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Pack Volume Calculation Doesn’t Add Up
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May 25, 2011 at 9:18 pm #1274429
I am editing my post since everyone has seemed to miss the point..
Ok say you have a backpack that has a circumference of 40" and a height of 26". If you try to find the volume of this pack using the cylinder equation here is what you come up with. 40" circumference / 3.14 = 12.738" diameter. If you divide the diameter by 2 to find the radius this gives you 6.369". To check that this is right. 6.369" radius x 2 = 12.738" diameter x 3.14 = 40" circumference. Now to find the area of the cylinder you take the radius which is 6.369" x 6.369" x 3.14 = 127.371 Sq Inches. To find the volume you would take 127.371" x the height of 26" = 3,311.658 Cubic Inches.
Say you want to find the area of a rectangle using the 40" circumference and the height of 26". This would give you a rectangle that measures 12" wide x 8" deep x 26" tall. (Common 60L pack size) So using the area formula for a cube L x W x H this gives you 12" x 8" x 26" = 2,496 Cubic Inches.
A backpack's shape is closest to a rectangle but most backpacks have an overstated size closer to a cylinder. Why is this? Why are pack makers incorrectly stating their pack sizes? Is it marketing or is it they are using the wrong calculations? Furthermore why is there no standard?
May 25, 2011 at 9:35 pm #1741244A circle and rectangle with the same circumference do not have the same area.
Area of your circle = Pi * r^2 = 3.14 * 6.369 * 6.369 = 127 square inches
Area of your rectangle = L * W = 12 * 8 = 96 square inchesYou are multiplying both of these areas by the same height to get pack volume.
(127 / 96) * 2496 = 3300. That is where your discrepancy comes from.
Andrew
May 25, 2011 at 9:40 pm #1741248Your math is correct Lawson, but you are making an incorrect assumption:
–A backpack is a mix of a cylinder and a rectangle depending on how its packed and if both the cylinder and the rectangle have the same circumference and the same height they should have the same volume but they don't.–
Cylinders and boxes with the same circumference and height do not have the same caculated volume. Imagine in your example given above if you had given the box dimensions of 11*9*26= 2574; with dimensions of 10*10*26=2600; with dimensions of 15*5*26=1800; etc. A circle of a given circumference has a definite area; as shown, the circumference of a rectangle does not directly infer it's area.
May 25, 2011 at 9:56 pm #1741253A backpack is not a fixed object like a cylinder or a rectangle. For instance you can take a piece of material 40" long x 26" tall and it will fit perfectly around a cylinder with a 40" circumference and a rectangle that measures 12" wide x 8" deep..I have done it so I know it works. Dan McHale is the only person I have seen provide a method to this madness. He calculates packs as cylinders. Does the industry as a whole use the same calculations? If so why? A backpack is closer to a rectangle then a cylinder.
Side Note: Before making camping gear I owned a concrete construction business for several years and before that I was a concrete foreman, so I am very familiar with calculating volume but this does not add up.. Maybe it does and everyone else is doing it wrong. Just think your 40L pack may really be a 25L pack… Food for thought..
May 25, 2011 at 11:38 pm #1741270True that a pack is not fixed in that the sides are somewhat flexible. To a certain extent this will be determined by the shape of the bottom panel. I would think the most accurate way to precisely determine the maximum capacity would be to consider the pack as an ellyptical(sp?) cylinder. Of course, the figure would be somewhat irrelevant, as a pack has a fair amount of empty space when packed with a real load. I like Dan McHale's method for comparing packs more than for determining the actual volume.
May 25, 2011 at 11:46 pm #1741271Oh, and on the math front, it's just mathematical fact. The circular shape will ALWAYS have a larger area than a rectagular shape for a given circumference. The rectangular shape will maximize it's area as the two dimensions approach equivalent values.
May 25, 2011 at 11:48 pm #1741272Andrew's ansd Scott's answers explains most of this.
But to cut through all of this, pack volumes are not measured that way. Guess why? They are measured by filling them with small balls or similar, then measuring the volume of the small balls in a suitable rectangular box. See our articles on Internal Frame Packs for more information.
http://www.backpackinglight.com/cgibin/backpackinglight/lw_internal_frame_packs_part_1a.html
http://www.backpackinglight.com/cgibin/backpackinglight/lw_internal_frame_packs_part_1b.html
http://www.backpackinglight.com/cgibin/backpackinglight/lw_internal_frame_packs_part_1c.html
http://www.backpackinglight.com/cgibin/backpackinglight/lw_internal_frame_packs_part_2.htmlCheers
May 26, 2011 at 5:04 am #1741304What's so special about a rectangle 12" by 8"?
It could be 10" by 10", or say 20" by 0" and still have a circumference of 40".
In this last case the volume would be zero.
This just illustrates that the shape does matter.
