Cool Science

Let’s do the time-lapse again (with math)

By Stephen Smith on 03/18/2013

Did you know that there is a connection between math and creating time-lapse videos? In January, I shared a time-lapse video on our Facebook page during our annual maintenance period. The video showed the deconstruction of the ring above the old Techlab on the 4th floor.

Time-lapse video is taking video of an event that happened over a long period of time and compressing it to make the event look like it happened much more quickly. Using math to understand time-lapse will help you best create the effect you want. The video below took nearly 8.5 hours to record, yet the final video is only 1 minute and 41 seconds long. That’s because I set the computer to capture only one frame every ten seconds, then played those frames back at 30 frames per second (or fps), giving the illusion that the action happened much faster than it actually did. How did I decide to capture one frame every ten seconds? That’s where math comes in.

I knew that the work was being done over the course of a whole day, so 8.5 hours was a good number to start with. But since we’re talking about frames per second, let’s convert 8.5 hours to seconds by multiplying it by the number of seconds in an hour, 3600.

8.5hr x 3600sec/hr = 30580 sec

I wanted my final video to be around 1 minute and 40 seconds long, or 100 seconds, and play at 30 frames per second, which means I needed around 3000 frames total.

100sec x 30 fps = 3000 frames

If I have 30580 seconds of action but only need 3000 frames, I have to divide to figure out how often to record a frame:

3000 frames / 30580 sec = 0.098 fps or about 1 frame every 10 seconds

Trying to figure out how many frames you should record to create the perfect time-lapse depends on many factors, but ultimately for me it comes down to the overall quality and time I have to work with. How many images are recorded will determine the overall length of the video as well as the smoothness and quality of the time-lapse recording when it is played back at normal speed. Changing those variables to create a time-lapse can be fun. In the equation below, I am solving for x.

x = Interval in Seconds between recorded frames.
H = Total Hours taken for time lapse in real time.
FR = Frame Rate in which the images will be displayed (24, 25, 30, 60 etc.).
Dtrt = Desired Total Running Time of your final video in seconds.

Time-lapse equation

So if you understand this, I have a challenge for you: if you wanted to record the movement of clouds in the sky over a six and a half hour period during the day and you wanted your final time-lapse video to be 27 seconds long playing back at 24fps, use the equation above to solve for x, where x is the interval in seconds between recorded frames.

Post your answer as a comment to this post below or on our Facebook page.

Watch the time-lapse video below:

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