Impact location, using four sound sensors.

Using Arduino Sensors
14

I might be missing something in this formula,
the problem i see is that Xi and Yi is unknown to me, thus i cannot manipulate the formula to give me the results Yi or Xi,

or am i just not understanding what you are trying to show me ?

johnwasser:
Based on timing and the speed of sound you have the length of line segments A1, B2 and C3. You want to find the point of impact in the center of the circle. Call the radius of that circle R. The distance of the impact from the four corners is 0:R, 1:A1+R, 2:B2+R, 3:C3+R. Write out the four equations and solve for the three unknowns: R, Xi and Yi (the coordinates of impact).

For example:
SQRT((Xi-X0)**2+(Yi-Y0)**2) = SQRT((Xi-X1)**2+(Yi-Y1)**2) - AI = SQRT((Xi-X2)**2+(Yi-Y2)**2) - B2 = SQRT((Xi-X3)**2+(Yi-Y3)**2) - C3 = R

You can probably just drop out the R and solve for (Xi,Yi).