Airplane specific weight (hohohoho!..)

[LEM]

I was wondering if any math fan has ever calculated the "specific weight" of an airplane, I mean the total volume versus the weight...
not too difficult to calculate, but certainly to me, yes...

What could that be compared to? light wood?

In case my question is clear as mud: what material could we use to build a 1:1 scale aircraft model in one solid piece resulting in a realistic total weight?

[Notso Fantastic]

No way! Not even plastic. I think if you molded the full size aeroplane out of poystyrene you'd be closer (the solid sort that packs video recorder boxes).
There was that dreadful Jack Lemmon 70s Airplane movie where the 747 ditches, then there's a gurgling sound and you see the water moving up over the cabin window and the air-filled aeroplane sinks to the bottom. My gasp of disbelief was audible- this was not just ignoring physics, it was chaining it down and violating it most cruelly.
(Ever tried to get an inflated balloon in a bath and hold it underwater? Makes the wife laugh if nothing else).
Actually, thinking about it, maybe somewhere between that soft extremely light balsa and polystyrene might be there.

[Milt]

Interesting question

Does anyone have a handle on the relative densities of some typical aircraft at max weights.

Makes one wonder about the mass of the air in a heavy which may become a consideration in manoeuvre. The aircraft has to move that mass of air around as well as the hard bits.

As a guess there may be about 500 to 1000 pnds of air in a jumbo pressurised to 8,000 ft.

1 pnd of air occupies about 13 cubic feet at sea level.

Probably insignificant.

[Milt]

Have made a few estimates for a typical 747.

Rough volume of fuselage and wings is 100,000 cubic feet.
If air occupies about 20% of the volume then we end up with about 6000 pnds content of air at sea level.

Using volume of 100,000 and a weight of 450,000 pnds then density is close to 4.5 pnds/cubic foot.

That puts the relative density (to water at 62.5 pnds per cubic foot) at about 4.5/62.5 = 0.07. This is a lot lower than expected perhaps similar to a model made from something lighter than balsa.

Am I close?

[Young Paul]

Pounds per cubic foot??????!!!!! Scary!

[Specnut727]

Numbers are only ballpark, because who outside Boeing would know the volume of a 747. Could submerge a model in a bucket and measure displacement I suppose. What we really need is a 3 dimensional cumputer model of the aircraft ! Back to Boeing.

I estimated 2,600 cu.metres, not far from Milt's 100,000 cu.ft.

Based on (round number) MTOW of 400 tonnes, this gives about 150 kg/cu.metre (about 9 lb/cu.ft). Density relative to water of 0.15

For comparison, polystyrene foam is about 50 kg/cu.metre (about 3 lb/cu.ft). Balsa ranges from 3 to 30 lb/cu.ft

I think Milt's figure for air volume of 20% is a bit low. Maybe more like 40% when you consider how much of the PAX and freight space is air. Using 0.9 kg/cu.metre (air at 8,000 ft) I get about 1 tonne of air.

Milt, within the accuracy of all our guesses, you're not far off the mark. Obviously using MTOW or empty weight makes a big difference.

I hope someone finds all this info interesting !

Spec.

[Notso Fantastic]

Some of the above posts appear to ignore Archimedes Principle: When a body is suspended in a fluid (in this case air), it loses weight by the weight of fluid displaced. Therefore to calculate the mass of air in an aeroplane and ignore the fact that it is displacing a lesser mass of lower pressure air inflight or on the ground is an error!

[Specnut727]

Notso,

Yes I agree, but the mass of air displaced is small. I haven't calculated air density at 35,000 ft, but I guess it will be about 1/4 of density at 8,000 ft. So aircraft contains about 1 tonne of air, and displaces about 250 kg. Nett weight of air is 0 up to 8,000 ft, increasing to about 750 kg at 35,000 ft.

This is insignificant compared with 400+ tonnes of Aluminium/Jet A1/PAX/Freight etc.

All these calcs are a bit of a futile excercise without better starting data anyway.

Hopefully someone may be able to come up with a better figure for the aircraft total volume.

[swh]

Table Aircraft Volume Ratios

Aircraft Type Cabin Volumes in Cubic Feet Ratio

DC-9 vs CE-650 5,840 vs 576 10:1

B-737 vs LR-55 8,010 vs 502 16:1

B-727 vs NA-265 9,045 vs 430 21:1

L-1011 vs G-1159 35,000 vs 1,850 19:1

B-747 vs Learjet 59,000 vs 265 223:1

Data Source: Physiological Considerations and Limitations in the High-altitude Operation of Small-Volume Pressurized Aircraft.
E. B. McFadden and D. de Steigner, Federal Aviation Administration (FAA) Civil Aeromedical Institute (CAMI).