Rotation about the CG

[Dick Whittingham]

We all say from time to time that if we apply new force to an aircraft, in stable flight, not passing through the Centre of Mass that this will result in rotational movement about the CM. For example in the effect of rudder input.

Is this rigidly and universally true?

Dick

[acunningham]

Yes. The laws of physics (backed up by an enormous volume of scientific evidence) state that:

Force * Perpendicular distance from centre of mass = Moment of inertia about the centre of mass * Angular acceleration

Since the first three are all non-zero in your scenario, the angular acceleration must be non-zero too. If applied for a non-zero length of time, this will result in a non-zero change of angular position.

[Checkboard]

No it's not true. The centre of rotation is different from the centre of mass. You usually measure torque from the centre of mass in order to simplify the calculations involving the centre of mass (as you are defining those distances as zero).

The centre of mass is usually pretty close for aircraft, however, so it's easy to teach that the two are the same, with out the confusion of teaching year 12 physics to those with a *ahem* imperfect understanding. :rolleyes:

[Dick Whittingham]

Thank you. I thought I remembered that from (ahem) some years ago, but I couldn't replay the maths.

Dick

[Checkboard]

As an illustration: to say that the rotation is always about the centre of mass, is to say that it is impossible to apply forces to a body which will cause it to rotate about any other point. Two seconds with a pencil and two fingers on a table will show you practically that it is possible (using two fingers) two get the pencil to rotate about any point, if you use sufficient force.

[Dick Whittingham]

Thanks again Checkboard, but I don't quite understand the pencil trick. With the pecil flat on the desk and two fingers astride you can spin the pencil from the point where the fingers are, true. but this is constraining the system. In the "rudder" case you have a single linear input into a freely suspended system. Are we still on track?

Dick

[Checkboard]

Still on track. Don't think of it as 'constraining' the system - you are just applying two forces. If you like, think of a broom stick floating in orbit. Two sky rockets attached, pointing in opposite directions - and you can slide them to any position. You can always choose positions in which, when you fire the rockets, the broomstick will rotate around a point which isn't the centre of mass. (Which is the point of the thought experiment - that an object isn't magically constrained to rotate around the centre of mass when affected by external forces.)

Beacause an aircraft has a tailplane at one end, and the wing lift (the largest force being applied) is close to the centre of mass (call it the second largest force - although it depends on what the aircraft is doing), then the centre of rotation is very close to the CofM - so it is easy (although not technically correct) to say the two are the same.

[MD83FO]

without a conceptual back up, on the md 80 i learned how on the landing flare for example, how applying nose down elevator actually raised the main landing gear, as the initial force applied also acts on the opposite side of the center of mass.
i believe this is why the space shuttle reaction control system has thrusters on both sides. for a nose down axial rotation the tail thruster fires down while the nose thruster fires up.

[BOAC]

actually raised the main landing gear, - (we know what you mean:D) - it is actually far simpler than couples and c of g/m's etc - rotating the a/c nose down moves the nose gear (ahead of the c of m) closer to the ground and the mains (behind the c of m) further away - try it using your hand. Standard 'Boeing push' technique.

[FCeng84]

In general, a force applied to a body will cause both a rotation and a translation. In the special case of a force applied in a direction through the center of mass, the body will only translate (no rotation). In the special case of a pair of equal magnitude forces applied in opposite, parallel directions displaced laterally from each other there is no translation, only rotation. With very few exceptions, airplane control surface motions result in both rotation and translation.

In the case of a tail mounted elevator, a trailing edge up motion causes downward translation and nose-up pitch rotation. For most airplane configurations the initial response of the CG (and the main gear) will be downward while the cockpit will initially rise. There will be a point along the forward fuselage where the translation and rotation are matched and opposite such that the initial reaction at that point to an elevator input does not involve any vertical acceleration. This body station (given the name "initial center of rotation" of "ICR" will experience only rotation at the initial response to an elevator position change. The ride at the ICR will be quite smooth - no surprise that this point is usually found somewhere within the First Class section!

