Tractrix Horn Vs Exponential Horn Series Of Measurementsnumbers

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Its contour (parabolic, conical, exponential, hyperbolical, geometrical or tractrix).

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I hate to open up this can of worms, but I cant help it, I think of these things.

Tractrix Horn Vs Exponential Horn Series Of Measurementsnumbers

When we use a tractrix horn calculator to give us the expansion rate of a proposed horn, we are given a series of measurementsnumbers that correspond to points, that when plotted out on graph paper, provide us with the angle of the top and bottom of the horn pathway, and also for the curve of the sides of the horn pathway.

When we plot out the angle for the top and bottom, its pretty straight forward, its simply a straight line that is plotted at an angle, that when built, will give us the desired height of the throat and mouth of the horn.

When we plot out the curve for the sides of the horn, the resulting curve provides a controlled expansion (in the tractrix curve) that when added to the expansion provided by the top and bottom angled pieces, adds up to the total expansion needed for the horn.

Microsoft outlook.

How are we doing so far O.k., heres the thing.

I think the curve that is being calculated AND plotted out on graph paper according to the measurementsnumbers provided by the program, for the sides of the horn, is the center plane of the horn, the mid-plane of the horn; and thus, when cutting the curve into the top and bottom pieces of the horn, that curve must be modified slightly because those pieces are at an angle to the center of the horn.

In the picture below, there is a template of the top or bottom of a horn on the left and the calculated curve on the right (cut into a piece of wood).

I have adjusted the curve of the template on the left, so that when it is tilted up (at the angle it will be at when the horn is built), the curve matches the calculated curve of the center plane of the horn, or the piece of wood on the right.

If I hadnt made this adjustment in the curve of the top and bottom pieces, the curve of the sides of the horn would be slightly different than the calculated curve.

Another thing - the curved side of the horn is a curved plane; in other words the curve isnt different from top to bottom of the curved side.

The reason there is a difference in the curve of the top and bottom pieces is because they are sitting at an angle.

So, Im sure there is a slight difference in the curve of the cut of the top and bottom pieces of the horn, versus the curve at the center plane of the horn.

What Im not sure of is which curve the tractrix calculator is giving me.

Im also not sure it matters with the sound of the horn in the end.

Because the side plane of the horn is the same up and down the side, I believe this is the curve that is being given to us by the calculator (which, BTW, is the same curve as the center plane of the horn).

Furthermore, because we are plotting it out on a flat surface (the graph paper), just like we are the angle of the top and bottom pieces, this too leads me to believe that the curve given by the calculator is the center plane of the horn.

So, in conclusion, I believe the curves of the top and bottom pieces need to be modified slightly to account for the difference of angle, so that the side curve of the horn stays the same as the calculated curve.

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