where does the 70 in the formula come from ?

[Ralph Burgess]

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

Bob, we have:

z = x – (70-y)/2
z’ = 5/9(z – 32),  x’ = 5/9(x-32),  y’ = 5/9(y-32)

then

z’ = x’ – (21-y’)/2

If you check the algebra, you will find that for this particular formula, the equivalent formula in Centigrade units does just involve changing the 70 to 21.   Everything else cancels.

 

[Bob Moulder]

Thanks for the correction.

In the immortal words of Emily Litella,

 

 

[James Marco]

Rather than looking at the constant (70F or 21C) I would look at the actual relation as described.

He is assuming that the second bag is roughly half as effective as the first bag:

So if we start at freezing (using the 0C as the initial condition) we find:

x=first bag, y= second bag, t=resultant combined warmth

x – (0 – y)/2=t,

x-(-y/2)=t,

x+y/2=t

Taking two 5C bags we have

5+2.5 =7.5 which is entirely unreasonable. Something wrong with the base formula. Personally, I wouldn’t bother to use this formula and simply use the loft values, comparing it to a known reference.

 

 

[Woubeir (from Europe)]

Like I said: “Maybe something for BPL.” Perhaps even more because it’s not only used for layering bags/quilts, but also for the use of liners in bags/quilts or the use of clothing inside bags/quilts.

Measuring the loft is an alternative, but it remains arbitrary.

[IVO K]

I am rather disgusted by the appalling attempts at algebra in this thread.

Ralph Burgess correctly introduced the substitutes

z’ = 5/9(z – 32),  x’ = 5/9(x-32),  y’ = 5/9(y-32)

but then did not follow through with correct math.

These substitutes should be used to express rather x, y, and z in the original equation – like this:

z = 9/5z’ +32; y = 9/5y’+32; x=9/5x’+32, where x,y,z are temps in °F, and the “prime” values are in °C.

After substituting, we arrive @

9/5z’+32=9/5x’+32-(70-9/5y’-32)/2

After further solving this for z’, the result in °C that Woubeir was seeking is this:

z’ = x’+1/2y’-10.55

This is the accurate translation of the original formula of z = x-(70-y)/2 in °F. Cheers!

 

Separately, I agree that measuring the loft is not a good alternative as it disregards the fill power, hence – the actual insulating capabilities.

4″ loft of 550 fill is not the same as 4″ of 900+ fill.

[Woubeir (from Europe)]

z’ = x’+1/2y’-10.55

Absolutely correct although it’s closer to 10,56 ;-)

 

[James Marco]

Well, I would disagree on loft not being more accurate. Loft at 4″ is loft of 4″.

The fill power measures the volume of material. Generally, the 550 loft stuff will be roughly the same as the 900 fill stuff. I say roughly because the 550fp stuff actually conducts a bit more(and maintains it’s loft better in muggy conditions) than the 900fp. But, generally they do the same insulating.

The weight is calculated at 550/900 and is clearly different. Or, 10oz of 550fp down would only require 6.1oz of 900fp. But this has very little to do with the temperature rating of a bag. They would be roughly the same temperature rating because of the loft.

Of course this does not take into account weight of materials below, clothing, shape, or compression caused by 1 bag in the other. And the original formula depends on the order.  Using an 20 degree bag inside a 40degree or a 40degree bag inside a 20degree bag will effect the outcome of the calculation. Again, something is wrong and an indication that the formula is not correct. Just totaling loft and looking up where the average loft falls on a temp scale discounts the type of fill, be it synthetic or down and regardless of the type of down. It only deals with temperature. The shells will stop convection between them, but not conduction or radiation. So, you are roughly in the “slightly warmer” category for two bags.  I would suggest strongly not to rely on this formula. But following it will only mean you are too warm. Wasted weight but not life threatening (as in the case of getting too cold.)

[Woubeir (from Europe)]

And the original formula depends on the order.  Using an 20 degree bag inside a 40degree or a 40degree bag inside a 20degree bag will effect the outcome of the calculation.

Well, actually that formula sais that x is the warmest bag and y the coldest bag and sais nothing about the order of bags (but I guess assumes that the coldest is always put in the warmest).

[Ralph Burgess]

I am rather disgusted by the appalling attempts at algebra in this thread.
Ralph Burgess correctly introduced the substitutes
z’ = 5/9(z – 32),  x’ = 5/9(x-32),  y’ = 5/9(y-32)
but then did not follow through with correct math.

Oh dear, Ivo.

In your disgust at the algebraic incompetence of others, two advanced mathematical concepts seem to have escaped your attention.  10.5 is half of 21; and two negatives multiply to a positive.

Your formula

z’ = x’+1/2y’-10.5

is, rather obviously, exactly the same as the formula that I wrote

z’ = x’ – 1/2(21-y’)

The only difference being that the way I wrote it is the only sensible way, of course, similar to the form of the Fahrenheit equation.

[James holden]

http://www.enlightenedequipment.com/blog/quilts-106-quilt-layering-for-cold-temps/

personally i use a more conservative estimate that adding a 40F bag adds ~ 20F to the rating, an 30F bag adds 30F, etc …

IMO conservative is better as the fit of the bags is key

• if its too tight the down will be compressed
• if its too wide then there will be dead air gaps between the bags
• it can be BOTH too wide and too tight in different areas on the same bags

a much more important benefit is the moisture management benefits when using 2 bags, especially if the top one is synth

overall the published media is pretty silent on the benefits and downsides of layering bags and poofayz

which is a shame as the moisture management benefits are immense … and it lets folks extend the temp range of their system as they are more likely to own or borrow 2 lighter bags than a winter bag

theres a whole bunch of “tips and tricks” like this which passes mostly by word of mouth … with very little research or literature on em … but when you get hit by a cold snap could save you

;)

[IVO K]

Oh dear, Ivo.

@Ralph:

I hang my head, ashamed of my ineptitude at math while having my 1st cup of coffee in the morning.

 

Credit goes to Ralph for algebraic prowess. And mathematical sensibility.

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