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*From*: Paul Nord <paul.nord@valpo.edu>*Date*: Mon, 5 Nov 2012 11:49:07 -0600

If I've got a blimp inflated to neutral buoyancy and I hang a small mass from it, what will the acceleration of the blimp be immediately after I attach the mass?

Since we're still at zero velocity we can ignore the viscous effects of the air for just a moment. I believe that I need to know the un-inflated mass of the balloon and the payload, the volume of the helium, the mass of the helium, and the mass of the displaced air. Let's assume a very small pressure is held by the balloon so that we can think of it as simply a volume of helium at the ambient pressure. The mathematics of a simple Attwood's Machine would seem to apply.

The total mass going down:

balloon and payload

helium mass

extra ballast weight (call this 'm')

Total mass going up:

mass of displaced air

Let's call the sum of all of the mass except for the ballast weight 'M'.

M = balloon + payload + helium + displaced air

The acceleration of the balloon is then:

a = g * m / (m + M)

Question 1: Of course Pascal's Principle says that air pressure will distribute itself equally on all sides. In the static case I can ignore the effects of pressure and air mass. The net force is zero (ignoring the vertical pressure gradient of the air, yes). However, for a balloon to move down, an identical volume of air needs to move up the same distance. The mass of that air cannot be ignored. Is this a valid assumption?

Question 2: Flow through a vicious fluid is typically modeled with a term which rises as a function of the square of the velocity. There is a force resisting the passage of a moving object. If it use the mass of the displaced fluid in the calculation above, am I already accounting for some of the "drag" force which is normally accounted for in this velocity squared term?

Paul

**Follow-Ups**:**Re: [Phys-L] Dirigible Flight Question***From:*"John Clement" <clement@hal-pc.org>

**Re: [Phys-L] Dirigible Flight Question***From:*brian whatcott <betwys1@sbcglobal.net>

**Re: [Phys-L] Dirigible Flight Question***From:*John Denker <jsd@av8n.com>

**Re: [Phys-L] Dirigible Flight Question***From:*Bernard Cleyet <bernardcleyet@redshift.com>

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