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Originally posted by kmax87On a point of clarity, the negative result indicates that if the balloons were only pumped to a 4ft diameter, there would be no capacity to carry ballast as the chair would not even be able to float anyway. Equating the nett buoyancy to Larry's weight only gives the minimum amount of balloons inflated to 4ft that will put his own weight in an equilibrium floating position.
===> Wb = V*(Da-Dh) - Wm
Da = 1.293 kg/m^3; Using your density values
Dh = 0.178 kg/m^3
V of 45 balloons = 42.7 m^3 (V of 1 = 0.9489 m^3)
===> Wb = 42.7*(1.293 - 0.178) - 100
===> Wb = -52.388 kg
A negative ballast result indicates that in this configuration the chair would not even lift off as the ...[text shortened]... r densities.
Either way as you worked out the chair would not be able to take off at all.
The only performance qualifier given in the wiki article is that he rose quickly to a height of about 16,000 ft. If the time he had taken was accurately recorded we may have had some way to calculate the initial volume he inflated his balloons to, assuming of course that they all were inflated to the same size. This would be because if we knew Larry's initial volume we could calculate his actual buoyancy and we would know how much buoyant force acted on his craft at liftoff. For the rest you would have to adapt the standard equations of motion.
Going back to the equation and using the densities you quoted, it would be clear that the minimum diameter of each balloon for him just to get off the ground without any ballast, would be:-
Wb = V*(Da-Dh) - Wm
Da = 1.293 kg/m^3;
Dh = 0.178 kg/m^3
=====> Wb = 0 = V*(Da-Dh) - Wm
0 = V*(Da-Dh) - 100
100 = V*( 1.293 - 0.178)
100 = V*( 1.115)
======> V = 89.686 m^3 is the total volume of air required to be displaced by the 45 balloons just to account for Larry's weight.
Each of the balloons must therefore be (89.686 / 45 )m^3 in volume
==> V_ea. = 1.993 m^3
therefore the minimum size of each balloon would have to be
V = 4/3*pi * R^3
R^3 = (V /pi)*3/4
R = (R^3)^1/3
=======> R = 0.7806 m
=======> D = 1.561 m = 5.123ft ( 1)
The minimum diameter of each balloon would have to be 5.1 ft just to make Larry weightless.
To work out what he might have started with we could look at his final position, the altitude ceiling of 16,000ft and try some back engineering, but there are still dead ends associated with this approach.
If 16,000ft became his ceiling we can work out the Buoyancy required to float at that altitude and from that maybe we can infer how much inflation he had started with.
Using International Standard Atmosphere (ISA) data, we know that at
16,000 ft the following relations hold:-
~ http://www.aeromech.usyd.edu.au/aero/atmosphere/index.shtml#atmtab~
4876 m 16000ft -16.5(oC) 0.542(P/Po) 0.609 (rho/rho_o)
This data is handy because we can work out the density of air at 16,000 ft.
Taking your reference sea level value for air density of 1.293 kg/m^3, at 16,000ft the Da would now be Da16 = 1.293* 0.609 = 0.787.
However what this approach does not help us with, is finding the density of helium at this altitude. This is for two reasons. One we don't have an ISA table that gives values for helium at different altitudes and secondly the helium pressure would not just equal the external pressure of the air at that altitude. If it did we could use the perfect gas relation of P = rho*R*T and then knowing density (rho~Dh) we would be able to work out how big the balloons need to be at this altitude to provide floating buoyancy. This is when the circular reasoning and rubberized uncertainty really takes hold. As the perfect gas relation indicates, increased Pressure can only mean increased density of the helium. Because it is a highly compressible substance this is quite easily achieved.
A large unknown would be the pressure exerted on the helium by the rubber weather balloon trying to restore itself to its uninflated size.
From the weather balloon website you quoted
~ https://secure.scientificsales.com/weather/Details.cfm?ProdID=129&category=18~
Uninflated diameter Inflated diameter Burst diameter
18.9 in (48 cm) 3.9 ft (118 cm) 8.9 ft (270 cm) Pilot type
23.6 in (60 cm) 5.0 ft (154 cm) 12.8 ft (390 cm) Sounding type
27.6 in (70 cm) 5.1 ft (156 cm) 14.1 ft (430 cm) " "
32.7 in (83 cm) 5.7 ft (175 cm) 17.7 ft (540 cm) " "
The factor by which these balloons expand is dependent on the initial size, so in order of Inflated size, the factor of expansion is 2.26(3.9ft); 2.56 (5.0ft); 2.76 (5.1ft); 3.1(5.7ft)
In terms of the pressure it exerts on the helium because the factor of expansion in most cases from uninflated state to burst diameter is of the order of 5.6 - 6.5. How much pressure over and above atmospheric is required to affect this change is anyones guess and this is where the calcs sort of grind to a halt.
Any assumptions would have to be made on the basis of the equipment typically used to inflate balloons with helium. Normal atmospheric pressure is about 14.7psi.
