H.A.C

And according to Newtonian Aerodynamics, a Bee can'fly! Tell that to them the next time you disturb a hive full of them.

Do it the simple way:

The Lockheed report gives the range of the 10E as between 4100 and 4500 miles on 1200 gallons of fuel. Use the midpoint 4300 miles and divide by 1200 and get 3.5833 miles per gallon.

The Lae to Howland distance is 2556 miles, divided by 3.5833 eequals 713.3 gallons which when subtracted from 1100 gallons leaves386.7gallons, multiplied by 3.5833 m/g gives 1386 miles, enough to go to Gardner and back 3 times.

Which of course we gcould have gotten by subtracting the distance Lae to Howland, 2556 or so from 4300 to get 1744.

Conclusion: They had more than enough feul to fly to Gardner, land, and run the starboard engine to charge the batteries to operate the radio to send out distress calls.

------------------------------------------------------------------------

Further fuel analysis.

Looking at figure VI on page 12 of Lockheed Report 487 we can see that 1200 gallons would provide

a maximum range of 4060 statute air miles;

1150 gallons will take you 3940;

1100 gallons will take you 3800 and

1050 gallons will take you 3645 statue air miles.

The minimum fuel needed to go the 2556 statute miles distance to Howland in still air is 680 gallons

meaning that if the plane took off at the light gross weight of 13,324 with just 680 gallons it could fly

that many miles. Taking off with more fuel weight causes the plane to burn more fuel en route so more

fuel will be consumed on the way to Howland when starting with a greater fuel load.

Boswell did an analysis and, starting with 1150 gallons, calculated the maximum range of 4160 statute

air miles, 220 miles more than report 487. Analyzing his report, you find his calculations shows the

plane burned 871 gallons in 18:32 minutes needed to fly the 2556 miles to Howland leaving 279 gallons

remaining and a further range of 1604 statute air miles.

There is a third way to do this calculation, using the Breguet formula, which needs very few inputs and

produces amazingly accurate results.

Range (statute air miles) = 863.5 times L/D (max) times propeller efficiency divided by specific fuel

consumption times the Log of the starting weight divided by the finishing weight. See attached pages 186 and 187

from “Airplane Performance Stability and Control" by Perkins & Hage.

formula 4-40 on page 186

R= 863.5 L/D n/c LOG (W0/W1)

To use this formula we only need to find coefficient of lift / coefficient of drag that is maximum, or

maximum Lift over Drag,

L/D (max)

This information is found on page 30 of the Lockheed report. (There are a number of typos on this

page that I have marked on the attached page.) Looking in the first column under “CL” for 16,500 #

we find the coefficient of lift at 150 mph is .63. We find the coefficient of drag (CD) for the same speed

and weight (after correcting the typo) is .053. Dividing CL by CD we find CL/CD = 11.89. We can do

the same calculation with other pairs of values and we will find that 150 mph produces the maximum

L/D at 16500#. We can also calculate the maximum at the other listed weights and we will find that the

speeds for maximum range varies with the square root of the weight ratio just as the laws of

aerodynamics predicts and the power for these speeds also change with the 3/2 power of the weight

ratios just as predicted by the same laws.

Next we find propeller efficiency on page 32. It varies a bit but we can choose .75 Similarly we find

SFC on page 34 of .46 pounds per hour per horsepower. Substituting these values into the formula we

end up with a constant times the LOG of the weight ratio.

.75/.46 x 11.89 x 863.5 = 16739 so range = 16739 times LOG of the weight ratio.

The finish weight is 9300# per the Lockheed report. Starting with 1200 gallons, gross weight 16500 the

calculated range is 4154 statute air miles.

1150 gallons produces a range of 4021, 1465 remaining after flying the distance to Howland;

1100 gallons ...............................3886, 1330....;

1050............................................3748, 1192.....

Further manipulation of the formula allows us to calculate the weight after flying 2556 statute air miles.

Starting with 1200 gallons the weight after 2556 miles will be 11596 meaning 817 gallons used;

Starting with 1150.................................................................11384..............803....................;

....................1100..................................................................11174..............788....................;

.....................1050................................................................10963................773 gallons used.

Also it would take 656 gallons if starting at a gross weight of 13234 and ending up with empty tanks

and a gross weight of 9300 pounds after flying the 2556 miles to Howland. This compares to the 680

gallons for the same conditions on figure VI.

Notice the maximum ranges calculated by the three different methods are quite similar.

A ten mph headwind component would have added about 200 statute air miles on the way to Howland

and a 25 mph headwind component would have added about 500 miles leaving more than 692 statute

air miles remaining even if the plane had left with only 1050 gallons.

So it doesn’t make sense that she ran out of fuel shortly after 2012 Z. Long’s explanation also doesn’t

make sense since there was no reason for AE to add power to speed up into the headwind since she

didn’t need to stay on a schedule and could just arrive later. The Lockheed report shows that to obtain

maximum range you should increase your airspeed only about 6 mph for a 20 mph headwind so if AE

had decided to increase her speed and power it would have been just a small amount and should not

have consumed all of her fuel. However, you only do this if you were flying at the optimum speed for

range, max L/D, and it appears that Earhart was flying at a higher speed when their weight got lighter.

If you are flying above the max L/D speed then, for a headwind, you should slow down so that your

speed is closer to the max L/D speed to achieve maximum range.

(If you look at graph II in Report 487 you will see this illustrated for 16,500 pounds. However, the curves

on this graph for the lighter weights are not located properly, they need to be further to the left because the

optimum speed is less at the lighter weights, so don't rely on them.)

To get the most accuracy out of the Breguet formula, which is based on the weight change from

takeoff to tanks dry, you should allow for the loss of weight from burning the oil, there was a reason for

carrying those 75 gallons of oil. Unlike modern flat engines, round engines consume a great deal of oil.

The specification for the Wasp is .32 oz per hour per horsepower which doesn't sound like much

but it does add up. Another way to state this specification is .02 pounds per hour per horsepower. Since

the SFC is .46 this means that for every 23 gallons of fuel that is burned the engines also burn 1 gallon

of oil. Burn 1,100 gallons of gas and you also burn 47.8 gallons of oil weighing 358.7 pounds. An easy way to do

this is to simply add the .02 pounds per hour to the SFC, totaling the burn off of all the liquids on board.

If you do this you get approximately 129 miles greater range estimate from the Breguet formula.

Something to keep in mind when using the Breguet formula is that it is optimistic in that it makes no allowance for taxi and take off and for climbing at higher power settings with a higher SFC and also assumes that the plane is flown at all times at the correct airspeed that results in L/D max which requires constantly slowing down as fuel is burned off. Flying either faster or SLOWER than the targeted airspeed will result in a shorter range.

But, she said she only had a half hour left...............

gl