For the takeoff at Lae the plane weighted about 14,000 pounds. 14,000/16,500 = 0.848 which squared equals 0.719 times 2100 feet means the takeoff at Lae should have taken 1,512 feet. Adding 243 pounds of fuel, and doing the same calculation results in a takeoff distance of 1,565 feet, only 53 feet longer, not much to worry about.

gl

Is your point that she should have considered 3000 feet plenty enough runway since the plane theoretically should have been able to get wheels off the ground in 1565 feet? And does that figure take into account the unpaved runway surface and an elevated density altitude (high humidity and mid-morning temperature in the 80's)?

LTM,

Mona

That estimate did account for the unpaved runway but did not account for the density altitude. I used the wrong weight, 14,000 pounds, her weight at Oakland. Her actual weight at Lae was probably only about 500 pounds more than at Oakland, she had about 150 gallons more fuel, weighing 900 pounds, but she was also short two people, Manning and Mantz, and their baggage, totaling about 400 pounds. So the weight was probably about 14,500 pounds but I will be conservative and overestimate the weight and use 15,000 for this calculation.

I have attached three years of data for 14 weather reporting stations in Papua New Guinea. This should be a representative sample and should validly predict the temperatures for 1937. Similar data would have been used in making the decision on whether more power was needed for the takeoff at Lae. The nearest reporting station to Lae is Nadzab located 22 SM inland from Lae. The highest July temperature recorded there during the three year period was 30.1 ° C (86 ° F. ) The temperature should be lower at Lae since it is located on the coast. A 30 ° C temperature at a sea level airport produces a density altitude of 2,000 feet which would increase the takeoff distance by only 6% from the sea level density takeoff performance. Lockheed report 487 states that a sea level takeoff takes 2,100 feet so increasing this by 6% would predict a takeoff at a 2,000 foot density altitude would take 2,226 feet, well short of the 3,000 feet available at Lae. But even this distance is based on a gross weight of 16,500 pounds and we know the plane actually weighed no more than 15,000 pounds at Lae. Takeoff performance varies with the weight ratio squared. Dividing 15,000 by 16,500 gives 0.909 which squared makes 0.826 which multiplied by 2,226 feet gives the predicted takeoff run at Lae at a gross weight of 15,000 pounds and at a two thousand foot density altitude of 1,840 feet giving a safety margin for takeoff at Lae of more than 1,160 feet, a 63% safety margin.

The runway was grass at Lae and not paved. Modern takeoff performance data is calculated for paved runways but Lockheed did the calculation for a turf runway since paved runways were a rarity in 1937. Page 2 of report 487 states that it takes 2,100 feet to take off "on a hard run-way" so I can see why you would think the calculation was for a paved runway. But look at page 21, where they go through the actual calculation, where is shows that the calculation was for "a good field with hard turf." The calculation uses a coefficient of friction ( μ, mu) of .04 for the calculation which is the μ for turf. The μ for pavement is .02, for short grass μ is .05 and it is .10 for tall grass. The coefficient of friction affects the takeoff roll because it retards the acceleration, the greater the μ the slower the acceleration. This retarding force gradually drops to zero as more and more of the weight of the plane is carried by the wings as speed increases. At the same time the drag due to increasing air resistance increases which slows down the acceleration as the plane approaches takeoff speed. All of these factors are accounted for on pages 21-23 which steps you through the calculation and you can redo the calculations yourself by substituting your chosen value for μ. If you don't want to go through the entire calculation you can use a rule of thumb to come up with a reasonable adjustment for longer grass at Lae. The rule of thumb is to increase the distance for takeoff from a paved runway ( μ = .02) by 7% for turf, 10% for short grass and 25% for tall grass. First back out the 7% for the turf runway that the calculation assumed and then apply the percent increase for different runway surfaces. But the runway at Lae was also described as "turf" and it looks like "turf" on the video, so the value calculated in report 487 should be applicable. At the worst, the runway is "short grass" and not "tall grass." Using the rule of thumb would increase the takeoff distance only 50 feet more for "short grass" rather than "turf."

If you want, you can also use these formulas for calculating the takeoff distance for different gross weights and for density altitude. If adjusting for gross weight you must first calculate the takeoff speed using the normal formula for lift. The takeoff speed also determines the dynamic pressure, "q", which you need for the takeoff formula and also is needed for determining the final thrust from the table on page 21.

If you want to do the calculation for a different density altitude then you again calculate the takeoff speed but you must substitute the density of the air at the altitude that interests you. ρ at sea level conditions is .002378 slugs per cubic foot but gets less at higher density altitudes. You also use the air density in the takeoff formula as the divisor under the gross weight. In this case it is used in the form of pounds per cubic foot. You can calculate this value by multiplying ρ by 32.17 pounds per slug conversion factor. The other number that shows up in the formula, "458" is the wing area and is a constant.

I don't know if you fly supercharged airplanes but density altitude is not the bugbear for takeoff of supercharged airplanes that it is for naturally aspirated airplanes. This is because there are two ways density altitude (another way of describing the density of the air, rho, that changes with actual height above sea level and with temperature) affects takeoff performance. The first effect is that the airplane must accelerate to a higher true airspeed in order for the indicated airspeed (and q, the dynamic pressure) to increase to the level that the wings can make enough lift for the plane to get off the ground. If the Electra at standard sea level conditions took off at 85 mph indicated airspeed which is also 85 mph true airspeed at zero density altitude, it would still takeoff at 85 mph indicated airspeed but the true airspeed at 2,000 foot density altitude would be 87 mph. It takes a bit longer to accelerate to 87 than it does to 85.This effect on takeoff is equal to the inverse of the density ratio. Air at standard sea level conditions, zero altitude and 59° F, has a density of .002378 slugs per cubic foot while air at standard temperature at 2,000 feet (a 2,000 foot density altitude) has a density of .002242 making the density ratio of .9428. One divided by .9428 equals 1.06 so the takeoff should take about 6% more runway than at a density altitude of sea level.

The second effect that the air density has on takeoff performance is that the power output of the engine also drops off as the air gets thinner so the engines produce less thrust which then reduces the rate of acceleration so it takes even longer for the plane to reach the higher true airspeed needed to takeoff at a density altitude above sea level. This is a problem for airplanes with naturally aspirated engines but is NOT a problem with supercharged engines below the critical altitude since these engines produce full sea level power up to the critical altitude. The type certificate data sheet for the S3H1 engine shows that the critical altitude for takeoff power of 600 horsepower is a 3,000 foot density altitude. This means that her S3H1 engines would produce full 600 hp takeoff power for the takeoff at Lae even if the temperature was 110 ° F but we know that it was no more than 86° F. The engines will also produce the 550 hp continuous rating up to a density altitude of 5,000.

Since these two effects parlay for an airplane with naturally aspirated engines, such a plane would use about 36% more runway at a 2,000 foot density altitude compared to zero density altitude. But since the Electra had supercharged engines and the density altitude did not exceed the critical altitude, the increase to the takeoff distance would be only the 6% previously mentioned.

And looking at the runway gradient, Long states that they had to taxi uphill to get to their starting position on the runway which would mean that they had a downhill gradient for takeoff which would help them and shorten the takeoff roll.

gl