Suite Spot for modeling free fall in metric
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I have been following the discussions regarding frame rates, physics time steps, and the fact that the Physics Engine is not perfect and finally took some time to tweak my settings to get a free falling object in a metric world to behave like it would in that theoretical "vacuum".
This was sparked of late by this question posted on http://www.khanacademy.org in the physics sections.
"A ball is launched with a horizontal velocity of 3.2 m/s. How long will it be until its velocity doubles". (about 0.6 seconds...I think). Anywho, using Sketchy Physics 3.2 and setting linear damping to 0.0 I ended up needing to set gravity to 4.38 in order to get the correct vertical velocities for the first 4 seconds. (-9.8, -19.6, ...). Curiously, I also had to multiply my initial velocity by the same factor,4.38, to get everything to behave "correctly". This was true whether my frame rate was set to 3 (aka 20 frames = 60 physics steps of 1/60th sec) or 1 (60 frames = 60 physics steps of 1/60th sec). Does anyone have any insight on this.
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I have struggled for 10 years to get my college students to respect the units. Little did I know that I had the ruby slippers inside the machine. I presume someone collects the "blown units" stories so here is one related. A son of a friend's first job when involved in the International Space Station was to figure out how to make the 4 prong power receptacle on one country's module accept the 3 prong plug from the other partner. I will digest your most thorough and excellent post and move onto the music portion of the sketchy physics show.
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I'm looking forward to when USA will follow the rest of the world and go metric.
AFAIK there are now only 3 countries in the world that uses Imperial units, Burma, Liberia and USA...
At least you're driving on the right side of the road
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This is what I have worked out. (Assume 60 frames = 1 second.) The actual velocity (v) is determined by:
v = (world scale)(setVelocity)(frame rate) inches/second.
In your model your world scale is set to 9.0 and you have scaled the velocity up by 4.38 which gives 9.0*4.38 = 39.4 which in effect has converted metres to inches because there are 39.37 inches in a meter.
The actual acceleration (a) is determined by:
a = (1/4) * (world scale) * (gravity) * (frame rate)^2 meters/second^2.
The vertical displacement (z) of the falling object is then given by z = (1/2)a(frames/60)^2
Yes, velocity is set in inches and acceleration is set in metres, no matter what units you have set Sketchup to use in the Window/Model Info menu! Well NASA crashed a Mars probe and wasted millions of dollars and years of work over a mixup between metric and imperial units, so SketchyPhysics is in good company. It seems to be just a coincidence that the magic figure of 4.38 works.
So for example to set an actual acceleration of 9.8 m/s in a metric model, set (world scale = 1), (gravity = 9.8) and (frame rate =2.0). Using the same parameters in the same model, to set an actual initial velocity of 3.2 m/s in the x direction, you would have to use setVelocity([63.04,0.0,0.0]) because 3.2*39.4/2 = 63.04
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Bjorn...I am in complete agreement however offer this contrary view to all of you multilingual Scandinavians and Europeans. Just as knowing at least two languages makes one in many ways better at both I do see a value in knowing at least two sets of units. The unfortunate part for most Americans is that we struggle at even knowing one. My favorite thing about the metric system however is that it makes it easy to remember how far it is around the globe (about). How many Metric first people can actually tie it all back to the French pulling a proverbial string from the north pole through Paris to the equator and "calling it 10,000,000 metres? One of most favorite fun facts. Enjoy the coming sunshine.
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@mptak said:
Bjorn...I am in complete agreement however offer this contrary view to all of you multilingual Scandinavians and Europeans. ...
Well, I am of the view that the whole world should only be allowed to speak English and use only Metric units. It would save a lot of translation resources and confusion. That is just my radical (biased) view.
I have attached an updated file in which I have tried to get the units for distance, velocity and acceleration to work in a consistent way. It also reports the time and location when the speed of the falling ball doubles, if it starts with an initial horizontal velocity of 3.2 m/s.
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Thank you for the explanation, Kev. It was really helpful. However, I would like to know why when you calculated the acceleration you multiplied all by 1/4.
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