wc_y# = 600.0
    If ( CAR1_car_position_wc_y# > 600.0 ) CAR1_car_position_wc_y# = 0.0
    
End Function

Comments

Shagwana

2005

I know this is one of the oldest snippets on the arcs ...

I have just tried running this in blitz+ and the accleration / braking works - but im not getting any rotation of the cars.

Vorderman

2005

trying printing CAR1_car_angle# to the screen and see if it's changing - I wrote this sooooo long ago that I can't recall how it works, but I do remember having the exact same problem getting to the car to rotate when porting the code from one program to the next.

It could be that CAR1_car_angle# is actually in radians (so from 0 to 6.28), so you might need to convert it to degrees to get a rotation between 0 and 360.

Shagwana

2005

Your right, CAR1_car_angle# looks like its not getting updated ...

Just after the controls being read and the debug text being displayed,

Text 0,24,Str(CAR1_car_steerangle#)

I placed this line ...

CAR1_car_angle#=CAR1_car_angle#+(CAR1_car_steerangle# * 0.25)

It may not be correct, but it gets the car rotating!.

Phoenix

2005

Is there any version with keyboard control?

2005

Phoenix: You're new, so I'll be gentle...

If you want keyboard control, I would start off by changing the code by replacing all the joypad stuff with keyboard stuff. You will be able to find many examples of how to use keyboard input within the code archives.

Phoenix

2005

I'm definately not new, just don't post here very often. Anyway, I'll check the manual for those joy commands...

Code Archives Forum