To follow the scientific method, you ask a question, do background research, form a hypothesis, test your hypothesis with an experiment, analyze your data and draw a conclusion, and communicate your results. By "test your hypotheis," I mean disprove it. The statement might be, "The XP-39 went 390 mph in 1939."
Well, lets see, we have.
1, no test report the XP-39 did fly 390mph.
2. reports of continued oil overheating and/or high temperatures causing at least one flight to be cut short.
3, At least one report of high coolant temperatures.
4, reports or accounts of modifications done to oil and radiator ducts. Which did not solve the problem
5, accounts of how the AAC wanted a new drive shaft installed in the plane because of vibration problems or worries if the engine misfired. Until new drive shaft was fitted engine rpm was restricted to either 2600or 2700rpm. The New drive shaft was not fitted until after the plane went to Langley. No full power flights?
6 time available.
a, first flight April 6th, 15 minutes.
b 2nd flight April 7th cut short due to oil temp
c. 3rd and 4th flights on April 22 total 47 minutes.
d 5th flight April 23, Nose wheel fails after manual lowering of landing gear, 1 hour 40 minutes total flying time in 5 flights.
e. accounts do not say what flying or tests were done in May of 1939. could have been some.
f. Plane is delivered to Langley on June 6th. After arrangements made at the end of April.
7, Langley claimed that the oil cooling problem was resolved or minimized during initial flight tests by using a higher drag duct than originally fitted.
So,
if the XP-39 did do 390mph or anywhere near to it it had to be done in May, (none of the April flights were long enough to get to 20,000ft, do a high speed run and get back down on the ground again.) with a high drag oil cooler duct, a radiator that had problems (like at 350mph the radiator was supposed to have 16,900 cubic ft of air going through but only 10,250 cu ft was needed to cool the engine) and the engine was limited to 90% or less of rated rpm, unless the pilot disobeyed instructions.
I can't
prove the XP-39 didn't hit 390mph but the chances of it are pretty slim. And if it hit 390 mph with all those problems it should have been a real rocket once they got fixed.