DATA ACCURACYThis is a curve of tip friction you already saw, (or, to say better, a curve of the total braking torque in the vacuum chamber, but, as we are going to see, residual air drag in the vacuum is extremely low, so we can consider this actually as a curve of tip friction), more precisely the curve Nr. 15, (a spin with oil).
I wanted to add error bars to it, but these resulted too short...
... so I expanded the vertical axis by ten times, then I inserted the error bars, (below):
the horizontal black segments are the measured values of the total braking torque.
The red bars are errors of timing, (up to +/- 1 second error, which is possible because my tachometer makes one reading every about 0.6 - 1 seconds).
The blue bars represent the highest and most pessimistic values of the residual air drag in the vacuum chamber;
the values of the blue bars at 950-1000 and 1000-1050 RPM are calculated, the values of the other blue bars are only predicted approximately, (but certainly at lower speeds the air drag is lower).
They are only below the black segments because the black segments represent the total braking torque.
The real values of the tip friction are about at the center of the blue segments.
But the difference is really so negligible, (about 0.01 millionths of Newtonmeter at high speed), so I used the data of the total braking torque as they were the data of the tip friction in all the curves I exposed.
The vertical expansion can be misleading. See below, how much difference there is between the Total braking torque curve, (green), and the tip friction curve, (purple); at the left the first one is above the other one by 0.01 millionths of Newtonmeter.
I have had a confirmation of this 0.01 millionths of Newtonmeter residual air drag in the vacuum chamber through a more refined version of the
Test for to know residual air drag relevance in the vacuum chamberI added to my top Nr. 30 two pieces of scotch tape, like so;
(the pictured top is another one, the picture is just to give an idea. I used the Nr. 30, which is lighter, for to have less tip attrition and more stable friction).
The aim of the scotch tape is to dramatically increase the air drag on the top, without changing its weight/distribution of weight, (the two scotch tape pieces together weigh only 0.03 grams, the top weighs 119 grams).
The top, with or without the tape, would spin for practically the same time in a perfect vacuum.
In normal room pressure conditions instead, the top spins, (from 1050 to 1000 RPM), in 42 seconds without the tape, and in only 3 seconds with the tape. A huge difference.
This top is a useful and very sensitive instrument for to reveal residual air drag in the vacuum chamber.
I spinned this top at different air pressures in the vacuum chamber, with and without the tape, and timed the lapses 1050-1000 RPM, and 1000-950 RPM. The value of 767 mm Hg represents the normal room pressure.
RPM lapse mm Hg Time Time
with tape without tape
1050-1000 767 00:03.0 00:41.7
950-1000 767 00:03.2 00:44.9
1050-1000 2.2 03:49 04:56
1050-1000 0.5 04:40 05:16
1050-1000 0.2 04:30 05:33
1050-1000 0.2 04:35 05:21
1050-1000 0.1 04:46 05:27
950-1000 2.2 04:02 04:46
950-1000 0.5 04:29 05:30
950-1000 0.4 04:53 04:55
950-1000 0.2 04:43 05:15
950-1000 0.2 04:48 05:35
950-1000 0.1 05:02 05:40
I translated these spin times into values of total braking torque, (the rotational inertia of this top is kg-m
2 0.0000705), then I calculated the difference of torque due to the scotch tape:
RPM lapse mm Hg Total braking torque, millionths of Newtonmeter
With tape Without tape Difference
1050-1000 767 123 8.86 114.1
950-1000 767 115 8.23 106.8
1050-1000 2.2 1.61 1.25 0.36
1050-1000 0.5 1.32 1.17 0.15 (?)
1050-1000 0.2 1.37 1.11 0.26
1050-1000 0.2 1.34 1.15 0.19
1050-1000 0.1 1.29 1.13 0.16
950-1000 2.2 1.52 1.29 0.23
950-1000 0.5 1.37 1.12 0.25
950-1000 0.4 1.26 1.25 0.01 (?)
950-1000 0.2 1.31 1.17 0.14
950-1000 0.2 1.28 1.10 0.18
950-1000 0.1 1.22 1.09 0.13
"Difference" is practically the air drag of the scotch tape alone.
The same scotch tape, which has 107-114 millionths of Newtonmeter air drag at room pressure at the tested speeds, has 0.13-0.26 millionths of Newtonmeter air drag in the vacuum at the lowest pressures I can use, at the same speeds.
The highest measured residual air drag at 0.1-0.5 mm Hg is
0.26 : 114.1 = 1/439
of the air drag at normal air pressure.
Using the other numbers, other ratios are found that range from 1/439 to 1/ 822 in the 0.1-0.5 mm Hg range.
I overlooked the two (?) values, too little plausible.
(also I expected littler differences at 0.1 and 0.2 mm Hg).
Wanting to be conservative, I used the ratio found at 2.2 mm Hg, (1/317), for to calculate the length of the blue error bars;
The top Nr. 27b, which I used for the tip friction measurements in this thread, has about 5,3 millionths of Newtonmeter air drag at normal room pressure, at 900-1000 RPM;
In the vacuum chamber, (0.1-0.5 mm Hg), it can be expected to have less than
5.3 : 317 = 0.017 millionths of Newtonmeter air drag.
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Conclusions:
Residual air drag in the vacuum chamber at the used pressures for the tip friction measurements, (0.1-0.5 mm Hg), is extremely low, and, for our aims, can be neglected.
The total braking torque curves practically coincide with the tip friction curves, and can be treated as such.
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Topic: Tip friction and air drag measurements (Read 47092 times)