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If the aerofoils are creating lift they are doing the work to lift the helicopter. When the helicopter is hovering, the blades are carrying the weight of the entire ship. The forces on the aerofoils are acting in the opposite direction to gravity which is pulling the ship down. These opposing forces create a situation where the ship is now hanging from the aerofoils.

So would this mean that the weight and balance calculation for the pilot should not include the weight of the aerofoils as this weight difference would affect the C of G?

A fixed wing aircraft would suffer the same results?

My question is, should the weight of the section of the aerofoils of an aircraft that provide lift be deducted from the weight used to calculate the C of G of the aircraft?

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    $\begingroup$ Hello Devon, welcome to aviation.stackexchange! That is quite a wll of text you have posted there, making it difficult to read. Perhaps you can cut it into paragraphs by adding a few line breaks for better readibility and/or cut out part of text to get to the point more quickly. What is your question actually?To me it is unclear what would you like to have answered. $\endgroup$
    – DeltaLima ♦
    Jan 16, 2020 at 9:02
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    $\begingroup$ Hi Devon, I'm with @DeltaLima on this. Please make sure that there is an actual question in your post. aviation.SE is a Q&A site, not a forum to share thoughts. Edit your post to fit the Q&A format and I'm sure you'll find plenty of experts here to help you :) In any case... Welcome ! $\endgroup$
    – Quentin H
    Jan 16, 2020 at 9:23
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    $\begingroup$ ...and make sure to check aviation.stackexchange.com/tour to see how things work around here ! :) $\endgroup$
    – Quentin H
    Jan 16, 2020 at 9:26
  • $\begingroup$ Thanks guys, apologies for the long text. I edited the post to include my actual question at the end. I will edit the post a bit later. $\endgroup$
    – AME
    Jan 16, 2020 at 9:35
  • $\begingroup$ I think I understand your question is "is the airfoil taken into account the same way for helicopters and for fix wing aircraft when computing CG?" but I'm not quite sure. $\endgroup$
    – Manu H
    Jan 16, 2020 at 10:21

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The center of gravity is relevant for all inertial forces. For example, if you turn, the centrifugal force would be calculated with the mass of all aircraft parts, including wings and rotor blades.

If you want to calculate the loads on the aircraft structure, things depend on the location. If, for example, you want to know the load on the wing root or the helicopter rotor shaft, you use the total mass minus wing / rotor mass times the acceleration to calculate the force.

While there are cases where the wing mass needs to be subtracted, center of gravity calculations must include it.

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You may choose to model the wings (or helicopter rotors) and the rest of the airplane as separate entities linked by springs/dampers to simulate structural connections. Or if the structures are rigid enough for the purpose of your simulation, you may consider the whole thing as one single rigid-body.

But no matter how you model it, the mass of the wing (or helicopter rotors) is there!

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  • $\begingroup$ JZYL, thank you. Surely though, the aerofoils are not linked to the surrounding “air” mechanically. The interaction between the aerofoil and the air create the lift and that air is not connected to anything else. So I agree the weight is still there but it is being supported by something not connected to the aircraft. The weight goes into the air that that is helping create the lift? $\endgroup$
    – AME
    Jan 16, 2020 at 13:08
  • $\begingroup$ @AME That's a negative. You don't need weight (i.e. gravity) to generate lift. And in any case, in a free body diagram, the lift is just another external force. $\endgroup$
    – JZYL
    Jan 16, 2020 at 13:18
  • $\begingroup$ Another way to think of it is the blades are generating less lift because of their mass; some of the lift goes to supporting the blades' mass. The amount of lift generated by each blade is different (depending on cyclic position), but the subtraction of lift is the same, therefore the percentage of lift removed is different, therefore affecting the CG. $\endgroup$
    – HiddenWindshield
    Jan 17, 2020 at 5:23
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On a fixed wing, for the dynamic purposes of balance, no. In the end, other than rotational moments (flywheel effects), aerodynamic forces are unaware of the origins and placement of the mass they are working to affect and whether mass is concentrated in the wings or fuselage are the same thing as far as CG is concerned.

The wing still has to produce 2000 pounds of lifting force for a granite winged airplane that weighs 2000 lbs all up, vs a foam winged airplane that weighs 2000 lbs all up, except for the effects of having mass closer to (foam wings) or farther from (granite wings) the rotational axis and its effect on dynamic behaviour (for example, the inertial effects of having fuel in wing tip tanks). In other words I can install 500 lbs of lead ballast attached to the wing trailing edges, or put 500 lbs of ballast at the same station in the baggage compartment, and I'll have the same aft C of G problem either way because I can think of the wings and fuselage as a single rigid object.

