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### AuthorTopic: Physics Question  (Read 8411 times)

#### Ric Gillespie

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##### Physics Question
« on: March 09, 2022, 09:20:51 AM »

The available evidence strongly suggests the aircraft struck the rocky island in the pond and blew up. No engine or prop has been found on or near the island, so we have to assume the engine and propeller separated from the aircraft and went ballistic.   How far they could go would seem to be a fairly straightforward physics question.

The engine weighed about 960 pounds.  We don't have a weight for the enormous aluminum prop, but 40 pounds seems conservative, so a total weight of 1,000 pounds for the whole assembly should be close.  Our best guess is that the aircraft was moving at about 40 mph at the time of impact/explosion.
1. How far would a 1,000 pound cannon ball travel before it hit the ground (or water) if fired from a cannon at a muzzle velocity of 40 mph (58.66 ft/sec) if the muzzle was 4 feet off the ground?
2. How fast is it going when it hits the ground (or water).
3. Assuming it hits water, how far will it travel before coming to a stop?

Of course, and engine and prop will have more drag than a cannon ball, but this is a good starting point for figuring how far the engine might be from the island.
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#### Bill Mangus

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##### Re: Physics Question
« Reply #1 on: March 09, 2022, 11:11:16 AM »

Not a physicist, but have to consider spherical expansion of the "three explosions in rapid succession" heard by Nicholas McGrath.  Not all of the force would have been focused on the engine.  Maybe even consider reflection off the rocks/water also.  All the explosions may have done is break the engine free of the aircraft and the momentum of the a/c's forward motion would have propelled it forward some distance, say around 30 or 40 feet as a guess.

Addition:  Have to consider that when the bow of the hull of the a/c hit the rocky island it wouldn't just stop. the bow would have certainly crunched but at the same time it would have been forced upwards and tried to ride over the pile of rocks as the engine/fuel tanks collapsed together and detonated.  There's still some residual forward motion present.  How much would depend on speed at moment of impact, the depth or draft of the hull at impact, perhaps changed by any last second instinctive yanking back of the stick/wheel when the rocks were seen.  I'll change my estimate to somewhere between 50 and 100 feet from the rocky island.

Sounds like a problem for a naval architect/engineer, maybe a class project at Air Force or Naval academy since both aspects apply.
« Last Edit: March 09, 2022, 12:42:12 PM by Bill Mangus »
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#### Martin X. Moleski, SJ

• Posts: 3006
##### Re: Physics Question
« Reply #2 on: March 09, 2022, 11:32:10 AM »

1. How far would a 1,000 pound cannon ball travel before it hit the ground (or water) if fired from a cannon at a muzzle velocity of 40 mph (58.66 ft/sec) if the muzzle was 4 feet off the ground?

The weight of the projectile is relatively unimportant.

Galileo and the guys in the moon hoax  showed that a canonball and a feather are accelerated toward the center of a massive object at the same rate.

You will have make guesses about the coefficient of drag because that will cause the velocity of the engine and prop to fall off continually from the time your cannon is fired until the projectile hits the ground.

I am pretty sure that this means you need calculus to get an excellent answer to your question.

Here is a free fall calculator.  The time that a projectile will be in the air is identical to the time that it takes to drop something straight down.  The same force that makes something fall straight down will act continually on the projectile, assuming that it is not in the shape of a lifting body.

Gravitational acceleration (g) 9.80665 m/s²

Initial velocity (v₀) heading straight down = 0 ft/s

Height (h) 4 ft

Time of fall (t) 0.4986
-----------------------------

58.66 feet per second times 0.4986 seconds = 29.247876 feet

In other words, probably in or near the pond.

One source among dozens, if not hundreds: Does a Fired Bullet Hit the Ground at the Same Time as a Dropped One?
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2. How fast is it going when it hits the ground (or water).

I'm going to say fractionally less than 58.66 fps, but not enough to make any difference.  The impact of 1000 pounds going somewhere near that velocity is going to hurt whatever it hits.

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3. Assuming it hits water, how far will it travel before coming to a stop?

Not far!  It's not going to skip like stone, which must be lyric from some 1960s folk song.  The straight-down velocity after 0.4986 seconds of free-fall will be 4.89 meters per second.

"Banking off of the northeast winds,
Sailing on a summer breeze,
And skipping over the ocean like a stone."

