Dot Physics

AutoTracker and a landing plane

If you know me, you know I love Tracker Video Analysis. Basically, it is a free-java program that allows you to get position-time data of a moving object from a video. In Tracker version 3.10, there is now the autotracker feature. This will automagically mark the location of an object moving in a video. How do you use it?

First, the video. This is a video I made of a plane landing at an airport. Not much exciting going on, but that never stopped me before. I put this video on vimeo instead of youtube because vimeo allows you to download the original video.

Landing Airliner from Rhett Allain on Vimeo.

Now what? Well, here is a short screen-cast tutorial on using the autotracker feature.

More details

In order to scale the video, I used the size of the plane. That looks like a SouthWest Airline plane. I am pretty sure they only fly 737′s. According to Wikipedia, the 737 is 30.5 meters long. Really, that is the only thing I had to look up for this video.

How fast was the plane moving?

The aircraft is probably slowing down as it comes in for a landing. This means that the “how fast” question doesn’t have one answer. However, it it appears the acceleration isn’t too high. Here is a plot of the horizontal position vs. time for the plane with a linear fit.

i-305e325ea4d062e546b3ccd0ba2c570e-2010-01-14_data_tool.jpg

The slope of this line has a magnitude of 76.4 m/s. This is about 170 mph. I guess that is an appropriate. I remember playing Microsoft Flight Simulator and that seems like an ok speed. What about the vertical speed?

i-56cdc1823ec768d89d5b255072c8e99b-2010-01-14_data_tool_1.jpg

1.5 m/s or 3.4 mph.

What is the horizontal acceleration of the plane?

Instead of fitting a linear equation to the horizontal data, I am going to fit a parabola. Doing this gives:

i-f6349014703b624d13f103a6b656f77b-2010-01-14_data_tool_2.jpg

This equation is similar to the form:

i-bc7d780c6472f6d382a8847a41c5d422-2010-01-14_la_te_xi_t_1.jpg

Where the “a” term in this equation is the acceleration. This means the “a” from the fitting equation is 1/2 the acceleration. The horizontal acceleration of the plane is then 1.5 m/s2 or 0.15 g’s.

Comments

  1. #1 john
    January 14, 2010

    Rhett,
    When you tried to use the autotracker on this video, did you find it failed to find a match on a few frames?

  2. #2 Rhett Allain
    January 15, 2010

    @John,

    If I set the “accept scores above” at anything other than 1, tracker will stop and ask me if I want to accept some points. If I set it at 1, it goes without stopping.

  3. #3 CCPhysicist
    January 15, 2010

    Your value for the rate of descent, about 300 feet per minute, seems low but maybe the plane was below the glide slope. I’m impressed with that software!

  4. #4 hs teacher
    January 22, 2010

    It is interesting that the plane is speeding up rather than slowing down (as you originally expected). I guess this makes sense since it is descending onto the runway.