Calculating resolution

[ElectricGuy]

Hey everyone;

Help one on this one, because i'm not getting there alone.

I have a system that measures the velocity across two points. Thoses points are separated from each other 30cm.
My PIC micro starts a timer when the projectil travels across the first sensor and stops on the second sensor.
My Timer is configured to tick every 4uS (8Mhz/4/(1:8 prescaller)^-1.

In software i'm multiplying my timer value by 4 so i can get the time traveled in uS.
So, my velocity in m/s is V=300000/(timervalue*4)

All is working fine great, i get the velocity. but now i want to figure the resolution of the system, and i'm not getting there.

Can somebody help out?
Thank you!

[KerryW]

Your resolution is 3uS.  You probably want to know the resolution in M/S, though. don't you?

The resolution in M/S changes with the velocity.

1 tick = 75000 M/S, 2 ticks = 37500 M/S, resolution = 37500 M/S

10000 ticks = 7.5 M/S, 10001 ticks = 7.49925 M/S, resoluyion = 0.00075 M/S

[IanB]

If you are measuring time intervals, your resolution is 4 µs (the smallest resolvable difference between two measurements is 4 µs).

If you are measuring speed, the resolution is a function of the time resolution dt, the distance between measurement points s and the speed you are measuring, v. Your speed resolution is given by:

    dv = [s / t] - [s / (t + dt)]

where

    t = s / v

hence

    dv = v * [1 - s / (s + v * dt)]

Therefore the resolution is better at lower speeds, greater distances, and smaller clock intervals.

[ElectricGuy]

Ok, i understand now. And yes, i want the m/s resolution.

Thank you IanB and KerryW.

Actually i was getting those values, but didn't understand them.

I think for each measure i will calcule and print also the resolution. So i can always know the resolution that i'm getting.

[babysitter]

Hi,

your resolution with this timing setup will always be the same as long as you don't change one of the contributing values sensor distance or timer settings. I think it would be more interesting to printout the interval you dont know about in m/s, like in Speed between X1 m/s and X2 m/s. X1 is the corresponding speed according to the timer value, X2 the speed that corresponds to timer-1, as the actual trigger event is inbetween those two, not earlier than timer-1 but before timer.