Fred Neil and Harry Nilsson, "Everybody's Talkin,'" 1966, featured in Midnight Cowboy in 1969.

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Of course, and engine and prop will have more drag than a cannon ball, but this is a good starting point for figuring how far the engine might be from the island.
LTM,

Marty
TIGHAR #2359A

« Last Edit: March 10, 2022, 12:45:18 AM by Martin X. Moleski, SJ »
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#### Ric Gillespie

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• "Do not try. Do or do not. There is no try" Yoda
##### Re: Physics Question
« Reply #3 on: March 09, 2022, 02:24:02 PM »

There's something wrong. The island is roughly 60 feet (18 meters) long by 40 feet (12 meters) wide at its widest point. I'm not arguing with the math, but if the plane comes to a screeching stop and explodes as soon as it hits the island, and the engine/prop assembly breaks free and travels only 29 feet before hitting the ground, it never even gets to the water unless it bounces there. (In the photo below, the yellow line is 29 feet long.)  As you can see, the rocky bottom is visible in the photo for quite a way all around the island and that area has been well-searched.  There ain't nothin' there.

So, somehow, the engine and prop assembly ended up further from the island than it would have if the airplane came to a screeching stop and exploded as soon as it hit the island - and yet a significant amount of debris, including (possibly) fragments of the fuel tanks and a landing gear support attachment form the hull, was left on the island.
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#### Don White

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##### Re: Physics Question
« Reply #4 on: March 09, 2022, 02:38:28 PM »

The engine fell off before it got to the island? Not a serious suggestion. Then again, if there was an explosion in the air first...

This seems to have as many variables as figuring out Earhart's fuel consumption.

Visualizing this, I picture the engine possibly not going in a straight line after it detached due to the imbalance of its mass and resistance (air or water) of the propeller. Also thinking about whether the engine was pushed away by an explosion or only detached by explosion or impact and carried away by momentum.

One of those three explosions could be impact, another an explosion of the remaining fuel, and the third? Or an explosion in air, impact, final explosion? Perhaps an impact with water, then island, then exploding fuel?

I've asked before whether Nungesser and Coli had practiced water landings before their departure. Were there any tests of this landing system? It seems like they just built it and took off. In their way, they seem to have the same kind of contradiction as Earhart, of preparation for some aspects of the flight combined with no preparation for others, and those the most important, like would this thing actually land as designed.

LTM,
Don W
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#### Bill Mangus

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##### Re: Physics Question
« Reply #5 on: March 09, 2022, 03:49:59 PM »

Thats a very interesting picture!  Thought experiment:

Superimpose a clock face on the picture with 12 o'clock straight up at the top.

Now look at roughly the 8 o'clock position.  No partially submerged rocks in that area.  If you look at 9 -10 o'clock there's a ridge of partially submerged rocks heading outwards in that direction.  Same at roughly the 6:30 direction.  Could those rocks have been pushed into those two "ridges" by the impact of the bow on the island?  Think of a power boat beaching itself on a sandy beach.  The bow pushes up the sand in a vee-shape on either side.  Ric, your yellow line may be nearly perpendicular to the direction of travel.

Now look at roughly 3 o'clock.  Note how the island sort of bulges out in that direction.  Could that bulge be rocks that were displaced from the top of the island as the a/c rode up and over the island?  That would account for landing gear support attachment debris and perhaps fuel tank pieces being found on the island, scraped off as the rest of the a/c continued on into the pond exploding as it went.  remember McGrath three explosions in rapid succession.  To me that means about 1/2 second apart.

Ric, if you extend a line from the 8 o'clock position out to the shore of the pond, is it along the long axis of the pond?

« Last Edit: March 09, 2022, 04:06:46 PM by Bill Mangus »
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#### Simon Ellwood

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• Posts: 34
##### Re: Physics Question
« Reply #6 on: March 10, 2022, 02:42:35 AM »

As Martin X mentions above, the weight of the engine/prop isn't important - a more important variable is the trajectory angle (from horizontal upwards).

Calculus (and any artillery/gunnery guys) will tell you that you get maximum range for a gun with a given shell velocity at an elevation angle of 45deg up from the horizontal, so the same would go for our hypothetical ballistic engine/prop mass after hitting the island (neglecting air resistance).

