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Oct 15, 2003, 08:28 PM
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shaneyee's Avatar

Fuselage Bending moment

What is the maximum bending moment on a fuselage? I supppose it would be a pullout after a vertical dive. So the lift force pulls the wing up at the Mean Aerodynamic Chord or the Neutral point or wherever....and the CG pulls the plane down. The distance between these 2 points multiplied with the maximum lift force on the wing is the max bending moment? How do I find the mean point where the lift force acts?


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Oct 15, 2003, 09:54 PM
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There are two kinds of loads that bend the fuselage. The inertial load due to a rapid pull out form a dive and aerodynamic loads due to the pitch down moment of the wing at high speed and the down load on the horizontal times its moment arm which is aproximately equal and opposite to the wing's pitching moment. Both of these bending loads go up as the square of the airspeed. The design criteria are usually established by the do-not-exceed air speed limit.

The aerodynamic forces and moments of the wing and tail are applied to the aerodynamic centers which are at 25% of the respective mean aerodynamic chords.

The inertial load increases inversely as the radius of the pull out circle. The centripital force is simply the lift produced by the wing minus the down load on the tail. The minimum radius of pull out occurs when the wing is operating near its maximum lift coefficient. How the inertial load is applied to bending the fuselage depends on the mass distribution of the fuselage and the things in it.

The criteria for designing the structure of the fuselage is usually determined by stiffness rather than strength considerations. If the tail boom bends too much it can adversely affect the decalage and the ability to control the plane in pitch.
Oct 16, 2003, 01:14 AM
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shaneyee's Avatar
The aerodynamic forces and moments of the wing and tail are applied to the aerodynamic centers which are at 25% of the respective mean aerodynamic chords
I understood that this is an approximation only. The Allegro Lite plan has a marked "Neutral Point", 3.75" from the LE, and the CG is supposed to be 0.3" to 0.6" from this "Neutral Point". Could this be the ACTUAL Mean Aerodynamic Center? If it is then the max bending moment would be 0.6" x 150lb ( max lift force )= 90 inch lbs.

Oct 16, 2003, 05:15 AM
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The neutral point is the aerodynamic center of the whole aircraft. The trouble is that at model sizes and speeds the neutral point is not always fixed but may shift some with changes in the pitch atitude of the model. This is caused by shifts in the aerodynamic centers of the flying surfaces. Those shifts are caused by shifts in laminar seperation bubbles and boundary layer thickness along the airfoil chord with changes in angle of attack. The flow beyond the boundary layer behaves as though the shape of the airfoil were changing with angle of attack and the boundary layer were not.

The maximum coefficient of lift occurs at a particular angle of attack and the exact aerodynamic center of the wing can be found at that angle of attack. The lift force of the wing acts through that aerodynamic center.

When the plane is in dynamic equilibrium the sum of all the moments is zero. And the sum of all the force vectors is zero. Knowing every force and moment will allow you to find the bending moment on the fuselage. During a high speed pull out, the inertial forces come into play and the mass distribution along the fuselage determines the inertial force distribution. Those inertial forces have to be added to the aerodynamic forces and moments to determine the bending load on the fuselage.

If the plane weighed 1.5 pounds and the lift force was 150 pounds then the plane would experience roughly 100 G's of inertial forces. If the tail weighed 0.8 ounces, then during this maneuver, the inertia of the tail would contribute five pounds to the bending load on the tail boom. In addition to that, the aerodynamic down load by the horizontal tail would contribute an additional bending load on the tail boom. The mass of the tail boom itself would also contribute to its distributed inertial bending load. At 57 meters per second, how much down load by the stab would be needed to balance the nose down pitching moment of the wing?
Oct 16, 2003, 06:52 AM
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vintage1's Avatar
Actually I'd say the worst forces are put on a fuselage in a high speed snap roll. You may need to dive to get the high speed, admittedly..
Speed + control surface deflection will do the worst. And a heavy engine on a long nose will load that up as well in pitch and yaw excursions.

Of course heaviest loads are in crash situations.
Oct 16, 2003, 07:44 AM
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shaneyee's Avatar
Seems like a bit difficult to analyse for an armchair engineer like myself...I'll just do the TLAR method of design but at least I know the minimum requirement.

Ouch.... coincidentally, I just crashed my repaired Picojet into a canal.. the plane bent its nose, the motor broke off and fell into the water and I ruptured 2 cells from my battery pack. I haven't looked at it since but I did soak the motor in distilled water before I dried it. This hobby has its heartwrenching moments...
Oct 16, 2003, 10:29 AM
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The greatness of Dr. Drela's designs is that he has taken all the important forces and moments into account and designed his structures accordingly. They are designed for worst case conditions yet not over designed. You just can't do much better than that.
Oct 16, 2003, 11:54 AM
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Sparky Paul's Avatar
To engineer this situation, one would examine the fuselage alone, finding its deflection under the load. Then add the forces of the wing and tail to see their contribution to the assembly.
Note a fuselage alone doing a loop say, would tend to try to leave the path outward, with the nose and tail ends bent "down", up being to the center of the loop.
The wing and tail would be pulling the fuselage around the path, altering the forces on the fuselage. The tail lifting down for instance adds to the bending of the aft fuselage over the fuselage isolated from the other influences.
Possibly looking at wing bending is more enlightening.. Lockheed found that the removeable tip tanks on the P-80 were better left on permanently, as their presence decreased the bending moment on the wing under load, so the ultimate load the wing could take was increased by the addition of the tanks.
Oct 16, 2003, 08:39 PM
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shaneyee's Avatar
Sparky Paul,
I was trying to come up with a formula for the bending moment so I could design a fuselage with less fudging. I figured the product of the distance between the CG and the MAC or the Neutral Point plus something for the inertial forces would get me in the ballpark.

