# Tanks Physics • ### Question

• I am making the tanks and have never dealt with programming Physics. So I was wondering what is the best way to program the trajectory path for the tank shell?
Thursday, June 25, 2009 6:10 PM

• First of all the best way to handle this is to break the movement down into x and y components. The x movement is unaffected by gravity. There are basic equations to do with Newtonian mechanics which I advise you to look up in case my memory is failing. (Look up "Equations of motion").

v = u + at

where v = velocity
u = initial velocity
a = acceleration (in this case 0)

This will give you your x velocity which unless there is any drag will be a constant u  as there is no acceleration a.

s = ut + 0.5at^2

s = distance travelled
a = acceleration (in this case g = 9.81 m/s^2)

Note that if y is up then a will be negative.

Try these to start with. You may then consider adding atmospheric drag or wind effects. See Small Basic Gorillas; banana, tank shell, they behave the same way.
Thursday, June 25, 2009 6:32 PM
• If you ignore air viscosity this way should be OK:

```alpha=45
velocity=50
xpos=200
ypos=200
gravity=10
wind=-1

xvel=velocity*Math.Cos(alpha*Math.Pi/180)
yvel=velocity*Math.Sin(alpha*Math.Pi/180)
GraphicsWindow.Show()
GraphicsWindow.PenColor=0
For i=1 To 200
oldy=ypos
oldx=xpos
yvel=yvel-gravity*i*0.1
xvel=xvel+wind
ypos=ypos-yvel 'Y axis is reversed in graphics window!
xpos=xpos+xvel
GraphicsWindow.DrawLine(oldx,oldy,xpos,ypos)

EndFor```

Grzesio
Thursday, June 25, 2009 6:42 PM
• Nice,

If The Hacker wants to include air resistance (friction - not a big issue for a heavy tank shell but why not) we need a term to modify xvel and yvel accordingly.  For turbulent flow in air it is reasonable to assume the frictional deceleration is proportional to the square of velocity, using the Math.Abs to keep the sign correct.

Try:

yvel=yvel-gravity-friction*yvel*Math.Abs(yvel)
xvel=xvel+wind*0.1-friction*xvel*Math.Abs(xvel)

where friction = 0.001

Also if we want to work in real units we can assume 1 pixel = 1m.  Then gravity = 10 m/s2.  Wind is m/s etc.  To run with this we should use smaller timesteps (currently dt = 1s) since these are set by i incrementing by 1.

If we set dt = 0.1 (s) (or smaller - consider velocity is now hundreds of m/s)

Then:

yvel=yvel-gravity*dt-friction*yvel*Math.Abs(yvel)*dt
xvel=xvel+wind*dt-friction*xvel*Math.Abs(xvel)*dt
ypos=ypos-yvel*dt 'Y axis is reversed in graphics window!
xpos=xpos+xvel*dt

Also initial velocities are then in m/s (typically around 300m/s)

xvel=velocity*Math.Cos(angle*Math.Pi/180)
yvel=velocity*Math.Sin(angle*Math.Pi/180)

The only advantage of considering the units is that we can more easily set up more realistic tank shots (low angle & high velocity) rather than big lobbing 'cannon balls' and the 'normalisations' have physical significance.

Thursday, June 25, 2009 8:11 PM

### All replies

• First of all the best way to handle this is to break the movement down into x and y components. The x movement is unaffected by gravity. There are basic equations to do with Newtonian mechanics which I advise you to look up in case my memory is failing. (Look up "Equations of motion").

v = u + at

where v = velocity
u = initial velocity
a = acceleration (in this case 0)

This will give you your x velocity which unless there is any drag will be a constant u  as there is no acceleration a.

s = ut + 0.5at^2

s = distance travelled
a = acceleration (in this case g = 9.81 m/s^2)

Note that if y is up then a will be negative.

Try these to start with. You may then consider adding atmospheric drag or wind effects. See Small Basic Gorillas; banana, tank shell, they behave the same way.
Thursday, June 25, 2009 6:32 PM
• If you ignore air viscosity this way should be OK:

```alpha=45
velocity=50
xpos=200
ypos=200
gravity=10
wind=-1

xvel=velocity*Math.Cos(alpha*Math.Pi/180)
yvel=velocity*Math.Sin(alpha*Math.Pi/180)
GraphicsWindow.Show()
GraphicsWindow.PenColor=0
For i=1 To 200
oldy=ypos
oldx=xpos
yvel=yvel-gravity*i*0.1
xvel=xvel+wind
ypos=ypos-yvel 'Y axis is reversed in graphics window!
xpos=xpos+xvel
GraphicsWindow.DrawLine(oldx,oldy,xpos,ypos)

EndFor```

Grzesio
Thursday, June 25, 2009 6:42 PM
• In the absence of wind or air resistance we should have a parabolic flight.  The change in y velocity arising from gravity should be proportional to gravity * timestep and not gravity * time.

