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Recently, while fretting about an air trip I had to make, I wondered why airplanes don't carry parachutes for passengers in case of a mid-flight disaster.  Turns out the answer is both practical and logistical: the parachutes would add a lot of weight, the percentage of disasters that happen in mid-flight is in the single digits, and skydivers require four hours of parachute training which is impossible to do for every passenger on every flight.  So then I thought, why not just train the crew and pack only a few parachutes large enough to support a crew member and several passengers?

And then that unexpected bolt of inflation inspiration (inspflation?) hit me again: make the crew the parachutes... so to speak.

Then I needed to figure out how big each crew member needed to be to make a soft landing.  So I scienced.

WARNING: MATH AND PHYSICS NERDINESS CONTAINED HEREIN

If Earth were a vacuum, its gravity would cause a falling object to continue accelerating at 9.8 m/s^2 all the way down until it landed.  However, Earth is not a vacuum, and the air applies drag forces on anything that travels through it.  In the cases of falling objects the drag creates a terminal velocity, which is the velocity at which the object will stop accelerating because the upward forces of drag and buoyancy equal the downward force of gravity.  It doesn't cause the object to stop falling, but it does prevent the object from falling faster.

On average, the terminal velocity for humans on Earth is about 53 m/s in a standard skydiving posture, and a skydiving parachute will slow a person down to a terminal velocity of 6 m/s.  That wasn't good enough; I wanted an even softer 3 m/s landing for the airline's paying customers.

The terminal velocity equation is as follows:

velocity = √( 2 * mass * force of gravity / ( drag coefficient * density of air * cross-sectional area of object ) )

And since our object is a sphere, a cross-section of a sphere is a circle, with area = pi
 * radius^2.  So the whole equation would be:

velocity = √( 2 * mass * force of gravity / ( drag coefficient * density of air * pi * radius^2 ) )

The above equation determines the velocity given all the other values, but in our case we knew the velocity (3 m/s) and wanted to determine radius.  Reworking the equation to solve for the radius is easy:

radius = 
√( 2 * mass * force of gravity / ( drag coefficient * density of air * pi * velocity^2 ) )

The values we know are:

mass = weight of female crew member (59kg / 130lbs) + (average weight of US citizen (80kg / 175lbs) * number of passengers carried)
force of gravity = 9.8 m/s^2
drag coefficient of a sphere = 0.5
density of air = 1.29 kg/m^3 (it's closer to 1.5 at sea level but thinner at higher altitudes)
pi = 3.14159265358...
velocity = 3 m/s

With all of that, I had a formula primed and ready for a spreadsheet to help me write the story: docs.google.com/spreadsheets/d…

One thing I would've liked to do is calculate how long it would take (in seconds and in altitude) for the person to decelerate to 3 m/s while they are inflating, but that would've been much more difficult.  Since the radius would still be changing as she inflates, and even the mass would change as people land on top of her, that would've required a differential equation and it's been too damn long since I've even attempted one.  So I was intentionally vague on a lot of that, and we can just assume that they inflate very very quickly.

As for how they inflate, just assume that it's a combination of the force of air as they fall and a high-speed fan in the harness that adjusts the airflow as necessary.  I didn't think it was important so I didn't want to take up story space explaining it.

Hope you enjoyed it.
Published:   |  Mature
© 2017 - 2021 doubleintegral
Comments29
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I would have climbed on he breasts and started squeezing with her breasts between my leggs
gener8onslost's avatar
nice job! I was expecting some inflation-related shenanigans (considering the author), but this gave me a few surprises. it's also very interesting in the details, and you know exactly what needs to be left slightly vague. =D (Big Grin) 
heliumgirl77's avatar
Yay for science-ness!

*Thinks a little harder.....*

Ooooh...... *goes into that wide-eyed-oh-dear-just-thought-of-this-sort-of-look*

Does Miranda....keep her normal body temperature? While she is inflated, I mean? Either because of her metabolism or the sun warming the trapped air inside her? It must be like a greenhouse in there..... I just ask because...you know...hot air rises.

If she is 20 degrees or so warmer than the surrounding air....and 277 feet wide....someone else do the maths!

Sunburn might be the least of her problems.
doubleintegral's avatar
Well I'll be damned.  I hadn't thought of any of that.
heliumgirl77's avatar
But this story manages to be smutty and funny and character-warming at the same time. It made me smile at the end of a long day. Big hugs for writing!
heliumgirl77's avatar
en.wikipedia.org/wiki/Hot_air_…

Thank you wiki people ! *imagines wiki people to be like magical clever elves*

So.....20-degrees-warmer Miranda experiences an upwards force of 0.060 kg per cubic metre. She has a radius of about 41 metres. So a volume of..oooh...288,000 cubic metres. So she has a net buoyancy of about 17 tons!

