Game Development Reference
In-Depth Information
The Gas Tank Simulator
Let's use the 1-D heat conduction equation to simulate how long it will take a gas tank to explode
when exposed to a flame. A typical screen shot of the Gas Tank Simulator is shown in Figure 12-4.
At the top of the GUI is a display window showing a not-too-bright soldier aiming a flamethrower
at an aluminum or concrete gas tank. At the bottom left-hand corner of the GUI are text fields
that allow the user to set the flame temperature, tank material, and tank thickness. At the right-
hand side of the GUI are text fields that display the elapsed time for the simulation and the
temperatures at the inner and outer walls of the gas tank.
When the Start button is pressed, the soldier fires his flamethrower at the gas tank. The
heat from the flame conducts into the gas tank wall. The ignition temperature of gasoline
3
is
about 550
K
. When the inner wall temperature reaches this value, the gas tank will explode. In
real life, the heat conduction from the flame would be three dimensional, but in this simulation
the 1-D heat conduction equation will be used to compute the temperature through the gas
tank wall as a function of time.
Figure 12-4.
A typical Gas Tank Simulator screen shot
The temperature at any location inside the gas tank wall at any time can be determined
from Equation (12.18). The
A
and
B
constants in that equation can be calculated based on the
boundary conditions. The gas tank will initially have a temperature of
T
0
= 300
K
throughout its
thickness. When the flamethrower is lit, the temperature at the outer wall of the gas tank will be
maintained at the flame temperature. Based on these boundary conditions, the values of the
constants
A
and
B
can be obtained from Equations (12.20) and (12.22).
B
==
1000
(12.23)
1
AKTT
π
=−=
300
−
1000
=−
700
(12.24)
0
1
If the boundary conditions are incorporated into Equation (12.18), the equation for the
temperature at any point in the gas tank wall at any time is equal to the following:
