- #1
natai
- 2
- 0
The problem below is actually in reference to determining the location of a unknown gamma radiation source. However, I believe the solution lies with relatively simple calculus.
First, the equation that defines the relationship between the radiation exposure rate and the distance from the source is defined by:
y = k / x^2
Where y is the dose rate, x is the distance from the source, and k is a constant which may vary depending on the specific situation and source.
Next, this needs to be applied in three dimensions (x,y,z). So I believe it needs to be rotated around the y-axis to form a surface of revolution. If I remember correctly, the equation for such a surface should look something like:
x^2 + z^2 = 1 / y^2
On this curve your distance from the y-axis on the x-z plane would be equivalent to your distance frlom the radiation source, and the y-coord corresponding to each (x,z) would be the dose rate at that distance.
Think of it this way. At point (x,y,z) x and z are like latitude and longitude while y is the radiation dose rate.
This curve could be rotated around any line parallel to the y-axis, so the highest y reading would not always be at x-z point (0,0).
Here is what I am trying to accomplish:
If I have multiple (x,y,z) points where x and z are latitude and longitude (or just points on the x-z plane measured in feet) and y is the radiation rate, I want to be able to locate the highest y-reading on the x-z plane. In other words, if I know a radiation reading at two or three points and the latitude and longitude at those points, I want to be able to locate latitude and longitude of the radiation source.
Any ideas?
First, the equation that defines the relationship between the radiation exposure rate and the distance from the source is defined by:
y = k / x^2
Where y is the dose rate, x is the distance from the source, and k is a constant which may vary depending on the specific situation and source.
Next, this needs to be applied in three dimensions (x,y,z). So I believe it needs to be rotated around the y-axis to form a surface of revolution. If I remember correctly, the equation for such a surface should look something like:
x^2 + z^2 = 1 / y^2
On this curve your distance from the y-axis on the x-z plane would be equivalent to your distance frlom the radiation source, and the y-coord corresponding to each (x,z) would be the dose rate at that distance.
Think of it this way. At point (x,y,z) x and z are like latitude and longitude while y is the radiation dose rate.
This curve could be rotated around any line parallel to the y-axis, so the highest y reading would not always be at x-z point (0,0).
Here is what I am trying to accomplish:
If I have multiple (x,y,z) points where x and z are latitude and longitude (or just points on the x-z plane measured in feet) and y is the radiation rate, I want to be able to locate the highest y-reading on the x-z plane. In other words, if I know a radiation reading at two or three points and the latitude and longitude at those points, I want to be able to locate latitude and longitude of the radiation source.
Any ideas?