Q: Would you rather land on water or marshmallow?

[MattSimmons]

Hello,

Having a little chat in the pub last night, we got on to skydiving vs bungee jumping. I said I would rather try a http://en.wikipedia.org/wiki/Halo_jump" than a bungee jump.

This took a slightly odd turn, and we were trying to figure out whether in the absence of a parachute, one would be better off landing on water or a cushion of marshmallow.

I am aware that landing on water from a great height can kill you. Would the same be true of marshmallow? What are the contributing factors - surface tension and density?

Any thoughts appreciated!

Matt.

 

[Ranger Mike]

having made over 65 jumps from helicopters, prop and jet cargo planes
I'll take the marshmellow..water is " hard" ( surface tension}, if i reacll my notes from Jump Master School,
you reach terminal velocity at about 120 MPH..reagrdless of 25000 ft AGL Halo or 600 ft static line jump

 

[tiny-tim]

Welcome to PF!

Having a little chat in the pub last night … we were trying to figure out whether in the absence of a parachute, one would be better off landing on water or a cushion of marshmallow.

I am aware that landing on water from a great height can kill you. Would the same be true of marshmallow? What are the contributing factors - surface tension and density?

Hi Matt! Welcome to PF!

I think the main factor is the incompressiblity of water …

the sea has no "crumple zone" …

while marshmallow is a foam, and is highly compressible!

Try googling compressible +marshmallow. ​

(btw, good to know you aren't wasting your time in the pub discussing matters of no conceivable application to reality! )

 

[russ_watters]

It would have to be a combination of both density and compressibility.

 

[Cyrus]

100% marshmellows.

Take a plunger and try to compress water - good luck.

You can squeeze a marshmellow flat as a pancake with your fingers.

(Im actually eating a bag of them as we speak! LOL) Yum.

 

[tiny-tim]

skiing down marshmallow!

(Im actually eating a bag of them as we speak! LOL) Yum.

oooh :!) … gimme! gimme! ​

Can you ski down marshmallow , or would you just sink into it?

of course, you could survive by making a cave,
and then eating your way out! ​

 

[Vanadium 50]

After you land, it's a heck of a lot harder to drown in marshmallow.

 

[MattSimmons]

Lol

Thanks all for responses, I think compressibility was the term / concept missing from our (very important and not at all time-wasting) discussion in the pub!

And as for application to reality, well you just wait until I open the new Theme Park I've always dreamed of!

Best - happy eating,
Matt.

 

[thaddeus]

just as a foot note ,, a 2hp motor attached to a Floating barge will make way as well as a speed boat with the same motor until as i recall the speed reaches about 3knots .. the water gets out of the way well enough upto that speed pretty much regardless .. at higher speeds a streamlined hull shape plays a greater role ..

 

[tiny-tim]

eliminate global warming!

And as for application to reality, well you just wait until I open the new Theme Park I've always dreamed of!

Best - happy eating,
Matt.

Will this be a general Land of Chocolate theme park , or will it be specialising in food you can sink into, like marshmallow and candy floss and Baked Alaska?

On a more serious note, why has nobody thought of eliminating global warming by covering the North Atlantic with marshmallow?

This would vastly increase reflectivity, yet would not be an obstruction to shipping, since ships could just plough their way through it. ​

 

[FredGarvin]

Hmmm...baked Alaska is served on fire...

 

[Dale]

we were trying to figure out whether in the absence of a parachute, one would be better off landing on water or a cushion of marshmallow.

That depends, do you have a backpack full of graham crackers and chocolate instead of the parachute?

 

[schroder]

It seems to me the marshmallow would be almost like quick sand. You would not be able to swim out, and then, and then the red ants come and...well its too horrible to mention!

 

[MattSimmons]

Follow-up question: would you die hitting the marshmallow after a 30,000 foot fall?

What depth - if any - of marshmallow would "save" you?

 

[MattSimmons]

I think graham crackers and chocolate is as good a reason as any for not having a parachute when jumping out of a plane.

Mum packed the wrong thing again...

 

[Dale]

Mum packed the wrong thing again...

 

[Dale]

Follow-up question: would you die hitting the marshmallow after a 30,000 foot fall?

What depth - if any - of marshmallow would "save" you?

The height of the fall doesn't matter very much, only the conditions at impact. Not all falls are created equal, if you do a "spread eagle" fall you will hit much faster then if you did a "headfirst" fall. If we assume a hefty 100 kg skydiver, a respectable 60 m/s freefall, and a very squishy (barely able to keep him from sinking) 1000 N marshmallow cushion then the KE on impact is:
1/2 100 kg (60 m/s)² = 180 kJ

and the required stopping distance is
180 kJ/1000 N = 180 m

All of this changes for stiffer marshmallows, smaller skydivers, or different impact speeds, but I think that is a reasonable upper limit. Make it 400 m for an engineering safety factor of 2.2. I hope mom packed a LOT of graham crackers and chocolate.

 

[tiny-tim]

terminal velocity

Follow-up question: would you die hitting the marshmallow after a 30,000 foot fall?

What depth - if any - of marshmallow would "save" you?

ah … well, you would reach terminal velocity in air well before 30,000 feet …

then the marshmallow would slow you down to terminal velocity in marshmallow …

I think the two important questions are:

i] what is terminal velocity for an average human through air?

ii] what is the drag coefficient for an average human through marshmallow?

