flange throat radii. A side effect of this difference is that the "tangent angle" associated with the above radii is quite shallow.
The "tangent angle" is an angle from the horizontal defined by a line that passes through the two points of tangency that exist between wheel and rail when the wheel is located in the EF position. The first point of tangency (and apex of this angle) is located where the tread is tangent to the major top radius of the rail. The second point of tangency is where the flange root radius of the wheel becomes tangent to the rail shoulder radius. As one incrementally increases the rail shoulder radius, this latter point of tangency will change location and proceed further and further around the arc of the rail shoulder radius; thus, the "tangent angle" will progress from being shallow toward becoming more steep.
The drawing associated with this experiment illustrates the cautionary warning related by Joe S. Brook Smith [Brook Smith, 1997]. In that article, and as he concluded his thoughts regarding the significance of the "tangent angle," Joe said; "The rail shoulder radius must never be greater that the flange root radius. On the other hand in modeling terms the rail should never have a sharp corner between its edge and the head, which should itself be radiused as is the prototype."
The rail (BS 95R prototype) shoulder radius specified for P4 is 0.17 mm, a dimension which becomes 0.15 mm when reduced to P87 terms.  Reviewing the drawing, one can see how a small increase in rail shoulder radius would allow a rather dramatic displacement of the side of the rail toward the wheel. The result would be a reduced EF and an increase in the magnitude of the "tangent angle."
More than a simple comparison, this experiment yields practical information of interest to any " P87 basher" of P4 wheels. Since the intent is to end up with a hybrid wheel that retains the P4 flange throat radius but is "bashed" to achieve a close proximity to the flange width and overall wheel width of a P87 wheel, some metal must be removed from the back of the P4 wheel and the flange reduced to a new shape and depth.
The drawing reveals the offset between the backs of the P4 and P87 standard wheels, when both are located in the EF position. The offset is

0.065 mm. This is greater than the 0.06 mm set forth in the hypothesis used at the outset of this experiment. And, it is less than the 0.07 mm that Dave Doe mentions [Doe, 1998]. Here, the pertinent observation is that removal of less than 0.065 mm of metal from the back of a P4 wheel will result in a wheel with an EF that is even further over the max limit than the EF exhibited by a "proper" P87 wheel (Again, this is when both wheels are placed on track constructed with ME Code 70 rail.) In view of the fact that a "proper" P87 wheel has here ended up with an EF at 0.02 mm over max, it looks like Dave Doe's suggested dimension of 0.07 mm has a lot going for it.
One final bit of useful information derived from this experiment is that the difference in flange depth between the two standard wheels when in EF position is 0.050 mm. The drawing also shows that, when both wheels are in EF position, the P4 contour takes away metal (not much - but some) that exists further down the face of the flange of a P87 wheel. At this point, the ramifications of this latter factor, as it may relate to actual operation, are speculative at best.
I think if I were playing Bucky Beaver at my kitchen table with the Emery paper on a piece of plate glass, I'd reduce the P4 wheel flange depth as the first operation (though for this operation it would be the file held against the wheel being revolved by whatever was handy to spin it.) I'd aim at first for a flange tip that is flat and horizontal across the width of the flange. It is easier that way to control the diameter reduction and measure progress as you go. After the wheel diameter, as measured over the flange, was correct, then I'd start "figure eighting" the back side on the emery paper.  After that, it's basically a kiss with the file on each of the corners of the flange to dispose of the remaining excess metal and the flange side of the wheel would be done. Then it's scrubby - scrubby - scrubby in a figure eight pattern on the front of the wheel to get the whole shebang down to desired width.
In conclusion, modifying a P4 wheel will not result in a "perfect" P87 wheel, but the modeler can come pretty darn close.
The Practice - René "Bucky" Gourley