I love the slow-moving motion video clip on the iPhone 6. Not simply does it record 720p video at 240 fps, it likewise allowed’s you instantly change exactly what component of video is in sluggish movement and also what component is in genuine time. I can not quit making slow activity videos. Help me.
But there is something fascinating. Exactly how does the apple iphone manage this shift from genuine rate to slow down activity rate? In various other words, what is the moment price of modification of the structure rate during the shift. Allow’s find out.
A Sample Video
We need a video that shows something we already know the solution to. Exactly how around projectile activity? Below is a sample video clip tape-recorded with the apple iphone 6. It has normal rate video clip at the start and also end with slow motion in the middle.
Typically, I would create a story of both the vertical and also straight activity however in this instance merely the horizontal will certainly work. Making use of Tracker Video clip Evaluation and also that meter stick on the window for scale, I obtain the following plot.
Just a fast note. Yes, you can make stories with Tracker Video clip Analysis. I locate it easier to suit a number of functions to the same set of information with Plotly.
But what does this all suggest? Right here is a ball after it has been tossed (dismissing air resistance).
Since there is only a force in the vertical instructions, I could create the following two equations for the velocity of the ball.
Since the acceleration in the x-direction (straight instructions) is absolutely no, the rate in the x-direction need to be constant. A plot of the x-position versus time should be a straight linear feature with a slope that amounts to the straight rate of the ball.
You could view in the story that the x placement of the ball does NOT look like a steady velocity. Obviously the reason for the non-constant incline is because of the results from the apple iphone 6 slow movement thingy (perhaps it has a technical name). Notice that the slope of the line prior to as well as after the slow activity has concerning the same value at around 8 to 7 m/s. Yes, these ought to be specifically the same. I suspect the issue is that I do not have significantly information for ‘after’ the sluggish motion to obtain a good fit. I am going to choose the consistent rate of 8.07 m/s.
Dealing With Transforming Frame Rates
The typical rate part of the apple iphone video clip dips into 30 structures per 2nd (fps). This indicates that from one framework to the following is a time period of 0.033 secs both in real life and in the video clip. During the slow-moving movement part of the video, it is tape-recorded at 240 fps which would indicate there are 0.0042 secs for each framework period. However, the iPhone plays this back at 30 frameworks each 2nd to provide it that ‘sluggish activity appearance’.
Let me write the two horizontal speeds (before as well as during the slow-moving activity) as:
Here I am using the moment system of s‘ to represent the moment during the slow movement place of the video. Because the two speeds are in fact the exact same (in reality), I can establish them equivalent to each other with some ‘price factor’ multiplied by the slow activity part.
This “a‘ factor informs us just how slow the framework rate is contrasted to genuine life.
But what regarding the transition? The rate factor goes from a worth of 1 to a value of 9.72 in a couple of frames. Exactly what is the rate of change for this an aspect? Below coincides information as in the past. Nevertheless, as opposed to suitable a linear function to the data I am suitable a square function to the parts of the data where the video is in a change from actual speed to slow down motion.
For both of these ‘time acceleration’ phases, I have a time velocity of concerning 16.6 s’/ s2. In the initial shift, this is a ‘unfavorable time velocity’ and also after that a ‘favorable time velocity’ to return to normal time. I am beginning to despise this post as a result of my perplexing expressions – it’s not simply you, it’s me too.
You Do not Recognize Something Up until You Design It
Forget all this stuff about changing time prices. If I can make a version that reveals the movement of the sphere that looks MERELY LIKE the video, I win. That’s the regulations of the game.
Just taking a look at the story of the sphere’s horizontal position, it appears like it relocates at a continuous rate, after that eventually accelerates to a lesser speed as well as finally speeds up back to the initial speed.
Here is my basic model.
- Start with some initial rate (similar to the values in the video clip).
- Use an upright acceleration of -9.8 m/s2 as well as a straight velocity of 0 m/s2.
- Use this velocity to calculate the brand-new velocity after a short time interval.
- Use the rate to compute the new placement after the very same brief time interval.
- If the time is in the range of the initial reduce, provide the ball an adverse horizontal acceleration of -16.6 m/s2. If the moment is in the accelerate variety, placed the acceleration at 16.6 m/s2. Do the very same tip in the vertical direction.
That’s it. Right here is the design I obtain using GlowScript:
It’s not best, yet it’s close sufficient. You can view that it has the exact same basic form as the information from the actual video. I believe that if I experiment with the acceleration times, I could acquire a near best suit. I’m happy.
There are still some inquiries that continue to be. I will leave them as a homework assignment for you.
- What regarding the upright movement? Can you merely use the very same suggestion for the upright activity? Can I provide it an acceleration to make a design work like the sluggish motion video?
- Is the horizontal rate in my video actually consistent? Should it be steady? Estimation the air resistance on a tennis ball moving these speeds.
- It appears that the sluggish movement shift takes around 12 frameworks. Suppose I make my slow-moving activity place of the video clip simply 10 frameworks long to ensure that the reducing transition and also the speeding up transition overlap (you may require an apple iphone 6 of your very own to address this thought).
The a lot more I consider it, the more I don’t have a firm understanding of just what’s happening in the y-direction. Visit this story of the upright movement of the very same ball.
This looks strange. It looks like during the slow motion place of the video the ball has a constant upright rate. Nonetheless, I think this is simply an illusion. If a tossed sphere has an upright velocity of -9. m/s2 and also after that you slow the video clip time down by an aspect of around 10 the noticeable vertical acceleration would certainly be extremely near absolutely no. Maybe I comprehend the vertical motion a bit better than I thought.