By "velocity curve" do you mean that meaningless curved line that does not follow the dots?
You need to listen carefully.
The text you are critiquing is from your NIST quote.
By "velocity curve" NIST meant the shape of the datapoints in their derived velocity profile...
The "dots" as you call them, form a curve. Forget the straight line. Forget the solid curved line. The datapoints themselves form a varying curve.
By "The slope of the velocity curve is approximately constant" NIST mean just that, that for a part of the time the points can be said to form a slope which is approximately constant. It's not constant. It's approximately constant, with the resoluton and fidelity of the data they had available.
The "meaningless curved line that does not follow the dots" is the NIST derived velocity profile fit. In the same way that the linear fit (the straight line) does not "follow the dots" exactly, neither does the derived velocity curve, given by NIST as...
v(
t) = 247.52(0.18562
t)
2.5126exp[-(0.18562
t)
3.5126]
They are talking about the curved line.
Whether from the datapoits or curve fit makes no difference. Both are "approximately constant" for a whie. Again, not constant, approximately constant. Therefore any derived acceleration is also approximate during the region of interest.
The data points are not perfect because they are taken from a video
Correct.
but the average gives the actual acceleration - FFA.
Incorrect. Average, approximate acceleration.
You cannot avoid this.
NIST said it was free fall.
NIST say their
estimation of
approximate and
average acceleration is
equivalent to the acceleration of gravity during that period.
The bolded words are important.
The words are from NIST themselves.
Language is not independant of local context.
You just refuse to accept that.
I accept that NIST said what I wrote above. NIST say quite a lot of daft and lazy things. In this instance what they say is relatively clear. It's based on shoddy data, but NIST say their
estimation of
approximate and
average acceleration is
equivalent to the acceleration of gravity during that period.
the entire upper portion falls as a single unit.
"A single unit" is terminology that you will find meets resistance. There are thousands of interconnected elements which make up the "upper portion", and there's all sorts of flexure. In essence the upper portion of the North facade descended as a unit, sure.
That inclusion is, however, intended to help de-glitch traces rather than anything else, and it won't "smooth" ). Translation to real-world units, and derivation of velocity and acceleration was performed separately, as I've already said earlier.
