Why would the point at which the transistors conduct be off AK ? This bit I don't understand. If these values are known then why can't the transistor turn on be worked out.
Because the point is NOT a point. As the voltage across the base-emitter junctions increases, the transistors turn on over a range of values anywhere from 0.3 V for a single small transistor to 1.5 V for a giant power darlington. AND, that value increases as the collector current increases. The standard approximation that Vbe = 0.6 V (0r 0.7 or 0.65 or whatever) for a single transistor is wrong 99% of the time. That is because it is an approximation describing the average behavior of thousands of part numbers, not any one part. Your circuit will use one part, it is a darlington, not a single small-signal part, and a power device to boot. These details matter way more than any rule of thumb. Many people spout these "rules" as if they are actual rules. They are not, and knowing that separates the professionals from everyone else.
Its hard to get my head round the huge differential between 25 ohms and 200 ohms and how the circuit is affected by both in terms of power values (Voltage and current) and the doubts I've seen in other posts, as to whether its possible to bias these transistors at all.
Of course it's possible. Steve and I present two different possibilities. Neither is right or wrong, something you clearly are looking for. Give it up; there is no one right answer. If the 7812 is in a place where it can't touch a heatsink, then adjust its current lower. If you want it to control the output more directly by increasing the ratio of its static (quiescent) current to its output current, adjust it higher. I keep pointing out that these are decisions to be made by the designer, you, based on how you want the circuit to perform.
Don't forget there have been two separate posts from two different members saying you don't need R7 at all. Although I've worked out that's a bad idea now. But early on in the thread, for a while I did think "really" no R7.
Eliminating R7 is just plain stupid. The 78xx parts have been made by dozens of manufacturers around the world for decades, and every datasheet that has this circuit has R7 in there for the same reason, so I'm glad to see you stick with that body of knowledge.
then some one said the regulators queicent would bias the transistors !
Technically, it can. But all possibilities are not equally smart. And, inside each power darlington transistor there already are resistors across the base-emitter junctions. If the 7812 were actually a 78L12, with a max output current of only 100 mA and very poor thermal properties, then we would be discussing using those built-in resistors as part of the biasing circuit, another uncontrolled variable that wiould affect the overall circuit performance. But fortunately we don't have to.
"Really" I thought queicent current was the regulators no load resting state.
Quiescent current *is* the regulator's resting state, the static or no-load current it needs to function. Internally the regulator has a voltage reference, an error amplifier, a power amplifier, a current sense circuit and a temperature sense circuit. All of that takes a small amount of current to function even when the output is disconnected from any load, and that current flows from the input pin to the ground pin. It also varies from part to part, and with temperature, and with the load current, which is why I don't think it should have a major role in determining when the boost transistors start to kick in. Working from memory, the 78xx series static current is around 8-10 mA. Choosing R7 so the boosters start up at 100 mA means that their startup is determined 90% by the load current and 10% by the static current. Again, a design choice based on my opinion, based on my experiences.
I can take voltage and current measurements in circuits easily, yet I can't pin down a value for R7 on paper for the MJ11015 transistor.
Then stop trying. There is no one right value. There wouldn't be even if the boost transistors weren't darlingtons (which does make things less precise). You have a range of acceptable values. Pick one, take real voltage and current measurements, let us know the results, and we can discuss any adjustments. It is T.H.E O.N.L.Y W.A.Y to determine how the circuit performs in the real world.
You don't know me, or Steve, or Colin, etc., which makes this risky. Rather than just spout unsupported assumptions, Steve and I have presented two positions that are the boundaries for R7, complete with the supporting math. Now, as it has been from the beginning, it's up to you.
ak