A

#### Andy Sandford

I have a formula that converts the diameter of a circular duct into it's

equivalent rectangular counterpart. This formula is used to populate a

table, a section of which is detailed below:

Width

100 125 150 175 200 225 250 275 300 325

100 110 123 134 145 154 163 171 178 185 217

H 125 138 151 162 173 183 192 201 209 240

e 150 165 178 190 201 212 222 231 260

i 175 193 206 218 230 240 251 279

g 200 220 234 246 258 269 297

h 225 248 261 274 286 313

t 250 275 289 301 329

275 303 316 344

300 330 358

The top row of the table is the width of the rectangular duct, the left hand

column is the height.

The cells within the body of the table are the circular duct equivalents.

e.g. The rectangular equivalent to a circular duct of diameter 201mm is

therefore either 275mm x 125mm OR 225mm x 150mm

I need to search the body of the table for the closest match to a given

diameter (n1) and return the numbers in the corresponding top row and

left-hand column (width and height).

I need to return a single result based on the following constraints:

1) The initial circular match in the table needs to be equal to OR higher

than n1.

2) The height of the rectangular element needs to be less than or equal to a

specified value (h).

3) The ratio of width to height needs to be as close to 1:1 as possible.

e.g. Required circular duct diameter (n1) = 233mm, Maximum height of

equivalent rectangular duct (h) <= 175mm

Closest selection in the body of the table is 234mm, but this does not meet

point (2) maximum height (h)

The next nearest selection is 240mm, but this occurs twice.

Based on aspect ratio, point (3), the best solution is therefore 275mm wide

by 175mm high (1:1.57), rather than 325mm x 125mm (1:2.60).

I hope I've given you guys enough info.

Thanks to you all in advance!

Andy