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Parabolic vs Air Drag Trajectory revC is the same as revB except the graph is not auto-scaling. Some folks may prefer this.
Parabolic vs Air Drag Trajectory revB fixes a small error: the "launch height" user input parameter was not being imported into the parabola equation.
The physics and math for the computer numerical simulation (including topspin/backspin)
is explained in this paper.
Parabolic Equations and constants a, b, c, xp, and yp
y = a*x2 + b*x + c and y = a*(x-xp)2 + yp explained:
http://www.chiefdelphi.com/media/papers/download/3868
How to find constants a and b, given launch speed and angle:
http://www.chiefdelphi.com/media/papers/download/3871
How to find constants a and b, given desired scoring range:
http://www.chiefdelphi.com/media/papers/download/3872
How to find constants a and b, given yp and a point (x1,y1) on the trajectory:
http://www.chiefdelphi.com/media/papers/download/3877
Terminal Velocity calculator spreadsheet:
http://www.chiefdelphi.com/media/papers/download/3900
Attached Files
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Introduction
parabola.pdf
download file
uploaded: 20-02-2014 20:49
filetype: pdf
filesize: 48.16kb
downloads: 304
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Compute a&b from speed&angle
given speed&angle, find a&b.gif
download file
uploaded: 20-02-2014 22:21
filetype: gif
filesize: 11.06kb
downloads: 382
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Compute a&b from scoring range
scoring_range.gif
download file
uploaded: 20-02-2014 22:30
filetype: gif
filesize: 12.08kb
downloads: 233
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Compute a&b from yp,x1,y1
compute a&b from yp,x1,y1 rev02.pdf
download file
uploaded: 21-02-2014 11:21
filetype: pdf
filesize: 16.63kb
downloads: 234
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Parabolic vs Air Drag Trajectory
parabola vs air drag.zip
download file
uploaded: 24-02-2014 23:46
filetype: zip
filesize: 57.46kb
downloads: 158
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Parabolic vs Air Drag Trajectory revB
parabola vs air drag revB.zip
download file
uploaded: 27-02-2014 18:17
filetype: zip
filesize: 51.67kb
downloads: 221
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Parabolic vs Air Drag Trajectory revC
parabola vs air drag revC.zip
download file
uploaded: 04-03-2014 13:28
filetype: zip
filesize: 63.61kb
downloads: 514
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Terminal Velocity spreadsheet
Terminal Velocity.zip
download file
uploaded: 04-03-2014 14:02
filetype: zip
filesize: 26.53kb
downloads: 161
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Given launch speed and a point on the parabola, find theta
given Vo and (d,h) find theta.pdf
download file
uploaded: 17-02-2016 19:11
filetype: pdf
filesize: 44.59kb
downloads: 247
Discussion
view entire thread
27-02-2014 18:23
Ether
Re: paper: Parabolic Trajectory Calculations
For those of you who downloaded the Parabolic vs Air Drag Trajectory spreadsheet, please note that I just uploaded revB to correct a small error. The user input "launch height" was not being imported into the parabola equation.
28-02-2014 12:07
Ether
Re: paper: Parabolic Trajectory Calculations
|
Originally Posted by Ether
For those of you who downloaded the Parabolic vs Air Drag Trajectory spreadsheet, please note that I just uploaded revB to correct a small error. The user input "launch height" was not being imported into the parabola equation.
|
The parabola plot with the original version was correct as long as you didn't change the launch height.
And even if you did change the launch height, the error affected only the parabola, not the air-drag trajectory.
04-03-2014 09:55
Hugh Meyer
Re: paper: Parabolic Trajectory Calculations
Ether,
Would you more clearly define the launch angle? A drawing would be nice. Is that from the horizon, or a plumb line? Thanks.
-Hugh
04-03-2014 10:19
Ether
Re: paper: Parabolic Trajectory Calculations
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Originally Posted by Hugh Meyer
Would you more clearly define the launch angle? Is that from the horizon, or a plumb line?
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The reason you don't see the graph appear to visually correspond to the launch angle is because the X and Y axes are not scaled equally, and when you change the launch angle the scaling auto-adjusts to fit the graph.
While you're here, does your team happen to have any test data to confirm (or refute) the 37 ft/sec terminal velocity number for this year's game piece?
04-03-2014 10:36
Hugh Meyer
Re: paper: Parabolic Trajectory Calculations
Thank you.
We do not have any data, but we have been talking about it. How would we measure the terminal velocity?
-Hugh
04-03-2014 12:23
marccenter
Re: paper: Parabolic Trajectory Calculations
Ether,
The assumption appears reasonable with the shooting range we are seeing on our robot.
I just found the thread today. When we unbag the robot on Saturday, I will be attempting to increase our shooting percentage via angle and may be able to provide some data after that point.
We did overshoot the target a bit last weekend at Southfield, MI a few more times than I would have liked.
04-03-2014 12:28
Ether
Re: paper: Parabolic Trajectory Calculations
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Originally Posted by marccenter
The assumption appears reasonable with the shooting range we are seeing on our robot.
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04-03-2014 14:00
Ether
Re: paper: Parabolic Trajectory Calculations
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Originally Posted by Hugh Meyer
How would we measure the terminal velocity?
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I just posted a small revision (revC) to the air-drag spreadsheet. I turned off the auto-scaling in the graph and re-shaped it so the launch angle "looks" more like the real thing. It may make it easier to visualize what's changing when you change the input parameters. The downside is you lose some resolution.
http://www.chiefdelphi.com/media/papers/2946
17-02-2016 19:15
Ether
Re: paper: Parabolic Trajectory Calculations
Given launch speed and a desired point (d,h) on the trajectory, show the derivation of and formulas for the launch angles and the equations of the two parabolic (no air drag) solutions.
http://www.chiefdelphi.com/media/papers/download/4614
17-02-2016 23:44
GeeTwo
Re: paper: Parabolic Trajectory Calculations
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Originally Posted by Hugh Meyer
How would we measure the terminal velocity?
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If you don't have a speed gun, a strobe of some sort, including the video method suggested by Ether would be next.
As for 3946, we did the air-resistance-free calculation, added about 50%, tested that we had more than we needed to hit the goal at the ranges we wanted, then we'll back down based on empirical launch data until we hit the goal at the desired range (this year, with our rear bumper in the outer works). Not as elegant as the full-physics solution, but we've built several high-percentage launchers using this paradigm.
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