digidocs
Well Known Member
I've been curious about the wing stresses in airplanes with extra fuel tanks or gross weights in excess of Van's recommendations, so I did a little study.
Disclaimer:
I am an electrical engineer that only dabbles in structural analysis. I am only analyzing static structural loads and may have made incorrect assumptions or not done the math correctly. Please do not use any of this data to justify flying your airplane at elevated gross weights.
Scenario 1:
An RV-10 is loaded with 2698 lbs in the fuselage and 1 lb of fuel in the tanks. The airplane is below its max gross of 2700 lbs, so from a stress perspective it should be good to go.
I've heard several times on the forums that adding fuel in the wings reduces wing stress. Does that mean that it would be okay to fill the tanks in this scenario?
In the following three graphs, the RV-10 wing has been divided into 10 span wise stations. Station 0 is at the root and station 9 is near the tip. The blue line represents a -10 with 1 lb fuel (2699 lbs total) and the green line a -10 with full fuel (3059 lbs total). The forces/moments indicated result from a +3.8g load.
Its pretty easy to see from these graphs that the airplane with full fuel (green) is placing considerably more stress on the wing structure. Its also possible to see why this is the case and maybe why the original misconception was born.
The lighter airplane has a mass of 1223 kg. The wings most produce 45,545 newtons of lift to apply a +3.8g acceleration to the aircraft. The heavier airplane has a mass of 1386 kg, and its wings must generate 51,614 newtons to provide the same acceleration. In short, the heavy airplane's wing is having to generate a lot more lift (about 1368 lbs-f). This lift is generated along the full span of the wing (lift distribution taken into account). The basic premise behind the "more wing fuel = less stress" theory is that the extra weight of the fuel cancels out this extra required lift.
So does it work?
The net force graph shows that yes, at stations near the root the weight of the fuel reduces the net force. However at stations nearer to the tip, the net force is increased.
Remember that moment (bending) is the product of force and distance. The tip stations have a large distance AND they have larger net force. The result is that they generate a lot of extra moment. As we mentioned, the stations near the root see less force, but because their arm (distance) is shorter their effect on the total moment is smaller. Overall the increase in moment from the tips overpowers the decrease in moment near the root, and the net moment at the root is bigger.
Lastly, take a look at the shear graph. I think this graph illustrates the birth of the misconception. Since shear loads are not dependent upon the distance from the root, the extra weight of the fuel exactly cancels the extra lift required and the root shear is identical in both cases. Of course at any other station than the root, the shear is higher with the extra fuel.
If you're still awake, consider scenario 2:
This time we build a crazy -10, where the fuel is only stored in the outboard wing section. There is no inboard fuel. Once again the no fuel airplane is right at gross, and the fully fueled airplane is over gross by about 160 kg (~360 lbs).
As you can tell, something interesting has happened. Basically we have reversed all the loading effects of the first scenario. The extra fuel near the tips greatly reduces the moment generated by the outboard sections. This time the decrease in moment (near the tips) is larger than the increase in moment near the root, and overall the wing sees less stress. Cool!
By now you're catching on, and you say what happens if the fuel is evenly distributed through the wing span?
You might think that now the loads on both airplanes would be exactly the same. Unfortunately, life isn't quite that simple. Because the lift falls off near the tips, the net force is reduced more in the outboard sections. This reduces the total moment a bit, but you can see the difference is much smaller now.
I hope you found my little study interesting. I had a good time putting it together and attempting to understand all the results. If I've made a mistake, please point it out. I'd be very grateful to see where I went wrong.
-David Carr
Disclaimer:
I am an electrical engineer that only dabbles in structural analysis. I am only analyzing static structural loads and may have made incorrect assumptions or not done the math correctly. Please do not use any of this data to justify flying your airplane at elevated gross weights.
Scenario 1:
An RV-10 is loaded with 2698 lbs in the fuselage and 1 lb of fuel in the tanks. The airplane is below its max gross of 2700 lbs, so from a stress perspective it should be good to go.
I've heard several times on the forums that adding fuel in the wings reduces wing stress. Does that mean that it would be okay to fill the tanks in this scenario?
In the following three graphs, the RV-10 wing has been divided into 10 span wise stations. Station 0 is at the root and station 9 is near the tip. The blue line represents a -10 with 1 lb fuel (2699 lbs total) and the green line a -10 with full fuel (3059 lbs total). The forces/moments indicated result from a +3.8g load.
Its pretty easy to see from these graphs that the airplane with full fuel (green) is placing considerably more stress on the wing structure. Its also possible to see why this is the case and maybe why the original misconception was born.
The lighter airplane has a mass of 1223 kg. The wings most produce 45,545 newtons of lift to apply a +3.8g acceleration to the aircraft. The heavier airplane has a mass of 1386 kg, and its wings must generate 51,614 newtons to provide the same acceleration. In short, the heavy airplane's wing is having to generate a lot more lift (about 1368 lbs-f). This lift is generated along the full span of the wing (lift distribution taken into account). The basic premise behind the "more wing fuel = less stress" theory is that the extra weight of the fuel cancels out this extra required lift.
So does it work?
The net force graph shows that yes, at stations near the root the weight of the fuel reduces the net force. However at stations nearer to the tip, the net force is increased.
Remember that moment (bending) is the product of force and distance. The tip stations have a large distance AND they have larger net force. The result is that they generate a lot of extra moment. As we mentioned, the stations near the root see less force, but because their arm (distance) is shorter their effect on the total moment is smaller. Overall the increase in moment from the tips overpowers the decrease in moment near the root, and the net moment at the root is bigger.
Lastly, take a look at the shear graph. I think this graph illustrates the birth of the misconception. Since shear loads are not dependent upon the distance from the root, the extra weight of the fuel exactly cancels the extra lift required and the root shear is identical in both cases. Of course at any other station than the root, the shear is higher with the extra fuel.
If you're still awake, consider scenario 2:
This time we build a crazy -10, where the fuel is only stored in the outboard wing section. There is no inboard fuel. Once again the no fuel airplane is right at gross, and the fully fueled airplane is over gross by about 160 kg (~360 lbs).
As you can tell, something interesting has happened. Basically we have reversed all the loading effects of the first scenario. The extra fuel near the tips greatly reduces the moment generated by the outboard sections. This time the decrease in moment (near the tips) is larger than the increase in moment near the root, and overall the wing sees less stress. Cool!
By now you're catching on, and you say what happens if the fuel is evenly distributed through the wing span?
You might think that now the loads on both airplanes would be exactly the same. Unfortunately, life isn't quite that simple. Because the lift falls off near the tips, the net force is reduced more in the outboard sections. This reduces the total moment a bit, but you can see the difference is much smaller now.
I hope you found my little study interesting. I had a good time putting it together and attempting to understand all the results. If I've made a mistake, please point it out. I'd be very grateful to see where I went wrong.
-David Carr
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