# TIGHAR

## Amelia Earhart Search Forum => Aircraft & Powerplant, Performance and Operations => Topic started by: h.a.c. van asten on August 14, 2011, 04:05:21 AM

Post by: h.a.c. van asten on August 14, 2011, 04:05:21 AM
Apply some Newtonian Aero Dynamics : The lift needed for an A/c in horizontal flight is from CL . 1/2 . r . S . Vt^2 = m. g . in th dimension Newton (N) . For NR 16020 @ 8,000 ft with r = 0.964 kg/m^3 , S = 42.6 m^2 surface wing , Vt = 69 m/s TAS , Vw = 8 m/s headwind , average mass = 4,932 kg in flight we find : m . g  = 48,383 N with CL = 0.459 lift coefficient . Reasonable glide ratio CL/CD Lockheed 10  is 10 (report Lockheed no.487) . Thence : 48,383 N / 10 =  4,843 is the propeller draft needed . The mechanical propulsive efficiency  ep was 21.6% (0.76 for propellers , Report 487 ; & reasonable 0.28 for the engines) so that for a range R follows : E = (m . g . R) ep^-1 , or by insertion : 4.63(4,838 N x 2,628 mls x 1,6092 m/mi x 1,000 m/km) = 9.47 x 10^10 kg . m^2 . s^-2 in the energy dimension  J  for Joule .  Divide by 47 x 10^6 J / kg gasoline chemical energy and find  2,015 kg , 4,438 lbs , or 740 US gallons for 2,528 mls Lae to Howland , zero wind , duration 19h12m , offset included . The power needed to pull 48,393 N is  CL . 1/2 . r . S . Vt^3  in zero wind , to be transposed to CL . 1/2 . r . S . (Vt + Vw)^3 in the event of headwind speed Vw . (Vt + Vw)^3 = 1.39 Vt^3 . Note that any acceleration factor against resistance translates to the  factor in 3rd power to energy needed  (2 x as fast = 8 x greater energy) . Hence : needed for 2,628 mls in headwind 18 mph , 8 m/s , Beaufort 6 is : 740 galls x 1.39 = 1,028 galls . Remaining @ GMT 1912  22 galls 87 oc & max. 25 galls 100 oc fuel from 1,100 initial store . The specific range was 2,628 mls / 1,028 galls =  2.56 mph , so that by extrapolation follows that after GMT 1912  a maximum distance  47 x 2.56 mls = 120 mls  could be additionally flown . This range is from the Howland region too small for reaching any other in the Pacific land point than Howland itself , or Baker .

Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on August 14, 2011, 10:28:05 AM
------------------------------------------------------------

Also see excerpts from Boilerman 3 & 2, the U.S. Navy training manual for boilermen 3rd and 2nd class which is attached. BTW, nowhere in this manual or in Knight's Modern Seamanship is there any mention of the horribles that inhabit Brandenburg's fertile imagination.

- Uneven heating among the tubes, etc. create all kinds of stress; relative cooling in one section / component and extreme heat in the next creates the potential for what amounts to a bomb - it's basics 101 in boiler-world.  Point is to do what was described is counter to good practices and it was not likely what really happened.  In any case, AE certainly never reported finding any smoke that we're aware of... the rest may be - speculation.  I appreciate your insight, but also happen to be long familiar with steam engines of many sorts. - Jeff
-------------------------------------------------------

Wow Jeff, I just realized that you must be very, very old! I think the last time an A&P worked on a steam powered airplane it was Langley's in 1903. ;)

gl
Title: Re: Fuel load, head winds, range
Post by: Harry Howe, Jr. on August 14, 2011, 02:30:40 PM

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.
Title: Re: Fuel load, head winds, range
Post by: Harry Howe, Jr. on August 14, 2011, 03:18:26 PM

Obviously I had a brain twitch in my last post

It should be BEES can't fly

and the 3 was wrong, they could only have flown from Howland and back and then back to Gardner. 1-1/2 round trips, not 3.
Title: Re: Fuel load, head winds, range
Post by: Monty Fowler on August 14, 2011, 03:39:18 PM
Maybe bees can't fly, but they can sure sting the bejesus outta you. I'm sure Mr. van Asten has a mathematical equation about 50 pages long for that, as well.

I know, my bad.

LTM,
TIGAR No. 2189CE, wishing the Discovery Channel would rebroadcast Finding Amelia in the mainstream instead of the backwaters.
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 15, 2011, 01:32:07 AM
A very good assessment indeed . Do not however , forget the continuous headwind pressure : your outcome must be for required energy multiplied by (Vg + Vw)^3 / Vg^3 = 1.44 for this case . I inserted an error figure iin the comment  (Vg was exchanged for Vt) , the reciprocal of the propulsive efficiency  1/ep = 4.46 giving 9.14 x 10^10 J , and 4,284 lbs fuel for 714 (your figure) galls . This figure to multiply by 1.44 gives 1,028 galls . The same figure appears when calculated by starting @ the s.c. wind regression factor . So , without  the headwinds asking for (1.13)^3 = 1.44 more energy w.r.t. to zero wind or moderate wind resistance , the GMT 1912 reserve would have been (1,100 - 25) - 714 = 361 galls maximum , for 924 mls flight (there and back Gardner) as you suppose . When different calculation algorithms lead to a same outcome , it is always a signal that computations are correct . Probably , in Report 487 was reckoned for incidental , moderate wind fields , not with actual Trade Winds averaging , head  or cross , an equivalent 18 mph for the endurance . The fuel consumption per hour was btw normally 310 lbs/hr (letter Putnam to De Sibour , Feb 13 , 1937) . The actual trip asked 321.3 galls/hr , 3.6% more only . In 2,628 mls is 32 mls offset detour included , leaving 40 mls detour w.r.t. 2,556 , given the navigation model I worked with for the EJN-2008 article .
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on August 15, 2011, 02:20:26 AM

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
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on August 15, 2011, 02:23:47 AM

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.

gl

Two more attachments
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on August 15, 2011, 09:41:37 AM

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.
-------------------------------------

You forgot to allow for the wind. The range values shown in report 487
are statute air miles, the distance that could be covered in still air.
If the plane was flying at  true airspeed of 150 mph into a 150 mph
headwind it would still be able to fly the same number of air miles but
the number of miles covered over the ground would be zero. It's easy
to allow for this affect, just multiply the headwind component times the
time in flight and subtract from the total air miles range values.

All the values for range in Lockheed report 487, and those computed with
the Breguet formula, are for still air and we know that Earhart had a
head wind on the way to Howland. One of the theories has her turning around
and returning to Rabaul and the wind would have become a tailwind. But the
same analysis holds for any "turn around" theory. Lets see how this works out.
Let's make up some numbers to make this easier to see. Let's say we are
going to fly, in a no wind situation, out 3,000 miles and then return
for a round trip of 6,000 miles in a plane that cruises at 150 mph. To
fly out 3,000 miles will take 20 hours (3,000 ÷ 150 = 20) and then it
will take an additional 20 hours to fly back for a total of 40 hours in
a no wind situation so we put on enough fuel to fly for 40 hours. Now
let's do it again, this time with a 50 mph headwind on the way out which
becomes a 50 mph tailwind on the way back. Since the winds are equal,
the same headwind and tailwind, the winds should cancel out so it should
still take 40 hours for the round trip. The average ground speed will
still be 150 mph ((200 + 100) ÷ 2 = 150) so this makes sense. Let's
confirm this. Going out, the ground speed will be 100 mph, the 150 mph
airspeed minus the 50 mph headwind. At 100 mph it will take 30 hours for
the outbound leg (3,000 ÷ 100 = 30). When the plane turns around the
ground speed jumps up to 200 mph, the 150 mph airspeed plus the 50 mph
tailwind. At 200 mph it will only take 15 hours to fly the 3,000 miles
back to our starting position, (3,000 ÷ 200 = 15.) Now adding the 15
hours for the return flight to the 30 hours for the outbound leg makes
the round trip take 45 hours. Wait a minute, that is more than the 40
hours it would have taken in still air, does that make any sense? Did we
commit a math error?

After double checking the math we see that this is correct, it will take
an additional 5 hours to fly the round trip with an equal 50 mph
headwind and tailwind than it did in still air. If we started with fuel
for 40 hours on board we would have run out 5 hours before reaching our
starting point. Since, on the return leg, we will have a ground speed of
200 mph, this means we will crash 1,000 miles short.

gl
Title: Re: Fuel load, head winds, range
Post by: Harry Howe, Jr. on August 15, 2011, 12:33:13 PM

No, I didn't forget the wind!
Looking at the lower number for range in the Lockheed Report (4100 miles on 1200 gallons) I realized that  the residual range when arriving at Howland (assuming still air) would have been about 1375 miles (4100 miles minus 2600 miles equals 1500 miles times 1100/1200 equals 1375 miles;  Even with a constant wind of 45 mph IN THEIR FACES for the entire 20 hour flight (45 times 20 equals 900 miles equivalent).  1375 miles minus 900 miles leaves 475 miles.  The distance Howland to Gardner is about 405 miles.

