# Ammount of heat needed to lift hot air ballon.

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I'm thinking about making a new type of hot air balloon, but I need to see if I can even make the math/physics work out let alone the engineering. I would be more than happy to collaborate on the effort, may be make some one very rich.

How much heat would it take to lift a spherical hot air balloon (r= 81.4) x ft in to the air?

How much heat at x altitude (function would be appreciated) would be needed to raise the balloon 200 ft?

I'm most concerned with the lift off, as once in flight I have a different source of power than a flame.

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PV = nRT for an ideal gas, which should be a good enough approximation

If the inflated volume is constant and the pressure is constant, then the density varies inversely with temperature (one must use an absolute temperature here, e.g. Kelvins)

The buoyancy force is the weight of the displaced air. 1 mole of an ideal gas displaces 22.4L at STP, which is about 29 grams of mass. If you doubled the temperature from 273K to 546K (i.e. 273 ºC), the air density inside the balloon drops in half, and you could lift 14.5 grams

I'm using 0º C and 1 atmosphere as STP here, which is apparently now an "old" definition according to IUPAC, but it's what I grew up on

http://en.wikipedia.org/wiki/Standard_conditions_for_temperature_and_pressure

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This is an approximate value.

First, we set up a force balance equation about the balloon.

We consider air as an ideal gas.

Vballoon Loballoon air + mload +mballoon mass= Vballoon Loair(h)

Vballoon{(MairP(h) ) /(R Tballoon) }+ mload +mballoon mass= Vballoon Loair(h)

So

Tballoon={ Vballoon Mair P(h)} / {R (Vballoon Loair(h) -mload -mballon mass) }

The required heat energy is like this.

Q =~ Vballon Loair (h) Cp air(Tballoon - Tair) + Qloss

Q/t = Qloss/t

The required energy from the beginning is

Q =~ Vballon Loair (h) Cp air(Tballoon - Tair) + Qloss/t ttravel

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Just a couple of practical points.You do not make clear the units of measurement. Is the balloon 81.4 ft radius or 81.4 something else to be raised X feet into the air? You also need to know the total weight of all you need to lift. This includes the balloon envelope, air heating mechanism, pilot and whatever is going to provide the source of power that you mention once your machine is in the air. Hot air balloons are pretty big structures which generally carry quite light loads. If you are going to force it through the air you will need a powerful motor which will surely be heavy.

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Ah yes: pv=nrt, fond memories.

(The units are ft sorry) The dimensions I used are based on a spherical version of a 3-5 passenger hot air balloon. The "power" source I'm planning to use weighs about 90lbs. Let's assume 150lbs is the weight of a "passenger". The "power" source can deliver 10% of the "average homes" "power".

My hope is to carry at least 2 people and their cargo.

Is this enough information? If so is this feasible?

Edited by wanabe
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Ah yes: pv=nrt, fond memories.

(The units are ft sorry) The dimensions I used are based on a spherical version of a 3-5 passenger hot air balloon. The "power" source I'm planning to use weighs about 90lbs. Let's assume 150lbs is the weight of a "passenger". The "power" source can deliver 10% of the "average homes" "power".

My hope is to carry at least 2 people and their cargo.

Is this enough information? If so is this feasible?

I'm not really into maths and anyway you will need to vary the heat required according to weather and load conditions. However this link makes clear you will need at the very least 2MW (possibly as much as 12MW). http://en.wikipedia.org/wiki/Hot_air_balloon

Edited by TonyMcC
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• 4 weeks later...

So unless my generator can create this power range 2-12MW, this thing can't get off the ground, am I correct?

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