Find x and y location from timer values

[Kisen]

Hi,
I am hoping that someone can help me with my problem.

I am working on calculating the impact point on a plate, when only provided with a few known points.
I have to say i am struggling quite a bit.

Below is my geometry setup and an example of a hit point x10,y20.

Speed of sound in the material is 3273m/s
Hypothetical timer values are as follows. (S2 was where the timer started) .td is the calculated distance travelled.

	S1	S2	S3	S4
Timer Value	514	0	931	1291
.td	16.82	0.00	30.47	42.25

From this information i need to find the missing value for (S1-S2) that when added to all 4 .td will result in the correct values.

I am lost at how to find x,y coordinates, with what i have available.

Can anyone help?

 

[Pommie]

If you truly believe your velocity in material then your top two readings give your hit point (except one is zero). Or, bottom two. I think that the total distance - all paths (from hit point to sensors) added together will always be the same. A bit of maths should solve it.

Mike.

 

[rjenkinsgb]

Imagine a circle around each sensor, with its radius the time value for that sensor.

Look for intersections.

Keep increasing the circle radii, all by equal amounts at each pass through the loop, until you get all four to intersect as a common point.

After looking at the initial intersections and distances a few times you can likely see some separation that can be used as an increment at each loop iteration, to rapidly zero on on the final position.