The wind was irrelevant to the conclusion, i.e.  AE/FN, diverting to land at Gardner, had enough fuel to fly there, land, fix  the radio, transmit distress calls, run the atarboard engine engine to charge the batteries as necessary.

The modern day equivalent to Occam's Razor (Look it up) is KISS (Keep It Simple Stupid).
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 15, 2011, 12:38:13 PM
With means and averages one should be very careful if , per your example , the tracks are equally 3,000 miles long . If tracks are different you never encounter a problem if you take the arithmetical mean of speeds etc . But if tracks are equal a treacherous trap comes up : for equal tracks the harmonical , not the arithmetical mean must be taken . If you make good 2 x 3,000 mls equal tracks @ 100 versus 200 mph the harmonic mean weighs with hours per mile :  2 / (1/100 hpm+ 1/200 hpm) = 2 / 0.015 = 133 1/3  mph for the mean speed , unequal to and lower than (100 + 200)/2 = 150 mph . That is the reason why you go in  undershot with fuel for 40 hours :  6,000 mls / 133 1/3 mph = 45 hours . Very treacherous this arithmetical gimmick , especially fo those computing for a combat range in war time . If the up/down speeds are equal (zero wind) , you have no problem for equal tracks and you can take the arithmetical mean of speeds . If the up/down tracks are unequal , you can also take the arithmetical mean of speeds .
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 15, 2011, 12:52:37 PM
Excuse sir, but that is too much solo : keep in mind that any acceleration against resistance , p.e. by 5% does not ask for 1.05 x , but for (1.05)^3 = 1,16 x the initial fuel flow . In the Earhart case , airspeed was increased to mean 155 mph to acquire 137 mean cross country speed , a difference of 13% , or factor 1.13 . The consequent fuel flow acceleration thence increased to (1.13)^3 = 1.44 x initial , or with 44 % . 714 galls x 1.44 = 1,028 gals , leaving 22 galls 87-octane and maximum 25 galls (but probably 16) 100-octane . The 22 galls (87-oc for the trip) covers Earhart´s GMT 1912 signal : 1/2 hour left .
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on August 15, 2011, 01:02:51 PM

No, I didn't forget the wind!
Looking at the lower number for range in the Lockheed Report (4100 miles on 1200 gallons) I realized that  the residual range when arriving at Howland (assuming still air) would have been about 1375 miles (4100 miles minus 2600 miles equals 1500 miles times 1100/1200 equals 1375 miles;  Even with a constant wind of 45 mph IN THEIR FACES for the entire 20 hour flight (45 times 20 equals 900 miles equivalent).  1375 miles minus 900 miles leaves 475 miles.  The distance Howland to Gardner is about 405 miles.

The wind was irrelevant to the conclusion, i.e.  AE/FN, diverting to land at Gardner, had enough fuel to fly there, land, fix  the radio, transmit distress calls, run the atarboard engine engine to charge the batteries as necessary.

The modern day equivalent to Occam's Razor (Look it up) is KISS (Keep It Simple Stupid).

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

But you didn't put that in your original post.

If you look at my post it also shows that they should have had enough gas to get to Gardner so it doesn't dispute your conclusion, it only illustrates for others that you must allow for the wind in this kind of analysis.

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

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

gl
Title: Re: Fuel load, head winds, range
Post by: Harry Howe, Jr. on August 15, 2011, 01:07:54 PM

I believe that the Chater Report states that all tanks were filled except one 81 gallon tank that was for 100 octane fuel and it was half full (40.5 gallons).  The reason that the 81 gallon, 100 octane tank, was not filled (topped off) was because Lae had no 100 octane fuel.
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 15, 2011, 02:15:42 PM
It concerned one 102 galls port wing tank containing 50 US galls 100-octane fuel for takeoff in lower density air . Fuels were Stanavo Ethyl. Engine oil was Stanavo 120 .
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on August 15, 2011, 02:38:38 PM

I believe that the Chater Report states that all tanks were filled except one 81 gallon tank that was for 100 octane fuel and it was half full (40.5 gallons).  The reason that the 81 gallon, 100 octane tank, was not filled (topped off) was because Lae had no 100 octane fuel.

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

There is definitely a conflict in the evidence regarding the fuel consumption. The tanks only held 1150 U.S. gallons so that puts an absolute top limit on the gas in the plane. Chatter said that 654 Imperial gallons (785 U.S. gallons) were put into the tanks so this puts an absolute floor on the fuel load of 785 U.S. gallons.

Both Collopy and Chatter state that the plane had 1100 U.S. gallons on board but there is a conflict in their statements. Collopy said that a 100 gallon tank was half full while Chatter said an 81 gallon tank was half full. There are no 100 gallon or 81 gallon tanks in the fuselage but there are 102 gallon and 81 gallon tanks in each of the wings. Earhart lost control of the plane on takeoff from Hawaii so she would be loath to have a lateral fuel imbalance on takeoff at Lae so is likely that she wouldn't just leave one tank in just one of the wings half full but would leave a tank on the other side half full also. Supporting this theory is the discrepancy in the size of the tanks described by Chatter and Collopy. If one of them looked in the tank and passed the information on the other guy then they would have the exact same size for the tank so it didn't happen this way. If they each looked in the same tank that was half full then, again,  they would have reported the same size. Based on this it is reasonable that they were each looking in different tanks, one in the right wing and one in the left wing. They both said they saw a tank half full and if they talked to each other neither would have reason to realize that the other guy was talking about a different tank since they both calculated 1100 gallons total. It is like the old story of the three blind men examining an elephant. Based on this I believe that it is quite likely that they only had about 1050 U.S. gallons on board when they took off from Lae.

This 50 gallons less explains only between about one hour to about two hours  of the lesser endurance but doesn't explain all of it. Using the data from Lockheed shows there should have been plenty of gas left at 2013 Z and the Breguet formula also, independently, predicts much greater range so it doesn't make sense that they ran out shortly after 2013 Z, so this is quite frustrating.

But there is another piece of conflicting evidence that trumps all the other calculations, this is Earhart's statement that they only had a half hour of gas left. She was there, and the change in the pitch of her voice lends additional credence to her being almost out of fuel when she transmitted the last message at 2013 Z.

gl
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 15, 2011, 02:50:44 PM
From the Bréguet formula derived is , for the mean speed of A/c  Vm = Range / Endurance = V0 {[ln (W0/W1) / 2[(W0/W1)^0.5 -1]} . For W0 = 16,500 lb , W1 = 16,500 - (1028 x 6 lb (gas) + 268 lb (oil)) = 10064 lb . For Vm follows  0.4944/0.5609 = 0.884 V0 . For V0 = 155 mph we find Vm = 137 mph , in keeping with Vgm = 137 mph for 2,628 mls offset included in 19h12m . This says that due to the actual windspeeds aloft the fuel weight diminished faster than expected from forecast : 2,628 mls / 18 hrs = 146 mph cross country lowered to 2,628 mls / 19h12m = 137 mph .
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on August 15, 2011, 03:05:15 PM
-------------------------------------------------------

Wow Jeff, I just realized that you must be very, very old! I think the last time an A&P worked on a steam powered airplane it was Langley's in 1903. ;)

gl

Well, I'm pretty old I guess, but I'm afraid Langley pretty well predated the first A&Ps.

Actually, my first mechanical love as a boy was steam locomotives - but I was born too late to experience them on a common scale (so not THAT old).  I learned all I could through the library and every other source I could find.  Always loved steam powered ships - the compound / triple expansion recips and Parsons turbines, etc. all fascinated me.  Have seen the guts of the N.S. Savannah as a small boy - and again as a young man - several times (you may know, she's nuclear powered, not bunker or coal - but 'steam' none-the-less).  I have spent quite a bit of time perusing the Norwich City information and pictures of her on this site and elsewhere - from proud 'tramp' to forelorn derelict.

The idea that something bigger than a house and made to the precision of a fine watch could sit in the guts of a ship and drive something like the Titanic across the ocean (well, part way as it turned out...) at 22 knots or more has always been enchanting to me.  And she was a wonder in her day - two recips and one turbine - all circuited to get the most out of the heat from her boilers.  The behavior of fuel, air and water to make it happen was equally as thrilling a pursuit.

