the deal betwen Packard and R-R was 50-50 production split and the P-40F/L consumed all of FY 42 Priority and funding for the Merlin XX (1650-1).
I don't know what the deal started out as but it wound up as an initial contract for 9000 engines, 1/3 for the US and 2/3rds for the UK with peak production at 800 engines per month.
aside from that I have no argument with anything in you post.
Follow up contracts and changes to contracts get short shrift in most common accounts.
It took Packard until March of 1943 to complete the original contract but I don't know when the follow up contracts were signed or what the details were.
We do know that Packard built almost exactly 800 engines a month for the last 6 months of 1942.
The US may not have taken delivery of the full 3000 engines from the first contract.
Packard did build over 26,750 two speed engines by the end of 1944 and just under 18,600 two stage engines by the end of 1944.
By the summer of 1944 Packard was building over 2000 engines a month.
That is from the historical production perspective. Changing the numbers of engines built in 1942 requires more factory space, more machine tools and more employees.
In some cases expanding Packard production may mean something else may not get built, tank engines? Landing craft engines? a different aircraft engine?
perhaps somebody could have beaten some sense into a few officers in material command to allow drop tanks and the needed plumbing and pumps sooner.
What you can't make somebody do is make a significant change in the rate of climb of a well over 8000lb airplane that was using the single stage Merlin engine at the higher altitudes (over 20,000ft). That is more physics.
Once you specify a certain amount of weight for guns and ammo, and the desired fuel and protection and the structural strength and so one, you are going to wind up with a over 8,000lb airplane for US service. And if your available engine only offers 1100hp at the crank at 18,500ft in climb you don't have lot of options to change the climb performance.
see.
http://www.wwiiaircraftperformance.org/mustang/Power_required_available_P-51A_P-51B_P-47B.pdf
Yes this report was from late 1943 but engineers could have done (and probably did ) similar studies earlier. In fact teh P-47Ds were in production when this report was issued.
Please note that the power curves are for thrust HP and figure in the efficacy of the propellers.
Similar curves could have been done for higher altitudes.
The power you have to climb is the surplus power you have between the required power to actually fly at the desired speed and the max power of the engine.
In the case of the 3 planes shown the P-51A at 180mph needs about 250hp to fly and has 800hp available so it has 550hp thrust to climb with.
The P-51B needs 275hp to fly but has1150hp available so it has 875 hp thrust with.
The P-47B needs 435hp to fly ( a lot more drag and weight) but has 1600hp available and has 1375 hp thrust to climb with, however that horsepower needs to deal with almost 50% more weight.
engineers and engineering officers could make charts and predictions on performance based on charts/formulas like these.
A Merlin V-1650-1 is going to fall in between the P-51A and the P-51B in both needed power (only a small change) and the available power.
The problem for this question is that the available power at 20-25,000ft is not going to be enough to give the plane the performance it needs. And they could figure that out without actually building the plane.
Now as used in 1943-44 the B-17s and B-24s often did not fly at 25,000ft but flew 2-5,000ft lower but they didn't know that in 1941-42, they were planning on 25,000ft (or close) altitudes and in the US only the P-38 and P-47 offered the desired performance at altitude,
until The two stage Merlin showed up.
we can see that a P-51B could reach 30,000ft in just under 10 minutes and being climbing at 2175fpm. The engine was making 1075hp and could make 51.6in of boost.
