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W/D³ Explained
Written by Justin Weaver
To quote Dr Jim Watts."If a wool fibre produced at different levels of nutrition retains the same ratio of fibre length to fibre diameter and the same cross sectional shape, the weight of the fibre will be proportional to the cube of its diameter. It follows that since the number of fibres does not change at different levels of nutrition (except under very severe and sudden under nutrition) the ratio of fleece weight to the cube of fibre diameter must be constant at different levels of nutrition." *
What Jim is saying, in layman's terms, is that W/D³ gives you a figure that you can use to compare between animals of different micron and fleece weight. The higher the figure the more productive the animal. This is an oversimplification but this is all most breeders will need to know about the figure.
The next question is why we need this figure in the first place? The answer to that is far simpler. To quote Dr Jim Watts again, "Consistent increases in W/D³ values for a flock or mob over an extended period of time show that genetic improvement is occurring in your enterprise." So, in other words, we can use the figures to show how our herd is progressing from a production (micron & weight) perspective.
The figures that we use in the formula are common ones, which most breeders record at shearing time each year - clean fleece weight and fibre diameter.
Clean fleece weight (W) is the weight of fibre from one alpaca, worked out by multiplying the total fleece weight shorn off one animal by the yield. The yield is the percentage of clean fibre present, and can be tested or estimated. Alpaca yield ranges from 80-90% according to AAFL.
Fibre diameter (D) is the micron measurement taken from a midside sample, and then cubed (e.g. 23x23x23= 23³). Some more examples of workings are shown below using Halcyon figures.
Shearing |
Ave Micron |
Ave Flc Wgt in grams |
Workings |
W/D3 |
1999 |
24.12 |
2350 |
(2350 x 90%) / (24.12 x 24.12 x 24.12) |
0.15 |
2000 |
23.40 |
2570 |
(2570 x 90%) / (23.40 x 23.40 x 23.40) |
0.18 |
2001 |
23.68 |
2580 |
(2580 x 90%) / (23.68 x 23.68 x 23.68) |
0.17 |
2002 |
22.93 |
2730 |
(2730 x 90%) / (22.93 x 22.93 x 22.93) |
0.20 |
2003 |
21.18 |
2960 |
(2690 x 90%) / (21.18 x 21.18 x 21.18) |
0.28 |
2004 |
21.04 |
3260 |
(3260 x 90%) / (21.04 x 21.04 x 21.04) |
0.32 |
2005 |
21.60 |
3500 |
(3500 x 90%) / (21.60 x 21.60 x 21.60) |
0.31 |
2006 |
20.35 |
3560 |
(3560 x 90%) / (20.35 x 20.35 x 20.35) |
0.38 |
For reasons of uniformity and to allow progress to be tracked over time, we suggest that the second shearing alpaca be tracked. That is the whole of your second shearing alpaca have W/D³ worked out and an average taken for this group only each year. This will give you a figure that can be tracked via a line graph to show trends in genetic progress. An example of the graph which can be produced is shown below using Halcyon's figures as a guide.
References
* Watts , J.E. and Hicks, J (2002): The Soft Rolling Skin® (SRS®) Breeding System for Alpacas: Australian Alpaca Association National Conference 2002 - The finer future: AAA Inc.: Pg 159
**Australian Alpaca Fleece Limited (AAFL), Fairbairn Rd, Sunshine, VIC, Australia .
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