Hope this helps.

[MD83FO]

thats what i was trying to say with my poor english.. i learnt this in high school physics 20 years ago, i wander if this is more pronounced on long objects though, ill give it a googling. thanks.

[Dick Whittingham]

Thank you, FCeng84. Very clear.

Seattle? Are you perchance from a large aircraft manufacturers?

Dick

[FCeng84]

Dick - you are correct. My location is a bit of a give away!

[flyera343]

Would anyone have the data available for a calculation in the following incident?

http://www.mlit.go.jp/jtsb/eng-air_report/FGSPD.pdf

It would be interesting to know, with the rapid 2.3G pull, what the initial negative G factor would have been in the aft galley as well a for how long. Thanks.

[FCeng84]

flyera343,

I don't have any more data than that presented in the report that you linked. The data there is rather course with some of it updated at a rate of 1 Hz or less. The sensors on the 777 are located in the EEbay found below the front end of first class, just aft of the nose gear post. From there to the aft galley is approx. 30 meters. The instantaneous center of rotation for the 777 is about 10 meters aft of the EEbay (20 meters forward of the aft galley). The key parameters of interest for calculating the local vertical acceleration at any point along the body are the Nz at the sensor location, the pitch acceleration at the sensor location, and the distance between the sensor location and the point of interest. The data provided shows pitch attitude with a sharp change from -1.2 deg to +3.0 deg in one second. It is hard to infer pitch acceleration from this.

Another way to look at it is how high must the pitch acceration have been to result in negative g at the aft galley? With the aft galley 20 meters behind the ICR (where initial incremental vertical acceleration would have been zero) the pitch acceleration must have been >30 deg/sec^2 in order to result in negative g in the aft galley. The comment from Steward A that "I was strongly hit against the ceiling" indicates that the local acceleration was well below zero (i.e., much more than -1g incremental).

The full negative g event for those unlucky to have been standing in the aft galley did not last much more than 1 second at the most as the pitch acceleration turned negative (nose down) within a second of the event initialization and the elevators were only displaced for one data sample.

Another thing that must be taken into consideration is that for very sharp inputs like this event at high speed there would have been some flexing of the fuselage. The elevators are located very close to the aft galley so the accelerations seen there could have been much different than what is predicted by looking at the sensor data from the front of the airplane and translating back assuming that the structure is rigid.

In my opinion the blame for these injuries falls squarely on the FO who was PF at the time. A potential minor overspeed event was replaced by a very abrupt maneuver. Due to the courseness of the data I cannot tell how far the elevators moved. Limit elevator at this flight condition for the 777 is only 11 degrees.

Lessons learned:
1. Wear your seat belt at all times. Particularly if you are seated aft of the wing! If you are up and about, keep in mind what you are going to grab onto if the bottom drops out - it is sure to come back in a hurry and the further you are from the floor at that time, the bigger chance for injury.
2. Force override of the pilot controls is not the preferred means of disengaging the autopilot!
3. 777 stick force per g target of approximately 40 lbs/g must be respected. Big force = big g = injuries if applied abruptly.
4. Pilots need to realize that on the 777 with the autopilot engaged, moving the pilot controls has zero impact on flight path until enough force is applied to result in an overrride disconnect at which point the manual control laws will respond to the full force being applied. There are only three reasons to touch the 777 controls when the autopilot is engaged:
A. Gain tactile feedback as to what the autopilot is doing.
B. Hold the controls in preparation for disconnect via the disconnect switches.
C. Command immediate disconnect and a large maneuver.

[flyera343]

FCeng84..

Thanks for your reply.

I'm on the line, where the theory of physics and aerodynamics quickly loses out to the practical side. When I first looked at this, I initially dismissed the falling of the crew in the aft galley as simply caused by the strong +2.3G. I thought that any negative G along any part of the fuselage would be fairly instantaneous as it gave way to the positive, especially with that kind of pull at that speed.
The fact that some crew hit the ceiling indicates that the negative G occurrence was rather significant and no small measure of time.

