# L/D -Bell vs Eliptical spanload?

look at this video from 18:00-21:00 ,Al Bowers talk about benefits of bell spanload compare to classic eliptical..Can someone explain what does it mean in practice examples when design aircrafts:

1)So if we have plane with 3000kg and we must have best L/D and if wingspan is not constrain,then we must choose bell spanload so our new wing will be 22%longer and it will has 11% smaller induced drag?

2)Why Al Bowers talk like airplane overall weight and wing bending moment are same thing?If some plane have bigger wing bending moment,that dont neccesery mean that it has larger weight than plane with lower wing bending moment...

3)Why all gliders use eliptical spanload if bell spanload has better L/D?

4)What do you think,when will aircraft industry switch to the bell spanload solution(if ever)?

• Hi, and welcome to Aviation.SE. Please summarize the content of the video you refer to; your question should stand on its own if that link rots away (or if the video is not accessible in some areas), and note that opinion-based questions (what do you think...?) are discouraged here. Also, consider taking our tour to learn how ASE works. Apr 28, 2020 at 11:10
• Ok I will delete last video and put it in new topic.. Apr 28, 2020 at 11:16
• I was referring to your first video, since you do not give much of an introduction to your questions outside of "watch this". Apr 28, 2020 at 11:17

1)So if we have plane with 3000kg and we must have best L/D and if wingspan is not constrain,then we must choose bell span-load so our new wing will be 22% longer and it will have 11% smaller induced drag?

All other parameters except span held constant this is true.

2)Why Al Bowers talk like weight and wing bending moment are same thing?If some plane have bigger wing bending moment,that dont neccesery mean that it has larger weight than plane with lower wing bending moment...

Wing root bending moment corelates to the load factor N * weight. Also spar cap sizing is done with REF to the the root bending moment which in turn drive the wing weight.

3)Why all gliders use elliptical span-load if bell span-load has better L/D?

To be precise, all gliders do not use elliptical span-load. However, it's not wrong to say all gliders tend to use span-load distributions which are very close to elliptical loading. What elliptical span-load gives is the lease induced drag per given span. Say you start with an airplane with a given span and increase the span by 22%. Yes, you will get 11% decrease in induced drag but if you use elliptical loading on that increased span, your induced drag will be even smaller. (32% decrease)

4)What do you think,when will aircraft industry switch to the bell span-load solution(if ever)?

I am not qualified and/or knowledgeable to answer this. Just for the info, there are many more viable and attractive solutions available with lower risks involved, such as the ones investigated in the NASA N+3 program.

• Are you also aeronautical enginer what is your background? May 1, 2020 at 20:30
• Say you start with an airplane with a given span and increase the span by 22%. Yes, you will get 11% decrease in induced drag but if you use elliptical loading on that increased span, your induced drag will be even smaller. (32% decrease) If you do that you will end up with higher bending moment=higher mass=higher lift,so overall drag will increase..
– user52248
Sep 5, 2020 at 6:20

1) So if we have plane with 3000kg and we must have best L/D and if wingspan is not constrained, then we must choose bell spanload so our new wing will be 22% longer and it will has 11% smaller induced drag?

Induced drag is not all. At high speed friction drag will dominate and at best L/D it will already contribute half of total drag. Those 22% will also add more surface area which adds friction drag. Real designs are a compromise which looks at both components, friction and induced drag.

2) Why Al Bowers talk like airplane overall weight and wing bending moment are same thing?

He simplified things, as did Prandtl in his article which is the source of Al's wisdom. If the mass that counts (the payload) sits in the middle of the wing (i.e. in the fuselage), this simplification is justified. Airplanes need to have practical value and a big payload fraction means more practical value for the operator.

3) Why all gliders use elliptical spanload if bell spanload has better L/D?

Because they need to minimize drag with a given wing span. Given their high aspect ratio, the speed of best L/D is close to the stall speed already, so in most of the speed range friction is the dominant source of drag. By keeping wing area low, this drag contribution is kept low as well. There have even been attempts at reducing wing area in flight (fs-29, SB-11) in order to improve L/D at higher speed.

4) What do you think, when will aircraft industry switch to the bell spanload solution (if ever)?

You may not have noticed but they did move away from the elliptical lift distribution long ago. Only in the times of biplanes a constant chord over span was favored, but as soon as cantilever wings were used, wings became tapered (exceptions apply, of course). But witness the taper ratio of most wings - they would have atrocious stall characteristics if they relied on elliptical loading. Of course they use proportionally less lift near the tips in order to minimize drag.

You can see that the outer contrails of this Boeing 747's engines wrap around the contrails of the inner engines (picture source). This shows how the air is pushed down in the wake of the wing and that the centers of the vortices are slightly inboard of the outer engines. The outer wing contributes little lift; however, this is not an ideal bell-shaped distribution with download at the tips. Again, it is a compromise to minimize overall drag.

• 1)Do you think that AL Bower forgot to consider frictional drag in calculations?He prove that bell spanload can reduce overall drag by 60%. 4)I think this is not examples of bell spanload,bell spanload has resultant force at wingtip tilted forward,so lift produce small thrust Apr 29, 2020 at 7:26
• @ROTOR: Without knowing Al personally, I am convinced that he considered friction drag but chose an operating point where it matters little to make the advantage of a non-elliptical distribution obvious. For 4, see the extended answer. With enough angle of attack, every wing designed with the bell-shaped distribution will create lift also on the tips. Apr 29, 2020 at 8:21
• Wing with bell spanload at wingtips allways produce lift,just lift is tilted forward from vertical axis,this cause small thrust.Strong upwash at wingtips change effective airflow..there is no download at wingtips..see picture on this link:aviation.stackexchange.com/questions/77662/… Apr 29, 2020 at 9:00
• @PeterKämpf He simplified things, as did Prandtl in his article which is the source of Al's wisdom. If the mass that counts (the payload) sits in the middle of the wing (i.e. in the fuselage), this simplification is justified I really cant understand what is link between payload and bell wing,can you explain what you mean behind this?
– user53913
Feb 5, 2021 at 20:52
• @EBV821 Root bending is caused by the non-lift-carrying mass. The wing carries itself; it is the stuff in the middle which needs to be lifted with a force at some distance. This creates the root bending moment and causes heavy wings. Now please stop stalking me and do the rest of the thinking yourself. Feb 5, 2021 at 21:04