COG limits help please!

[baleares]

I am having trouble understanding a seemingly contradictory explanation.

When the centre of gravity is beyond its forward limit the tailplane is more effective due to a longer moment arm.

My book tells me that: [I]"with the COG outside the forward limit, the elevators may have to be permanently displaced upwards in order to provide sufficient balancing download from the tailplane for straight and level flight."

This seems to contradict the first paragraph ? Can anyone help ?

They go on to explain how the opposite occurs with the COG beyond its aft limit with the opposite - that the tailplane is less effective [which I understand to mean there is less downforce from the tail and thus more of a net (nose) pitch down moment.]

They continue that: "the elevators may have to be permanently displaced downwards to provide sufficient balancing upload from the tailplane for straight and level flight"

Would love some help! :)

[SpannerInTheWerks]

Imagine a ruler balanced in the middle resting on a pencil.

Put a weight on one end and the ruler tips down towards the weight.

Now move the pencil until the ruler is balanced again.

The CoG has moved towards one end - the moment arm (between the pencil and the other end of the ruler) has increased.

If the CoG moves forward the aircraft is becoming nose heavy - as with the weight on the ruler.

So, whilst the moment arm has increased if may not be possible to raise the nose because the elevators don't have enough authority (aerodynamic force) to overcome the effects of the aircraft being nose heavy - due to the CoG being outside its forward limit.

Same goes for being tail heavy when the CoG is outside the rear limit.

The aircraft will be in balance and controllable when the CoG is inside the limits. It will become uncontrollable if the CoG is outside these limits.

Practical examples:

With passengers in the back of a 4-seat light single, it will require nose down trim (up trimmer, down elevator, force 'pushing' up) to counter the rearward movement of the CoG due to the weight of the passengers.

Some aircraft can't carry out aerobatic manoeuvres, such as spinning, if the CoG is too far back, as the aircraft would have a lack of (down) elevator authority to recover from the spin. So there are limitations on weight and balance (no rear passengers, for example) on some aircraft types.

[BabyBear]

My reading of it is that the elevator will be more efficient in either direction for a particular deflection due to the greater leverage. I see the consequence of the COG being out of limits as not being directly related to the efficiency due to leverage. Indeed in spite of the greater efficiency there may still be insufficient elevator movement to counter the out of limits COG.

BB

[SpannerInTheWerks]

My reading of it is that the elevator will be more efficient in either direction for a particular deflection due to the greater leverage.

Yes, more effective due to the increased lever arm.

I see the consequence of the COG being out of limits as not being directly related to the efficiency due to leverage.

No, if the CoG is out of limits the elevator will not have sufficient authority (effectiveness due to amount of movement, surface area, airflow over it) to overcome the out of balance condition.

Indeed in spite of the greater efficiency there may still be insufficient elevator movement to counter the out of limits COG.

Yes, although it is unlikely to happen in practice in 'normal' flight, the theory is that the elevator, even with the effects of increased lever arm, would not be able to overcome the effects of a CoG that is out of limits.

The spinning example I mentioned above is one of the best practical demonstrations of the effects of a too rearward CoG. These issues have caused innumerable spinning accidents over the years.

This topic is valuable in that it highlights the importance of calculating the weight and balance of an aircraft.

There was the sad example of a PA28 a few years ago when two highly experienced pilots decided to spin the aircraft off the coast of Blackpool. The aircraft never recovered and both were killed - the CoG being outside of limits for spinning that type of aircraft. Only two on board, no rear passengers but nevertheless outside the 'utility category' limits set out in the Pilot's Operating Handbook.

Although of academic interest only in this Thread, the practical consequences of paying scant regard to weight and balance can be serious.

[Crash one]

COG too far forward the elevator is not more effective as an elevator, though it may be easier to move.

Laws of levers. A lever length of 12feet with the load 6inches from the pivot your kid could lift a ton, but not very far. Move the pivot back closer to the mid point and several fat people might lift a few Kg quite a distance. Which one is "more effective"?

[keith williams]

We can test the effects by carrying out a few calculations.

Let’s suppose that we have the following initial conditions:

2000 lbs of lift being generated at the wing C of P.

C of G is 1 ft forward of the wing C of P.

Tail plane down force 200 lbs acting at the tail plane C of P.

C of G is 10 ft forward of the tail plane C of P.


In the initial condition we have the following:


Nose-down moment = wing lift multiplied by distance from wing C of P to C of G

Nose-down moment = 2000 lbs x 1 ft = 2000 ft lbs.


Nose-up moment = tail plane down force multiplied by distance from tail plane C of P to C of G

Nose-up moment = 200 lbs x 10 ft = 2000 ft lbs.

