Greybeard has sound advice in this matter, so I'd follow everything he's suggesting. Your tillering stick/tree & spring scale will serve you well in tillering.
Preston wrote:The width I can't choose as its already been cut to 38mm, the depth is 19mm and the length is 69 inches
As a guide, I would leave the bow at 69" length (the longer the limbs, the less concentrated the force acting on them & the better your string angle at full draw, assuming a straight limb bow. Tim Baker discusses this in the Bowyer Bibles) and 38mm/1.5" width.
A wider limb spreads the compression loading on the limb across a wider area, so the weaker a material is, the wider the limb needs to be. 1.5" is a fairly standard limb width but it would seem you would benefit from an additional 0.25" width as a factor of safety. You don't have that option, so be careful as you tiller. The point to take home here is that
compression or tension failures for a straight-limbed bow of a given, uniform material are a function of the limb width and the working limb length, assuming workmanship/finishing is up to an appropriate standard.
Personally, I'd take a string and mark the centreline along the length of the board. Then I would find centre, and mark this. I like rigid handle bows, so I would mark 2" either side of centre (Part A - the handle), then 6" either side of centre (Part B - the fade). From the 2" mark to the 6" mark I would taper the board depth from 19mm to 1/2". I would then continue that 1/2" depth for the length of the limb. This will provide you with a 4" handle on a 12" riser with 27" working limbs (assuming 1.5" nocks). A 27" working limb is fairly generous, longer would be better though, for safety. (Edit: I tend to overbuild risers, so you could make the riser much shorter and allow for a longer working limb, say, 2" handle section with 3" fades would provide an additional 2" working limb length).
Then I would cut the profile, that is, the pyramid limb shape. At 6" from centre (the end of the fade) you want the limb full width (1.5"), tapering linearly to 1/2" at the nocks. Always, always, always cut outside the line and then sand/file/rasp to it. From there, I'd measure 1" in from either tip & cut shallow nocks. You can glue nocks on before this or if you're in a rush, shallow nocks on the board will suffice. Using a long string, begin flexing the limbs an inch or so on the tillering stick/tree. 1/2" thickness will probably create a bow that is overweight (I know it would for Spotted Gum, at least, although your timber is somewhat less dense), so you can start balancing the limb bend with only a few inch draw. As you draw further on the tillering tree, you reduce weight. For instance, you want a 50lb bow, so draw a few inches and thin the limbs where/if required to ensure they bend evenly. Once the limbs are bending equally in a smooth arc, draw to 50lb. If this is at 26", or 14", or 5" or anywhere in between, reduce the limb depth a little and retest it on the tillering tree. When you next hit 50lb you'll be closer to your 28" goal. Although I would leave it at 50lb @ 26" or 27" as this allows for the bow to take a little set and still be in the 50lb range at 28" draw.
That's a pretty easy, straightforward, step-by-step guide there. Don't try anything fancy and just keep it simple.
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