This paper is adapated from the book “Firework Displays:Explosive Entertainment” by Dr Tom Smith (BPA Secretary) – details of the book and ordering information are available at http://www.fd-ee.com
Shellcalc © has been adopted by the BPA and many other organisations around the World as the de facto means of predicting shell and comet trajectories. It does not address “normal” fallout but it can be used with other calculations to predict “normal” fallout from aerial fireworks.
Shellcalc© is a tool developed by John Harradine(1) of Queensland, Australia following investigation into an incident at Bray Park and modified by the author of this book (2) which produces numerical and visual representations of shells and comets in flight for use in planning “safety” distances.
The program, written in Microsoft® Excel for convenience, has been extensively modified and allows inputs as shown in the table below:
Table – Shellcalc© input parameters
|Type of effect
Shell or comet
|If “Shell” is selected a burst diameter is calculated and a possible fallout trace is produced. If “Comet” is selected then the projectile is assumed to be consumed during flight|
|Units||Metric or Imperial|
|Calibre||Diameter of projectile|
|Mortar angle||Direction fired from vertical|
|Muzzle velocity||Entered if known, otherwise standard values used|
|Fuse delay||Entered if known, otherwise standard values used|
|Shell mass||Entered if known, otherwise standard values used|
|Tumbling/mortar drift||Allows a factor to be introduced to simulate barrelling and tumbling effects. If this is not present a shell fired vertically would land exactly where fired if no wind parameters are entered|
|Wind speed||At ground level|
|Relative wind direction||Relative to the firing angle|
|Elevation of launch site||To allow for changes in atmospheric density etc|
|Height of launch||Height of launch point above the ground – introduced to allow for firing from buildings and to permit debris to extend below launch height|
|Terrain category||To accommodate open, wooded or built up areas.|
Output from the calculations is produced graphically and in a tabulated form. A selection of typical outputs is given below. Note that the depiction of the shell burst diameter may be distorted depending on the axes that the program selects to display the results – the alternative would be a highly extended “y” axis in the majority of cases.
Figure – 4” (100mm) shell – Fired 5 degrees from vertical with low wind
Shellcalc© can also be used to model the trajectories of comets and this is particularly useful for the risk assessment of firing single shot items from buildings. In this case Shellcalc© allows modelling of below horizontal firing and allows modelling of “blow back” onto the building in extreme conditions.
Figure – Comet fired from a building
Taken together the calculated data from “normal” debris distances (which are relatively low hazard but high frequency) and shell failures (which are high hazard but low frequency) allow the display designer to design a display which presents an acceptably low risk, whilst also provides objective criteria for curtailment or cancellation of the display.
We usually work on a normal maximum wind speed of Force 4 – this allows a display to be designed to accommodate the vast majority of conditions that would normally be encountered for displays. If the wind is stronger than this then it is likely that other safety considerations will need to be considered anyway.
Figure – 6” (150mm) shell with deliberately extended fuse time (i.e. shell fuse failure) – note the position and extent of the predicted burst
From all the data we have amassed and calculated, and with a knowledge of the material chosen for the display we usually then prepare an objective “contingency” table for the display which details what curtailments will need to be made as a function of wind direction and strength. Direction is important because it may be that from certain directions an additional risk is posed (i.e. towards the audience or other hazards) but if the wind is blowing in the opposite direction then a greater wind strength can be tolerated before curtailment or cancellation is necessary.
(1) J Harradine & T Smith, Journal of Pyrotechnics, 22, 2005, 9-15 – http://www.jpyro.com/wp/?p=23
(2) See revised version of Shellcalc© at http://www.jpyro.com/wp/?p=1193