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Equal Measures Part 2 - Scaling Up or Down

   written by Jean Turner
Published: FlyDresser - ??

Having started up a card system for the quick and accurate duplication of a minimalist number of flies (my 'windows' for any activity are around 20 minutes max), I sat down one fine afternoon, ready to whip off a few examples of a fly to use in a competition that was coming up.

I fished out all the necessary ingredients for the fly, stuck my hook in my vice and pulled out the relevant card with a flourish. Holding the card up to the hook I had chosen, I was dismayed. The marks on the card did not match up at all to the hook sitting in the vice. How to solve the problem?

Firstly, I had to decide what the problem was. The difference in the make of the hook meant the scale of the hook was not the same - the gape was different in proportion to the hook shank length, and the bend was in the wrong place. Hearing my sighs of frustration, my ever-supportive husband came to the rescue. Being Rick, he never, ever gives a straight out solution to anything. He will simply throw a term or two into the conversation from which one is required to self-help. This occasion he divulged his little secret formula in one word: 'Perspective.'

Yeah, right.

But he was right. Once I thought about perspective, all became clear.

Western world artists centuries ago came up with the principle of perspective - a vanishing point on the horizon toward which all lines go. Remember art classes at school where they made us draw little boxes with slanted sides, and then extend and join up the lines on the sides so that they all disappeared neatly into a single point further on? Then we had to draw more little boxes within the lines between the original box and the vanishing point and compare what they looked like.

Point one: The principle of perspective is that no matter where you are along those lines, so long as the same points on the item drawn touch the same perspective lines, the item will be in proportion to any other item in a different place within those perspective lines - irrespective of its size. (fig 1)

Point two: No matter where you start within the closing funnel of the perspective lines, any item which falls between the first item and the vanishing point will look proportionately smaller than the first item. (fig2)

So using this 'optical illusion' to our advantage...

If you place a card directly in front of you (marked up with your 'equal measures' lines), and then position a second card further away from you then the first - perspective laws dictate that the second card will look smaller in all proportions. By manipulating this vision, and by marking similar size markings on a proportionately smaller card - we can increase the relative size of the marks to the size of the card we are marking on.

Likewise if the new card is in front of the old - we can relatively decrease the sizes of the marks to the size of the card. It sounds very complicated, but is in fact the simplest method available to scale pattern sizes down and up. Thus we can change any pre-marked pattern card proportionately to fit any size hook. What a boon!

Let's be practical and give an example:

I had a size 10 hook in the vice. The old card I had made up was for a size 12 hook. On the new card, I marked the exact new hook shank length (size 10 hook) by referring directly to the hook I wanted to use.

For any scaling operation we need two reference points on both cards. The first will be the corner of each of the two cards, held so they line up with each other visually. The second is the hook length mark on each card. (fig3)

I held up the new card behind the old - that is to say on the other side of the old from my eyes. I then moved it back and forth within my plain of vision until the two marks and the two corners of the cards lined up together. Carefully holding the card in that position, I made light marks with an easy-mark pen on the edge of the card to coincide with the rest of the marks on the original card, constantly checking that the hook shank length marks and the corners of the cards still lined up. Make all your marks, take the card away and voila! You have an altered pattern size. (fig4)

Gape width sizes can be altered independently the same way. Mark the new gape with and a starting point, then by visually comparing the marks on two cards, intermediate newer marks can be proportionately changed.

Scaling up is done by holding the card between the original and the vanishing point. The card looks proportionately smaller, and so by copying the marks, you actually proportionately scale things up. Scaling down is achieved by holding the new card between the original and yourself - i.e. further away from the vanishing point.

The alternative to this method - (and perhaps the most accurate one if you have the shakes at all) is to start from scratch with a new card using the method I described in the first article.

This 'Scalar Method' is used for proportionately-correct scaling up and down in all sorts of areas of life. Pipe-organ pipes in relative sizes (and thus tones) are made by using this method (with slight viewing adaptation) and turners also use it regularly to size items up or down on a lathe.

This system requires little brain power - which is a good thing when your children interrupt you for something every few minutes. It certainly beats using a ruler.

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