No, the numbers are not wrong, at least I don't think I made a mistake coding the formulas in Excel and I did sample checking with DOF Master. The numbers I used are all there, you are welcome to reproduce my calculations: I gave you the focal length that I measured for each scope and if that was measured wrong at least I measured them the exact same way. You know the diameter of the objective lens.
I did state I was using a CoC of 0.030mm for everything. This last one is definitely something that can be argued and modified. I've long asserted that at high zoom values, one should reduce the CoC accordingly and I am a big proponent of a CoC of 0.020 past 3-4X zoom. I can tell you that when I focus my 4.5-28X52 at 200 yards and stay below 15X, the DOF is huge.
That said, my goal here was not to present guide numbers but to try to answer Bill's question regarding the relationship between length, objective diameter and DOF and I think my numbers tell the story. A smaller objective will produce a deeper DOF. That's the reasoning behind the modifier disk provided by March for many of its top end scopes. But the difference between the 5-42X56 and the 4.5-28X52 to which Bill alluded had the added twist of the 4.5-28X5s having a shorter focal length than the 5-42X56 as well as a smaller diameter objective. One would have thought that reducing both FL and Objective would produce the same DOF for the 4.5-28X52 as the 5-42X56. As the numbers show, in this case, the reduction of the focal length trumped the reduction of the objective length, for the DOF.
Now, If I change the CoC from 0.030 to 0.020; the 200 yard values change dramatically, as I expect them to: For the 5-42X56, the DOF runs from 145 yards to 354 yards. For the 4.5-28X52; the DOF runs from 130 yards to 483 yards. This is what would would find "empirically" if you were using a higher zoom setting.
First of all, I apologize that it looks like I am picking on you. I am not. However, you are trying to port calculations from the photography world into this and are making some rather incorrect assumptions. The internet retains everything, so I really want to make sure this is corrected or someone will dig this up a year from now and walk away with all these pseudo-technical half-truths as the holy grail because they sound impressive.
The numbers are wrong because of the exact things you pointed out: depth of field varies with magnification. The statement when focused at 200 yards "For the 5-42X56, the DOF runs from 145 yards to 354 yards" is completely and utterly meaningless without saying what magnification it is at (however, since you your CoC reasoning is grossly wrong, if it is accurate somewhere that is purely coincidental).
Depth of field depends on the F-number of the objective lens (ratio of focal length to the objective diameter, assuming that is the aperture stop. You are kinda saying it, but not explicitly unless I missed it. That is an important thing to make clear.
Objective diameter we know. How exactly did you measure the focal lengths? If you are trying to be rigorous, you should ask March what the focal lengths are. There is no way I can think of to measure it exactly without talking to the designer of the scope, or taking the whole thing apart and doing some measurements. You do not know where exactly the FFP is located. It is not always right under the turrets. Also, March has used a somewhat complicated objective design in the past, at least once that I can think of, where even if you knew exactly where the FFP was you would not be able to figure out the focal length. I do not know if March is OK with the exact focal lengths of their objectives published, but you can ask if you want to be serious about it. If I was them, I would probably not release it. From a competitive info standpoint, a couple of numbers like that and I can figure out all sorts of stuff about the internals of a scope.
Another point: how do you know the erector system is not limiting the DOF at one of the portions of the magnification range? Those lens systems have F-numbers too.
Finally, your CoC assumption copied over directly from the photography books can only be correct by accident.
If you really want to figure out the CoC, you need to map the resolution limit of the human eye, via the eyepiece and the erector, onto the FFP. That will give you a CoC that is likely different at every magnification if the objective is indeed the limiting factor here.
Standard photographic CoC assumptions absolutely and unequivocally do not apply to riflescopes.
If you really want to figure this out in a somewhat rigorous matter and if March is comfortable with you releasing the focal length numbers (I sure as hell will not be releasing them), you can calculate appropriate CoC to a reasonable degree from a set of uncomplicated empirical measurements.
Set up both scope at the closest or thereabouts focusing distance on a range where you know distances with great granularity and physically measure the DOF at each marked magnification.
From that, you can figure out appropriate COCs and extrapolate the rest numerically. The results will be accurate for your eyes, but if you have reasonably healthy eyes it should be close to most other people.
If you really want to get to the bottom of this, you should also repeat the measurements in low light when your eye pupil is dilated.
Now, onto the good part: while quantitatively, there is definitely some work to do here, qualitatively, you are absolutely correct.
Here is a brief history of how the 4.5-28x52 design came to life:
I was testing a prototype 5-42x56 for March and I also had the 3-24x52 on hand. I thought that new 5-42x56 March absolutely kicked ass, but turrets could be a little different (that's how we ended up with the new locking turrets) and that there was also room for a smaller scope between the 5-42x56 and 3-24x52. That could also be an interesting opportunity for March to have a riflescope with a little more depth of field, and somewhat different erector optimization that more traditional March designs.
I reached out to March with a few suggestions that are mostly proprietary, but one of them was: if you dialed back on erector ratio a little and optimized it to be as good as humanly possible between 15x and 20x (which is there I do a lot of shooting), what could you come up with?
The 4.5-28x52 is what they could come up with and it is really excellent.
Fast forward to today and when I look around my office, there are two early production 5-42x56 March scopes within arms reach, one early 4.5-28x52 and they are building another one for me. For what it is worth, I also still have that 3-24x52 on a large frame AR. As I said these are really nice scopes.
To be clear, there were other people providing feedback to March. It wasn't just me. However, I was in those conversations and the request for the 4.5-28x52 or something along those lines came from steel shooters.