For structural purposes however, the location of the mass matters a lot. The wing root bending moment is much higher for the styrofoam winged airplane since load is concentrated in the fuselage, and the granite winged airplane with most of its mass concentrated in the wings could get away with much lighter root fittings. This is the basis of "zero fuel weight" limits on airliners - the effect of mass concentration on wing bending, and taking credit for mass located out on the wings in reducing wing bending vs mass in the fuselage.

On a helicopter, the rotor blade has to support its weight as well as the weight of the hub and the machine hanging below it, so the weight of the machine has to include the weight of the blades in terms of the total weight the blades have to lift. But the rotor disc has a flexible connection to the rest, so the disc's C of G is effectively disconnected from the body once the disc is holding the machine in the air (the rotor disc is the "helicopter"; the fuselage is the sling load hanging under it - though this is a more accurate concept for teetering rotor machines than articulating rotor machines).

C of G limits on a helicopter are largely a function of articulation limits between the rotor and fuselage, that is, how far off perpendicular the fuselage's vertical axis can be relative to the rotor mast's axis when in flight. So helicopter weight and balance calculations allow for the fact that the rotor's mass is part of the G of G of the machine when it is weighed statically, but is factored out of the calculation to establish C of G limits that apply while in flight.

So in the case of the helicopter, the weight of the blades has to be included in all up weight the engine has to lift, but does not affect center of gravity in flight.

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  • $\begingroup$ Thank you John K - I tried an experiment yesterday when conducting a reweigh on a helicopter. With the helicopter hoisted and left to hang freely, I took a measurement from the tail to the ground. I then got guys to lift the main rotor blades off the stops (this head allows the blades to flap freely on hinge bolts) which removes some of the weight of the blades. The tail measure two centimeters lower during while the blades are lifted which means C of G had changed. Maybe where this experiment is wrong, is that the blades are not yet taking any load and are not actually lifting the helicopte. $\endgroup$
    – AME
    Jan 17, 2020 at 4:32
  • $\begingroup$ @AME I think hanging it from the rotor mast means the blades are acting on the CG somewhat the same as when sitting on the ground, so that when the blades are lifted the CG moves toward the fuselage-only CG, which with no pilot aboard would be slightly aft of the mast axis, so I would expect the tail to drop. So I think you got the correct result. $\endgroup$
    – John K
    Jan 17, 2020 at 13:03
  • $\begingroup$ This is a very interesting play on modeling based on the center of lift. Does a plane just "hang" from its wing? Is the wing the actual "pivot" for pitch? In reality, all unbalanced forces cause acceleration (acting at the center of gravity) until drag force re-balances to a steady state. So, like John says, your CG is simply behind your lift point. Where does the POH say it should be? $\endgroup$
    – Robert DiGiovanni
    Jan 17, 2020 at 16:42
  • $\begingroup$ The CG when loaded will have a range with limits forward and aft of the mast's axis, which determines how much the machine hangs at an angle while hovering, and also affects the pitch attitude in cruise. The pilot and front pax have the largest effect. On very early B-47s you have to move ballast weights between the front of the skid and the tail depending on single light pilot (weight forward) and 3 seated (weight aft) to keep the CG close enough to the rotor mast. The huge horizontal tail of the Blackhawk helped extend the CG range. $\endgroup$
    – John K
    Jan 17, 2020 at 22:31
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For a helicopter, yes indeed the fuselage hangs from the rotary hub, although there is interaction between rotor disk and fuselage (the rotor angle is directed by the flight controls, fuselage angle follows).

The weight of the lifting surfaces can be subtracted from the total weight, but that complicates the computation unnecessarily: the weight and position of the lifting surfaces is a known constant. So the moment equations all add and subtract this known constant, and presto: the CoG of the whole helicopter.

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    $\begingroup$ For a fixed wing aircraft, suppose #1 has wings made of styrofoam, and #2 has wings made of granite. Exact same shape, very different weight. Can we omit all that weight in the case of #2 simply because it's part of the lifting surface? Or does it still affect CG calculations? $\endgroup$
    – Ralph J ♦
    Jan 16, 2020 at 11:46
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Well, it's tax time, so why not ask about deductions?

No, you do not change CG, unless weight changes from burning fuel, or weight is removed from the aircraft by dropping items from it.

Thrust forces from rotors and props, aerodynamic forces from motion (lift and drag), and G forces from turning act on the center of gravity. The net center and magnitude of pitching, rolling, yawing, and lifting forces around the center of gravity determines what the aircraft does. Once in motion, drag forces must be considered.

Gravity force vector is constant.

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