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How long is this roll of tape?

mc2fool
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How long is this roll of tape?

#425545

Postby mc2fool » July 7th, 2021, 1:08 pm

Almost certainly a simple one for the mathematical types around here, but this is a practical problem which I think (hope!) I've got a good-enough-for-me answer to but thought I'd throw in as a "How do you figure this properly?" question ... and to double check my good-enough-for-me answer!

Image
https://www.steelroofsheets.co.uk/products/20mm-x-9mm-grey-self-adhesive-pvc-foam-tape-8m-roll/

I've been sent a roll of adhesive foam tape similar to the above (but not that one). It's a gift and I'm not sure how long it is, and prefer to measure its length myself and just email back a grateful "Thanks! That's great!" rather than a question about it. Of course I could stretch it out, measure it, and then rewind it before putting it in the cupboard for later use, but being adhesive backed that risks all sorts of hassles, from it falling onto the floor and picking up carpet fluff to personal entanglement, as well as possibly weakening the adhesive.

So instead, measuring the roll itself as is, the diameter across the whole disc is 20cms.
The diameter of the outside of the inner plastic ring (i.e. the diameter of the inside of the foam roll itself) is 8cms.
Counting from the outside one to the inside one, there are 10 "rings" (not actually rings of course) of tape.

So, my rough-and-ready take on it (not going for massive accuracy here! :D) is that the outermost ring of tape is 20*Pi = ~63cms long, and the innermost is 8*Pi = ~25cms long. So, the average length of a ring is (63+25)/2 = 44cms and there are 10 rings so I have around 4.4 metres of tape.

Fair enough, or likely to be way off? And what's the more accurate way of calculating it?

jfgw
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Re: How long is this roll of tape?

#425550

Postby jfgw » July 7th, 2021, 1:24 pm

That looks right.

You could also calculate the area and divide this by the thickness of the tape.

The area in sq cm is 10^2 pi - 4^2 pi = 264

The thickness of the tape in cm is (10-4)/10 = 0.6

264 sq cm / 0.6cm = 440cm = 4.4m.

It is an interesting gift. Birthday? Anniversary?


Julian F. G. W.

Gengulphus
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Re: How long is this roll of tape?

#425622

Postby Gengulphus » July 7th, 2021, 5:18 pm

mc2fool wrote:So, my rough-and-ready take on it (not going for massive accuracy here! :D) is that the outermost ring of tape is 20*Pi = ~63cms long, and the innermost is 8*Pi = ~25cms long. So, the average length of a ring is (63+25)/2 = 44cms and there are 10 rings so I have around 4.4 metres of tape.

Fair enough, or likely to be way off? And what's the more accurate way of calculating it?

Fair enough, as is jfgw's method of getting essentially the same result.

As regards improving the accuracy, I can make two suggestions:

* Determine accurately how many 'rings' of tape there are. For the roll of tape in your image (rather than the one you've been sent), for instance, it looks to me as if the innermost 'ring' starts roughly between the 2 o'clock and 3 o'clock positions in the image, loops around the centre of the roll 13 times clockwise and a bit more, ending roughly at the 4 o'clock position. So I would work on the basis of about 13 1/8th 'rings'. I'd estimate that that last 1/8th of a 'ring' probably makes a difference of a bit over 10 cm to the calculated length.

* Determine whether you're interested in the length along the outside edge of the tape, its inside edge, or somewhere in the middle of its thickness (I'd guess for the tape in your image, it's probably the outside edge, as it looks to me to have a non-stretchy outside layer, then foam which will presumably expand a bit when unrolled and finally adhesive on the inside edge adhering to the outside layer of the next 'ring' in - but looking at the actual tape could quite easily reveal a different story!). The outside length vs inside length difference will be about 2pi times the thickness of the tape per 'ring', which I would estimate to be somewhere of the order of 75 cm for the tape in the image, or half that for the roll you've been sent.

