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where does the 70 in the formula come from ?


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Home Forums Gear Forums Gear (General) where does the 70 in the formula come from ?

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  • #3381267
    Woubeir (from Europe)
    BPL Member

    @woubeir

    For combining 2 sleeping bags, there’s a formula; x – (70 – y)/2. As I want to convert it to °C, does anyone know where the number 70 comes from ?

    #3381272
    Roger Caffin
    BPL Member

    @rcaffin

    Locale: Wollemi & Kosciusko NPs, Europe

    Probably out of Cleo.
    I have never seen that formula and have no idea what it means.
    Um?

    Cheers

     

    #3381275
    Woubeir (from Europe)
    BPL Member

    @woubeir

    I’ve seen it only here and It is used for estimating the temperature of two sleeping bags with one bag into the other (x is the warmest bag and y the coldest). But it uses (of course) °F and I’m looking at converting it to °C. But for that, I need to know what that 70 is.

    #3381276
    Dean F.
    BPL Member

    @acrosome

    Locale: Back in the Front Range

    At a guess, 70F is a comfortable room temperature.  So it looks like you’re taking the temperature rating of the thicker bag and improving it by half the difference between the temperature rating of the second bag and a comfortable room temperature.  So just change the 70F to Celsius, which IIRC is around 21C, and use your Celsius ECN ratings.

    #3381277
    Larry De La Briandais
    BPL Member

    @hitech

    Locale: SF Bay Area

    Well, the new formula would be:

    ( ( x – (70 – y)/2 ) – 32 ) / 1.8

    That can possibly be factored down some, but that should work.

     

    #3381280
    Ralph Burgess
    BPL Member

    @ralphbge

    Larry, your formula assumes that x and y are entered in F, and then converts the result to C. That isn’t really what’s wanted – the OP wants everything in C.

    The equivalent formula with all temps in Centigrade is:

    x – (21-y)/2

    For example,
    20F and 40F bags,   20 – (70-40)/2 = 5F
    -6.7C and 4.4C bags,   -6.7 – (21-4.4)/2 = -15C

    You don’t need to know where the 70 “comes from” to restate this empirical formula in Centigrade – it’s just algebra.   But no doubt it’s something to do with 70degF (21degC) being a comfortable reference temperature, as Dean already said.

    #3381284
    Woubeir (from Europe)
    BPL Member

    @woubeir

    The 21 I already figured out but I just like to know why just that number and not another one. It’s just that knowing why makes things easier to explain than just using it but not knowing why. :-)

    #3381287
    Larry De La Briandais
    BPL Member

    @hitech

    Locale: SF Bay Area

    Larry, your formula assumes that x and y are entered in F

    Yup, messed that one up.  ;)

    #3381289
    Ralph Burgess
    BPL Member

    @ralphbge

     

    Woubeir, if you already knew how to convert the formula to centigrade, then perhaps not asking how to do just that in the original question might have saved us some time….

    Anyway, your real question is “where does this empirical approximation come from”?

    I’ve never seen it before, but as Dean said 70F (21C) is probably a temperature when we’re perfectly comfortable, so it makes sense that this is the reference.    So, relative to that 70F reference,  let’s call a 20F bag a “delta-50F” bag,  and a 40F bag a “delta-30F” bag.     If you layer a delta-50F bag with a delta-30F bag, it would make sense that you add the deltas in some way, since the deltas represent the maximum gradient across which you will be insulated to maintain 70F inside.  However, it’s presumably not a simple sum because of non-linear heat loss across the same delta at lower temperatures.   Presumably the non-linearity is approximated by the factor of 1/2 in the empirical formula.

    So anyway, I have no idea if the empirical formula is at all accurate, but the general approach seems fairly reasonable.   All temperature ratings are very approximate in any case, there is no industry standard.

    #3381293
    Woubeir (from Europe)
    BPL Member

    @woubeir

    Sorry for that.

    So semi-scientific. But like 70 was probably chosen because it’s a round number, 20 is ’rounder’ than 21. So any reason why I shouldn’t opt for that 20 ?

    #3381299
    Richard May
    BPL Member

    @richardm

    Locale: Nature Deficit Disorder

    I knew I’d seen it too. I did some digging hoping to find a better answer and it appears to have jumped over from hamockforums.net. Peter_Pan mentions it early and WV follows up saying he found it it in “Articles”.

    I stopped there, dinner has to be made for the family.

    Personally, I’d have thunk that measuring (or adding) the loft of the two bags would give you a good temperature rating.

    #3381300
    Ralph Burgess
    BPL Member

    @ralphbge

    As far as Enrico Fermi is concerned, until a number exceeds 3, it’s about 1.

