Numerical Integration (Trapezoid) on live data in Python

Question

A question on numerical integration (Trapezoid) on live data in Python-

Background: In real time I'm measuring a moving object which has a mean speed of 100 metres/min, and I'm sampling every 100ms for 60 seconds - therefore at the end of the minute I'll have 600 samples. My method of measurement is not accurate and has 10 metres variance per measurement. A typical graph after a minute interval would be:

Question: I know roughly that the object travels 100 metres in a minute, however when integrate over this period (just use Trapezoid for now) a I get an answer which is 60x more than expected, what am I doing wrong? I suspect it's the 'width' or deltaT = 100ms which is incorrect(?)

My python code is below - this is idiomatic i.e. not pythonic, for a reason; to mimic the real time measurements:

# Trapezoidal rule integral
testData = []       # store all vel. measurements
width    = 100e-3   # sample every 100ms
total    = 0
currVel  = 0
prevVel  = 0
t = 0

while( t < 60 ):
    # take a live sample and save it
    currVel = np.random.normal(100,10,1)  
    testData.append( currVel )
    # only complete the integral after the second sample
    if( t >= 100e-3 ):
        total += width*(currVel+prevVel)/2
    # update previous flow and increment 
    prevVel = currVel
    t += 100e-3
#total /= 60  # fudge factor, why this factor out?
print "Total distance covered over 1 minute", total

Answer 1

An integral can be thought of as an area calculation. You essentially have:

(100 m/min) * (60 s)

and you are getting an answer of 6000 because the program has no representation of units. (The answer is 6000 meter-seconds per minute.) If you write your calculation this way instead, the mistake might be more obvious:

(100 m / 60 s) * (60 s)

Now the seconds will cancel out properly. See this thread for a discussion of Python unit libraries.