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EducationHow to properly measure a sphere?
21st May 2012 21:20 UTCKristi Hugs
Ok, there seems to be some issues here on how to most accurately measure and list a sphere. I was always told to find the accurate diameter I should measure the circumference and divide by 3.14.
So that is what I have been doing. However, a lady I know, told me that my measurement was off and that when she used her calipers on the same sphere, she got a different number. She told me I was wrong. I do not like being wrong :) but I would like to know for sure :)
So, do calipers give a more accurate measurement? or does measuring around the sphere and dividing by 3.14 give a more accurate measurement?
Thanks all!!
Mira
21st May 2012 23:57 UTCAmir C. Akhavan Expert
And there are no general rules for determining the best way of measuring some value. You can do all sort of things, and as long as you "do it right" they will all give the same result.
Except maybe one "rule": Because complex methods come with pitfalls and the errors of the steps involved in the method add up, one should choose a simple method, and whenever possible, measure the value "directly" with a reliable instrument.
So I'd use a caliper until the diameter gets too large or small for the calipers I got.
One thing is important, though:
Every scientist knows that who does the experiment/measurement is very important.
A.k.a as "wishful thinking".
So instead of aguing with the lady about the methological problems in your measurement, you should take a caliper and compare what you find to what the lady finds ;-)
22nd May 2012 00:15 UTCDon Saathoff Expert
a couple of mm's different.....are they?
Don
22nd May 2012 00:19 UTCDean Allum Expert
Your questions bring our the Geekiness in many of us mindaters (Amir has really shown restraint here).
While most "quartz spheres" are only approximate, There was a NASA project a decade ago to create perfect quartz spheres. While it met the goal to confirm part of the General Relativity theory (principle?), creating the spheres is pretty cool also.
Here is a link that tells the story:
http://science.nasa.gov/science-news/science-at-nasa/2004/26apr_gpbtech/
It took a team of scientists several months to "measure" these spheres to the required accuracy.
Regards,
Dean Allum
22nd May 2012 02:01 UTCOwen Lewis
If your method of measurement of circumference is a tape measure wrapped around a sphere (assumed perfect (which it won't be) just to simplify the basic discussion), you are unlikely to be able to measure with greater accuracy than about +/- 0.5mm (worse for small spheres) So, at best, a suitably flexible but non-elastic tape should let you determine diameter to an accuracy of about +/- 0.17mm. OTOH a decent (not expensive) gauge will give you a direct read out of diameter to +/- 0.01mm for all diameters of <1mm up to the capacity of the gauge (150mm?). Accordingly, I suggest that a direct measurement of diameter with a good gauge should be at least one order of magnitude more accurate that is the method of circumferential measurement with a good tape and then dividing by pi.
22nd May 2012 14:39 UTCGord Howe
I agree with Owen. An inexpensive pair of digital calipers taking diameter measurements across centerline would be more than adequate to define the diameter. I would also measure it across several different axis and average it out. 150mm calipers won't measure a 150mm diameter but with a little inginuity a simple jig can be made up that will allow it to. If you have access to micrometers, even better. What you are trying to do with circumferences is tricky and as soon as you start multiplying or dividing you are multiplying any errors accumulated in your procedure.
Gord
22nd May 2012 19:22 UTCKristi Hugs
Thank you all again. You are awesome!!
22nd May 2012 22:57 UTCDouglas Merson 🌟 Expert
Doug
28th Sep 2012 04:52 UTCKeith Wood
Amazing what they can figure out!
Mira, maybe those guys could give you some tips on measuring spheres! They seem to be doing a pretty good job!
28th Sep 2012 09:28 UTCJolyon Ralph Founder
Unless in Alabama, when you have to divide it by 3 ;-)
28th Sep 2012 11:03 UTCOwen Lewis
You mis-remember or had a bad teacher :-) Measuring a circumference (a little harder to do accurately by any other method) is best done by measuring the diameter (easy to do accurately) and then multiplying that value by π (pi) (3.146.......etc).
If you can't measure the diameter accurately, it can be calculated as follows:
1. For objects of large diameter (a planet even), measure the maximum angle subtended between accurate observation of the points furthest apart on the opposite sided of the sphere. Call that angle θ. Call the diameter d, (d=2r where r is the radius of the sphere). Call the distance from the observer to the centre of the sphere D; measure or calculate D.
tan θ = 2r/D from which, by substituting the determined values for tanθ and D, out pops the value for 2r (=d).
2. If the object is of a more handy size and you have no calipers suitable to measure d, but you have an accurate balance, then determine first the SG of the sphere by the hydrostatic method and hence determine its volume. The formula for the volume (V) of a sphere is stated as:
V=(4/3)*π(r^3)
Since we know π and have determined V, getting the value of 2r (=d) becomes a matter of simple maths.
P.S. Alabama. I had often wondered why the holes in the doughnuts and bagels one buys there are never round :-D However, I've noticed the same phenomenon in some other places too!
28th Sep 2012 15:40 UTCDennis Tryon
Dennis
28th Sep 2012 17:08 UTCOwen Lewis
Nicely sniped!
28th Sep 2012 17:08 UTCEugene & Sharon Cisneros Expert
14th Apr 2014 08:46 UTCarunima banerjee
14th Apr 2014 17:22 UTCAdam Kelly
How many rockhounds does it take to measure a sphere?
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Copyright © mindat.org and the Hudson Institute of Mineralogy 1993-2024, except where stated. Most political location boundaries are © OpenStreetMap contributors. Mindat.org relies on the contributions of thousands of members and supporters. Founded in 2000 by Jolyon Ralph.
Privacy Policy - Terms & Conditions - Contact Us / DMCA issues - Report a bug/vulnerability Current server date and time: April 25, 2024 16:53:56