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Old 31st May 2012, 08:27 AM   #2259
Robert Muehlenkamp
New Blood
Join Date: May 2012
Posts: 18
Let's have that again uniformly using the Anglo-Saxon decimal separator (dot instead of comma):

Item_Provan's test group_Test group with 3 adults 43 kg and 5 children 16 kg
(a) Number of bodies in Provan's test group_8_8
(b) Volume m of Provan's box_0.44_0.44
(c) Volume m per body = (b) (a)_0.06_0.06
(d) Concentration of bodies per cubic meter_18.18_18.18
ST's formula:
(e) Total weight of adults kg_174_129
(f) Total weight of children (1) kg_85_64
(g) Total weight of children (2) kg_7_16
(h) Total weight of test group kg_266_209
(i) Average weight of test person kg_33.25_26.13
(j) Volume occupied by adult m_0.095940_0.090526
(k) Volume occupied by child (1) m_0.035150_0.033684
(l) Volume occupied by child (2) m_0.011579_0.033684
(m) Total volume m (j)+(k)+(l)_0.142669_0.157895
(n) Average volume per person = (m) 3_0.047556_0.052632
(o) Persons per m = 1 (n)_21.03_19.00

Now let's look only at the 3*43kg + 5*16 scenario and do the following exercises:
a) cut the weights in half (21.5 kg for adults, 8 kg for children)
b) double the weights (86 kg for adults, 32 kg for children).

The results are quite amazing:

Item_43/16 scenario_21.5/8 scenario_86/32 scenario
(e) Total weight of adults kg_129_65_258
(f) Total weight of children (1) kg_64_32_128
(g) Total weight of children (2) kg_16_8_32
(h) Total weight of test group kg_209_105_418
(i) Average weight of test person kg_26.13_13.06_52.25

(j) Volume occupied by adult m_0.090526_0.090526_0.090526
(k) Volume occupied by child (1) m_0.033684_0.033684_0.033684
(l) Volume occupied by child (2) m_0.033684_0.033684_0.033684
(m) Total volume m (j)+(k)+(l)_0.157895_0.157895_0.157895
(n) Average volume per person = (m) 3_0.052632_0.052632_0.052632
(o) Persons per m = 1 (n)_19.00_19.00_19.00

With ST's formula, it doesn't matter whether you double the weights, cut them in half or multiply them by or divide them through any given factor. As long as you use the same multiplier or divider for both and the relation between adult weight and child weight is not changed, the average volume occupied by one person in the test group will always be 0.052632 m, and the concentration of bodies per cubic meter will always be 19.

Great formula, ST. You should obtain IPR protection for it.

Last edited by Robert Muehlenkamp; 31st May 2012 at 08:40 AM.
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