So back to Grade 7 physics for me: Does your acceleration of >30degs/sec^2 take into count the distance from the galley to the ICR? My guess is it does and that the tangential vector in the galley exceeds 9.8m/sec^2 at that point. That would of course assume that the CR remains rigid in space, which it doesn't.
The extra data I was wondering about was how long does it take for the ICR to experience translation to positive G in this situation? Does the ICR move during an abrupt pull like that? Even though the event turned nosedown within a second, would it be safe to assume that neg. G lasted significantly shorter than that due to that section of the fuselage experiencing pos. G from translation? I never thought about the fuselage flex altering things that much but at that length I can see it now..
Thanks for your patience as I try to wrap my head around this...

[FCeng84]

flyera343,

I agree that the time period of negative g in the aft galley must have been less than one second. Assuming the crew member whose head hit the ceiling must have risen one meter off the floor, the g level must have been more negative than -0.5g. Keep in mind also that while positive pitch acceleration at the beginning of this event reduces Nz at the aft galley, the sharp negative pitch acceleration at the end of the maneuver increases local load factor experienced at the aft end. While the front of the airplane saw a peak of 2.3g, the peak in the aft galley may have been considerably higher during the recovery. I know that designing tail loads occur during the recovery from a pull-up and are most critical in the airplane nose down direction.

The way that I like to think about this is that there are two basic means of generating local load factor. The first is angle of attack combined with the status of the wing surfaces that influence wing lift. The second is the pitch acceleration / lift increment of the elevator. The folks at the back end of the airplane get quite a ride as the response is what we call non-minimum phase (initial response is the opposite direction of the long term response). For this event, the first response of the tail is to drop as the elevator forces the tail down to increase angle-of-attack on the wing. Then when angle-of-attack is well established and the whole airplane is experiencing positive g the pilot returns the column to detent and the elevator moves to cause nose down pitching moment. The tail sees a higher peak load factor than body stations further forward.

The effect is very much like the situation on a school bus with the aft wheels well ahead of the last row of seats. Adventuresome students vie for the back seat because corners are so much fun. When the bus turns left, the last row first goes right and then quickly swings left to catch up.

I did use the distance from the ICR to the aft galley to compute the required pitch acceleration: 20 meters requires 0.5 rad/sec^2 to generate a net Nz increment of 10 m/sec^2 (i.e., 1g). If you think of the ICR with respect to the elevator alone, it does not change. This is the sweet spot if you will - it is the location that does not experience any local Nz increment due to the elevator. This spot only feels the Nz due to overall lift generated via changes in angle-of-attack.

[scrubba]

FCeng84,

So it would seem that, in long airplanes (in particular), the empirical approach to saving some (not all) bad landings when the rate of descent gets away from you has some merit, ie that there is a point when continuing to flare (at a high rate) may make it worse, and "rolling it on" short of nosewheel contact may be a better option. Not because the typical "rotating the main gear into the ground" is true, but mostly because the downward translation occurs before any increase in wing lift can compensate - true?

[FCeng84]

scrubba,

You are correct. If your metric for a good landing is touchdown sink rate, a late agressive pull will only make it worse. This is particularly true for a T-tail configuration where the horizontal tail is not as impacted by ground effect lift as much and thus is not significantly "cushioned" as it approaches the runway. I have heard some pilots talk of a technique where a slight nose down command is made just as the mains are touching down in order to "lift" the tail and further soften the landing.

It seems that a soft landing is really a matter of hitting the sweet spot of not flaring too late such that sink rate has not been arrested and not flaring too early such that you float, lose speed, and eventually end up dropping in the last little bit.

Its a bit off topic, but a curious side effect of a very soft landing is that the auto speedbrakes may end up firing before the main gear strut oleos are fully compressed causing the airplane to settle abruptly with an undesirable bang when the oleos reach their fully compressed position. I'm curious how many pilots notice this and on what models they have found it. Is this enough of a factor to lead pilot to avoid auto speedbrakes electing for manual speedbrake extension following touchdown? This is quite possibly worth a separate thread.