Boy, that term "Point Of No Return" runs shivers down my spine and has been used in many movies to heighten tension. "We can't turn back, we must go forward, no matter what!"

In reality, it's not that dramatic.

The "point of no return" is just another example of the more general "radius of action" calculation. This was known in 1937 since it was published by Noonan's friend Weems in *Air Navigation*, 1931, and in *Navigation and Nautical Astronomy*, Dutton, 1934.

The formula is quite simple and there are various ways to write it depending on how you want the result. The inputs are the endurance (based on the fuel on board divided by fuel flow) the head (or tail) wind component for the approximate first half of the flight and the true airspeed of the plane. The true airspeed and the wind component are combined to determine the ground speed out (on course towards the destination) and the ground speed for the return leg.

So:

Time (to PNR) = (Endurance X GS return)/(GS return + GS out)

Since the wind component causes an equal but opposite effect on the ground speed for the GS out and the GS return the divisor is simply 2 X TAS so the formula can be rewritten:

Time PNR = (Endurance X GS return)/(2 X TAS)

We know for sure that the plane had an endurance of at least 20:13. Using the TAS of 130 knots (150 mph) and the wind component of 23 knots as determined in flight, and reported by Noonan, we can substitute into the formula:

GS out = 107 K

GS return = 153 K

2 X TAS = 2 X 130 = 260 K

T = (20:13 X 153)/260

T = 11:54

If we multiply this time by the GS out we find the distance to the PNR.

Dist PNR = 107 K X 11:54 = 1273 NM

Alternatively, if you just want the distance to the PNR you can use the formula:

Dist PNR = (Endurance X GS out X GS return)/(2 X TAS)

D = (20:13 X 107 X 153)/ 260

D = 1273 NM

To confirm that his is a correct result we can divide the distance by the GS return:

1273 NM / 153 K = 8:19

8:19 + 11:54 = 20:13, the endurance.

So we can be sure that had they turned around prior to 11:54 Z they could have made it back to Lae. If, in fact, the endurance was only 20:13 then we also know that if they turned around any time after 11:54 Z that they could not make it back to Lae, they would have been past the "point of no return."

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Using a 15 knot wind component from the July 1st forecast you get:

11:16 and 1297 NM

Using the 25 knot wind component from the July 2nd forecast you get:

12:03 and 1265 NM

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If Noonan thought he had a 24 hour endurance using the 23 knot wind component then he would have calculated the PNR as 14:07 at 1511 NM. Using a 15 knot wind component then he would have gotten 13:23 at 1539 NM and with a 25 knot wind he would have gotten 14:18 and 1502 NM, just past Nauru, so the decision had to be made more than 100 NM west of the Gilberts at about the time that Itasca first heard from the plane at 1415 Z.

See attached excerpt from the Navigator's Information File.

gl