Thought about this last night, you are probably right about the dick thing but the complete explanation is long. Oh well, maybe I deserve this ...
First off, that page's explanation of how to figure the DP is
1) impossible. There is no way to "measure the addendum" so how are you expected to deduct two addendums from the o.d. ?
2) mentally retarded. Do this instead
Count the number of teeth and measure the o.d. Add two to the number of teeth and the o.d. of the part will be the pitch diameter of the +2 part. For example, if there are 30 teeth and the o.d. is 3.200, then the pitch diameter of a 32 tooth gear with the same size teeth is 3.2" therefore the DP is 10. (32/x=3.2, x=10)
Easy and the normal way to guess at the DP of a tooth. No idea where they picked up that weird-ass plan.
However ....
The basic flaw in all of these discussions is a misunderstanding about gear engineering. All of the calculations in charts are a myth. Like eastern religions, the numbers we talk about are pointers to a concept, not the thing itself. I have never even seen this correctly explained in gear books, since engineers are seldom mystics. They just gloss over the discrepancies with words like "
operating pitch diameter" and so on. But just like religion, it's all wrong and all lies if you take it literally.
For example : imagine that you want a 3:1 ratio on 8" centers. Shafts are exactly 8" apart and you place a friction-driving disc on each one in 1:3 proportions. Now you have a 4" diameter disc on the driving shaft and a 12" diameter disc on the driven shaft. These are your pitch diameters. The REAL pitch diameters. This is the fiction upon which all gear engineering is based.
Is there perfection in real life (tm) ? Of course not. It's a hot day in Phoenix and an aluminum housing in the sun. Expand the shaft distance a tiny bit, say .005" Do the friction discs touch ? No power transmission. The real pitch diameters MOVE with circumstances.
It is not possible for a gear to have a pitch diameter or a pressure angle by itself. It only has these features in relation with another gear at a real distance.
Since we cannot have perfect teeth on perfect center distances with absolute stiffness and no backlash, it is impossible for these "standard" numbers to ever be the truth. So when we say that a 10 DP gear with 32 teeth has a 3.2" pitch diameter, that's a convenience. And it works well enough 90% of the time. But if you depend on this when trying to back-calculate a gear, you can get into big trouble by expecting it to be reality.
It gets worse. Lets take our 3:1 ratio example and put it into practice. I want to transmit 15 hp with this thing, so I'll choose 8 DP teeth. I have tinnitus and appreciate quiet, let's use 14 1/2* pressure angle. Standard sizes, people will have cutters, can transmit that much power no problem. 8" is huge, let's use 4" centers. It's only 15 hp, we don't need a box big enough for the
Enterprise. Numbers of teeth will be 16 on the pinion and 48 on the gear. Perfect.
Oops. Maybe not perfect. I'm going to get undercut on the pinion making it weak and at 16 teeth to 48 teeth, it will wear much faster than the gear. I can make it harder than the gear to help with wear but how about the undercut ?
Take the 16 tooth blank and cut 15 teeth on it. You can do this quite easily with off-the-shelf hobs or shaper cutters. It works great, it's common and the slang term is "drop-tooth gear"
but if you go to reverse engineer this thing with charts off a website, you're going to be in deep poo. Using the simple formulas nothing is going to calculate out correctly. We say it's 8 pitch because it rolls with an 8 pitch rack but it isn't really 8 pitch.
Due to the generosity of the involute curve, different chart pitches and pressure angles will roll correctly together if the base pitch is the same. All the standard formulae are more of a guideline or a shorthand than they are factual, in many real world applications.
Another very common situation is in automotive use. The maker is stuck with some arbitrary center distance but he wants to achieve a specific ratio. The gear designer will drop a tooth here or add a tooth there to change the ratio. In many cases you can do this with off-the-shelf "standard" cutters. But the teeth themselves are nowhere near "standard" anymore. Try to reverse engineer it strictly from charts and you're going to be up shit creek.
Another common case would be replacements. Real world example, Ducati gearboxes were not up to snuff. Metric center distances. I made replacements, DP teeth. Even worse, to make it all fit I used stub tooth cutters and
then for reasons related to dog diameters, interfering shafts in the enclosure, wear and strength desires and so on, all the teeth on both shafts were non-"standard." Reverse calculate that from simple charts and see where you end up.
Let's do another because I like this one. Rear end gears. One drawback to hypoids is the massive amount of sliding they incur. Sliding = friction, friction = heat, heat = bad. With involute teeth there are three basic zones - approach action, where the teeth are sliding against each other, the middle mostly rolling area, then recess action where the teeth are sliding away from each other. Approach is obviously the worst from the standpoint of friction. So the people designing rear ends modified the teeth to have mostly recess action. This is why backing up is way noisier than going forward. Try to reverse engineer these teeth off a chart.
There is more but I will stop
I hope you can see that this isn't just "being a dick." The fictions about pitch, pitch diameter, pressure angle and so on are useful. In many cases they are close to the truth. But it is not realistic to assume that they are
always going to be the truth and you can just insert measurements into a chart to reverse engineer a gear.