A cylinder gives the largest volume for a given circumference.May 26, 2011 at 7:45 am #1741346Also if you pack poorly you do reduce your pack volume. If you place some rigid piece of gear in your pack which is wider than the perscribed width it will reduce the depth of your pack. If you depth is reduced from say 12 to 10 while your width is increased from say 16 to 18 your circumference remains constant but your volume will decrease. If you pack in this manner your 40L pack, packed poorly, might only be a 25L pack. Maybe a large tent or synth bag could do this.
May 26, 2011 at 7:58 am #1741350I think you all are missing the point. I am not looking to debate how to calculate volume or why a cylinder of the same circumference and height has more space. What I am trying to understand why there is no "standard" all pack makers use? If you buy a gallon of water from store x and and a gallon of water from store y both are going to be the exact same. Sure one might have a different shape but 1 gallon is 1 gallon no matter how it comes. Yet pack volumes can grossly vary. A 50L pack from company x and a 40L pack from company y can be the exact same size. As Roger said the only true way to measure a packs volume would be to fill it with some unit of measure like foam blocks but its apparent that most companies are not doing this.
Andrew,
>>>"A circle and rectangle with the same circumference do not have the same area. Area of your circle = Pi * r^2 = 3.14 * 6.369 * 6.369 = 127 square inches. Area of your rectangle = L * W = 12 * 8 = 96 square inches. You are multiplying both of these areas by the same height to get pack volume. (127 / 96) * 2496 = 3300. That is where your discrepancy comes from.""<<< My math is correct. I am not looking for a math lesson. I am looking to understand what unit of measure pack makers use since there seems to be no standard..Scott,
>>>""I like Dan McHale's method for comparing packs more than for determining the actual volume."" Why? McHale's packs look much more like a rectangle then a cylinder to me.. So why wouldn't he measure pack volume by filling the packs as Roger suggested?? >>>""Oh, and on the math front, it's just mathematical fact."" Duhhhh…Roger,
>>>"Andrew's and Scott's answers explains most of this." <<< No they don't. They are trying to give me a math lesson.. My calculations are correct. I am just trying to make sense of it all.>>>"But to cut through all of this, pack volumes are not measured that way. Guess why? They are measured by filling them with small balls or similar, then measuring the volume of the small balls in a suitable rectangular box."<<< Can you confirm that all pack makers use this method? If so then why did your testing have an average ratio of 86% of stated volume? If they are all using this method then why were some pack ratio's as high as 101% while some were as low as 61%? On a 50L pack thats an average of a 7L difference. This is no standard.. You only tested a few packs from a few pack makers so whats the real average?? Could there be more ULA's and lower the ratio or more Mont Bells to raise the ratio??
Stuart,
>>>"What's so special about a rectangle 12" by 8?""<<< Its a pretty average backpack dimension and also has a 40" circumference.>>>"It could be 10" by 10", or say 20" by 0" and still have a circumference of 40".<<< I have never seen a backpack that is 20" wide by 0" deep. Have you???
>>>"'In this last case the volume would be zero. This just illustrates that the shape does matter. A cylinder gives the largest volume for a given circumference.""<<< I agree and thats why I brought up the question. Have you ever seen a cylinder backpack? If not then why are listed pack volumes more in line with cylinders then rectangles?
May 26, 2011 at 8:53 am #1741381Ok, so I missed your point – perhaps it was not all that clear in your original post.
To try to answer what I think is your question, I believe that manufacturers deliberately overstate the capacity of their packs in order to make a pack appear lightweight for it's size. They realise a purchaser can easily verify the quoted weight but not many will verify the quoted volume. The latter is not difficult to do using polystyrene beads (beanbag filler) and a measuring jug.
May 26, 2011 at 9:01 am #1741387You should have made your point better originally Lawson, rather than continually editing your original post and then discrediting and ridiculing the answers you got. And if you can't understand that a 40" x 26" piece of fabric will perfectly encircle both a 12" x 8" rectangular shape and a circular shape with a 40" circumference, and that these two shapes have different areas, you need a math lesson. As to why pack makers don't use standardized volume measurements, I doubt anyone here could answer that accurately.
May 26, 2011 at 9:07 am #1741389Lawson,
I agree with your initial post, both the math and the logic of your question.
I've had a similar problem when trying to include an estimated volume in postings for my home made packs. My packs are typically just big stuff sacks so the stuffed shape depends a lot on how I pack it. I could assume a cubelike, cylindarlike, sphericallike, etc. shape and the volume estimates would all be different.
One time I lined the pack with a garbage bag, filled it with water and then measured the water. I wish I had small balls….foam balls…. because they would be much lighter than the water.
I think the small ball method would be a great improvement over the current randomness of pack volume estimates. Perhaps balls with weight designed to approximate typical pack weights would be best. The weight of the balls with my packs, for example, would influence its filled shape.
Perhaps the testing and discussions from this website will inspire some of the industry leaders to adopt a standard? They could call it the CaffinKline test.
May 26, 2011 at 9:12 am #1741394Huh?