`yvel=yvel-gravity*i*0.1`
Should be
`yvel=yvel-gravity*dt`
Where dt is a constant (timestep) scaled to fit the units and window size being used, say dt = 0.8 works for starters OK here.

Thursday, June 25, 2009 7:00 PM
• Of course you are right.
Velocity changes in linear way.

Grzesio
Thursday, June 25, 2009 7:25 PM
• I've added some comments, normalizations, GraphicsWindow resizing etc. and published on: http://smallbasic.com/program/?KDM274

Grzesio
Thursday, June 25, 2009 7:44 PM
• Nice,

If The Hacker wants to include air resistance (friction - not a big issue for a heavy tank shell but why not) we need a term to modify xvel and yvel accordingly.  For turbulent flow in air it is reasonable to assume the frictional deceleration is proportional to the square of velocity, using the Math.Abs to keep the sign correct.

Try:

yvel=yvel-gravity-friction*yvel*Math.Abs(yvel)
xvel=xvel+wind*0.1-friction*xvel*Math.Abs(xvel)

where friction = 0.001

Also if we want to work in real units we can assume 1 pixel = 1m.  Then gravity = 10 m/s2.  Wind is m/s etc.  To run with this we should use smaller timesteps (currently dt = 1s) since these are set by i incrementing by 1.

If we set dt = 0.1 (s) (or smaller - consider velocity is now hundreds of m/s)

Then:

yvel=yvel-gravity*dt-friction*yvel*Math.Abs(yvel)*dt
xvel=xvel+wind*dt-friction*xvel*Math.Abs(xvel)*dt
ypos=ypos-yvel*dt 'Y axis is reversed in graphics window!
xpos=xpos+xvel*dt

Also initial velocities are then in m/s (typically around 300m/s)

xvel=velocity*Math.Cos(angle*Math.Pi/180)
yvel=velocity*Math.Sin(angle*Math.Pi/180)

The only advantage of considering the units is that we can more easily set up more realistic tank shots (low angle & high velocity) rather than big lobbing 'cannon balls' and the 'normalisations' have physical significance.

Thursday, June 25, 2009 8:11 PM
• Sorry to be picky, but isn't drag proportional to the cube of velocity?
Thursday, June 25, 2009 9:30 PM
• My apologies. After checking, it seems that the drag is proportional to the square of the speed, but the power required to overcome the drag at a constant speed (in a car for example) is proportional to the cube of the speed which is not relevant to this problem.
Thursday, June 25, 2009 9:36 PM
• Stendec,

Projectiles is not an area of physics I have any particular expertise, but if you look at (for example) http://en.wikipedia.org/wiki/Drag_coefficient : Fd is the deceleration force proportional to -acceleration and Cd is a constant (drag coefficient), where v is velocity.  I am more certain that turbulent flow pressure gradient is proportional to v^2 and think the analogy to projectile friction probably holds.  I am certainly interested to learn differently.
Thursday, June 25, 2009 9:54 PM
• The deceleration is proportional to velocity squared.  Line 719 of the last stargates uses it to slow down the ships exploding bits, visually looks pretty real, although i made up all the drag coefficient & gravity numbers to make it look pretty.

Making games realistic is fun, but many times unrealistic behavior is even more so...

Friday, June 26, 2009 1:28 AM
• The only advantage of considering the units is that we can more easily set up more realistic tank shots (low angle & high velocity) rather than big lobbing 'cannon balls' and the 'normalisations' have physical significance.

You are right but real tanks don't change their shot power. Aiming relies on angle only and trajectories are quite flat.
Setting angle+power and looking at steep lobs heavily changed by wind seems to be more funny in computer games. ;)
Even when it is not very realistic...

Grzesio
Friday, June 26, 2009 4:30 AM
• Better rename the game "Artillery".  Then you can fiddle with charge, elevation, etc.
Friday, June 26, 2009 4:21 PM
• You do change howitzer gun charges, but in only a few steps.
Friday, June 26, 2009 7:54 PM
• maybe you dont need this anymore, but, are you trying to make realistic and complicated physics? or just something that looks good?
Rape OR GET RAPED!
Saturday, August 15, 2009 6:52 PM