To review the New Guinea to Howland flight for the via Choiseul Island detour as deployed in the addendum of EJN article no.3 , we check the physical flight system by a mathematical model for which we use the analytical Breguet Formula for range:


    R = H/g . L/D . ŋov . ln [ Winit / Wfin  ]


In which  R  is the ferry range of NR 16020 in km ,  H  the avgas energy density in kg m2/s2 (Joule) per kg mass , L/D the lift to drag rate for the aircraft , ŋov the overall efficiency of the propulsive system , and Winit , Wfin  the respective weights of aircraft before takeoff and after any part of, or all the gasoline has been burnt during one single flight . The integral R = ʃ (W , H , g , L , D , ŋov) δW can only result in the above Breguet formula if the between brackets latter five figures are constants , which they actually are on long haul flights with a small fraction only of range and endurance for takeoff and landing operations to and from a given flight altitude. With empirics H = 42 x 106 J /kg , L/D = 8 , ŋov = 0.25 , ln [Winit / Wfin] = 0.536 we find Rmax = 4,590 km , 2,852 SM @ altitude 8,000 ft . The via Choiseul Island Lae-Howland (erroneous coordinates) distance was (2,628 + 59) SM = 2,687 SM .  When against 1905 GMT Howland should have run in sight the mean groundspeed amounted to 141 SM per hour , at 1912 GMT the signal “We must be on you . . fuel is running low” was transmitted , probably with the addition “Only ½ hour left” . By naming the product [H/g . L/D . ŋov] = Z = 8.562,691 we can establish the amount of fuel remaining when the 2014 GMT transmission was running , distance 2,687 SM , 4.324,189 m ex Lae made good  : ln [ Winit / Wfin ] should be 0.505 . We here find Wfin to be 9,594 lbs for 49 USG (24 + 25) remaining . 2,852 SM / 141 MPH gives   20h13m37s, 23 seconds from 2014 GMT , for the fuel run out time .  (2,687 / 2,852) x 20h13m37s is the by the crew supposed ETA , 1904-1910 GMT approximately . The acquired figures are close to the empiric ones presented in EJN , article no.3 of the series : the conclusion remains that , even by reaching the Howland region  directly by the shortest 2,556 SM path,  Gardner at 410 SM off was beyond the for that event 296 SM remaining range. Mr.Noonan knew it, he will not have set course to the south-east with the intention to find land,  other than Howland. Eventually,  checking for the endurance with 1,100 USG gasoline we find , as derived from integration in the Breguet algorithm:


          Tfinal = - L/D . ŋov . H / g.V  . ln [Wfin / Winit]


 with V = 63 m/s (work is exclusively done by motion w.r.t. Earth) ,  Tfinal  measures 72851 s / 3,600 s / hr = 20h14m11s  when the NR 16020 radio transmission signed off , against Earhart´s intention to come back on the air .

March 31 , 2013             H.A.C.van Asten


Addendum #2 to July 2008 Article in the

European Journal of Navigation