That's more than enough for her 20 passengers to be worried about their next direction of travel! If they don't get help soon, then they had better disembark...quickly!

*puts on bobble hat of extreme cleverness*
SkeletalBookeeper's avatar
Great concept here, and wonderfully executed! Very practical, enjoyable, and just a great way to indulge this lovely fetish while also forging a solid story. I like that Richelle has consequences from blowing up that enormous, that quickly- though I hope there's nothing too problematic with her- she seems the kinda gal who would *grow* to enjoy being a blimp. 

Awesome to see more from you as always :) 
doubleintegral's avatar
Don't forget about Jessi, too.  When it comes to problems, those two are peas in a pod.  Very large peas, amirite??
SkeletalBookeeper's avatar
Heh, oh yeah! :D The larger the better!! ;) 
With your stories, do you usually have one protagonist far larger than others? 
doubleintegral's avatar
I don't often have more than one inflatee in my stories, but yes, I have made use of that plot element before.
SkeletalBookeeper's avatar
Ahh, alright! Awesome, thank you for answering! :) 
perchedontheloon's avatar
First, your creativity is impressive. You managed to write a great story that features inflation in the most low-key and unassuming way possible, and it was highly enjoyable. For that, I applaud you. You have a deft hand when it comes to crafting stories. Keep it up! 
doubleintegral's avatar
Thanks!  It feels good to finally claw my way out of the idea drought I had for the last couple years, and it's particularly rewarding to see that an unusual, non-sexy idea is well-received.
dkfenger's avatar
The understatement in the third paragraph greatly amused me.

Will you do any followup to show what happens to Jessi and Richelle later?
doubleintegral's avatar
I'm glad someone appreciated that.  Understatement is a really... um... understated comedic tool.

It's not in my nature to do sequels so we've likely seen the last of Jessi and Richelle.  I debated continuing the story to expound on their ultimate fate, but the honest truth is that it wasn't shaping up to be very interesting.
heliumgirl77's avatar
The understatement was great....but I thought "therefore" was perhaps the wrong word; you established Mark as relatively clueless and yet still capable of recognising a serious problem. Maybe "However" or "Despite this" would be more appropriate?
doubleintegral's avatar
Good point.  I think I may have used "therefore" to intentionally mislead the reader just prior to revealing the problem, but you are correct that it doesn't really fit there.
dkfenger's avatar
Fair enough.  Leaves something to the imagination for fans of either fate.
doubleintegral's avatar
Indeed.  Even I couldn't decide how I wanted them to end up, so I didn't want to pigeon-hole it too much.
dkfenger's avatar
That is some remarkable handling and fast thinking.  And it looks like he more or less was using the engine to keep the plane in the air *just* long enough to land.

I'm pretty sure a twin engine 40-plus passenger plane missing a wing and an engine doesn't have the control authority for that kind of stunt.
lopni's avatar
aviation-safety.net

Every plane would behave differently and we don't know which one flies in the story ^_^ 

Complete loss of wing is some of the most fantastic elements in the story, for Tu204 it took to land in Siberian forest to get wings physically chopped off by trees. Everyone survived

On 26th September 2006 USAF KC135 Stratotanker landed in Manas (Kyrgizstan) and was told to free the runway, however when Tu154 of Kyrgizian president started to land - KC135's long tail was still perpendicular to the runway making landing impossible. Tu154 noticed it too late and lost a part of the wing around 9 feet long, it then took off, gained 2300 ft altitude and landed safely. KC135 lost its tail and cought fire, but all three crewmembers we evacuated to safety

These are big ones, small ones usually have a better lift to weight ratio. It's always a gamble, but yeah, a pilot is a pilot because he/she can fly and land anything, without part of the wing, without wheels, without engines, on the water, in the desert, in the mountains, and it's still one of the safest ways to travel ^_^
dkfenger's avatar
You are... remarkably thorough about this.
doubleintegral's avatar
I actually researched this for the story, and the best consensus I could gather was that a passenger jet could never land on one wing, and the plane would more likely break apart before it reached the ground.  So, for the story, Miranda and Richelle only had to fly on one wing for 4-5 minutes.  That probably isn't very plausible in real life, but it also isn't plausible for them to evacuate the plane in the necessary fashion in a shorter amount of time.

Of course, this is to say nothing of the infinitesimal chances that an airplane wing would just suddenly break off mid-flight.  Some forum posts I read simply called it "impossible".

BTW, that video posted above is fake.
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