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Question:

What is the difference between a Crane Fly (or a Wren) and a 747 - 400?

Answer:

About 400 tonnes.

And a good deal of aviation spirit, and a few hundred passengers. But in many ways these three fliers are very similar; none is out of the ordinary.


Lift:

The lift which can be generated by the wings of any flying machine, animate or otherwise, depends on the following factors:

  • the wing area, A
  • the airspeed, V
  • the density of the air, r
  • the angle of the wings with respect to the direction of flight – the angle of attack.

The lift generated must equal the weight W of the aircraft in level flight. This lift is proportional to A and also to  rV2:

L   =   W   µ    ArV2

W =    kArV2

The relationship with the angle of attack is complex, and it is this which determines k; zero angle of attack generates no lift since no air is being deflected downwards and hence no force is being directed upwards, whereas high angles of attack generate greater drag. Most of us have experienced this with a hand (not far) out of the car window. The effect can be heard with an aircraft on final approach. Where I live in London is just where the inbound Heathrow traffic is slowed to around 180 or perhaps 160 knots. To do this the pilot will bring the nose of the aircraft up to increase the angle of attack. However this means that more power will also have to be used, and so the engine revolutions rise.

Since lift also depends on the air density r, this leads to the necessity for an aircraft to alter its cruising height as its journey progresses if it is to maintain the same airspeed. Aircraft get significantly lighter as they fly on long journeys, in the case of a 747 by about 10 tonnes an hour. As the aircraft becomes lighter, it flies higher in air of lower density to maintain the same airspeed.


Wing loading:

A comparison between different flying machines is easier if the wing loading L is used rather than the weight; the wing loading is the weight per unit wing area, so that

                                                                             L = W = krV2
                                                                                    A

For air of a given density – that is for flight at a given height – the airspeed V depends only on L and the angle of attack. In the cruise all aircraft have more or less the same angle of attack, so to a reasonable approximation the airspeed depends only on the wing loading. This ignores the lift which is produced by the fuselage and the tail-planes.

This idea illuminates some features of commercial airliners. The 737 has undersize wings; this means its wing loading is higher than its weight would suggest as the optimum, so that it flies faster than might be thought necessary. This is simply so that it isn’t too slow in the presence of other traffic especially its bigger brothers. It means the aircraft doesn’t look (to me, at any rate) quite right.

Concorde is another example. At high altitude and moving at supersonic speeds, Concorde doesn’t need very big wings. However with small wings the loading would be high which would necessitate a high landing speed and long runways. Concorde has to use ordinary airports; so it has oversize wings. It has oversize fuel consumption to match. However elegant it is and however majestic the achievement in engineering terms – it is majestic – it doesn’t look quite right either. Not like the 747.

A possible solution is to have swinging or folding wings so that A can vary. This solution is used by military aircraft which do not have to carry more than two passengers, and by birds which – as far as I know – carry no passengers, parasites excepted.

So what is the relationship between the Jumbo, the Wren and the Crane Fly? They have very different wing loading – but they have very different cruising speeds too. If all of these fliers are ‘ordinary’ fliers, and have no unusual characteristics, it should be the case that since

                                                                               L = krV2
                                                                                  
then                                                                         L = kr  = constant (at a given height).
                                                                                V2

The values for these three fliers are shown in the table.

W/N

A/m2

L/N m-2

V/m s-1

V2/
m2 s-2

L/V2
Crane Fly

3 x 10-4

7.5 x 10-5

4

3

9

0.44
Wren

0.11

4.8 x 10-3

22.9

7.8

60.8

0.38
747 - 400

3.95 x 106

530

7500

140

19600

0.38

 

Their flying properties are therefore quite similar. Just let me know if you come across any crane flies or wrens weighing 400 tonnes. Other than those marked ‘Boeing’, of course.

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Rod Beavon   17 Dean's Yard  London  SW1P  3PB

e-mail: rod.beavon@westminster.org.uk