Mass - Velocity and Kinetic Energy Curves

I hope that the above charts will be useful for people selecting a bandset and tailoring the shot weight, band length and draw length to their needs.

Some comments on the measurements:

• Temp: 29.9°C
• RH: 75%
• Altitude: ca. 150m MSL

The exercise is on a best-efforts basis; the method is not totally scientifically rigorous, but it's the best I can do for now. Each datapoint is an arithmetic mean of between 3 and 5 shots depending on how close a velocity grouping there was. Outliers were excluded if they resulted from a fork-hit.

Some comments on the charts:

You can calculate elongation by the second length divided by the first length minus one. The force figure is the draw force at full elongation. In the BB White chart this is (711mm/216mm)-1 or 230% and the force is 53 Newtons
The X-Axis shows the mass in grams
The Left hand Y axis shows the velocity in m/s (red line) at a given mass
The Right hand Y axis shows the kinetic energy in Joules (blue line)at a given mass

The velocity is less for heavy shot
The kinetic energy is more for heavy shot

Where the velocity line would intercept the left hand axis if extrapolated is the speed the band would achieve if there was no mass. This is finite and limited by the bandset at a given length and elongation.
The kinetic energy is zero at if the mass is zero. It reaches a maximum. If you don't stretch the band to the elastic limit, there is still some slope left in it at heavy masses but you obviously can't exceed the maximum if you pulled it as far as it would go.

Look at the top right chart ZDP-189 Fastbands 152mm slack length of elastic drawn to 711mm. At 370% elongation, it's at the elastic limit. Firing masses above 30g, it delivers no more energy and the velocity is less.

Don't take your bands to these limits! Over drawing and using weights too high or low is dangerous and strongly reduces band life. You want the sweet spot where there is a lot of slope in the lines. For my standard Fastbands, I recommend no less than 90gr (6g) and no more than 170gr (11g) with an ideal midpoint being 140gr (9g).

I like about 40-50m/s. More is nice, but I don't want a big draw weight penalty. Less than 35 m/s feels slow.

Over drawing gives more speed and energy, but it is less efficient. You can get similar results at a lower draw weight with about an inch more slack band and 6" more draw.

Heavier bands give more velocity and kinetic energy, and are more tolerant to heavier weights, but are less efficient at lower weights so you pay a penalty in much increased draw weight.

I have tuned my bands so that they give high velocity at the ideal weights of 6g to 9g, but are light enough to draw so that they are easier to draw, aim and release in a straight line. They wouldn't be much more accurate if they were lighter; 13-14 lbs is about the cut off where more weight is less accurate and less weight isn't much better.

A band can shoot a range of shot weights. As you reach the top end, you can always draw a bit more to make up for the extra inertia. That's why you can get different answers from different people. However, it is best to find bandset, mass and anchor point combination that suits you and your style of shooting and stick with that as much as possible. I hope these charts help you start to find your best combination. I will post more bandsets from our vendors in this blog post later.

Thank you very much for this Dan, I've wanted to do something similar myself for a while now but you've saved me the enormous expense and effort involved, you are a gift to the slingshot community!

We've needed this data for a while, now we can extrapolate it and use it to determine the optimum projectile weight for the rubber materials you've tested by simply using their mass! Might be something good to add to my 'Slingshot Calculator Compendium' ? Anyway I must retire to bed now as I'm very tired!

Most satisfactory.

Excellent!

Were the bands drawn and quickly released?

I would love to see the results of a quick release compared to a 1 minute hold and release.

Thanks.

boyntonstu, on 30 August 2010 - 11:47 PM, said:

You can do that yourself, with a simple pair of fishing scales...

boyntonstu, on 31 August 2010 - 06:47 AM, said:

Yes, they were released within 1-3 seconds of reaching full length. I may do such testing of the effect of hold delay later with a variety of bands exploring different variables (thin/thick, hot/cold, various materials), but these bands are designed to be shot by hand and are not optimised for a sling-bow. This particular round of testing is intended for the datasheet that is supplied with my bandsets.

I also wanted to test some other bands for comparison purposes. They look pretty good in the 3g-11g range, but it's not totally fair because Ultimate Bands are "big ball bands" that are optimised* for steel ball of about 18mm diameter and above and Bunnybuster's white bands are for the traditional-styled buyer. I should do some Express Bands. I expects those to be very similar and it will be down to the lighter pouch of the Fastbands vs Tex's special natural latex. My bands stack up well against Express bands, but in longevity, rather than velocity.



{*Optimised in terms of efficiency. They're faster than my bands even down to about 6g, but only just a bit and the pull strength is almost double; enough to make my hands shake, my elbow creak and risks damage to the tendons in my thumb with prolonged use.}

Well let's be frank, your Fastbands slaughter just about everything else on the market in terms of longevity, although I believe the improvement may also be partially down the smoothness of the forks they're attached to?

BTW if anyone hasn't seen Joerg's excellent review of Tex's Express Bands you simply must watch it now - 20.5ft/lb with only a 16lb draw weight!

very, very interesting!
Thank you for your work.
Thomas

thanks for your info.

Very helpful. More bandset studies please ! :)Also, it'd be great if the axes could be labeled, so they can be read at a glance, without having to scroll down several posts to find the key.BTW, I'm a little confused by the chart groupings. For example, for the "A+ Ultrabands" you have 2 charts, one for 197mm slack length with a max draw length of 711mm (102 newtons), and another for the same length of bands with a max draw length of 846mm (120n) ... how can the same length of bands have 2 significantly different max drawlengths and draw forces ?Did I miss something ?

Darb, on 27 October 2010 - 10:08 PM, said:

If you pull it harder, you will draw it further. The distance is the draw length at that peak force. Not everyone will draw a band till the very elastic limit, especially Ultrabands and Hunter Bands. Different anchor points, arm lengths and strength sets people apart. If I just assume everyone ties their bands the same length and draws to the very elastic limit, it would be incorrect for the majority of people. By showing multiple tie lengths and in this example on tie length pulled hard vs not so hard, users can guestimate using interpolation how far they may draw it with a certain force, how much energy is stored and how much velocity they will get out for a given mass. OK, it's not linear, but I've published force-elongation curves elsewhere and I seem to remember that I discussed above how to fit the data to a formula for energy to mass for a given bandset.

Forgive the complexity, but there are many variables that factor into velocity and I am being complete by stating as many variables as possible so that people can replicate the results or integrate them into their own models.

Darb, on 27 October 2010 - 10:08 PM, said:

This blog is my own notes (which I'm happy to share) and not intended as a text book, so I no plans to redo my charts.

Remember how I'm presenting the data - I've put them in charts uploaded as images. I have to include lots of variables not normally included in charts, like what kind of bands, the initial length and max draw length and force so that if they get jumbled up or moved around in cyberspace or reposted by somebody then they still show context. I don't want a dataset showing bands tied short and under-drawn to be used to make a bandset look weedy. Likewise, I don't want someone to show a bandset tied at butterfly length and drawn to the elastic limit to be used as a representation that that's what the average user can expect to get with a more conservative draw. There is a limit to how much information I can show. Besides, it is useful to make people come back to this page for an explanation. The only unlabeled axis is the X-axis and that's in grams of projectile mass. The others are (kind of) represented by the legend showing Velocity to the left and Kinetic Energy on the right.

Darb, on 27 October 2010 - 10:08 PM, said:

All in good time. I'm not holding back, I just have limited time and I'm focused on the Fastbands right now.