It's been a long time since I was much of an active A&P.  Now my work is done on paper and revolves around 'kerosene' (Jet A) and modern turbofans - but I still enjoy those steam roots and the thoughts of all that grand machinery from the past.  Look at the legacy we have from it all!

I'd love to see the examples you wrote of in California some day; I never tire of it.

LTM -

-----------------------------------------------
-------------------------------------
I remember the excitement when the Savannah was launched, too bad it was an idea who's time never came. You can also go aboard the first boat with that type of tea kettle when you are in Groton, Conn., the 571 boat.
I am attaching two photos, one of the links, and the other a diagram on the engine on the Jerimiah O'Brien. There is also a photo of the Walschaerts gear on a Big Boy in Ohaha (woman for scale.)

gl

gl
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 15, 2011, 03:27:58 PM
Vt/F.(1 - Vw/Vt) is the fuel flow rate fromula for in head- or equivalent crosswinds , the term in brackets is the wind regression factor . For this we find f = 0.905 for the forecast wind speeds and directions , giving 1/0.905 = 1.105 , or 10 1/2 % for the factor by which the initial supply had to be multiplied for 2,750 mls in the headwinds . Noonan , at the July 1 press conference , said to take in 950 gallons for 2,750 mls in still air . 950 galls x 1.105 = 1,050 87-octane . Add 50 galls 100 octane and the result is 1,100 US galls at apron Lae Airport , in accordance with the Collpy - Ivedale testimonies .
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 15, 2011, 03:44:13 PM
(1,100 - 25 - 1,028) galls = 47 galls , 25 of 100 oc & 22 of  87 oc , this latter for 1/2 hour @ nominally 44 gph low speed low altitude is a reasonable match with " 1/2 our left" @ 1912 GMT . If only 27 gals were left for 5 galls 100 oct remaining , additional endurance was also 1 / 2 hr if reckoned with the specific hourly consumption  1,028 galls / 19h12m = 53.5 gph .
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 16, 2011, 12:43:51 AM
Somewhere in the 487 Report there must be an underestimate , probably for continuous headwind Beaufort 6 translating to to 3rd power effect on energy needed , but I have not yet found the omission , the SFC/hr/hp figures should by recomputation deliver the outcome .
Title: Re: Fuel load, head winds, range
Post by: Jeff Scott on August 16, 2011, 10:50:17 PM
But, she said she only had a half hour left...............

gl

Which, of course, leads to the inevitable dispute over what that statement means:  did she literally have only 30 minutes worth of fuel left or only 30 minutes left until she had to start using her reserve?
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 17, 2011, 01:04:42 AM
It was for the fuel for the fuel as planned for the flight , not for the special avgas reserve , since GMT 1815 - 1912 = 1h03m .
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 17, 2011, 01:31:16 AM
If , p 12 Rep.487  / graph you take the fuel figures for 1,050 & 1,100 stores , and divide 3,645 and 3,800 mls range by factor 1.44 shown earlier for 3rd power effect , you get resp. 2,531 mls and 2,639 mls , the first close to 2,556 , the latter close to 2,628 mls , zero wind . This supports that Rep 487 registered marginally for continuous adverse wind as during the actual flight .
Title: Re: Fuel load, head winds, range
Post by: Harry Howe, Jr. on August 17, 2011, 01:40:35 PM

Perhaps the 1/2 hour fuel comment didn't really happen but was "invented" after the fact to cover butts and justify the ship steaming off to the NW and the "Search"  being done there primarily.

If I remember correctly, the men in the Radio Shack didn't hear that transmission Someone came in from the deck and asked those in the radio room whether they heard her.  "She was just on, didn't your hear her?"
Title: Re: Fuel load, head winds, range
Post by: Martin X. Moleski, SJ on August 17, 2011, 02:21:41 PM
Perhaps the 1/2 hour fuel comment didn't really happen ...

From "The 1937 Search: The First 24 Hours" (http://tighar.org/Projects/Earhart/Archives/Research/ResearchPapers/first24hours.html)  by Randall S. Jacobson, Ph.D.:

Thompson’s actions apparently were based upon his conviction that Earhart had said, at 07:42 (1912 GMT), that she only had half an hour of fuel left. Because there is no land other than Howland and its sister island Baker which could possibly be reached within that fuel limitation, the conclusion that the  airplane went down at sea is inescapable. If the quote is accurate Thompson  was certainly correct in beginning the search rather than sitting at Howland  waiting for an airplane that was already in the water. Where does the  quotation come from? The only source is what Thompson calls the “Other Log” which he quotes in his July 19th report as saying “Earhart on now  says running out of gas only 1/2 hour left.” The entry was made by Radioman 3rd Class O’Hare who had been on watch since 02:00. Evidence that the phrase was not said includes:
• Radioman 3rd Class Galten’s entry in the Itasca’s radio log, “KHAQQ calling Itasca. We must be on you but cannot see you but gas is running low. Been unable reach you by radio. We are flying at a 1,000 feet.”11 (http://tighar.org/smf/../Projects/Earhart/Archives/Research/ResearchPapers/first24hours.html#11)
• An entry in the Itasca’s deck log by Lt. (jg) W. J. Sevarstan, “0742 Planes position reported as near the island and gas running low.”
• Lt. Cooper’s report, “0741. Earhart. We must be on you but cannot see you but gas is running low...”12 (http://tighar.org/smf/../Projects/Earhart/Archives/Research/ResearchPapers/first24hours.html#12) However, this is a second-hand report, as Cooper was still on Howland Island.
• The July 4th press release sent by Itasca, “0730 Quote we must be on you but cannot see you but gas is running low...”13 (http://tighar.org/smf/../Projects/Earhart/Archives/Research/ResearchPapers/first24hours.html#13)
• At 08:43 (2013 GMT), a full hour after Earhart supposedly said she had “only 1/2 hour gas left,” Earhart was still aloft and transmitting.
• Not once in the three messages received by Itasca after the 07:42 message did Earhart repeat her concern over fuel.
• In Thompson’s typed report the quote from the “Other Log” is followed by the parenthetical comment “(unverified as heard by other witnesses)” but the “un” in “unverified” has been lined through by hand.14 (http://tighar.org/smf/../Projects/Earhart/Archives/Research/ResearchPapers/first24hours.html#14) However, it is impossible to determine when this line-out occurred and/or whether it was there when originally delivered to the Coast Guard.
• The available evidence argues strongly that the phrase “½ hour gas left” was never said. It may,  in fact, have been a simple misunderstanding. In three of the nine transmissions heard by Itasca, including the next message received 16 minutes later, the ship’s radio log recorded Earhart’s use of the phrase “half hour,” but always in reference to the radio schedule, never to fuel.
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 17, 2011, 02:50:51 PM
@ GMT 1912 Earhart , communicating that for 1/2 hour fuel was left , referred to the fuel store as planned for the flight to destination , not to the 100 octane gas in the separate container . The fuel for 1/ 2 hour as by re-computation must have amounted to +/- 22 gallons whereas ;  if 16 galls 100-oct remained , also the GMT 1815 fuel run out time finds explanation . At GMT 1945 no on cue radio signal was on air from A/c : at that point of time regular avgas was exhausted and cocks had to be set for flow from the 100 oct reserve ; shifting to the proper line disabled the pilot for operating the microphone .
Title: Re: Fuel load, head winds, range
Post by: Jeff Scott on August 17, 2011, 09:43:19 PM
The 100 octane tank was *not* her reserve.  By all accounts, Earhart routinely carried at least 20% more fuel than required to reach her destination on all her previous flights.  This fact is borne out by her carrying enough fuel for 24 hours flight time even though the trip to Howland only took 19-20 hours.  That 4-5 hours extra fuel was her reserve, far more than the 100 octane supply alone.
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 18, 2011, 01:03:51 AM
The reserve based on the forecast weather was 10.5% , the 100-oc gas was for take off in low density air due high temperatures @ Lae & Howland .
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on August 18, 2011, 03:52:04 AM
Perhaps the 1/2 hour fuel comment didn't really happen ...