From these (and http://en.wikipedia.org/wiki/Terminal_velocity), you can calculate the depth of marshmallow needed to bring you to a speed at which it would be safe to hit sugar rock. ​

 

[csprof2000]

Well, assuming we model the marshmallows as massless springs with spring constant k, and you fall from rest at a height h, and assuming that the resistive force is approximately constant, ...

mgh = 1/2 k x^2 => x = sqrt(2mgh/k) is the distance the spring compresses... so the height of the marshmallows

The average force would simply be: F x = mgh => F = mgh/x = sqrt(mghk/2)

So holding m, g, and h constant, we can find the maximum spring constant k if we know the maximum force F; in fact,

k <= 2 (F_max)^2 / mgh

If somebody wants to check the numbers, please do so. I'd be interested to see. F_max is probably online somewhere, and k can be found for a marshmallow by simple experiment. Then just put in your m, g = 10 m/s^2, and h = 10000 m and see how it turns out!

 

[csprof2000]

My guess:

F_max... a person will die, say, at 10 g's... so F_max = 10mg = 100m.
Say m = 100 kg. So 100m = 10000 = 10^4.

mgh = 100*10*1000 = 10^6.

So k <= 100.

So if the spring constant of a marshmallow is under 100 N/m, we may be in luck. Let's assume this is the case.

Then the depth of marshmallows must be around sqrt(2*100*10*1000/100) = 141.

So you'd need ~ 150 meters of marshmallows if my model is accurate (and we assume the worst-case spring constant; for more stretchy marshmallows, you could need many more, up to 10 times as deep).

 

[Ranger Mike]

30,000 feet means you got to jump with air bottle as you are at altitude where air is too thin
height does not matter since you ar at max terminal velocity after a few seconds
i had compamy commander pan cake into sand drop zone from 1200 ft..chute manfunctioned
he lived but spent 6 months in traction
the sky even more than the sea, is less forgiving...
what is depth of marshmellow to stop compression of 200 pound jumper at terminal velocity?

 

[schroder]

I must have way too much time on my hands……..anyway

Since the jumper will be at terminal velocity we can say 1/2 MV^2 = 1/2 KX^2
Now the need the spring constant of marshmallow. A slinky toy has a k of 1 and a marshmallow is about the same, maybe a 2. I will go with K of 2 and terminal velocity of 60 m/s. and M of 100 Kg.

Forget about the 1/2 factor as they cancel so (100) * (60)^2 = 2X^2 so X = 425 meters of goo.

But even if you live, the red ants will still get you!

 

[csprof2000]

Yes, I think I like your answer better, schroder. Although, were you falling in the cold and unforgiving vacuum of space, you must agree my method is more appropriate. ;D

 

[Dale]

what is depth of marshmellow to stop compression of 200 pound jumper at terminal velocity?

My 100 kg jumper would be about 220 lbs, so I still say 400 m which is close enough to schroder's 425 m.

 

[Ranger Mike]

NO WAY!
There is not way that you need a quarter mile of marshmellows to slow you from a jump!

A marshmallow is put into a bell jar and the bell jar is evacuated. The atmospheric pressure air trapped in the marshmallow forces the marshmallow to expand. ergo..it is a min air bag


you are forcing me to go to the store to buy a bag of them. drag out my posta lscale , cut open a shotgun shell to get some buck sot and start to do a drop test to calulate the deformation of said marshmellows..

but..i got nothin to do over Christmas so I just may..what info do we need to do the math?

 

[schroder]

NO WAY!
There is not way that you need a quarter mile of marshmellows to slow you from a jump!

A marshmallow is put into a bell jar and the bell jar is evacuated. The atmospheric pressure air trapped in the marshmallow forces the marshmallow to expand. ergo..it is a min air bag


you are forcing me to go to the store to buy a bag of them. drag out my posta lscale , cut open a shotgun shell to get some buck sot and start to do a drop test to calulate the deformation of said marshmellows..

but..i got nothin to do over Christmas so I just may..what info do we need to do the math?

It would probably be easier to put a marshmallow on a good kitchen scale, and depress it with a known weight, maybe 1 kg, and measure the deformation while noting the scale reading. From that we can get a better idea of the spring constant. My guess at a k of 2 is just that, a guess. But I doubt it will be higher than 5. I think all the estimates given are pretty good; maybe we should just average them all out?

 

[Ranger Mike]

good idea
i just thawed the lock on the race car trailer..got the Pelouze digital postal scale out.reeads to .1 oz or 1 gram increments
soon as the drive way thaws..off to buy sum marshmellows
meanwhile what else do we need/ scale to measure amount of deformation?
keep those ides acoming in..physics at its most practical level

 

[Dale]

NO WAY!
There is not way that you need a quarter mile of marshmellows to slow you from a jump!

A marshmallow is put into a bell jar and the bell jar is evacuated. The atmospheric pressure air trapped in the marshmallow forces the marshmallow to expand. ergo..it is a min air bag


you are forcing me to go to the store to buy a bag of them. drag out my posta lscale , cut open a shotgun shell to get some buck sot and start to do a drop test to calulate the deformation of said marshmellows..

but..i got nothin to do over Christmas so I just may..what info do we need to do the math?

We need the spring constant and the rupture stress (the initial slope and the final stress of a http://en.wikipedia.org/wiki/Stress-strain_curve" ). schroder and I made different assumptions about which dominates and also the magnitude of each. Both of us intentionally made conservative estimates for the strength of the marshmallows (better to have too much than too little, after all how can you have too much marshmallow) and then I doubled my result for additional safety.

 

[tiny-tim]

not a spring

… put a marshmallow on a good kitchen scale … the spring constant …

But is marshmallow springy …

does it return to its original shape?

If not, then "spring constant" isn't the issue.

A spring absorbs energy, and then returns it …

a "crumple zone" absorbs energy, but keeps it …

I thought that was why MattSimmons chose marshmallow in the first place?

 

[schroder]

I would never trust a marsmallow that “crumpled”!