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## COG Location with Cruising Speed

• yourgurltans
• Topic Author

### yourgurltans created the topic: COG Location with Cruising Speed

Hi

Which of the following statements is true regarding an aeroplane's COG location and it's cruising speed?

a) If loaded with the COG at it's aft limit, the aeroplane will cruise at a lower airspeed because of an increase in drag
b) If loaded with the COG at it's forward limit, the aeroplane will cruise at a faster airspeed because of a reduce in drag
c) If loaded with the COG at it's aft limit, the aeroplane will cruise at a faster airspeed because of a reduce in drag
c) If loaded with the COG at it's aft limit, the aeroplane will cruise at a slower airspeed because of an increase in lift

• Posts: 1169

### Richard replied the topic: COG Location with Cruising Speed

G'day,

Lift can be considered as acting through the centre of pressure and weight acts through the centre of gravity. These two points are rarely in alignment so as lift acts upwards and the weight acts downwards in straight and level flight, there will be a pitching moment created by the two forces. Since the centre of lift is usually behind the centre of gravity, this pitching moment becomes a nose-down pitching moment which the designer balances with the help of tail down force (TDF) generated by the horizontal stabilizer (as well as arranging the centers of thrust and drag but that's another matter).

The greater the pitching moment, the greater the down force required from the tail. If centre of gravity is far away from the centre of pressure, such as with a forward centre of gravity, a greater pitch down moment is produced and a greater TDF will be needed to help counteract it.

An aft centre of gravity means the CofG and the centre of pressure are closer and the pitch down moment is reduced. Therefore, you will need less TDF to help counteract the pitching moment.

TDF acts in the same direction as weight, so it needs to be balanced by lift. More TDF is like adding effective weight to the aeroplane. One rule of thumb I stumbled across estimated the TDF to be roughly 10-15% of the gross weight! That's about 110kg of extra "weight" as TDF in a typical Cessna 172 for example!

Anyway, if the CofG is aft, there is less nose down pitching moment, less TDF required and it is as if the aeroplane is lighter. Therefore, less lift will be required at any given speed which therefore means less drag. Setting cruise power will also result in a higher speed due to the reduced drag.

The answer must be (c) .

Cheers,

Rich

• John.Heddles
• Offline
• ATPL/consulting aero engineer
• Posts: 702

### John.Heddles replied the topic: COG Location with Cruising Speed

Another observation to expand on Richard's comments, if I may.

The question is not really well thought out .. yes, for constant power, a more aft CG will see a small increase in speed. However, looking at the usual performance equations, the significant speed influence on power (and fuel flow for the lightie brigade) is V cubed (eg web.mit.edu/16.unified/www/FALL/thermody...cs/notes/node97.html so the speed increase will be more academic than really useful. In the link, look at the first term on the RHS of the equation immediately above the graphic).

The more useful flight management option, and the reason that the heavies look to an aft-ish CG for cruise, is to maintain the optimum speed (particularly if a cruise-climb option is available) and save a bit on fuel burn. For instance, going back a few years ago now, QF did some sums for the 744 regarding ultra longhaul range-payload. By a more imaginative than standard fuel use plan, they increased the range-payload capability sufficiently to carry several extra (fare-paying) passengers across the pond ... not something to be sneezed at, looking at annualised figures. If I recall correctly, it was a fleet pilot who started the ball rolling and he did quite a bit of work on the figures off his own bat before he excited much interest in the support organisation.

Engineering specialist in aircraft performance and weight control.