From "The 1937 Search: The First 24 Hours" (http://tighar.org/Projects/Earhart/Archives/Research/ResearchPapers/first24hours.html)  by Randall S. Jacobson, Ph.D.:

Thompson’s actions apparently were based upon his conviction that Earhart had said, at 07:42 (1912 GMT), that she only had half an hour of fuel left. Because there is no land other than Howland and its sister island Baker which could possibly be reached within that fuel limitation, the conclusion that the  airplane went down at sea is inescapable. If the quote is accurate Thompson  was certainly correct in beginning the search rather than sitting at Howland  waiting for an airplane that was already in the water. Where does the  quotation come from? The only source is what Thompson calls the “Other Log” which he quotes in his July 19th report as saying “Earhart on now  says running out of gas only 1/2 hour left.” The entry was made by Radioman 3rd Class O’Hare who had been on watch since 02:00. Evidence that the phrase was not said includes:
• Radioman 3rd Class Galten’s entry in the Itasca’s radio log, “KHAQQ calling Itasca. We must be on you but cannot see you but gas is running low. Been unable reach you by radio. We are flying at a 1,000 feet.”11 (http://tighar.org/smf/../Projects/Earhart/Archives/Research/ResearchPapers/first24hours.html#11)
• An entry in the Itasca’s deck log by Lt. (jg) W. J. Sevarstan, “0742 Planes position reported as near the island and gas running low.”
• Lt. Cooper’s report, “0741. Earhart. We must be on you but cannot see you but gas is running low...”12 (http://tighar.org/smf/../Projects/Earhart/Archives/Research/ResearchPapers/first24hours.html#12) However, this is a second-hand report, as Cooper was still on Howland Island.
• The July 4th press release sent by Itasca, “0730 Quote we must be on you but cannot see you but gas is running low...”13 (http://tighar.org/smf/../Projects/Earhart/Archives/Research/ResearchPapers/first24hours.html#13)
• At 08:43 (2013 GMT), a full hour after Earhart supposedly said she had “only 1/2 hour gas left,” Earhart was still aloft and transmitting.
• Not once in the three messages received by Itasca after the 07:42 message did Earhart repeat her concern over fuel.
• In Thompson’s typed report the quote from the “Other Log” is followed by the parenthetical comment “(unverified as heard by other witnesses)” but the “un” in “unverified” has been lined through by hand.14 (http://tighar.org/smf/../Projects/Earhart/Archives/Research/ResearchPapers/first24hours.html#14) However, it is impossible to determine when this line-out occurred and/or whether it was there when originally delivered to the Coast Guard.
• The available evidence argues strongly that the phrase “½ hour gas left” was never said. It may,  in fact, have been a simple misunderstanding. In three of the nine transmissions heard by Itasca, including the next message received 16 minutes later, the ship’s radio log recorded Earhart’s use of the phrase “half hour,” but always in reference to the radio schedule, never to fuel.

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

﻿It is Friday evening and you are leaving the office. One of your office mates suggests that a few
of you stop for a beer at the sport bar that is on your way home. So you guys stop for a beer and
while ordering a second round, watching a Cubs game on the big screen TV, you strike up a
conversation with a stranger standing at the bar. He introduces himself as “Jim.”.  He says he just
recently moved to this town and asks you if there are any good restaurants in the area. You say to
him, “I live down near  the corner of First Avenue and Main Street and there are a number of
very good restaurants right at that corner.” Jim says, “wow, that is good to know,  I live at Third
and Main so those restaurants will be convenient for me and my wife.”

When you get home you tell your wife that you met a newcomer named “Jim” and “that he lives
at Third and Main.” Later you tell your son about this meeting and tell him, “Jim lives close to
us.”

The next Friday you are again at the same bar and this time you meet “Bill.” Pretty much the
same story as with Jim and you tell Bill the same thing, “I live down near  the corner of First
Avenue and Main Street and there are a number of very good restaurants right at that corner.”
Bill says, “that is good to know since I live close to there.”

You go home and tell your wife about this meeting.  You tell her, “Bill lives close to us.” But
you cannot say to her the same thing you told her about Jim something like “Bill lives at the
corner of Third and Main” because you do not have that piece of detailed information. If you just
made up a detail like that then you would be lying.

In Jim’s case, both of your two statements tell the truth, you know from his address that he “lives
close to you” so your generalized paraphrasing of his actual words is still telling the truth and is
commonly done, especially when making notes. But when making notes you do not make up a
detailed “fact” when you only have a general statement to work from. Think back on your own
experience, I’ll bet that you have often paraphrased information into a general form but that you
haven’t made up detailed “facts” from just a general statement.

One of the radio logs contains:  “Earhart on now, says running out of gas, only ½ hour left, can’t
hear us at all.”

The other log records: “We must be on you but cannot see you, but gas is running low, been
unable to reach you by radio.”

If Earhart had said only “gas is running low” or “running out of gas,” if you were the radio
operator would you have made up the specific and detailed “only ½ hour left” and entered it in
your log? I thought not.

Or is it more likely that she actually said "half hour of fuel left" and the other radio operator
paraphrased that to the more general "running low on fuel?" Writing down a more general
summary  from a specific statement is still speaking the truth, a ”half hour left” IS “running out
of gas.” But going the other way means "making up" the "half hour" fact and so is NOT a true
statement if she didn't actually say it

The Niku people and the Mili people and the New Britain people do not like Earhart’s statement
but if your keep an open mind I think you will agree she most likely actually said “only ½ hour left.”

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

But she was still flying a full hour after her statement was logged so is this proof that she did not
say “only ½ hour left?”

Well, no.

The fact that the fuel lasted an hour after Earhart reported only one half hour left is unsurprising.
Fuel gauges in airplanes are notoriously inaccurate today and they were no better 74 years ago.
Federal regulations (posted below) requires that the fuel gauge only has to  be accurate at one
point, it must read "zero"at the level of "unusable fuel" which is fuel remaining in the tanks that
might not be usable in extreme flight attitudes such as holding the nose extremely high or in
slipping or skidding flight or if doing aerobatics. You can use this "unusable fuel"
if you fly at normal flight attitudes. Another way to look at this regulation is that the engine can not run out
of fuel prior to the gauge indicating "zero" but the engine may continue to run after that point if you maintain
normal flight attitudes.  So if Earhart looked at the fuel gauge and estimated that there was only a
half hour left until it reached "zero" then it is not surprising at all that there was an additional half
hour of "unusable fuel” remaining after the gauge got down to "zero" and that this “unusable
fuel”continued to feed the engines  since they were not doing any extreme maneuvering.

Here are the current Federal Aviation Regulations found in title 14 of the Code of Federal
Regulations “CFR.” Part 23 prescribes the requirements for certification of airplanes such as
Earhart’s Electra.  Prior to the current Federal Aviation Regulations, aircraft had to meet the
requirements in the Civil Air Regulations, Part 3. CAR 3.437 and CAR 3.672 spelled out the
exact same requirements for fuel gauges.

14 CFR 23.1553:

§ 23.1553   Fuel quantity indicator.

A red radial line must be marked on each indicator at the calibrated zero reading, as specified in
§23.1337(b)(1).

§ 23.1337   Powerplant instruments installation.
......

(b) Fuel quantity indication. There must be a means to indicate to the flightcrew members the
quantity of usable fuel in each tank during flight. An indicator calibrated in appropriate units and
clearly marked to indicate those units must be used. In addition:

(1) Each fuel quantity indicator must be calibrated to read “zero” during level flight when the
quantity of fuel remaining in the tank is equal to the unusable fuel supply determined under
§23.959(a);

§ 23.959   Unusable fuel supply.

(a) The unusable fuel supply for each tank must be established as not less than that quantity at
which the first evidence of malfunctioning occurs under the most adverse fuel feed condition
occurring under each intended operation and flight maneuver involving that tank. Fuel system
component failures need not be considered.

see:

http://ecfr.gpoaccess.gov/cgi/t/text/text-idx?c=ecfr&sid=f0270f2e0237f7e8240bd450104e78e0&
rgn=div8&view=text&node=14:1.0.1.3.10.6.100.17&idno=14

gl
Title: Re: Fuel load, head winds, range
Post by: Martin X. Moleski, SJ on August 18, 2011, 07:58:13 AM
One of the radio logs contains:  “Earhart on now, says running out of gas, only ½ hour left, can’t
hear us at all.”

The other log records: “We must be on you but cannot see you, but gas is running low, been
unable to reach you by radio.”

If Earhart had said only “gas is running low” or “running out of gas,” if you were the radio
operator would you have made up the specific and detailed “only ½ hour left” and entered it in
your log? I thought not.

Witnesses to stressful events (assaults, robberies, accidents) often give conflicting accounts of the same event.  I do not accuse the person who wrote down "one half hour left" of making this up deliberately; that person probably thought that is what AE said.

The two logs are not of equal value.  One is from the radio operators themselves.  The other is not.  See "Log Jam" (http://tighar.org/Publications/TTracks/12_2/logjam.html) for details.

Notice that in the next message received after the controversial 7:42 AM transmission (7:58 AM), Earhart asks the Itasca to transmit on 7500 kcs now or "on the next scheduled half-hour."  If she only had 30 minutes of fuel left at 7:42, she is now down to 14 minutes.  She does not seem to be anxious about splashing down shortly.  Her announced plan was to listen on the hour and the half-hour, so I presume she meant 8:30 AM:  Itasca Primary Radio Log entry for 03:45-4? a.m. July 2, 1937 EARHART HEARD FONE/ WILL LISSEN ON HOUR AND HALF ON 3105-SEZ SHE 45/4– .

