/[alcoholcalculator]/trunk/abv_calc_algebra.txt
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Contents of /trunk/abv_calc_algebra.txt

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1 Non-Alcoholic Volume: Vna
2 Alcoholic Volume: Va
3 Alcoholic abv: Vab
4 Final abv: Abv
5 Total volume: Vt = (Vna + Va)
6
7 Abv = ( ( Va(Vab) ) / Vt )
8 Vt = ( ( Va(Vab) ) / Abv )
9 Va = ( ( Abv(Vt) ) / Vab )
10 Vab = ( ( Abv(Vt) ) / Va )
11 Vna = ( ( Abv(Vt) ) / Va )
12
13 substitution values:
14 Vt = ( ( Va(Vab) ) / Abv )
15 Vt = ( vna + Va ) [symobolic]
16 Vna = ( ( ( Va(Vab) / Abv ) ) - Va )
17 Va = ( ( ( Va(Vab) / Abv ) ) - Vna )
18
19 ; Vna = 1oz water
20 ; Va = 1oz 70 proof (35%)
21 ; Vab = 0.35 ; (70/2)/100
22 ; Vt = 1oz + 1oz = 2oz
23 Abv = ( ( 1(0.35) ) / 2 ) = ( 0.35 / 2 ) = 0.175
24 Vt = ( ( 1(0.35) ) / 0.175 ) = ( 0.35 / 0.175 ) = 2
25 Vab = ( ( 0.175(2) ) / 1 ) = ( 0.35 / 1 ) = 0.35
26 Va = ( ( 0.175(2) ) / 0.35 ) = ( 0.35 / 0.35 ) = 1
27 vna = ( ( ( 1(0.35) / 0.175 ) ) - 1 ) = ( ( 0.35 / 0.175 ) - 1 ) = ( 2 - 1 ) = 1
28 va = ( ( ( 1(0.35) / 0.175 ) ) - 1 ) = ( ( 0.35 / 0.175 ) - 1 ) = ( 2 - 1 ) = 1
29
30
31 Example Usage:
32 * I want a final abv of 15% or 30 poof
33 * I want to make the total volume approx. 12 oz (12*0.15=1.8oz)
34 * I want to use 70 proof (35%) to make it
35 * note: I would like to use no more than 2oz of alcohol
36 * how much non-alcohol do I need?
37
38 Va=2
39 Vab=0.35
40 Vna=?
41 Abv=0.15
42
43
44 2(0.35) / 12 = 0.058 = 5.8% (11.667 proof)
45 Abv = ( ( Va(Vab) ) / (Va + Vna) ) ; where Abv = 0.15
46 Abv = ( ( 2(0.35) ) / (2 + Vna) )
47 Abv = ( ( 0.7 ) / (2 + Vna) )
48
49 Abv = ( ( 0.7 ) / (2 + 1) ) = 0.23
50 Abv = ( ( 0.7 ) / (2 + 2) ) = 0.175
51 Abv = ( ( 0.7 ) / (2 + 3) ) = 0.14
52 Abv = ( ( 0.7 ) / (2 + 4) ) = 0.1167
53
54 Abv = ( ( 0.7 ) / (2 + 2.5) ) = 0.1556
55
56 Vna = (Va(Vab) / Abv) - Va
57 Vna = (2(0.35) / 0.15) - 2 = (0.7/0.15) -2 = 2.6667
58 Vt = Va+Vna = 2 + 2.6667 = 4.6667 = Va(Vab) / Abv = 0.7/0.15 = 4.6667
59 vt = Va(Vab) / Abv
60
61
62 2.6667 oz water / other non-alcoholic flavor
63 2 oz 70 proof
64 total vol: 4.6667
65 Abv = 0.15, (4.6667*0.15) = 0.7 oz
66
67
68 empierical maths:
69 Vt=12
70 Abv=0.15
71
72 Vt(Abv) = 12(0.5) = 1.8oz pure alchol
73 Va(Vab) = 2(0.35) = 0.7 oz pure alchol
74
75 1.8oz pure alchol of 70 proof is: 1.8/0.35=5.143oz of 70 proof
76 Vt=12-5.143=6.857oz non-alchol
77
78 Vt=12
79 Abv=0.15
80
81 6.857oz water
82 5.143oz 70 proof (5.143*0.35)=1.8
83
84 calculation:
85 1.8/(6.857+5.143)=1.8/~12 = 0.15
86
87 7oz water
88 5oz 70 proof (1.75oz)
89
90 1.75/(7+5)=1.75/12=0.146 (14.6%, 29.2 proof)
91
92
93 So to re-iterate:
94
95 * you are given a final volume (Vf)
96 * you are given a final abv (ABVf)
97 * you are given the proof of alchol to use (Ap) or an ABV to use; ABV = proof/2, proof = 2(ABV)
98
99 Vaf = Vf(ABVf)
100 Va = Vaf/ABV
101 Vna=(Vf-Va)
102
103 Convert the proof/abv:
104 If given a proof: (proof/2)/100=ABV%
105 If given an ABV: ABV/100=ABV% ; assuming the ABV is not a percent out of 1 (0.5 out of 1) = 50%
106
107 How to calulate:
108 * start by calculating the total volume of alchol in the final product
109 Vaf = Vf(ABVf)
110 * using this formula you can calculate the amount of alchol required
111 Va = Vaf/ABV
112 * using the amount of alchol, determine how much non-alcholic content to add
113 Vna=(Vf-Va)
114
115 ** you now know how much alcohol and non-alcholic content to combine
116 ** to create a known volume of a certain proof

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