# The AFB (Amazing FleaBike)

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#### Hot Wings

##### Grumpy Cynic
HBA Supporter
Log Member
Could someone tell me where I've gone wrong here?
Calculating area in the wrong plane? Front view vs top view?

#### rtfm

##### Well-Known Member
Hot Wings - I think you have it in one!
The shear web area required is 631mm^2, which has to be divided by the height of the web, That gives us 5.639mm - the thickness of the ply required. It is so simple now. Thank you.

Which leaves me with a bit of an issue. I'm going to have to double the shear webs - something like this? In future builds I'll simply specify 6mm webs, and have done with it.

HOWEVER... doesn't the fact that this is a strutted wing make a difference?

Duncan

#### rtfm

##### Well-Known Member
In case anyone is interested, the entire rear wing weighs 11.24kg (with the double shear webs). Not too shabby.

#### rotax618

##### Well-Known Member
Being strutted changes everything, the stresses are less by a factor of 3. Best to re-do the maths, you are carrying too many passengers - it is easy to make an airplane strong, it is hard to make it strong enough.

#### Victor Bravo

##### Well-Known Member
HBA Supporter
We are very lucky to have engineers here who can elaborate on this much much more authoritatively than I. But I will bet you that the spar would be significantly stronger and more robust if you accepted the slight inconvenience of two-piece ribs, and went to a solid shear web with no gaps in it.

#### rtfm

##### Well-Known Member
Too late, Victor Bravo. Ribs cut, shear webs cut, first bonding stage completed. I'm eager to see how the load test goes...

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#### mcrae0104

##### Well-Known Member
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Log Member
That gives us 5.639mm - the thickness of the ply required. It is so simple now.
What you have done is compute the thickness required based on the average shear stress. That gets you in the ballpark. But the shear stress is not distributed uniformly across the height of the shear web. The distribution depends on the shape of the beam.

The maximum shear stress value for the plywood is also affected by the orientation of the plies (parallel and perpendicular to the spar vs. 45-deg). The grain orientation also affects the shear stress allowable at the glue line between the web and caps.

If you have a copy of Bruhn, chapter C.8 deals with the design of wood beams and it is an excellent resource. Also Jeff Hanson’s YouTube series on statics and mechanics are quite good as a starting place.

#### mcrae0104

##### Well-Known Member
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To follow up on what I wrote above, I checked the max shear based on the values provided.
• The shear is 3.6 times the allowable value, but there are caveats:
• I simply used the Fs = 1.20 kg/mm2 as allowable shear. Bruhn has an equation to determine allowable shear in plywood webs based on the spacing of stiffeners, and this would be preferable.
• I don't think the max. shear is actually 1,634kg. That is simply half the weight (well, mass, but whatever) times a load factor of 6. That would be correct for a cantilevered wing, but drawing a shear diagram of a strutted wing will reveal a maximum shear value that is less than this.
• Also, 1,634kg is half of the gross weight. This is the rear wing we're looking at, correct? Wouldn't the rear wings be carrying 40% of the aircraft weight, meaning each rear wing would see more like 654kg?
• I don't know the allowable shear for Hoop Pine, but the max. shear in the segments with the web missing ends up about 3-4 times the allowable values of the various pines listed in ANC-18 (with the same caveat that max. shear would actually be lower).
• I gave it some more thought, and I think it's reasonable to analyze the four caps as little cantilevered stub beams as @Hot Wings suggested. I suspect the slots could be OK but might require a doubler--perhaps a rather wide one. Duncan, if you'll let me know your span, I could give a shot at analyzing that condition. (Just bear in mind that I'm not a professional engineer, but it might get you closer to some confidence in your design or helping you to make some minor modifications before testing).

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#### rtfm

##### Well-Known Member
Aaargh!
OK, I have more foam, so I'm going to cut two-piece ribs and cut a continuous shear web. BUGGER! This will be the 5th set of ribs I'm cutting...

When you say:
I predict that the wing will fail in testing at a rib to either side of the strut attachment, where maximum bending is encountered.
what exactly do you predict?

Duncan

#### BBerson

##### Light Plane Philosopher
HBA Supporter
The wing outboard of the strut is cantilever. But the load is only that portion of the semi- span. (usually about 1/3)

#### mcrae0104

##### Well-Known Member
HBA Supporter
Log Member
Aaargh!
OK, I have more foam, so I'm going to cut two-piece ribs and cut a continuous shear web. BUGGER! This will be the 5th set of ribs I'm cutting...

When you say:
what exactly do you predict?

Duncan
Sorry, Duncan, I just edited the post and removed that part--maybe take another look. I do still think it's correct that somewhere around the strut would be the location of the failure because it has the most bending and shear--but I want to analyze the slot areas for bending. What is your wingspan? Also, am I correct that this wing is only supporting 40% of the plane's weight? Don't scrap it just yet!

#### rotax618

##### Well-Known Member
Think about not cutting the lightening holes in the foam, the gain is not worth weakening the rib.