From "Log Jam" (http://tighar.org/smf/../Publications/TTracks/12_2/logjam.html):

Itasca Primary Radio Log entry for 07:42 a.m. July 2, 1937

KHAQQ CLNG ITASCA WE MUST ON ON YOU BUT
CANNOT SEE U BUT GAS IS RUNNING LOW BEEN UNABLE TO REACH YOU BY RADIO WE ARE FLYING AT A 1000 FEET 42

Aboard Itasca
: The situation is growing more tense. It is clear that Earhart has not heard Itasca’s transmissions although they are now receiving her at maximum strength (S5) indicating that she is within at least one hundred miles and possibly much closer. A second, less detailed, radio log kept by the ship records this message as “EARHART ON NW SEZ RUNNING OUT OF GAS ONLY HALF HOUR LEFT CANT HEAR US AT ALL.” Lt. Cooper’s report and the ship’s Deck Log, however, both agree with the primary radio log that the phrase is GAS IS RUNNING LOW. Cmdr. Thompson knows that the flight should have enough fuel to stay aloft until noon.

Aboard NR16020
: The time is 19:12 and Howland has not appeared as hoped. Earhart has dropped down to 1,000 feet so as to get under the scattered deck of clouds. She and Noonan believe they are very close to their destination but really need to know which way to turn on the line to find Howland. With 188 gals. remaining, enough for just 4.95 more hours, they are now burning their reserve. Gas is running low. There is, however, a contingency plan that will guarantee landfall before the fuel is exhausted. By turning right (157°) and running down the advanced line of position, one of four islands is bound to appear. If they are now too far north they will come to Howland. If they are already south of Howland then Baker, Mckean, or Gardner Island will eventually appear, provided they begin running southeast on the line when they have roughly three and a half hours of fuel remaining. Their situation at this point is serious but not desperate.

Itasca Primary Radio Log entry for 07:58 a.m. July 2, 1937

KHAQQ CLNG ITASCA WE ARE CIRCLING BUT CANNOT HR U GA ON 7500 WID A LNG COUNT EITHER NOW OR ON THE SKD TIME ON 1/2 HOUR (KHAQQ S5 A3) 0758

Aboard Itasca
: Apparently Earhart’s transmissions are coming in so loud that the speakers are distorting her words. At first the operator thinks he hears “WE ARE DRIFTING BUT CANNOT HEAR YOU” but that can’t be right so he goes back, partially erases DRIFTING and types in CIRCLING, which seems more reasonable to him. There is also confusion about how much fuel she has left. If Earhart is really expecting to run out of gas at 08:12 (HALF HOUR LEFT at 07:42) why is she asking Itasca to “GO AHEAD ON 7500 KILOCYCLES WITH A LONG COUNT EITHER NOW OR ON THE SCHEDULED TIME ON THE HALF HOUR” by which time she will already be in the water?

Aboard NR16020
: The time is 19:28 and the situation is now serious enough that Earhart, for the first time, departs from her regular transmission schedule. She probably says, “WE ARE LISTENING BUT CANNOT HEAR YOU” then asks for a long count on 7500 either now or in two minutes. Having failed in repeated attempts to get the ship to take a bearing on her, she will try to use her direction finder to take a bearing on the ship.
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 18, 2011, 11:40:54 AM
@ GMT 1912 for 1/2 hr fuel for the planned journey was left (abt 22 galls) , the max. 25 galls (but probably 16 galls) special avgas allowed for additional flight time . @ 1945 GMT regular gas ran out and cocks were set for supply from special fuel , again for +/- 1/2 hr .
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 18, 2011, 12:14:29 PM
The 1/2 hr reserve GMT 1912 concerned the normal avgas store to fly from departure to destination . Besides the regular gas , 50 galls special fuel 100 oct was on board @ take off . The remaining quantity @ 1912 GMT allowed for more than 1/2 hr flight . If fuel run out time is taken GMT 1815 , the remaining special fuel was +/- 16 gallons .
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on August 18, 2011, 12:25:31 PM
One of the radio logs contains:  “Earhart on now, says running out of gas, only ½ hour left, can’t
hear us at all.”

The other log records: “We must be on you but cannot see you, but gas is running low, been
unable to reach you by radio.”

If Earhart had said only “gas is running low” or “running out of gas,” if you were the radio
operator would you have made up the specific and detailed “only ½ hour left” and entered it in
your log? I thought not.

Witnesses to stressful events (assaults, robberies, accidents) often give conflicting accounts of the same event.  I do not accuse the person who wrote down "one half hour left" of making this up deliberately; that person probably thought that is what AE said.

The two logs are not of equal value.  One is from the radio operators themselves.  The other is not.  See "Log Jam" (http://tighar.org/Publications/TTracks/12_2/logjam.html) for details.

Notice that in the next message received after the controversial 7:42 AM transmission (7:58 AM), Earhart asks the Itasca to transmit on 7500 kcs now or "on the next scheduled half-hour."  If she only had 30 minutes of fuel left at 7:42, she is now down to 14 minutes.  She does not seem to be anxious about splashing down shortly.  Her announced plan was to listen on the hour and the half-hour, so I presume she meant 8:30 AM:  Itasca Primary Radio Log entry for 03:45-4? a.m. July 2, 1937 EARHART HEARD FONE/ WILL LISSEN ON HOUR AND HALF ON 3105-SEZ SHE 45/4– .

From "Log Jam" (http://tighar.org/smf/../Publications/TTracks/12_2/logjam.html):

Itasca Primary Radio Log entry for 07:42 a.m. July 2, 1937

KHAQQ CLNG ITASCA WE MUST ON ON YOU BUT
CANNOT SEE U BUT GAS IS RUNNING LOW BEEN UNABLE TO REACH YOU BY RADIO WE ARE FLYING AT A 1000 FEET 42

Aboard Itasca
: The situation is growing more tense. It is clear that Earhart has not heard Itasca’s transmissions although they are now receiving her at maximum strength (S5) indicating that she is within at least one hundred miles and possibly much closer. A second, less detailed, radio log kept by the ship records this message as “EARHART ON NW SEZ RUNNING OUT OF GAS ONLY HALF HOUR LEFT CANT HEAR US AT ALL.” Lt. Cooper’s report and the ship’s Deck Log, however, both agree with the primary radio log that the phrase is GAS IS RUNNING LOW. Cmdr. Thompson knows that the flight should have enough fuel to stay aloft until noon.

Aboard NR16020
: The time is 19:12 and Howland has not appeared as hoped. Earhart has dropped down to 1,000 feet so as to get under the scattered deck of clouds. She and Noonan believe they are very close to their destination but really need to know which way to turn on the line to find Howland. With 188 gals. remaining, enough for just 4.95 more hours, they are now burning their reserve. Gas is running low. There is, however, a contingency plan that will guarantee landfall before the fuel is exhausted. By turning right (157°) and running down the advanced line of position, one of four islands is bound to appear. If they are now too far north they will come to Howland. If they are already south of Howland then Baker, Mckean, or Gardner Island will eventually appear, provided they begin running southeast on the line when they have roughly three and a half hours of fuel remaining. Their situation at this point is serious but not desperate.

Itasca Primary Radio Log entry for 07:58 a.m. July 2, 1937

KHAQQ CLNG ITASCA WE ARE CIRCLING BUT CANNOT HR U GA ON 7500 WID A LNG COUNT EITHER NOW OR ON THE SKD TIME ON 1/2 HOUR (KHAQQ S5 A3) 0758

Aboard Itasca
: Apparently Earhart’s transmissions are coming in so loud that the speakers are distorting her words. At first the operator thinks he hears “WE ARE DRIFTING BUT CANNOT HEAR YOU” but that can’t be right so he goes back, partially erases DRIFTING and types in CIRCLING, which seems more reasonable to him. There is also confusion about how much fuel she has left. If Earhart is really expecting to run out of gas at 08:12 (HALF HOUR LEFT at 07:42) why is she asking Itasca to “GO AHEAD ON 7500 KILOCYCLES WITH A LONG COUNT EITHER NOW OR ON THE SCHEDULED TIME ON THE HALF HOUR” by which time she will already be in the water?

Aboard NR16020
: The time is 19:28 and the situation is now serious enough that Earhart, for the first time, departs from her regular transmission schedule. She probably says, “WE ARE LISTENING BUT CANNOT HEAR YOU” then asks for a long count on 7500 either now or in two minutes. Having failed in repeated attempts to get the ship to take a bearing on her, she will try to use her direction finder to take a bearing on the ship.

