Wednesday, May 16, 2012

What evidence(s) are there of the speed of the Ferrari was traveling at140± 30 km/hr?

updated 10 july 2014: indeed the Ferrari car's black box report data was 168 km/hr matches the accelerating model A: x = 2.137E1*t^2+3.283E1*t-5.251E-2

http://weelookang.blogspot.sg/2012/05/what-evidence-of-speed-ferrari-was.html
updated with inputs on length of FERRARI car travel to be 13.0±  1 m with table of data showing 9 frames ending at time t = 0.30 s
model  accelerating model A: x = 2.137E1*t^2+3.283E1*t-5.251E-2
model constant velocity B:  x = 3.925E1*t-3.380E-1

hint for model A: model  accelerating model A: x = 2.137E1*t^2+3.283E1*t-5.251E-2

hint for model B: B:  x = 3.925E1*t-3.380E-1


Ferrari 599 GTO crashed a Taxi causing 3 dead, 2 injured in Bugis S'pore - 12May2012


http://weelookang.blogspot.sg/2012/05/what-evidence-of-speed-ferrari-was.html
updated with inputs on length of FERRARI car travel to be 13.0±  1 m with table of data showing 9 frames ending at time t = 0.30 s
https://dl.dropbox.com/u/44365627/TrackerDigitalLibrarySG/TrackerFerrari/ferrari.trz


updated with inputs on length of FERRARI car travel to be 13.0±  1 m instead of the older assumption of 10 m 

using Google map to locate and make sense of the actual video scene, a bit of an attempt to measure the distance on the map but the length is too small for accurate distance measurement of 10 m



Google map street view from the taxi camera position

Analysis




Step1: use any YouTube down-loader such as this http://downloadyoutubevideo.org/download.php?url=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DS80bDrxrCiI%26feature%3Drelated. But this may result in a video that is frame-frame at 30, though the answer don't not change.
alternatively,
you can use your iOS phone to download the video in a *.mp4 which is frame-rate at 25, which some people have emailed me to ask me, but the final answer  is still the same.


Step 2: save the video into the computer

Step 3: use tracker http://www.cabrillo.edu/~dbrown/tracker/ to open the video file, recommended to install on your computer.

new estimates of length of car travel in video is now 13.0 ±  1 m , still the cab bumper can be fitted by 1.81 m length

reason for readjusting the length of car traveled, results from a discussion with physics education expert D, Wong who suggested using nokia maps
to estimate the length of car in the video ( we measure from 2 white line of the pedestrian walking to the center of the junction box. )
to estimate the length of car in the video ( we measure from 2 white line of the  pedestrian walking to the center of the junction box. ) show about 13 ±  1 m, against the map scale on the bottom right 10 m
using tracker, the measurement of length is done easily using calibration tape (length to be measured)  and stick (10m)

even after some prompting by others physics experts to use Google map to calibrate the length this is what i found.

Google map this time, again the length from 2 white line to centre of junction box is about 13 m
use tracker to measure length



Step 4 :state assumptions made:
  1. taxi camera is stationary for the duration of the 0.3 seconds the Ferrari sped across
  2. the height of the traffic light post is approximately 2.0 m from base to green light center
  3. distance traveled by car is roughly 13 ±  1  10 m and bumper of taxi is roughly 1.8 m (see diagram)
  4. the video is properly time-frame as 30 frame/seconds as default in the video data, and read correctly by tracker.
  5. the Ferrari is traveling at constant acceleration = 0 m/s^2track the front of the Ferrari.
Step 5: calibrate pixels in video with known lengths, improved strategy after discussion on Facebook distance traveled by car is roughly 13 ±  1  10 m and bumper of taxi is roughly 1.8 m.

