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Varialift airships
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Notion is - 150m long, 50m wide, cover with solar panels, and use pure
solar electric power??
D ing said they will go at 250 km/h when at altitude.
Compare with my book's model.
claim 155-218 mph. (at sea level and at 20,000 feet) 155 mph = 69.3m/s
and 80-90\% less fuel.
ARH50:
150m long
52m wide
50 t payload
range 6000 nm.
cargo space 100x50x10m.
max altitude 30,000 feet.
uses 900 l/hr of fuel.
2 crew.
ARH250: 300m long 110m wide.
carries 250t.
Same speeds.
consumes 2500 l/hour.
range 8000 nm.
My model: [ let's do the ARH50] I'll guess height is 42m
Air resistance Force = 0.5 cd A rho v**2
Power required = 0.5 cd A rho v**3 / epsilon
Power required = 0.5 * 0.03 * 52*42 m2 * 1.2 (kg/m3) * (69.3 m/s)**3 / (1/4)
= 0.5 * 0.03 * 52*42 * 1.2 * (69.3 )**3 / (1/4) W
= 52 MW.
Fuel consumption 900 l/hour * 10 kWh/litre = 9000 kWh/hour = 9 MW.
Area of panels required, assuming 20\% efficient and 1000 W/m2 sun --
9e6W / (200 W/m2)
= 45\,000 m2
And actual area is 150*52 = 7800 m2.
Which is 6 times too little. But if the electric motor efficiency is 4x better than the
petrol one, then maybe you can almost get there on solar.
The bigger one, can it be solar?
2500 l/hour * 10 kWh/litre = 25000 kWh/h = 25000 kW = 25 MW.
Area of panels required, assuming 20\% efficient and 1000 W/m2 sun --
25e6 W / 200 W/m2
=
125,000 m2.
Actual area: 300*110 = 33,000 m2.
That is a short fall by a factor of 3.8. So as long as the electric motor efficiency is
4 times better, pure solar power might be an option.
They seem to be claiming a cd that is quite a lot lower than I imagined.
(About 5 times better.)
But maybe my efficiency of 1/4 was wrong. Say 1/2 instead. Then my cd is off by 2.5,
which is not bad. And maybe the height is less.
And maybe they are doing a bit of hybrid lift effect?
The density of air is 1.2\,kg/m$^3$.
energy per distance per mass =
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helium balloon by Hybrid Air Vehicles
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http://www.bbc.co.uk/news/magazine-26372277
Airlander "largest aircraft in the world"
because shaped like wing, generates lift
38,000 m3
width 34m
height 26m
length 91m (300 ft)
[NB the USS Akron was 239 metres long]
fuel consumption: 3100 litres per day aloft
max payload: 1225 kg (ie 10 people)
max speed: 80 knots.
300ft and 400ft vehicles planned.
In interview, claimed:
``up to 50 tonnes of freight
at up to 100 mph'' (but not for this
particular vehicle)
Lift:
60\% helium
40\% from hull
reaches unreachable; more direct;
can stay aloft for a long time.
Take their numbers:
energy per distance, assuming maximum speed and payload (both generous!!)
3100 litres/day * 10 kWh/litre / ( 80 knots ) / (1225 kg)
= 26 m/s/s
= 7.1 kWh / tonne / km [compare with ARH50: [21600 l/day] [much more weight, and faster]
10 kWh/litre * 900 litres/hour / (300 km/h) / (50 tonnes)
= 9000 kWh / (15000 t km)
= 0.6 kWh / (t km) -- Very different! (10x)
Need to sanity check both numbers against a physics model. I would be sceptical about the ARH50 numbers!
%%% see mgp/HydrogenBlimpIdea.mgp
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cf my book page 92 says 1.65 kWh/t-km for Air, and about 1.0 for Road.
To do a good job on this I need to understand the Finesse of
``lifting body'' aircraft.
%% http://www.nasa.gov/centers/dryden/pdf/87738main_H-479.pdf
%% http://www.nasa.gov/centers/dryden/pdf/87738main_H-479.pdf
Lift and Drag Characteristics of the M2-F2 lifting body
during subsonic gliding flight.
Pyle and Swanson.
NASA TM X-1431
They got maximum lift-to-drag ratio about 3.1.
Approach:
do everything for a given payload.
Assume payload and fuel are 2/3 of the mass and structure is 1/3.
Assume either lifting-body approach or wing approach.
Assume a given amount of anti-gravity, and assume an ellipsoidal
shape that is that of the HybridAirVehicle. (eg width:height:length
34:26:91)
going by picture on website, maybe the balloony bit is better
represented by:
2:1:4.5
Assume that lift to drag is 3 or 18 respectively.
Size the body or wings to give the required lift.