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before I continue I would like to thank you guys beforehand for the help. I am new to this forum and in aviation in general. I am helping my professor to obtain the C.G coordinates in x, y , z for a simulation of a Cessna 172 (we are using Tornado for Matlab). From what Ive read, the C.G in aviation is mostly obtained through the longitudinal axis (x), I assume that the y is centered in most cases, but I am wondering, how can I obtain the height of the C.G, can I use the same method as in the longitudinal axis?

I was also wondering, why is it that for the calculation of the C.G you take into account things such as fuel, passengers, luggage and so on, but not other things like the motor, propeller, fuselage, landing gear, etc.?

Sorry if my questions are a little stupid or obvious. Thank you for your help!

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  • $\begingroup$ Interesting question! I have seen questions on lateral CG before, but never vertical. However, I don't think there is any real practical value in this exercise since the vertical axis of the CG doesn't have any real effect on the flight characteristics. At least none that I have ever encountered or even mulled over theoretically... $\endgroup$ – Michael Hall Apr 30 '20 at 19:27
  • $\begingroup$ @MichaelHall Some models of the Boeing 767 have vertical c.g. limitations expressed as maximum vertical moments. If you want to see an example, go to 747.terryliittschwager.com. Dismiss the initial pop up window, then go to the SERVER box and under the Loads click on the second test file from the top, labeled 2222-01-07_TEST_B767cfgA_N760XX. A window for the load will come up with a problem notification. Dismiss that and then scroll down to the first envelope depicted graphically and you'll see it. It's entitled GROSS WEIGHT LIMITATIONS VERSUS CLIM AND DECK LOADING, VERTICAL CG UP TO 42". $\endgroup$ – Terry Apr 30 '20 at 23:08
  • $\begingroup$ Vertical CG may not vary much for pax and luggage for a 172, but for a "from scratch" design it is needed to determine side force torque from area above and below it. The builders of the 172 did a terrific job, and, judging by its reluctance to roll too much in a side slip, it would be near the midpoint of areas top and bottom, somewhere near the pilot's sitting place. $\endgroup$ – Robert DiGiovanni Apr 30 '20 at 23:17
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No that's a really good question. Weight and balance calculations for flying are only concerned with the location and value of the variable weights - fuel, pax, baggage. The C of G of the "empty" aircraft with all those components is considered a single unchanging value for the purpose of establishing a starting point before loading, and is established just by weighing the airplane while empty. The weight of the components is a factor in where the empty C of G will end up, but once established the entire "empty" machine is treated as a whole unit for W&B purposes.

Vertical C of G is not normally provided with A/C weight and balance data. Although the location is not too big deal with most types of aircraft, for gyrocopters it's quite important because they need to have the engine's thrust line as close as possible to the center of mass for safety reasons (if you unload the rotor on a gyro by pushing over or from turbulence, and the thrust line is significantly above the vertical C of G, the thrust line tries to spin the mass of the machine like a pinwheel about the C of G and the gyro tumbles, with fatal results; the tall and spindly look you see on small gyros today is driven by the need to mount the engine/prop lower to get the thrust line close to the vertical C of G).

On a gyro, the procedure is to hang the loaded ready-to-fly-state machine by the rotor hub, establish a vertical reference line below the hang point, then hang it by another point at the same level that is offset forward or aft using a special "2 hang point" rotor hub fixture, or alternatively if it'll work you can tip the machine back on its main gear until it balances, and establish a vertical reference line extending up from the gear contact point. Where the line extending down from the rotor hub, and the line extending up from the gear balance point (or the two downward lines if you had a dual hang point fixture) intersect, is the vertical C of G.

To figure this out on a 172 you would need to do something pretty radical, like support it along the fuselage at one point using a suitable resting fixture just forward of the main gear but aft of the C of G, and tip it back until it balances and establish a vertical reference through the balance point, then move the fuselage rest forward to ahead of the C of G and tip the plane nose down to establish a new balance point and vertical reference. Then where the vertical axis of each balance point intersects, there's your vertical C of G. Of course you'd want to do this while loaded with people, fuel and bags and you'd probably have to pay them or offer them free beer, after you've found an airplane to use, built a fixture, and all that. You could also probably do it by weighing on scales with the nose propped up high on a block so it points up at an angle, then reweighing with the mains propped up high on two blocks so it points down on an angle, then do some clever geometric calculations to work it out.

Or, if you are as lazy and cheap as me you could call Cessna's Tech Support organization and tell them what you are doing and what you need, and somebody somewhere should be able to find the data (hopefully) without charging you for it.

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  • $\begingroup$ Thank you for the reply John and the others that commented on my question! The problem is that I dont have access to the physical aircraft. I wish I could now since what you are proposing seems like an interesting way to obtain the CGH. I also find it interesting that the CGH is not as relevant in most aircraft. Thank you very much! I will start reading more about aviation it is really interesting! $\endgroup$ – Kaelan May 1 '20 at 19:07
  • $\begingroup$ The vertical CG is usually not that far from the engine's axis in most airplanes except amphibians with engines on pylons above and such. If you eyeball a 172 and consider the volume of the wings and fuselage, you could guesstimate that the assembly's vert CG would be somewhere around the lower half of the side window. The engine's center of mass is roughly about the same level; the gear would lower the CG a bit. I will bet that if you get any results from Cessna it will turn out to be not too far above or below the lower edge of the window. Be interesting to find out. $\endgroup$ – John K May 2 '20 at 1:39

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