Step 6: Make roughly 8 to 9 points as shown


Make roughly 8 to 9 points as shown
even if you use a video with a frame rate of 25, the answer is still quite the same.
notice in this video the frame rate is 25, because it is a *.mp4 taken from my iOS, the number of points is now 8 instead of 9 from frame-rate 30, making the time still 0.32 instead of 0.3





Step 7: .Analyze the speed




7.1 s vs t graph, which is roughly 39.23 m/s from as evidence from the

linear fit x = 39.231*t + -0.352 where a = 39.231 which means the average velocity assuming a constant velocity motion 








7.2 v vs t graph statistic mean v average = 39.75     30(wrong estimate)  60 (wrong estimate) m/s


data tool notice the mean for x is 3.975E1 which means 39.75, another evidence of average velocity




average it out = (39.231+39.75)/2 = 39.5 m/s

Error Analysis:

The average velocity $v_{average}$ of an object moving through a displacement $\delta d$ during a time interval $\delta t$ is described by the formula:
$v_{average}= \frac { \delta d}{ \delta t}$ 

error analysis suggests,

$ \frac{\Delta v_{average}}{v_{average}} = \frac { \Delta (\delta d)}{\delta d} +  \frac { \Delta (\delta t)}{\delta t} $ 
using estimates of 

$\Delta (\delta d)$ = 1 m (estimate from nokia map), $\delta d$= 13 (nokia map)

$\Delta (\delta t)$  = 1/30 (from framerate) , $\delta t$= 0.30 (from tracker) or

$\Delta (\delta t)$ = 1/25 (from framerate) , $\delta t$ = 0.32 (from tracker) 

v = 140 m/s 

therefore, $\Delta v $  = 0.18*v = 26 ≈  30 m/s (1 sign figure) the order of uncertainty remains ≈  30 m/s even for a frame-rate 25 video.


Conclusion:


when converted to km/hr, v = 39.5*3600/1000 = 142 km/hr  140 ± 30 km/hr ( follow the order of magnitude of the error) 



Claim:

The vehicle is likely to be traveling at speed of 140± 30 (current best estimate, as of 17May2012)  

Question:
What do you think ??

Source of errors:

  1. moving source camera and some parallax error taxi camera was not stationary for the duration of the 0.3 seconds the Ferrari sped across.
  2. the distance 13.0 m traveled by the car may not be corrected measure, thus, a Nokia map was used to check, also cross check with a Google map.
  3. the height of the traffic light post is not 2.0 m from base to green light center
  4. the source of the video could not be verified in the time frame used to capture the video, and the time-frame may not be  30 frame/seconds, though it is likely to be correct. even for 25 frame-rate for *.mp4 files, the answer for (8 pointers) t = 0.32 s would be about the same as (9 pointers) t = 0.3 s for frame-rate 30.

Physics & Science lesson learn could be:

  • Using current affairs to educate the children on everyday physics and making physics relevant.
  • using evidences to justify claim. 
  • science knowledge is socially constructed with newer evidences suggesting better ways of explaining the phenomena.


Moral lessons caught could be: 

  • Don't drive recklessly.
  • Don't beat red lights.
  • Be responsible 

Open Content Sharing of Educational resources creative commons attribution:
the video, trk files are downloadable at NTNU java Forum http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=2447.0 , available to registered users of the forum, registration is FREE.
* trackerF04.png (324.91 KB, 1280x994  )
* videoplaybackwee.trk (14.38 KB  )
* videoplaybackwee.zip (2382.25 KB ) based on incorrect light post height
* videoplaybackwee01.zip (2594.63 KB ) based on incorrect length of car traveled in video evidences and measurements
* videoplaybackwee02.zip (2996.85 KB) based on better estimates of length of car travel 
* mp4andgooglemap.zip (2822.43 KB ) source files for frame-rate 25 video and Google satellite map analysis


Disclaimer:

This post is made with the best intentions to share good active learning practices in physics education, any offenses taken please leave a comment, i will amend the post or/and to remove offensive content if any.

The mass media media corp 5 news also reported on the accident.


there are other estimates that may interest you


other links on this post:
my ex-student T Wee's Facebook photo https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-snc7/576540_10150978291483223_784348222_11692069_1677107363_n.jpg
SMS by ex-student T Wee, thanks!