If we assume 45deg up to get the maximum possible distance before 'splash down', the best method for calculating the distance is to first work out the time of flight using the (initially upwards) vertical velocity of the engine/prop and apply gravity downwards:-

So, considering only velocity in the vertical direction, initial vertical velocity = 40mph x Sin(45deg) = 28.3mph.

Gravity acts with an acceleration of 22.1mph/s in a downwards direction, so the engine/prop rises vertically for 28.3/22.1 = 1.28s until it reaches maximum height, then it follows that it then falls for a further 1.28s before hitting the water =>  total ballistic flight time = 2.56s

Since the engine/prop is also moving horizontally at 40mph x Cos(45deg) = 28.3mph and it travels for 2.56s

Distance (in feet) = (28.3mph x 2.56s x 5280feet/mile)  /   3600s/hour  =  106.26 feet

The above calculation does not take into account air resistance.

EDIT: One other thing not taken into account in the above - if there was an explosion on hitting the island and that gave the engine/prop extra impetus in the direction of travel i.e. speed > 40mph
« Last Edit: March 10, 2022, 11:04:02 AM by Simon Ellwood »
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#### Ric Gillespie

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• "Do not try. Do or do not. There is no try" Yoda
##### Re: Physics Question
« Reply #7 on: March 10, 2022, 01:21:53 PM »

Thanks Simon.  Excellent input.

Here's something else to consider:
The PL-8 was a modification of the PL-4 naval observation aircraft. The idea was to give carrier-based aircraft water-landing capability in case they couldn't get back to the boat.  The ship would go find them and hoist them back aboard.  The PL-4 not only had a watertight, boat-shaped hull, but also floats ("ballonnets") on the outer lower wing.  Nungesser and Coli decided to forego the floats on the PL-8, no doubt to save weight and drag - but there is no record of the PL-8 ever being tested in a water landing, nor is there any indication that Nungesser had any experience with flying boats.

The French documentary (https://youtu.be/J0wfgp-uVTE) includes film of a PL-4 making a demonstration water landing on a river. You'll find it at 38:59 into the documentary and it's only a few seconds long, but if you study it closely you'll see that, immediately after the aircraft first makes contact with the water, the right wing dips and the float on that side returns the plane to an even keel. Without the float, the wing would have grabbed the water and spun the aircraft uncontrollably to the right. According to an experienced seaplane pilot, when that happens, the flat-sided fuselage catches the water, the aircraft tries to roll inverted, and the right wing(s) collapse upward.

In any case, without wing floats, the PL-8 was almost incapable of a safe water landing.  Nungesser probably lost control of the machine almost immediately after the hull touched the water, which might explain why the plane hit the island.  Once a wing snagged, he and Coli were passengers.  The plane might have struck the island going sideways or even tumbling which, of course, would effect the trajectory of the engine and could produce the howitzer parabola described by Simon.

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#### Ric Gillespie

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• "Do not try. Do or do not. There is no try" Yoda
##### Re: Physics Question
« Reply #8 on: March 10, 2022, 02:15:39 PM »

The accident might have been much more violent than we thought.  After 34 hours of flight with six hours of fuel remaining, the aircraft weighed in the neighborhood of 5,400 pounds.  Imagine that much weight careening out of control at roughly 40 mph or maybe more; striking the island, and setting off 158 gallons (almost a thousand pounds) of avgas.
I don't see any way to configure a search other than to draw two concentric circles around the island. We know the engine is not within this circle, and it can't be outside this circle.  The smaller we can make that second circle, the better.
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#### Martin X. Moleski, SJ

• Posts: 3006
##### Re: Physics Question
« Reply #9 on: March 11, 2022, 12:17:24 AM »

Imagine that much weight careening out of control at roughly 40 mph or maybe more; striking the island, and setting off 158 gallons (almost a thousand pounds) of avgas.

OK, I've imagined it.

And in my imagination, I draw on lots of fireballs created by drag cars and other explosions caught on film.

And think about the stories of how ineffectual bombs are when just sitting next to a structure.

Bullets thrown into a fire or cooked in a microwave do not go far.  The fit between the barrel and the bullet makes sure that the burning gases push the bullet in the right direction.

Too much Mythbusters!

1000 pounds of avgas might make a great fuel-air explosive, but I can't see it adding much to the kinetic energy of the engine.  The structure of the airframe may have been crude by our standards, but I imagine that the engineers of that time knew how to build decent engine mounts.  Any force great enough to tear the engine off the mounts through a glancing blow is going to eat up a lot of the energy needed to follow a ballistic trajectory.