But probably the most important point I'd make is to use a conservative estimate, because it's much better to have a bit left over at the end of the job than to have a bit too little for it! In particular, don't rely on being able to use the innermost 'ring' if the central 'spool' is made of cardboard - the adhesive on the inner 'ring' may well 'lift' a layer off it, resulting in it ending up much less sticky than desired...

Gengulphus

mc2fool
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Re: How long is this roll of tape?

#425634

Postby mc2fool » July 7th, 2021, 5:46 pm

Gengulphus wrote:
mc2fool wrote:So, my rough-and-ready take on it (not going for massive accuracy here! :D) is that the outermost ring of tape is 20*Pi = ~63cms long, and the innermost is 8*Pi = ~25cms long. So, the average length of a ring is (63+25)/2 = 44cms and there are 10 rings so I have around 4.4 metres of tape.

Fair enough, or likely to be way off? And what's the more accurate way of calculating it?

Fair enough, as is jfgw's method of getting essentially the same result.

As regards improving the accuracy, I can make two suggestions

Ha! Practical suggestions noted and thank you ... although I did put it up thinking you maths types would go into debating a mathematically more accurate way of calculating it than my primary school method ... something over my head like https://math.stackexchange.com/questions/2825984/length-of-a-spiral (shudder!) :D

mc2fool
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Re: How long is this roll of tape?

#425638

Postby mc2fool » July 7th, 2021, 6:11 pm

jfgw wrote:264 sq cm / 0.6cm = 440cm = 4.4m.

It is an interesting gift. Birthday? Anniversary?

Thanks!

LOL, no, we had a new rooflight dome fitted a few years back and the foam tape that came with it is of better quality (no deterioration at all) than others I've used, so I emailed the dome manufacturer (who don't sell retail), asking what brand and/or type they use -- and the same day got a reply back saying if I gave them my address and said how much I needed they'd just send some to me, which they did (as 3 equal, I guess standard, sized rolls) ... very nice of them. :)

9873210
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Re: How long is this roll of tape?

#425905

Postby 9873210 » July 8th, 2021, 3:34 pm

Note that the methods given by mc2fool (averaging the inner and outer ring and multiplying by the number of rings) and Julian (calculating the area of the tape "disk" and dividing by the tape thickness) are mathematically equivalent and will always give the same answer

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Re: How long is this roll of tape?

#425943

Postby Gengulphus » July 8th, 2021, 6:11 pm

9873210 wrote:Note that the methods given by mc2fool (averaging the inner and outer ring and multiplying by the number of rings) and Julian (calculating the area of the tape "disk" and dividing by the tape thickness) are mathematically equivalent and will always give the same answer

Yes - provided that when applying mc2fool's method, you measure the length of the inner ring along its inner edge and the length of the outer ring along its outer edge, or measure the lengths of the rings halfway through their thicknesses, or various rather less natural possibilities like measuring the length of the inner ring along its outer edge and the length of its outer ring along its inner edge. They're not mathematically equivalent if e.g. you measure both rings along their outer edges, which as I observe above might be the more accurate way of measuring the lengths of the rings if the outer layer of the tape is non-stretchy, so that the foam in the rest of the thickness expands slightly when it is unrolled.

Gengulphus

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Re: How long is this roll of tape?

#430575

Postby AndyPandy » July 26th, 2021, 8:34 pm

Weigh it.

Cut 1cm off and weigh that.

Divide the first answer by the second. Gives you Length in cm *.

* OK, subtract '1' if you want to account for the 1cm you removed.


Bathroom scales might not be accurate enough.

mc2fool
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Re: How long is this roll of tape?

#430608

Postby mc2fool » July 26th, 2021, 11:24 pm

AndyPandy wrote:Weigh it.

Cut 1cm off and weigh that.

Divide the first answer by the second. Gives you Length in cm *.

What about the weight of the plastic ring in the centre that the tape is wound around? Likely to be significant given how light the tape is... ;)


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