So we have an equilibrium condition with nose-up moments equal to nose-down moments.


If we now move the C of G 1 ft forward and employ the same elevator deflection to generate the same tail plane down force we have:

Wing lift = 2000 lbs acting at the wing C of P.

Distance from wing C of P to C of G = 2 ft.

Tail plane down force 200 lbs acting at the tail plane C of P.

Distance from tail plane C of P to C of G = 11 ft.


Nose-down moment = 2000 lbs x 2 ft = 4000 ft lbs. This means that the nose down moment has doubled.

Nose-up moment = 200 lbs x 11 ft = 2200 ft lbs.
This means that the nose up moment has increased by only 10%


The 10% increase in the nose-up moment that has been generated by the tail plane means that the effectiveness of the elevators has increased.

But to restore balance we must increase the nose-up moment to 4000 ft lbs to match the 4000 ft lbs nose-down moment that is being generated by the wing lift. This means that we require a 100% increase in the moment generated by the elevator deflection.

Although the elevators have become more effective in generating a nose-up moment, this improvement is insufficient to offset the increased nose-down moment generated by the wing lift. To see why this has occurred we need to look at the way in which the C of G shift has affected the moment arms of the wing and the tail plane. The wing moment arm increased by 100% (from 1 ft to 2 ft) but the tail plane moment arm increased by only 10% (from 10 ft to 11 ft). So the wing has become 100% more effective in generating nose-down moments, but the tail plane has only become 10% more effective in generating nose-up moments.

[baleares]

fantastic, thanks so much Keith. I get it.

[Mach Jump]

Well done Keith:) A very nice explanation!


MJ:ok:

[Russell Gulch]

Thanks, Keith but



http://www.cruisersforum.com/forums/attachment.php?attachmentid=50727&d=1354688024

[keith williams]

Try this Russel.

Probable Pitchers | mets.com: News (http://newyork.mets.mlb.com/news/probable_pitchers/index.jsp?c_id=nym)

[baleares]

LOL, very good!

[Level Attitude]

Keith,
Excellent explanation.
Assuming the aircraft he talked about was in level flight, anyone want
to say how heavy the aircraft was?

When the centre of gravity is beyond its forward limit the tailplane is more effective due to a longer moment armMy book tells me that: "with the COG outside the forward limit, the elevators may have to be permanently displaced upwards in order to provide sufficient balancing download from the tailplane for straight and level flight."The first quote relates to stability:
An aircraft in level flight, and trimmed, encounters a disturbance that raises the nose slightly. The tailplane is attached to the aircraft so its Angle of Attack increases slightly. With a long momemt arm this change
in AoA is sufficient to pitch the nose back down to where it originally was.

The second quote relates to elevator effectiveness:
If the CofG is forward then the nose down pitching moment due to this
needs to overcome by changing the AoA of the Tailplane. Assuming
you do not want the aircraft's pitch to change then the only way to do this
is with elevator. If the Cof G is so far forward that full elevator deflection is
required then this is not an efficient way to fly (extra drag) and, most
certainly, is not safe.

Why are there CofG limits? The effectiveness of a tailplane (as with any
other lift surface) depends on the speed of the airflow over it and on its
Angle of Attack. The CofG limits are set so that the elevator can always
create an effective tailplane AoA at any speed likely to be encountered in flight.

So, flying slowly:
Rear CofG is determined so that there is always sufficient elevator
authority to recover from a stall (and therefore spin).
Forward CofG is determined so that there is always sufficient elevator
authority to Round Out/Flare.

PS: Sorry no pictures

[john_tullamarine]

Worth keeping in mind that this discussion relates to only one CG envelope consideration .. there is a whole bunch of design considerations which come into play when considering what the final envelope ends up looking like.

[Russell Gulch]

Keith, I wonder if you missed my meaning.

All the calculations under the sun are fine but (for example) a traditional diagram of a CG envelope helps explain a lot.

A picture paints a thousand words.

Russ

[rotorfossil]

Anybody who has flown a parachute dropping aircraft will have found out all about operating at the extremes of the C of G envelope. On takeoff with all the human ballast in the back, it's on the rear cg limit, elevator very sensitive and easy to lift the nose wheel. When they all depart in a bunch, suddenly a lot of nose up trim required as it is now on the forward CG limit and on landing with full nose up trim, it takes a big heave to touch on the main wheels.

[djpil]

http://aerosociety.com/Assets/Docs/Events/671/Gordon%20Robinson.pdf
"Light Aircraft Stability and Control - A Practioner's View
Just look at ä few of the pictures and a few bullet points from page 36 onwards.