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

I agree that witnesses often get things wrong when questioned about events later.

Watch this short video:

Watch the video before scrolling down, I don't want to ruin it for you.

There have
been studies done of this where a group of unsuspecting test subjects suddenly see an event
staged in front of them and it is videotaped. They are then asked what they saw and what is
striking in the research is that the witnesses miss seeing things that are obvious on the videotape.
Based on this research, it is much more likely that Bellarts missed hearing the "half hour left"
statement than that the other guy heard something that wasn't there. In addition, this log entry
was made at the time and it was not yet a particularly stressful time in the radio room as this was
the first report by Earhart that she was having difficulties, so no reason to anticipate the eventual
outcome.

------------------------------------------------------
I think it more likely that Earhart's idea of "on the next scheduled half-hour"  was the next scheduled half hourly scheduled time, 8:00 am, just 2 minutes from her "now."

gl
Title: Re: Fuel load, head winds, range
Post by: Martin X. Moleski, SJ on August 18, 2011, 04:44:43 PM
I agree that witnesses often get things wrong when questioned about events later.

Watch this short video:

Yes.  I flunked the test years ago when I first saw a version of this.  It had a gorilla walking through the crowd of ballplayers.

Quote
I think it more likely that Earhart's idea of "on the next scheduled half-hour"  was the next scheduled half hourly scheduled time, 8:00 am, just 2 minutes from her "now."

Well, her language in an earlier message was "on the hour and the half-hour," so that "on the hour" would mean 8:00 AM and "on the scheduled half-hour" would mean 8:30.  That WAS her announced schedule for listening, so it sounds to me as though she knew it was time for the 8:00 AM broadcast "now" and that she expected to be in the air 30 minutes later at 8:30.  In other words, these messages make me think that she never said "I'm going down 30 minutes from now."
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on August 20, 2011, 05:19:43 AM
I agree that witnesses often get things wrong when questioned about events later.

Watch this short video:

Yes.  I flunked the test years ago when I first saw a version of this.  It had a gorilla walking through the crowd of ballplayers.

Quote
I think it more likely that Earhart's idea of "on the next scheduled half-hour"  was the next scheduled half hourly scheduled time, 8:00 am, just 2 minutes from her "now."

Well, her language in an earlier message was "on the hour and the half-hour," so that "on the hour" would mean 8:00 AM and "on the scheduled half-hour" would mean 8:30.  That WAS her announced schedule for listening, so it sounds to me as though she knew it was time for the 8:00 AM broadcast "now" and that she expected to be in the air 30 minutes later at 8:30.  In other words, these messages make me think that she never said "I'm going down 30 minutes from now."

----------------------------
To help us decide if Amelia actually said "half hour left" it would help if we knew if it were even possible for her to have burned that much gas in that time period. In looking at the various fuel consumptions we have assumed that Earhart flew at the correct speed and ran her engines so as to get the maximum possible range from the fuel on board. What if she didn't, would it have been possible for her to be down to a half hour of fuel at 1912 Z?

The calculations made in the past assumed a BSFC of .46 (Lockeed report 487) and nobody believes that she was able to get the .42 optimistic value in that report which was based on the requirement for her to fly a much longer leg to Tokyo. Nor was there any reason for her to try, since she should have had an abundance of fuel for the significantly shorter leg to Howland.

(BSFC means Brake Specific Fuel Consumption, pounds per hour per horsepower, the amount of fuel burned per hour for each horsepower being produced.) Since AVGAS weighs  6 pounds per gallon we can convert the 1100 gallons on board to 6600 pounds for this calculation. With a BSFC of .46 pounds per hour per horsepower, burning one gallon per hour will produce 13 horsepower. With this shortcut you can just divide the power output by 13 to find the gallons of fuel consumed per hour. Using this BSFC makes it appear that there was no way for her to use up all the fuel so quickly. The trouble with assuming that she operated with that BSFC is that you can only adjust the engines' mixture controls to lean the mixture out the achieve that BSFC at lower power settings and at high power settings you need to run the engines at "full rich" and then the engines burn fuel at a higher rate so the BSFC goes up. Air cooled aircraft engines use this extra fuel flow to dissipate the high heat being produced at high power settings and this extra fuel is not burned and does not produce any extra power.

I have the power setting table from Pratt and Whitney for the S3H1.

According to Pratt and Whitney, each engine burns 65 gallons per hour at the full 600 hp power output making the BSFC .65. (65 X 6 /600 = 65), a total of 130 gallons per hour. Running the engines at full power would have used up the 1100 gallons on board in 8:28 and if only 1050 gallons were on board in only 8:05. But you are allowed to run at 600 HP for only 5 minutes.

Running the engines at 550 hp burns 55 gallons per hour (each side, 110 gph total) making the BSFC .60 and
burning all the 1100 gallons in ten hours causing the engines to fail at 1000 Z so she could have run out of fuel 10 hours and 13 minutes prior to her last transmission. If she departed with only 1050 the engines would have quit at 0933 Z.

Contrary to Lockheed report 487 and other documents that state the BSFC of .42, the best BSFC obtained according to this Pratt and Whitney (the people who manufactured the engines)  table is .48 and this was at 300 and 350 hp. Cruising with 350 hp per engine burns 28 gallons per hour per engine which would have used 1100 gallons in 19 hours and 38 minutes and 1050 gallons in 18 hours and 45 minutes. Cruising with 300 hp per engine uses the 1100 gallons in 22:56 and 1050 gallons in 21:52.

So the answer to the question is YES, it is possible for Earhart to have opperated her engines in such a way as to have consumed all of the fuel in that short period of time.

gl

Title: Re: Fuel load, head winds, range
Post by: Irvine John Donald on August 20, 2011, 10:30:13 PM
I believe if she was burning fuel at that rate she would not continue to Howland. Based on your calculations she would have seen her fuel reserve disappear early enough to divert or return to Lae. Interesting that you think she burned more on this leg than previous legs. Her calculations were based on historical fuel usage and fuel burn rates as calculated by Lockheed.
If she was burning fuel at a greater rate why wouldnt she also mention that in a radio transmission?
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on August 20, 2011, 11:56:09 PM
I believe if she was burning fuel at that rate she would not continue to Howland. Based on your calculations she would have seen her fuel reserve disappear early enough to divert or return to Lae. Interesting that you think she burned more on this leg than previous legs. Her calculations were based on historical fuel usage and fuel burn rates as calculated by Lockheed.
If she was burning fuel at a greater rate why wouldnt she also mention that in a radio transmission?

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

I didn't say that she did. I just said that it was possible.

gl
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 21, 2011, 01:23:48 AM
The as by experience specific  fuel flow weight was 310 lbs/hr (letter AE & radiogram Putnam , 13 feb 1937) , @ 65% CD power for 3.00 MPG specific flight length . For the Lae-Howland leg expenditure was 321 1/4 lbs/hr for 2.56 specific length , 3.6% more consumption which was not alarming so that it was unnecessary to return to Lae , or evade to any other place , let go that shortage would be signalled from aboard . The 321 1/4 lbs consumption was , it is true , for a longer endurance , but for the entire journey fuel stores were sufficient . It was not possible to reach from the Howland region other land points than the island itself (and Baker) , but for Lae-Howland there was no gap between supplies and expenditures .
Title: Re: Fuel load, head winds, range
Post by: h.a.c. van asten on August 21, 2011, 02:54:45 AM
BHP needed was  {(m . g . / CL/CD] . v ]} Watts / 746 hp/W giving for V = 69 m/s    4,838 kg m/s^2 x 69 m/s = 333843 kg m^2/s^3 = 0.334 MW / 746 hp/kW = 448 hp   averaged over the flight . For normal practice BSPC was 310 lbs/hr / 715 hp = 0.43 @ 65% CDP . 448 hp x 1.44 due the headwinds = 645 hp . BSPC for the flight to Howland was 1,028 galls / 19h12m = 321 1/4 lbs/hr , divided by 645 hp gives BSPC = 0.50  for 645 hp / 1,100 hp = 0.59 x 100% = 59% CDP . All figures within reasonable performance features show that there was no fuel supply problem (321 vs 310 lbs/hr/hp is 3.5% more only) for departure to destination , giving this latter found within 1/2 hour after first negative attempt , so that another phenomenon, i.e. one  allied with navigation must have triggered the ultimate breakdown .
Title: Re: Fuel load, head winds, range
Post by: Richard C Cooke on November 16, 2011, 07:33:04 PM

I have the power setting table from Pratt and Whitney for the S3H1.

gl
Any chance of posting this table?