Well, that's my report from my coulda-shoulda-woulda generator.
LTM,

Marty
TIGHAR #2359A

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#### Don White

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##### Re: Physics Question
« Reply #10 on: March 12, 2022, 07:05:39 AM »

Yes, Hollywood has conditioned our views of what explosions look like and how they are caused. You'd think every car crash ends in a fire, which they don't in real life.

1000 pounds of avgas would not actually explode. Rather, once ignited, it would burn rapidly until consumed. What explodes -- not the most accurate term, it's really rapid combustion -- are the fumes in the tank or wherever else they are sufficiently concentrated.

I learned in boating safety that a gasoline-engined boat is most fire-prone when the tanks are nearly empty, but less so when they are full, due to the greater amount of gasoline-air mixture present in the empty tank. Boats are particularly subject to fires because they are enclosed and the fumes, which are heavier than air, remain in the bilges. All it takes is a switch that sparks when turned on, when the boat is first started up. Hence the need to ventilate the space before starting. On airplanes or cars, the fumes that escape the tank will fall below the vehicle and dissipate.

So there is a likelihood of explosion on the White Bird when the fumes are ignited, then it crashes and continues to burn. If the tanks weren't where the fire started, there would be an explosion as the fumes inside caught fire. So you could have an impact, followed by one or two explosions, and then a fire continuing as long as there was fuel.

It appears we have been thinking in terms of an attempted landing gone wrong, that the pilot was in control of the airplane on the way down. It has occurred to me, what if there was an event while still in the air? The pilot might then be trying to land a damaged aircraft, or already out of control and crashing.

Also I note looking at the pictures of the airplane, that from where he was sitting, forward visibility in landing was probably nil. He couldn't have seen where he was going or that there was an obstacle (which also may have been less exposed than it is today).

LTM,
Don

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#### Bill Mangus

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##### Re: Physics Question
« Reply #11 on: March 12, 2022, 10:09:38 AM »

I believe the three explosions Nicholas McGrath heard were from the hot engine crashing through the half-full (or less) aluminum fuel tanks as the a/c ran up on the rocky island, igniting the fuel/air mixture therein.  Eyewitness accounts Ric detailed in the last TT describe the plane streaming white "smoke" or vapor, not black smoke as would be expected from and engine fire, so I doubt anything catastrophic happened until it touched down and hit the island.
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#### Ric Gillespie

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• "Do not try. Do or do not. There is no try" Yoda
##### Re: Physics Question
« Reply #12 on: March 12, 2022, 10:55:17 AM »

1000 pounds of avgas might make a great fuel-air explosive, but I can't see it adding much to the kinetic energy of the engine.

I think that's a reasonable conclusion.  We still need to come up with a plausible scenario that puts the engine and prop someplace where they have not been found.

At gross weight of 5,181 lbs., the PL-4 had a wing loading of 8.2 lbs/sq. ft which would give it a stalling speed around 40 mph. My best guess is the water landing run shown in the film is between 50m (164 ft) and 75m (246 ft).

At it's max gross of 11,089 lbs., the PL-8 wing loading was 17 lbs. giving it a stalling speed north of 60 mph, but (by my calculations) by the time it got Newfoundland after 34 hours of flight, it had burned off 5,657 lbs of fuel bring its total weight down to 5,432 lbs which meant a wing loading and stall speed similar to the PL-4 and a similar landing run in a normal landing.  For perspective, in the image below the White Bird is shown to scale with a 75 meter trail behind.

But the landing at the Gull Pond was not a normal landing, so I would expect the crash trajectory would be shorter than a normal landing run.
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#### Ric Gillespie

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• "Do not try. Do or do not. There is no try" Yoda
##### Re: Physics Question
« Reply #13 on: March 12, 2022, 11:14:01 AM »

So there is a likelihood of explosion on the White Bird when the fumes are ignited, then it crashes and continues to burn.

If the plane blew up in flight and crashed, the engine could be anywhere and the presence of wreckage on and near the island was pure coincidence.

A crash resulting from an explosion, rather than an explosion resulting from a crash, is possible - but I would not call it a likelihood.  What would cause an inflight fire in an airplane without an electrical system?
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#### Ric Gillespie

• Executive Director