    There’s a popular representation in TV and movies that extremely smart and numerate people express estimates to a preposterously unwarranted number of significant figures.   The archetype being Mr Spock, “Captain, with shields depleted to 43%, I estimate that we have a 24.713% chance of surviving the next attack of the giant floating space-head”.    Smart people don’t do that, only idiots with calculators.   I wholeheartedly applaud your effort to express the Centigrade equation with a sensible number of significant figures commensurate with the underlying approximation.

     

    #3381328
    J R
    BPL Member

    @jringeorgia

    I agree with Dean. 70 is considered a comfortable temperature, in F. That’s the same as 21C. It’s not about rounded numbers, it’s about comfortable numbers. But that also would suggest that if you tend to be a cold sleeper you might want to bump that number up a bit. Likewise, 70F is more likely to be considered a comfortable temp by men than by women, so a female might want to use a slightly warmer number in that formula.

    #3381335
    James Marco
    BPL Member

    @jamesdmarco

    Locale: Finger Lakes

    Yes, Ralph is correct, the formula is only an approximation of the general thermodynamics.

    Basically it says heat the heat flow is less the further you move through the insulation. This means that the process is actually a curve, not linear as x – (70 – y)/2 implies.  But it is fine for most small temperature changes and ignores things like the shells, various surface areas, compression of the down, etc on the bags.

    The 70 is an arbitrary comfort temp. This will work down to about 0F but will gradually become more and more “off.” For sleeping naked in a bag, I would use 80F I think. With clothing, 70 works but will be a bit warm.

    For examples:

    For example two 40F with 4″ of loft  bags do not actually work out to 15F.  By experimentation we find that it only requires around 6″ of loft to do the same job. Not the 8″ we would infer from the loft of the two bags together. I would not hesitate to take the two 40F bags down to 0-5F or so. Again the formula is only approximate, ie a rule of thumb, because it doesn’t really match anything but works generally.

    If we take two 15F bags, then it works out to -11.5. The two 15F bags would have a total loft of ~12″. This will easily take you to -40F.  So it breaks down relatively quickly, like most rules of thumb. And it generally looks to keep you warmer than the calculated temp.

    So just substitute in the Celsius conversion for the 70 and use the Celsius temps. The relation of the formula is linear, the number chosen as a base is arbitrary, and we ignore all the other factors about a bag so it really doesn’t matter.  It is a rough calculation.

     

    #3381346
    Jerry Adams
    BPL Member

    @retiredjerry

    Locale: Oregon and Washington

    If you had a flat surface and the insulations didn’t get compressed, then you would just add the R values.  Your skin temperature is about 92 F if you’re just barely comfortably warm, which is what EN13537 assumes.  The temperature rating of the combined would be x – (92 – y) or x + y – 92.  If you had two 42 F rated bags, the combined would be -8 F – much more optimistic than x – (70 – y)/2 = 28 F.

    But there’s a bigger surface area for the outer insulation.  Let’s say your torso is 48 inches around.  Assume you have a 2 inch single sided loft.  Then the circumference of the outside of the inner insulation would be about 60 inches – 25% bigger.  Then the temperature drop across the outer insulation would be about 25% less.  The combined temperature rating would be x – (92 – y) * 0.75.  You’d have to put the actual numbers for torso circumference and single sided loft.

    But, let’s say you used that and you had two 42 F rated insulations.  That would combine to 4.5 F.  That’s pretty cold, below my experience, but I think you’d need some extra features.  Like there’d be too much leakage around the edge of a quilt so you’d want to have a mummy bag with some extra flaps or whatever they do for really cold sleeping bags.  So maybe that formula is too optimistic.  Plus, you probably get some compression so the inner insulation’s effective R value is reduced.

    Maybe that x – (70 – y)/2 is as good as anything, even if it’s not based on any theory.

     

    #3381353
    Jerry Adams
    BPL Member

    @retiredjerry

    Locale: Oregon and Washington

    oh, EN13537 assumes a skin temperature of 93 F, my bad

    maybe x – (93 – y) / 2 would be better

    then two 42 F insulations would be 16.5 F combined.  That seems a little more reasonable

    x = (70 – y) / 2 would give 28 F combined which seems too conservative to me

    #3381393
    Woubeir (from Europe)
    BPL Member

    @woubeir

    I think I found the original post (and poster) of that formula. Looks like based on a mix of experience and knowledge and the ‘where does that 70 come from’-question isn’t answered. I also found answers from people that said the formula was fairly accurate based on their experience. But I also found a few posts that said the outcome of the formula is too conservative and at least one post mentioned a comfortable sleep of 15°F below the outcome.