There is a standard ASTM F2153 – 07. You don't have to go far to find it BPL even makes reference to it on on the Absaroka product page.
I don't know which manufacturers use the standard, but I'd wager that those that don't do so because they'd rather make an inflated claim than give a capacity closer to the truth.
If you're interested in providing an accurate capacity rating, the most honest thing would be to use the standard.
May 26, 2011 at 9:17 am #1741397"What I am trying to understand why there is no "standard" all pack makers use? If you buy a gallon of water from store x and and a gallon of water from store y both are going to be the exact same."
Because there are hundreds of companies that produce backpacks that all want to do things their own way. Your cylinder calculation is just as arbitrary as any of them – Roger's test may be the best one. But perhaps eventually an EN standard will be made (or already exists? I don't know.) Then we will have the much more transparent problem that many pack manufacturers will choose to ignore it or won't want to pay to have their packs tested.
Andrew
May 26, 2011 at 9:42 am #1741407Aaron,
Thanks for the AST standard link. It really simplified my pack volume calculations.
The opening paragraph says that volume will only be included for portions of the pack that are completely enclosed. My pack has an open top that is only partially closed with a drawstring closure. So, by definition, my pack volume is zero.
Daryl
May 26, 2011 at 10:22 am #1741422Nice..I didn't know there was an ASTM standard. Thanks Aaron.. Now all we need to do is get the pack makers to use it. I recently purchased a pack that is ALOT smaller then stated so thats why I am so annoyed. Maybe its time to make my own packs using the ASTM standard.
May 26, 2011 at 11:30 am #1741442Lawson,
I started doing volume measurements with packing peanuts about a year ago. I fill it, shape it to approximately what it would look like with gear, verses round or optimal or pretty, and then pour them into a tall box. I measure the height and multiply by area to get the volume. A couple of wine boxes taped together work pretty well as they approximate the tall narrow shape of a pack. "Tall and narrow" also reduces the error of leveling and measuring a uniform height. ( I recently applied this method to determine the usable volume of a Ursack versus a Outsak by using beans.)This is the only way I could compare a Granite Gear Vapor Trail, a ULA Ohm, and a Gossamer Gear Mariposa Plus. Very revealing. This exercise also highlighted the difference between design shape and packing efficiency.
This approach is what makes the BPL study so valuable – the easy, nomagic method of determining pack volume that is uniform and repeatable.
May 26, 2011 at 11:39 am #1741444You can play games with the standard, but the core of it is applicable and honest how many ping pong balls fit into your pack? I think it'd be fair for makers to use the standard, or technically a derivative of it, to measure other open areas like side pockets. This could be obviously be gamed the capacity of the front and side pockets on my ULA Circuit hold are drastically different if the main pack bag is full or empty
May 26, 2011 at 11:51 am #1741451Quote:This is the only way I could compare a Granite Gear Vapor Trail, a ULA Ohm, and a Gossamer Gear Mariposa Plus. Very revealing. This exercise also highlighted the difference between design shape and packing efficiency.If you don't mine sharing how did the usuable volumes of these 3 packs compare, the Ohm and the Mariposa plus are on my short list along with the swift.
May 26, 2011 at 12:23 pm #1741459Greg F.,
To avoid hijacking this thread, Look Here, and post questions or comments there. I'll put a "Watch" on it, and follow up there.May 26, 2011 at 12:52 pm #1741480I worked in a totally unrelated technical field. Our management observed that competitors overstated some specs, and so decided to "use similar assumptions." This meant that over time everyone lied equally, and slowly inched into Neverland.
Good thing Backpacking Light and others do their "as tested" numbers to keep folk from that drift.
May 26, 2011 at 3:33 pm #1741555Hi Lawson
<< Can you confirm that all pack makers use this method?
That's the ASTM method mentioned elsewhere. It uis fairly clear.I can confirm that European mfrs all seem to use the Standard. I have even found the odd 20 mm ball left in a prototype European pack during the Internal Frame pack survey.
I can also confirm that many American cottage mfrs do NOT use the standard. They make the same volume claims but don't tell the customer that they are quite deliberately doing things not permitted under the ASTM Standard. The trouble is that conformance to the Standard is not required by law afaik.
So when you find a pack in the survey that was measured to be within 5% (say) of the claim, they were probably using the Standard. When you find one that is seriously different, you may draw your own conclusions.
What does concern me is that it seems to be always the American companies which make unsupported product claims, for pack volume, sleeping bag ratings, etc. The Europeans seem to be quite scrupulous about conforming to Standards. That worries me.
Cheers
May 27, 2011 at 5:48 pm #1741973Dude, chill out.
May 27, 2011 at 6:01 pm #1741982"What does concern me is that it seems to be always the American companies which make unsupported product claims, for pack volume, sleeping bag ratings, etc.
+1 Roger.
There is No consistency, especially when it comes to pack volume.
It is always "Buyer Beware". 
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