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Calculation Resources

771 Views 0 Replies 1 Participant Last post by  ZDP-189
I have made available for download some of my calculation spreadsheets.

While I endavour to ensure the correctness of this data and calculations, they are only my own back of the envelope calculations and I accept no responsibility for their veracity or the consequences arising therefrom. You may use them for your own convenience, but please don't quote from them, share them, post links to them, or republish them in any way (certainly not without attribution). The spreadsheets are generally in the latest xlsx format and cannot be read by older versions of Excel. If you can't read them you will have to convert them yourself. If you have trouble understanding them, drop me a PM.A full list is available at the link above.

Below are some of the individual spreadsheets and their purpose:
Diameter and Mass

This is a conversion formula.

A conversion of Dr. Stephen Wardlaw's roundball.exe insofar as it applies to slingshots.

Terminal Velocity
The terminal velocity of projectiles shot directly skywards.I have many more spreadsheets on my PC and will upload them gradually.

Carnivore Fawn Dog breed Grass Terrestrial animal

Nov 26 2010 11:32 PM

I have added a model for the effect of changing mass on the speed of a projectile and its energy.

There are only two experimental inputs needed; the energy and the bandset-mass constant. Both these must be determined experimentally, so you'll need at least 3 good data points for any given bandset. You then have to fit the curve yourself. It requires a little experimental and Excel programming finesse; I'm sorry that you can't just weigh and measure your bands and run the model as a desktop exercise, but this gives good accurate and replicable results.

As a desktop exercise, you can examine the formulae and better understand the relationship between the bands, projectile and the way it flies.

Carnivore Fawn Dog breed Grass Terrestrial animal

Dec 07 2010 10:52 PM

I have added a model of slingshot band velocity and energy based on Melchior Menzel's paper (2006).Slingshot Physics

Carnivore Fawn Dog breed Grass Terrestrial animal

Jan 05 2011 02:09 AM

I have added a conversion utility to adjust bands for different mass (density and size).

Carnivore Fawn Dog breed Grass Terrestrial animal

Oct 30 2011 12:46 PM

Jorg has recently published a band cutting calculator on his website.


It's a good starting point, but if you are going to use it, I have a few comments for you to bear in mind.
  • I would agree with the length dimensions as long as you use his stretch factor between 7 and 9. The lower numbers give you an unreasonably low draw, especially for anything thinner than TBG. Presumably, you'd take one factor unit off is you are drawing in cold weather.
  • His tapers are a bit aggressive for my taste. I'd recommend a taper factor between three and four. Maybe I need to experiment with more aggressive tapers, but his higher taper factors are sure to cause rapid failure at the pouch tie, especially if coupled with higher elongations.
  • I think his width calculation underbands by about a quarter to a third of the width, producing low velocities somewhere in the 40-50m/s range.
  • His tapers do not adjust when you increase the projectile mass; heavy projectiles will be slower than lighter ones, even though the width has increased.
  • He also did not take into account of the dead mass of pouch and band ties plus excess rubber at the tie. You might want to fudge the dimensions to add a two or three grams.
  • If you use anything thinner than Theraband Gold, you will have to scale up the widths accordingly. Even for TBG, I'd add some, maybe as much as a third.
  • I personally think the pouch dimension output is a little generous for my liking, but that's a matter of personal opinion and some have said I make my pouches too narrow.
  • He doesn't ask the user how heavy (in Newtons, kilograms or pounds) their ideal and maximum draw is, he just says not to try and shoot too heavy a projectile and scales the band width according to the projectile mass.
  • He does not give any indication of a likely ballpark velocity estimate. Partly this would be because the calculation of band width is flawed and would give different results for light and heavy projectiles. Partly I think it's because he doesn't have the experimental data to plot curves for temperature and taper.
In summary, it's driven by three variables (length of draw, taper and projectile size), and is disconnected from velocity. Velocity is a pretty key thing most people would want to know about their bandset and projectile combination.

But all said, it's the only publicly available online band cutting calculator I know of and it's a good starting point for your own experiments. Nobody cuts a better band than the shooter himself, once he has a little experience.
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