Tuesday, June 1, 2010

Percentage of Error

I was on two flights yesterday, from London to San Diego.

The first pilot said our flying time would be 10 hours and 23 minutes. I decided to take him at his word. I set my Breitling Aerospace watch to 10:23:00 and clicked the button when we began our takeoff roll.

Upon landing at LAX, we had taken 10:25:45 to travel 5448 miles. There's my plane in the top center, the largest one.

The second pilot said our flight would be 24 minutes for 100 miles. I set my timer and clicked when we began the takeoff roll. This isn't my plane (I was inside!) but it looked like this one.

Here we are on the SAN approach from the north, looking south. This view shows Mission Bay at the bottom, the San Diego River in the middle, and San Diego bay at the top.

Upon landing at SAN, we had taken 26:45 flying time.

I was amazed that each flight was off by 2:45 seconds from the predicted flight time. I knew it was a coincidence, but it made me think about the percentage of error in the flight plans. And I also began to wonder how pilots actually measure "flying time."

So here's today's blog math challenge:

What is the percentage of error made by each of the pilots in their flight plans?

First we convert the recorded times so we have just minutes to deal with (as there are 60 per hour, not 100 as in decimal systems). We have to convert the seconds to decimal as well as hours.

Flight one
Plan    10:23:00 = (10 x 60) + (23) + (.00) = 623.00 minutes
Actual 10:25:45 = (10 x 60) + (25) + (.75) = 625.75 minutes

Flight two
Plan    24:00 = 24.00 minutes
Actual 26:45 = 26.75 minutes

Next we find the ratio of late time to predicted time

2.75/623  = .004  pilot #1 was four-tens of one percent off in his flight plan
and
2.75/24 = .11  pilot #2 was about 11% off on his prediction.

Now we can check the work by calculating the ratio of actual time to predicted time

623/625.75 = .996 and if we add .004 we get 100%

24/26.75 = .897 and if we add .11 = we get 1.007 which is close enough to 100%

Or we can check the work by calculating the ratio of total time to predicted time

625.75/623 = 1.004

26.75/24 = 1.11