Thanks
Richard Cooke
Title: Re: Fuel load, head winds, range
Post by: Richard C Cooke on November 21, 2011, 10:42:28 AM
Apply some Newtonian Aero Dynamics : The lift needed for an A/c in horizontal flight is from CL . 1/2 . r . S . Vt^2 = m. g . in th dimension Newton (N) . For NR 16020 @ 8,000 ft with r = 0.964 kg/m^3 , S = 42.6 m^2 surface wing , Vt = 69 m/s TAS , Vw = 8 m/s headwind , average mass = 4,932 kg in flight we find : m . g  = 48,383 N with CL = 0.459 lift coefficient . Reasonable glide ratio CL/CD Lockheed 10  is 10 (report Lockheed no.487) . Thence : 48,383 N / 10 =  4,843 is the propeller draft needed . The mechanical propulsive efficiency  ep was 21.6% (0.76 for propellers , Report 487 ; & reasonable 0.28 for the engines) so that for a range R follows : E = (m . g . R) ep^-1 , or by insertion : 4.63(4,838 N x 2,628 mls x 1,6092 m/mi x 1,000 m/km) = 9.47 x 10^10 kg . m^2 . s^-2 in the energy dimension  J  for Joule .  Divide by 47 x 10^6 J / kg gasoline chemical energy and find  2,015 kg , 4,438 lbs , or 740 US gallons for 2,528 mls Lae to Howland , zero wind , duration 19h12m , offset included . The power needed to pull 48,393 N is  CL . 1/2 . r . S . Vt^3  in zero wind , to be transposed to CL . 1/2 . r . S . (Vt + Vw)^3 in the event of headwind speed Vw . (Vt + Vw)^3 = 1.39 Vt^3 . Note that any acceleration factor against resistance translates to the  factor in 3rd power to energy needed  (2 x as fast = 8 x greater energy) . Hence : needed for 2,628 mls in headwind 18 mph , 8 m/s , Beaufort 6 is : 740 galls x 1.39 = 1,028 galls . Remaining @ GMT 1912  22 galls 87 oc & max. 25 galls 100 oc fuel from 1,100 initial store . The specific range was 2,628 mls / 1,028 galls =  2.56 mph , so that by extrapolation follows that after GMT 1912  a maximum distance  47 x 2.56 mls = 120 mls  could be additionally flown . This range is from the Howland region too small for reaching any other in the Pacific land point than Howland itself , or Baker .
I believe you are counting the headwind twice.

The planning flight time at 150mph was 17hrs, and the estimate when they took off was 18hrs, which would be a ground speed of 142mph, implying an average headwind of 8mph.

The actual flight time to Howland appears to be 19.2hrs to the "I must be on you call", which would give a ground speed of 133mph implying 17mph average headwind.

To deal with a headwind you have to choose between longer flight time, or more power, not both.  AE seems to have gone for the longer flying time hence arriving in 19.2hrs instead of 17.

Assuming AE followed the profile in Kelly Johnson's telegrams in 19.2hrs she should have used 870-880 gallons depending on what you assume for warm up and taxi.

Richard Cooke
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on November 30, 2011, 10:02:31 AM

I have the power setting table from Pratt and Whitney for the S3H1.

gl
Any chance of posting this table?

Thanks
Richard Cooke

Yep.

gl
Title: Re: Fuel load, head winds, range
Post by: Richard C Cooke on December 01, 2011, 05:59:34 AM
Thank You   :)

Richard Cooke
Title: Re: Fuel load, head winds, range
Post by: Heath Smith on December 21, 2011, 10:42:02 AM

I believe you are counting the headwind twice.

The planning flight time at 150mph was 17hrs, and the estimate when they took off was 18hrs, which would be a ground speed of 142mph, implying an average headwind of 8mph.

The actual flight time to Howland appears to be 19.2hrs to the "I must be on you call", which would give a ground speed of 133mph implying 17mph average headwind.

To deal with a headwind you have to choose between longer flight time, or more power, not both.  AE seems to have gone for the longer flying time hence arriving in 19.2hrs instead of 17.

Assuming AE followed the profile in Kelly Johnson's telegrams in 19.2hrs she should have used 870-880 gallons depending on what you assume for warm up and taxi.

Richard Cooke

This is a very interesting thread about the fuel consumption.

My question for Richard is this, didn't Earhart need to stick to the flight plan and adjust her heading based on the magnetic declination that she experienced during the flight?

Isn't it critical to adjust your airspeed to match the 150 mph ground speed so that the magnetic influences of the Earth are kept in check when it comes to following your compass heading?

It seems that if you deviate from the plan, as you suggested using a 138 mph ground speed, this would throw a wrench in the entire flight plan? Perhaps I am missing something?

Thank you in advance.
Title: Re: Fuel load, head winds, range
Post by: Martin X. Moleski, SJ on December 21, 2011, 12:10:02 PM
A third article has been published in the December 2011 European Journal of Navigation by the originator of this thread here (http://davidkbowman.com/EJN-New.pdf).
Title: Re: Fuel load, head winds, range
Post by: Heath Smith on December 21, 2011, 12:28:26 PM

Wow, excellent article. Many thanks!
Title: Re: Fuel load, head winds, range
Post by: Bruce Thomas on December 21, 2011, 02:48:10 PM
A third article has been published in the December 2011 European Journal of Navigation by the originator of this thread here (http://davidkbowman.com/EJN-New.pdf).
Although I'm about 5 weeks late doing so, seeing Mr. van Asten's name reminds me to wish him a happy 80th birthday!
Title: Re: Fuel load, head winds, range
Post by: Richard C Cooke on December 21, 2011, 02:59:23 PM
My question for Richard is this, didn't Earhart need to stick to the flight plan and adjust her heading based on the magnetic declination that she experienced during the flight?

Isn't it critical to adjust your airspeed to match the 150 mph ground speed so that the magnetic influences of the Earth are kept in check when it comes to following your compass heading?

It seems that if you deviate from the plan, as you suggested using a 138 mph ground speed, this would throw a wrench in the entire flight plan? Perhaps I am missing something?

Thank you in advance.
Hi Heath

I don't know of any reason for AE to hold a fixed ground speed.

To get optimum range your need to fly faster in the beginning, when the plane is heavy, (L487 starts out with a speed of 162mph) and slower near the end of the flight, so its not a fixed speed.

We know that AE did not hold a 150mph ground speed because if she had she would have covered the 2556 miles in 17hours, as per the strip chart.  Then she would have made her "I must be on you" call 17hrs after take off, not after 19hr 12min.  The 133mph ground speed I gave is from a simple calculation of dividing 2556 by 19.2hrs to give an estimate of the actual ground speed.

Richard
Title: Re: Fuel load, head winds, range
Post by: Heath Smith on December 21, 2011, 03:32:05 PM

Richard,

Didnt the flight plan require exact time and magnetic compass measurements with a fixed ground speed?

Maybe her showing up late is evidence that this was not possible for them, that they could not determine ground speed?

Thanks.
Title: Re: Fuel load, head winds, range
Post by: Martin X. Moleski, SJ on December 21, 2011, 06:13:25 PM
A third article has been published in the December 2011 European Journal of Navigation by the originator of this thread here (http://davidkbowman.com/EJN-New.pdf).
Although I'm about 5 weeks late doing so, seeing Mr. van Asten's name reminds me to wish him a happy 80th birthday!

Hear, hear!
Title: Re: Fuel load, head winds, range
Post by: John Ousterhout on December 21, 2011, 07:13:34 PM
Three things to keep in mind  - 1) best economy airspeed increases with weight,  2) best economy airspeed decreases with decreasing weight, and 3) "economy" gets worse with increasing weight.
In a heavy weight condition, the "best" economy airspeed still sucks gas at a prodigious rate, compared to fuel consumption when lightly loaded, but it gets you towards your destination.  As your weight decreases, you can slow down to a new, "better" most-economical airspeed.

Here's the heart of the conundrum - the most economical airspeed for the lightly loaded aircraft is too slow to even stay in the air for the heavy aircraft, so you're forced to fly faster, even though you're burning more fuel.  That's why the Lockheed engineer gave AE the information for airspeeds and power settings to obtain best range.  He gave the best "MPG" speeds as the fuel weight decreased during the flight in easy incremental steps.