    I’m thinking of changing the 70 in to 20 as

    1. °C could then be used for x and y
    2. 20 is here the classic number for a comfortable room temperature

    However, I also noted that combining sleeping bags can give an outcome temperature far below than I would suggest to some, particularly beginners. So I’m thinking of explaining it and mentioning it after some things or more sensible measures that you should be aware of or take afterall like all sorts of metabolic and physical factors, choice of sleeping pad(s), …

    #3381568
    Anonymous
    Inactive

    I thought 70 *F or thereabouts was related to standard clo measurement in relation to a typical suit keeping a person (male?) warm at rest at that temp?

    Seems a bit arbitrary either way.  Different people will have different starting ranges, and which will vary even individually at different times.  But without some kind of standard or generalization, it would be hard to talk about this more briefly and in non technical terms.

     

    #3381572
    Jerry Adams
    BPL Member

    @retiredjerry

    Locale: Oregon and Washington

    1 clo is the amount of insulation needed to stay warm at room temp ~ 70 F.  Maybe that’s when you’re exercising the amount you’d do working in an office?

    #3381609
    Bob Moulder
    BPL Member

    @bobmny10562

    Locale: Westchester County, NY

    I’m thinking of changing the 70 in to 20 as

    1. °C could then be used for x and y

    2. 20 is here the classic number for a comfortable room temperature

    If ’70’ in the formula is a ‘reference temperature’ based upon the Farenheit scale, then ’20’ cannot arbitrarily be substituted to convert it to Celcius without taking into account the temperature conversion formula (°F – 32) x (5/9) = °C

    Formula or not, when combining bags/quilts/parkas/whatever in order to sleep comfortably in very cold places, one should always do some serious empirical testing in a similarly cold place that has a warm bail-out option very close by, or be prepared to do jumping jacks all night.

    #3381633
    Woubeir (from Europe)
    BPL Member

    @woubeir

    Bob,

    first: that’s a sensible approach of course. Unfortunately, some people want a quick and easy answer and if you don’t provide it, they will look somewhere else untill they think they found an answer. And then of course they run the risk of finding something that is way off. You could say something like ‘such a shame’ or ‘well, you know, survival of the fittest’ and go on with what you were doing, or try to find an answer (that is, of course, sensible and not just getting any answer because people want an answer). I knew I saw this formula somewhere and now I try to understand the reasoning behind it and why certain values were used and I’m looking if I can convert it to an formula with every variable in °C.

    Now, the 70. If I understand you wright, you mean that if that 70 has a specific meaning in °F, you can not ad randomly replace it with a any value in °C. Now, if I convert 70 °F to °C, I get 21,11111… and here that doesn’t mean anything. Now, if I convert 20 °C to °F, I get 68. Again a number that you won’t easily remember or do some calculations with. Now, if that 70°F is just taken because it’s the ~room temperature, 20°C has here exact the same meaning.

    #3381660
    Ben H.
    BPL Member

    @bzhayes

    Locale: No. Alabama

    I am surprised this post is still going.  Within the uncertainty of that formula 20°C is just as accurate of a number as 70°F.  As pointed out multiple times in this thread the formula is just a rule of thumb to estimate the effects of layering two bags.

    #3381669
    Philip F
    Spectator

    @morty

    Locale: (null)

    I’ve read before that around 70* is where the human body has to work least to keep it self thermoregulated.  Upon searching a bit further I found this bit of info which should explain that number

    http://www.ncbi.nlm.nih.gov/pubmed/17929604

    Most helpful tidbit:   With thermoregulatory vasoconstriction/ vasodilatation the body heat balance can be maintained within a range of ca. 4 degrees C, the middle of the range being at ca. 21 degrees C when light clothing is used.

    #3381671
    James Marco
    BPL Member

    @jamesdmarco

    Locale: Finger Lakes

    Ben is correct. It is a linear relation.The exact numbers are of little importance and do not effect the calculation. It only effects the goal, 80F or 20C inside the two sleeping bags. It just plugs in a constant. But it really does not depend on the relationship, it tries to define how two bags work together.

    The fairly accurate description to calculate heat flow is here: https://en.wikipedia.org/wiki/Thermal_conduction#Fourier.27s_law  But it is a complicated mess to calculate. Just use the very simplified rule of thumb. And, as shown above, the simplification is not real accurate when it comes down to the camping world, especially at temps <0C.

     

     

    #3381686
    Woubeir (from Europe)
    BPL Member

    @woubeir

    Don’t worry, if that formula isn’t good, it won’t be used. And I’m glad this thread is still going on; the more voices, the more opinions and, thus, the more input.

    Actually, this may be something to research for BPL as the layering of bags and quilts and the possible temperature as a consequence thereof, is regularly asked ?

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