If I have a vertical cutterhead in a moulder with a 20 degree hook cut angle with a cutter knife ground to have a 45 degree angle, when the wood is passed through the machine the actual wood face will actually not be 45 degrees and it will also have a slight arc on the face and not perfectly flat?
If the cutter head had a zero degree hook this would make a true representation of the knife.
But the hook angle actually distorts the desired outcome, correct?
Is there a formula to overcome this phenomenon?
I can make the knife template any way its needed to be to counteract this.
Anyone out there with an idea or even know what I'm on about!?
Thanks

The hook angle only has to do with proper geometry to make the cut with the least amount of chip out. It will not change the angle produced by the angled cutting edge. Easy to prove, put on the cutter and cut scrap. I have more trouble with the 45 actually being a true 45 if I intend to make miter cuts.

Hi. This is exactly what I thought too, but a custom tooling company has told me otherwise. I intend on making the cutter head to see for myself.
The object I'm working on has many miters and they tell me the runout will compound to be quite substantial by the end..
Very skeptical.. I'll be back with results!!

"Angular distortion" or Circular Distortion" are the two names I have bestowed upon the effect you describe. As I know it, there is no formula.

I first noticed it in roundover knives where a nice quarter segment of a circle, ground into the knives would come up short. I'd have to lengthen it a bit to make it produce a quarter circle.

Commercial grinders that grind the knives in the head adjust for the Circular Distortion as a matter of machine design. The template is made to show exactly what is needed, not 'sorta' like. You mentioned a template, so does your grinder adjust for the distortion?

i just ran across an explanation of this in 'modern shaper practice' by WH Rohr. Chapter XIV, pages 135-148 give some explanation. I'd heard of the phenomenon, but have not enough direct experience to be much help - perhaps Rohr will. The book is available to view online, but i ordered an on-demand print copy for under $20. Despite being a century old i found much practical info in it. Lots of production oriented jigs, setups and geometric information i had not run across before. Also lots of less helpful - but cool! things like 'attache a leather strap to the spindle to blow away chips'.

If you have a piece of molding to match. You can cut the end off at 20 degrees (if 20 degree hook) and trace the template directly with the bevel held flat.
Another method, a bit more scientific is illustrated in the drawing. You layout the cutterhead then calculate the elongation by dividing the short projection at 0 degree hook into the longer projection of the 20 degree hook. Trace the profile on standard graph paper (.25 X .25 Grid) then using a custom grid paper with the horizontal dimension elongated by the factor calculated, layout the elongated version by matching the intersects. You can also use cad software to stretch the profile by this factor in the horizontal direction.
The amount of elongation is a function of the hook angle as well as the radius of the cutting circle.
When I first started grinding shaper knives on a bench grinder I would simply grind the profile directly on the knife knowing it would come up short, then run a piece and compare it to the desired profile, then adjust the grind accordingly thus sneaking up on the profile.

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Thanks for the replies!
It turns out I wasn't understanding the tool maker properly..
what he was trying to explain was the disconnect between grinding shaped knives on his grinder then inserting them into my head. If the tool radius wasn't the same the wood profile would be skewed after I run in my machine. Which makes sense, even if the both have the same hook angle..
I made a straight angled cutter and put a straight edge on it, it has a slight radius as I was told there would be. So for fun I moved the knife outwards and re ran.. its wasn't a flat cut anymore..

If the cutterhead pocket is vertical, the profile has to be stretched out according to the rake angle to cut the desired shape. There is an additional effect, which I suspect is what you are seeing, when the pocket is skewed from vertical as in a "shear" head. A straight knife in a shear pocket will indeed cut a curved profile. The amount of curve depends on the shear angle and cutter diameter. Here's a thread from another site that touches on this phenomenon.

flush trimming on shaper