With computer spreadsheets it is relatively easy to work out the formulas for a ballista. I have developed a "Ballista Calculator" using Excel that will calculate the correct diameter of the skein in dactyls, inches or centimeters based on the weight of a stone in minas, pounds or grams. I could not put the Excel spreadsheet into an html format but have provided an image of what the calculator looks like.
The actual Excel formula for calculating the diameter of the skein appears in the box directly below the header. The variables are color coded and the conversion factors are given in the sections following the formula. Using the information provided in the illustration, a person familiar with Excel can duplicate the calculator.
The calculator also computes the diameter of the stone shot -- based on the density of the stone entered into the formula. The sheet shown here uses a density of 2 grams per cubic cm (twice that of water). Average densities of typical stones such as granite, sandstone, shale are between 2.3 and 2.7. Taking measurements from Bishop's drawings of stones of various mina weights gives a wide range of densities, some above but none near 2.6. This may be due to irruegularities in the shape of the actual stones; flat spots or pits would reduce the weight. It could also be due to inaccuracies in the measurements since the scales given in the illustrations are only marked in 10 centimeter increments. Nevertheless, the calculator here shows a general agreement with the actual stones illustrated by Bishop. A more accurate match can be made by adjusting the density number.
The calculator is shown with data for a 10 minas stone, 9.61 pounds, 8,720 grams (the colored section) and a density for the stone of 2 gm/cm3. The predicted size of the stone is 16.09 cm; the illustration of a 10 mina stone in Bishop's book is 16.33 cm in diameter. The calculator is in close agreement with Bishop's actual stone.
As a by-product the calculator also gives conversion tables between the mina, pound and gram and between the dactyl, inch and centimeter.
© 2003, Gary Brueggeman. All rights reserved world wide. No part of this work may be reproduced in part or whole, in any form or by any means, without permission from the author.