I know that a suitable deflection for the boom on the Allegro Lite I am building is 0.56in for a 2lb load on the 2ft boom. But thats measured on Mark Drela's plane and is specific for this design.

For instance, if a wing were designed for a max load of 150lb... I could work out the minimum size spar caps and shear web that could handle that and double it and that would suffice. Is there a similiar analytical method I could use for a fuselage. What are good assumptions I could make? Like, where along the chord of the wing would the lift force act? 25%? 30%?


Oct 16, 2003, 09:19 PM
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Up to the 1930's or so the forces and moments on a wing were represented by a resultant force acting at a center of pressure that migrates with changes in angle of attack. That system was, in the early 1930's, replaced by lift, drag and pitching moment acting at the aerodynamic center of the wing. In full scale applications the aerodynamic center doesn't move much and is located near 25% of the mean aerodynamic chord. The aerodynamic center in the modern system is defined as the point about which the pitching moment coefficient is constant. The wing's lift and drag forces are defined as acting at the aerodynamic center of the wing. Modern airfoil data is expressed in terms of coefficients of lift, drag and pitching moment. It is easier to apply the modern system directly than to first translate it into the old system based on center of pressure.
Last edited by Ollie; Oct 16, 2003 at 09:24 PM.
Oct 16, 2003, 10:39 PM
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Sparky Paul's Avatar
Shane, fuselages are more considered envelopes around the stuff than lifting surfaces.
A rigorous fuselage design handles the masses of all the parts, from the spinner to the tailwheel.
Their (relatively) high fineness ratios could be considered to be very short spanned long chords, but treating them as simple beams holding the parts together is more common.
Form follows function, and all a fuselage is expected to do is keep all the parts in the same location for the duration of the flight.
What works for a design can be used for much different shapes, but still have the same basic load structure.
If you look for instance at an Aeronca C-3, one of first examples in the Aeronca line, you see a triangular tubing structure for the fuselage. Covering applied directly to the tubing.
It's not apparent from the outside, but the 50 year later Citabria has that -same- triangular load carrying structure, fleshed out with plywood formers and spruce longerons and covered.
For a model airplane evaluating ALL the mass's effects and the structures needed to support them is WAY too much work for the results, when all someone need do is look at what works for a similar size and shape.
FAA certification isn't looming in the future before the model flies, after all.
There's other things besides bending to consider. Torsional stiffness for one. This gets into materials as well as stress.
The choices for a "universal" design program would be overwhelming when all the parameters that are considered for full-scales are included.
Many full-scale requirements can be ignored, since we don't carry people.
Or fly really heavy things around.
Essentially, any design program has to make compromises to be of any utility for a model airplane. Such compromises result in the output of a "one-shape" design, usually. Anything more is just too complex for the rewards.
The end result will look like the basic airplane the programmer used for his basic concepts, for the most part.
That's why model design is generally simplified to tail areas as x% of wing area, nose moments x times chord, tail moment y times chord.. battery here, motor there, servos whereever...
The structure itself is left to the builder. Sticks or sheet, foam, in whatever amounts have been shown to be useful.
Your example of Mark's Allegro Lite for instance.. what are the conditions for the 2 lb. load.. is it really important to know that?
How is that load comparable to a larger/samller airplane with different surfaces and structure?
I've built an Allegro Lite with e-power, and used a completely different construction, and I don't fly it to the extremes Mark does with his.
I'm quite happy with mine.
It's possible to get so tangled up in the details the end product never gets built because there's so many unknowns in the system assigning priorities to each can be overwhelming, especially considering the lack of quality/material control that is normal in modelling. How much adhesive, where is it? The covering... Where are the fasteners, the wires, the ..... all of these are fixed values in full-scale design, but uncontrolled to any extent in a model.
There's another question like this on evaluating a wing design for the number of wing ribs required... The answer can be anything from 0 (full-span foam) to 1 every inch of so (really scale Gossamer Condor ).
Punching in a few design parameters, unless those parameters are directed towards a specific shape won't "design" the structure. That requires looking at what's needed, what has worked, and how much effort the project really needs.
Last edited by Sparky Paul; Oct 16, 2003 at 10:43 PM.
Oct 17, 2003, 04:16 AM
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shaneyee's Avatar
Ollie, Thanks for your information.

Sparky Paul,
I get what you are saying. The TLAR method is what I normally use for designing model airplanes and it has worked well for me so far. I also learned ( and relearnt ) some new things from Ollie about designing wings and that added to my knowledge. Granted that " evaluating ALL the mass's effects and the structures needed to support them is WAY too much work for the results " but its fun to get just a little step further than where I've been. Its the journey as much as getting there.

Oct 17, 2003, 11:32 AM
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Sparky Paul's Avatar
Shaney, when I look at the variations in the fuselages I have hanging from my ceiling right now, the thought of programming a system that could handle all of them.... Oi!
Arrow shafts, easy...
Longerons with diagonals, not so easy.
Sheeted with internal diagonals..
Fiberglass shells; profiles, both solid and hollow..
Wings is easy compared to that!

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