However a totally different way to look at this problem can be found at this site:-
http://www.howstuffworks.com/question185.htm
They have a basic way of looking at it and simply say 1 liter of helium can lift 1 g .
So using this relationship we can say that 1000L or 1m^3 of helium can lift 1000g or 1kg.
Therefore it would take 100 m^3 of helium to lift 100kg.
So if we know the volume required is 100m^3 then we also know that if we have 45, 4 ft diameter balloons, then each balloon has to contain 2.222 m^3 of helium and then we also know that each balloon has to be inflated to a Diameter of:-
====> D = 2*R where R = R = (R^3)^1/3 & R^3 = (V /pi)*3/4
====> R^3 = (2.222/pi)*3/4 = 0.5305
====> R = 0.80953 m ==========> D = 1.619 m ( 5.31 ft) (2)
This answer compares favorably with the answer produced in (1) using densities (5.1 ft)
If we knew what the effect of blowing up a 4ft balloon to 5.1ft or 5.3ft would do in terms of the pressure it would exert on the helium, by knowing that pressure we would know exactly the density of the helium in the balloon at take off. We know that that pressure would cause the balloon to expand as it rose into the air. Whether that expansion would cause the balloon to surpass its burst diameter is not clear, because what is not known is the actual strength of the rubber and if the balloon reached its burst diameter it might then simply increase the pressure of the helium inside. We only know the burst diameter property. We are not given a threshold pressure to go with this condition, so it would not be possible to say whether the balloon will simply expand to its maximum diameter and then pressurize the helium inside past that point.
Unless someone else has an insight we haven't thought of yet, I'm afraid that at this point we reach a stalemate. Sure we could produce lots of interesting data or 'facts' but they would be based on so many assumptions and pure guesswork, the results while interesting may not tell us anymore than we already know.
Originally posted by kmax87Sorry for the delay will have a better look at your Maths in a bit.
On a point of clarity, the negative result indicates that if the balloons were only pumped to a 4ft diameter, there would be no capacity to carry ballast as the chair would not even be able to float anyway. Equating the nett buoyancy to Larry's weight only gives the minimum amount of balloons inflated to 4ft that will put his own weight in an equilibrium floa ...[text shortened]... esswork, the results while interesting may not tell us anymore than we already know.
Meanwhile, it is interesting to note that the most recent attempt
used som 3 x the number of balloons for a similar flight.
"Mr Couch took off buoyed by about 150 balloons.
"I'd go to 30,000 feet if I didn't shoot a balloon down periodically," he said. "
http://news.bbc.co.uk/1/hi/world/americas/7491841.stm
LMAO!! Check this out!
http://darwinawards.com/darwin/darwin2007-13.html
(21 May 2004, Texas) Michael was an alcoholic. And not an ordinary alcoholic, but an alcoholic who liked to take his liquor, well, rectally. His wife said he was "addicted to enemas" and often used alcohol in this manner. The result was the same: inebriation.
The machine shop owner couldn't imbibe alcohol by mouth due to a painful throat ailment, so he elected to receive his favourite beverage via enema. And tonight, Michael was in for one hell of a party. Two 1.5 litre bottles of sherry, more than 100 fluid ounces, right up the old address!
When the rest of us have had enough, we either stop drinking or pass out. When Michael had had enough (and subsequently passed out) the alcohol remaining in his rectal cavity continued to be absorbed. The next morning, Michael was dead.
The 58-year-old did a pretty good job of embalming himself. According to toxicology reports, his blood alcohol level was 0.47%.
In order to qualify for a Darwin Award, a person must remove himself from the gene pool via an "astounding misapplication of judgment." Three litres of sherry up the butt can only be described as astounding. Unsurprisingly, his neighbors said they were surprised to learn of the incident.
Originally posted by kmax87You are just posting a load of pretentious nonsense.
On a point of clarity, the negative result indicates that if the balloons were only pumped to a 4ft diameter, there would be no capacity to carry ballast as the chair would not even be able to float anyway. Equating the nett buoyancy to Larry's weight only gives the minimum amount of balloons inflated to 4ft that will put his own weight in an equilibrium floa ...[text shortened]... esswork, the results while interesting may not tell us anymore than we already know.
Originally posted by Bosse de NageDo your genetic tendencies affect the brand of toothpaste you purchase?
"A genetic tendency to take risks"! You can have fun with that kind of language. Do your genetic tendencies affect the brand of toothpaste you purchase?
Incidentally, having a child is an enormous risk.
Yes. I tend to avoid toothpaste that tastes, smells and looks like diarrhea for example.
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Originally posted by Bosse de NageAnd yet somehow men seem to die more in life. More boys are born, but there are more old women then men.
"A genetic tendency to take risks"! You can have fun with that kind of language. Do your genetic tendencies affect the brand of toothpaste you purchase?
Incidentally, having a child is an enormous risk.
Do you have an alternative explanation? I only postulated that men tend to take more risks for genetic reasons. I did not say that it was true; just that it was one possible explanation.