An unexpected headwind would mean that the amount of fuel remaining after X hours is the same as if there were no wind.  The difference is that you might have further to fly after X hours to reach your destination.  The best speed and power setting for best fuel economy didn't change, and those things are determined by air miles, not ground miles.
Title: Re: Fuel load, head winds, range
Post by: Ricker H Jones on December 22, 2011, 11:27:15 AM
I would like to convey this message from Mr. Van Asten:
" Bruce Thomas , on the TIGHAR site , wishes me a happy 80th birthday . Would you plse thank him inmy name since I can´t do it myself , having no entrance to the site . Thank you very much in advance . H ."
Rick
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on December 23, 2011, 01:31:08 AM
Three things to keep in mind  - 1) best economy airspeed increases with weight,  2) best economy airspeed decreases with decreasing weight, and 3) "economy" gets worse with increasing weight.
In a heavy weight condition, the "best" economy airspeed still sucks gas at a prodigious rate, compared to fuel consumption when lightly loaded, but it gets you towards your destination.  As your weight decreases, you can slow down to a new, "better" most-economical airspeed.

Here's the heart of the conundrum - the most economical airspeed for the lightly loaded aircraft is too slow to even stay in the air for the heavy aircraft, so you're forced to fly faster, even though you're burning more fuel.  That's why the Lockheed engineer gave AE the information for airspeeds and power settings to obtain best range.  He gave the best "MPG" speeds as the fuel weight decreased during the flight in easy incremental steps.

An unexpected headwind would mean that the amount of fuel remaining after X hours is the same as if there were no wind.  The difference is that you might have further to fly after X hours to reach your destination.  The best speed and power setting for best fuel economy didn't change, and those things are determined by air miles, not ground miles.
Well actually, a headwind requires a slight increase in airspeed to minimize the deleterious effect of the headwind. The rule of thumb is to increase the airspeed 1/4th of the headwind component and Lockheed report 487 shows this. But this is only true if you are already flying at the most efficient airspeed. For example, let's say that the best range airspeed is 100 knots. If you are flying at 100 knots into a 100 knot headwind then just maintaining the airspeed at 100 knots means that you are going nowhere so you should increase your airspeed to 125 knots. If you are flying faster than the most efficient airspeed then maintaining that airspeed may be the best policy. Continuing the example, say you had been flying at 130 knots instead of 100 knots into the 100 knot headwind. Just maintaining the 130 knots gets you very close to the new best range airspeed of 125 knots.

What we know of Earhart's method is that she never flew slow enough to be at the best range speed based on the weight. The fuel capacity of he plane was enough so that it was not necessary to do so. She averaged about 145 mph on the other legs of the flight and this would not have been possible if she had been flying at best range speeds that were well under this number at light weights. On the leg from Natal to St. Louis she averaged 149 mph for the 1971 SM leg. From the chart for the Dakar flight, and from the Williams strip charts, it is clear that they based their preliminary flight planning on a ground speed of 150 mph but there was no necessity to stick to that number if there was a surfeit of fuel available as it was on the other legs.

The 1912 Z report shows that the ground speed had been at least 133 mph and possibly even faster if Earhart didn't make this report at the exact instant that they thought they had arrived and, as is likely, they had not flown directly to Howland but had added some miles for performing the sun line landfall approach. Since all the information we have shows about a 25 knot (28 mph) headwind component, to achieve a ground speed of 133 mph would have required an airspeed of 161 mph, well above the best range speed as the plane got lighter.

gl

Title: Re: Fuel load, head winds, range
Post by: Heath Smith on December 23, 2011, 07:46:40 PM
Quote
The rule of thumb is to increase the airspeed 1/4th of the headwind component and Lockheed report 487 shows this.

Are you referring to the chart on page 10?

I am wondering if this was not trying to calculate the air speed needed to achieve a ground speed but rather it was given only to show the change in the GPH efficiency?
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on December 23, 2011, 08:34:08 PM
Quote
The rule of thumb is to increase the airspeed 1/4th of the headwind component and Lockheed report 487 shows this.

Are you referring to the chart on page 10?

I am wondering if this was not trying to calculate the air speed needed to achieve a ground speed but rather it was given only to show the change in the GPH efficiency?
The graph on page 10 is the standard way for finding the best range airspeed, NOT ground speed. You plot fuel flow rate (or power required) on the X axis and airspeed on the y axis. You then draw a line from the origin tangent to the curve and read the best range airspeed from the point of tangency. Shifting the starting point of the line right or left is how you figure the best range airspeed depending on wind. This is all standard engineering.
gl
Title: Re: Fuel load, head winds, range
Post by: Jeff Scott on December 24, 2011, 05:22:04 PM
A third article has been published in the December 2011 European Journal of Navigation by the originator of this thread here (http://davidkbowman.com/EJN-New.pdf).

One of the puzzling aspects of Mr. van Asten's time with us was his very difficult to read writing style that made many of his points hard if not impossible to understand. Had he communicated with the same talent displayed in this article, he would have gotten along just fine!
Title: Re: Fuel load, head winds, range
Post by: Heath Smith on December 24, 2011, 06:27:11 PM
Quote
The 1912 Z report shows that the ground speed had been at least 133 mph and possibly even faster if Earhart didn't make this report at the exact instant that they thought they had arrived and, as is likely, they had not flown directly to Howland but had added some miles for performing the sun line landfall approach. Since all the information we have shows about a 25 knot (28 mph) headwind component, to achieve a ground speed of 133 mph would have required an airspeed of 161 mph, well above the best range speed as the plane got lighter.

Gary,

Have you ever created your own model of the entire flight from Lae to Howland and made an estimate of the fuel remaining? If so, can you post those results?

Thanks.
Title: Re: Fuel load, head winds, range
Post by: Gary LaPook on December 25, 2011, 03:46:17 AM
A third article has been published in the December 2011 European Journal of Navigation by the originator of this thread here (http://davidkbowman.com/EJN-New.pdf).

One of the puzzling aspects of Mr. van Asten's time with us was his very difficult to read writing style that made many of his points hard if not impossible to understand. Had he communicated with the same talent displayed in this article, he would have gotten along just fine!
I have read his third article and it is gibberish like the prior two. I am not going to get sucked into dissecting  every aspect of this article but I will point out four items.

1. He uses the wrong weight for the plane, 16,400 pounds, while the weight at takeoff did not exceed 15,000. What is interesting in that it demonstrates Mr. van Asten's lack of knowledge by the way he calculated this. He started with the maximum gross weight of 16,500 pounds and subtracts 1,200 gallons of fuel weighing 7,200 pound giving him an empty weight of 9,300 pounds. He then adds the 6,600 pounds for the 1,100 gallons of gas the plane carried on takeoff from Lae plus 500 pounds for the crew and equipment coming up with his 16,400 pounds. What is wrong with this is his assumption that the only payload of the plane was the 1,200 gallons of fuel, he left out the crew, equipment and any cargo from the beginning of his calculation. The documentation actually shows that the empty weight was 7,340 pounds not the 9,300 upon which van Asten based his calculations. To this real empty weight we add 340 pounds of crew, 6,600 pounds of fuel, 562 pounds of oil for a total of 14,842 pounds leaving some extra capacity for equipment before exceeding 15,000 pounds. The effect of weight on range is inversely proportional to the weight and van Asten overestimated the weight by 9 or 10% causing him to underestimate the range by the same 9 or 10%.

2. He calculated the time to fly from Lae to Howland as exactly 18 hours, 50 minutes and 8 seconds but he doesn't tell us where he started the timing from, was it at the beginning of the takeoff roll, or when the tail came up, or when the main wheels left the ground, or when they cleared the end of the runway, or some other blade of grass on the runway. Mr. van Asten uses impossible levels of precision in his calculations which mean nothing in the real world.

3. He uses the Breguat formula for part of his calculations but this formula is only valid if the plane is flown, at all times, at exactly its best range speed which get slower and slower as the plane burns off fuel and gets lighter and we know Earhart did not follow the Breguat regime but flew at considerably higher speeds, so the use of that formula is invalid for van Asten's calculations.

4. I get a real chuckle out of this one, he now admits the position report was received at Lae at 0718 Z when in his prior arguments he claimed it was sent at 0720 Z in support of his complex calculations that showed that Noonan took an observation of the sun at exactly 0719:30 Z to produce that position report but this claimed observation would have been taken one and a half minutes after the report had been received at Lae. Now that he admits that the report was received two minutes prior to the time that he thought the position report had been sent from the plane, this shows that he was wrong since you can't receive a radio report earlier than the time that it was sent. This was the subject of several months of postings earlier this year. A minute and a half error may not sound very significant to readers but it was absolutely critical to van Asten's theory in his two prior articles, everything flowed from that erroneous computation. In celestial navigation a one and a half minute difference in the time of a sight is HUGE since it produces an error of 29 SM because the plane is moving and, more significantly, the Earth is turning at a rate 1,035 mph - 17.25 SM per minute. (I wonder if he will now go back and retract his prior erroneous articles but I doubt that he will.)

Here are links to what I have written about the quality of van Asten's prior articles.