Calculating Loudspeaker Box Volume With Fibonacci Numbers

An alternative method of calculating loudspeaker box volume. The only information needed is the nominal driver size.

The program listing shown below can be copy and pasted into the editor window of the BASIC interpreter. Click the "Run" button to execute the program. Width, height, depth values shown are the interior dimensions. No adjustment for the displacement of the driver is needed. Dv is the nominal vent diameter. Multiply Dv by 0.75 for dual vent tubes.

The back and sides of the enclosure interior should be covered with acoustical cotton batts or some similar damping material. Consider rounding the backside of the cutout hole to allow air to escape from the backside of the driver.

20 rem Loudspeaker Box Volume Calculator
30 rem Copyright (c) Donald A. Swanson
40 clear
50 home
60 data 0.904,1.015,1.136
70 input "Enter nominal driver size (in) = ";dz
80 for i = 1 to 3
90    rem calculate width (wd), height (ht), depth (dp)
100   read s1
110   ds = dz * s1
120   wd = ds * 1.618
130   ht = wd * 1.618
140   dp = wd * (1 - (1 / (1 + 5)))
150   wd = int((wd * 4) + 0.5) / 4
160   ht = int((ht * 4) + 0.5) / 4
170   dp = int((dp * 4) + 0.5) / 4
180   rem calculate enclosure volume (Vb)
190   vb = wd * ht * dp
200   rem convert cubic inches to liters
210   vb = vb / 61.024
220   vb = int((vb * 10) + 0.5) / 10
230   rem calculate nominal vent diameter (Dv)
240   dv = ds / 3
250   dv = int((dv * 8) + 0.167) / 8
260   print"---------------------------------------"
270   print
280   print " ";vb;" (L)";"   Dv: ";dv;" (in)"
290   print
300   print " ";"w,h,d: ";wd;", ";ht;", ";dp;" (in)"
310   print
320 next i
330 restore
340 print
350 input " Hit enter to continue ";en$
360 goto 40

Calculating Thoroughbred Race Odds With Fibonacci Numbers

A subjective method of making odds from the analysis of thoroughbred horse races.

Symbols And Descriptions

The leftmost column in figure 1 shows the seven symbols used in the method. The left side symbol part (+, N, Ø) is the base. The right side symbol part (+, -) is the modifier. Symbols are usually hand-written with a forward slash "/" as a separator, for example: N+ / + / Ø+. Symbol selection starts with consideration of the base symbols before moving up or down. Symbols and descriptions are to be memorized. Column 3 in figure 1 shows the matching Fibonacci numbers which will be used to calculate the weighted percentages.

Contender Percentage And Confidence Levels

The race is analyzed to decide which horses will be contenders. The handicapper will have some level of confidence that one of the contenders will win the race. A symbol is selected to represent the confidence level. The rightmost column in figure 1 shows the matching confidence levels which are to be memorized. Horses that don't make the cut are labeled as doubtful or Ø.

cp - contender percentage
nc - number of contenders
fs - field size
wt - weight
cp = (wt * nc) / ((wt * nc) + (fs - nc))

Four contenders in a nine horse field with moderate confidence.
4 / 9 / N
N / N / N / N / Ø / Ø / Ø / Ø / Ø
5 + 5 + 5 + 5 + 1 + 1 + 1 + 1 + 1
cp = 20 / 25 = 0.80
cp = (5 * 4) / ((5 * 4) + (9 - 4)) = 0.80

One contender in a six horse field with maximum confidence.
1 / 6 / ++
++ / Ø / Ø / Ø / Ø / Ø
21 + 1 + 1 + 1 + 1 + 1
cp = 21 / 26 = .808
cp = (21 * 1) / ((21 * 1) + (6 - 1)) = .808

Factor Symbols And Combinations

Races with two or more contenders will use one to three factors which are to be arranged from left to right in order of importance, for example: class, distance, form. Factors can be a two-part compound, for example: form-surface, jockey-trainer, form-age, distance-surface.

The N symbol is extended to NN making the neutral base symbols N+, NN, N-. The factor symbols are the right side symbol parts (+, N, -) matched up with Fibonacci numbers 8, 5, 3 respectively. Figure 2 shows the six factor symbol combinations and weighted percentages. A symbol combination is chosen that indicates the relative importance of each factor. The entire contents of figure 2 are to be memorized.

Weighted percentage calculation for the "plus and minus" (+ N -) combination.

8 + 5 + 3 = 16
8 / 16 = .5
5 / 16 = .3125
3 / 16 = .1875

Factors can be doubled, for example: speed, speed, distance making a two factor race. The factor symbol representing the doubled factor must be duplicated in the combination as shown in figure 2. A single factor can be tripled (N N N) making a one factor race.

Example Race Calculation With Weighted Percentages And Odds

Two contenders in an eight horse field with high confidence.
2 / 8 / +
cp = (13 * 2) / ((13 * 2) + (8 - 2)) = .813

Three factors are chosen: class, distance, form with the "plus and minus" (+ N -) combination.

Calculate the factor percentages.

8 + 5 + 3 = 16
(8 / 16) * cp = .407
(5 / 16) * cp = .254
(3 / 16) * cp = .152

Each contender will get three symbols with one for each factor as shown in figure 3 second column.

Calculate the weighted percentages for each contender and factor.

13 + 3 = 16
(13 / 16) * .407 = .331  (#1)
(3 / 16) * .407 = .076    (#2)

5 + 8 = 13
(5 / 13) * .254 = .098    (#1)
(8 / 13) * .254 = .156    (#2)

5 + 13 = 18
(5 / 18) * .152 = .042    (#1)
(13 / 18) * .152 = .110  (#2)

Sum the three percentages for each contender.

.331 + .098 + .042 = .471  (#1)
.076 + .156 + .110 = .342  (#2)

Sort the percentages (pct) in descending order before converting into odds.

odds = (1 / pct) - 1

(1 / .471) - 1 = 1.123  (#1)
(1 / .342) - 1 = 1.924  (#2)

Select the increment (inc) for rounding off.

if odds < 0.3 then inc = 20
elseif odds < 1 then inc = 10
elseif odds < 2 then inc = 5
elseif odds < 5 then inc = 2
else inc = 1

odds = int ((odds * inc) + .5) / inc

int ((1.123 * 5) + .5) / 5 = 1.2  (#1)
int ((1.924 * 5) + .5) / 5 = 2     (#2)

Convert rounded odds into fractions.

n = 0.5  // numerator
d = 0    // denominator
while int(n) <> n
  d = d + 1
  n = odds * d
end
print n,"/",d

Finished calculation shown in figure 4 with percentages and fractional odds.

Figure 5 is a two factor race with the distance-surface factor doubled.
Note that the symbols for each contender are duplicated with the doubled factor.