Within a single comment I found myself in a debate regarding the value of skew vs. square when going across the grain and potential for changes in effective cutting angle. Instagram is not a good medium for discussions or explanations, so here we are.
First, skewing an iron in a plane does help performance when working across the grain. Here are a few pictures of a rabbet made going across the grain with a skewed iron and no nicker.
Due to the leading edge of the iron severing the wood fibers at the point that will be the vertex of the rabbet, you get a much cleaner rise (fillet). The fibers of the rabbet's floor are not being lifted prior to them being sheared (detached.)
If correctly skewing the iron does not increase the performance of the plane then it stands to reason that incorrectly skewing the iron (i.e. the trailing edge of the iron contacting the fibers at the vertex) must not decrease the performance, right?
Here is an example of a square iron going across the grain.
The quality of the fillet is kind of in the middle, right?
Adding nickers, of course, changes things.
Anyway, the debate was more about bedding angle vs. a perceived change in effective cutting angle due to skewing the iron in the body of the plane. The debate seemed to come to an end after a simile of walking up a mountain in various patterns. This is a correct comparison, but...
"People that speak in [similes] oughta shampoo my crotch."
A skewed plane works better across the grain because the leading edge is on the inside of the rabbet, makes contact and cuts first. The horizontal surface of the rabbet is ultimately cleaner because the vertical fillet is cleaner. The deterioration of the vertical can lead to the same in the horizontal.
The skew of the iron in the plane body does not change or reduce the effective cutting angle of the plane. A square rabbet plane bedded at 50 degrees has the same cutting angle as a skewed plane bedded at 50 degrees.
Thinking that the skew changes the effective cutting angle in the same manner that skewing a square plane reduces the effective cutting angle is not a direct comaparison. You are measuring two different angles.
To measure the same angles you must measure square to the mouth.
(Note the lines running perpendicular to the mouth)
I am holding the sliding bevel at the appropriate angle here.
Here I am holding the bevel against the body and you can see the slight difference between the two angles.
So a 15 degree skewed plane bedded at 50 degrees will have an effective cutting angle of about 52 degrees if you skew the plane body so that the iron is perpendicular to the direction in which you are pushing just like a square plane bedded at at 52 degrees will have an effective cutting angle of about 50 if you skew the plane 15 degrees from perpendicular in the direction in which you are working.
Still confused? Maybe all of this can be summed up in a picture, which brings us back to instagram:
The plane on the left is bedded at 50 and when pushed in the direction of the arrow probably has an effective cutting angle of 48. The plane on the right is bedded at 50 and when pushed up has an effective cutting angle of 50.