#### rtfm

##### Well-Known Member
Wingspan (front) is 6m, rear is 4m. Struts at 1.25m and 1m respectively ( also where the hinges are situated)
MAUW keeps changing as the build develops, but I think it will end up in the vicinity of 300kg

I am currently working on the rear wing: 30% loaded.

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#### rtfm

##### Well-Known Member
Well, I'm getting closer. I've increased my MAUW to account for the many unexpected weight additions as the build progresses, and have now factored in wing loading, but still working with a cantilever scenario. I figure that if my results work for a cantilever wing, they will certainly work for a strutted one. Here's where I am at present.

If this is correct, then my 3mm shear webs are going to be fine, and I'm never going to stress the wings to 6 g's in a Flea anyway.

As for the 30mm gaps in the shear webs, won't the main stresses in the spar caps be almost purely in tension and compression? And they're capable of withstanding over two and a half thousand kg in tension/compression. Anyway, I'm going to finish the rear wing as is I think, and am thinking of a continuous shear web for the more heavily loaded front wing.

Duncan

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#### mcrae0104

##### Well-Known Member
HBA Supporter
Log Member
Well, I'm getting closer. I've increased my MAUW to account for the many unexpected weight additions as the build progresses, and have now factored in wing loading, but still working with a cantilever scenario. I figure that if my results work for a cantilever wing, they will certainly work for a strutted one. Here's where I am at present.
View attachment 110425
If this is correct, then my 3mm shear webs are going to be fine, and I'm never going to stress the wings to 6 g's in a Flea anyway.

As for the 30mm gaps in the shear webs, won't the main stresses in the spar caps be almost purely in tension and compression? And they're capable of withstanding over two and a half thousand kg in tension/compression. Anyway, I'm going to finish the rear wing as is I think, and am thinking of a continuous shear web for the more heavily loaded front wing.

Duncan
Hi Duncan,

Here is a start on some calculations for the rear spar. Unfortunately I started before I saw the above post and I used 30% for the rear spar as you mentioned earlier. Nevertheless, I hope this will be of some value to you and others for the process if nothing else. I used a sort of graphical method to generate the shear and moment diagrams--they're not super precise but pretty close. Please beware that it is entirely probable that I have made errors and I would invite others who know what they're doing to offer their scrutiny. You will see on the first page (image below) that I have made some assumptions about the spar layout--it's probably not exactly the design you have. My drawing is not a suggestion--only a guess, but it is probably close enough as a first pass that could be cleaned up to dial in the precision. Sorry for the imperial units, but Bruhn and ANC and the FPL literature and charts use them and I'm more confident translating the basic dimensions at the start than trying to adjust all the literature into metric.

These pages deal with the basic scenario of a continuous shear web--the calculations for the rib slots will need to come after this. I have not yet checked the glue line shear strength, combined bending and axial stresses, or other load cases such as asymmetrical lift or the loads you get when the control surfaces (i.e. the entire wing panels) are deflected, which would need to be a part of a more complete analysis.

In this base case (cont. web, 30% weight on rear wing), it looks good so far (if not overdesigned). My guess is that increasing to 40% will erode the bending margin somewhat (current M.S. > 2) and that more shear strength may be needed (current M.S ~0.5). Of course the front wing will be a different animal, carrying more load and having a larger span.

I want to stress again (no pun intended) that the figures above in post #434 for web thickness are based on average shear stress for a cantilever (not strut-braced) wing, and do not account for the actual maximum stress, which is higher (but tempered by the fact that it's a strut-based design). You can see how this works in the attached file.

Yes, where the caps bridge the gaps, they will be in tension/compression due to the bending imposed from the portion of the wing outboard of the gap, but they will also have shear stress (and the axial stress imposed by the strut reaction needs to be added in as well).

I will see what I can do tomorrow night as time allows.

EDIT: I just saw that I made a dreadful mistake at the outset. I imposed the entire rear wing lift on just one wing panel. \$%@!!! At least it means your wing is stronger than my calculations show. I believe the process is correct for demonstration purposes, but I'll need to correct this (I'll probably make a spreadsheet so that adjustments can be made more easily than this manual method, but it won't show all the steps).

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#### Hot Wings

##### Grumpy Cynic
HBA Supporter
Log Member

Hand work like that takes me at least 3 iterations to make it readable for others. Generally two even if it is just me that needs to look at it next week.
Love my Excel.............

#### patrickrio

##### Well-Known Member

Hand work like that takes me at least 3 iterations to make it readable for others. Generally two even if it is just me that needs to look at it next week.
Love my Excel.............
You can mostly tell who took drafting before computers changed the industry by this skill alone.

#### BJC

##### Well-Known Member
HBA Supporter
You can mostly tell who took drafting before computers changed the industry by this skill alone.
Yup, lettering to the instructor’s satisfaction was a challenge.

BJC

#### Hot Wings

##### Grumpy Cynic
HBA Supporter
Log Member
You can mostly tell who took drafting before computers changed the industry by this skill alone.
Actually................
I started drafting when I was pre-teen. My grandfather was a very good architect and I too was/am pretty good at the paper, pencil and triangle drafting.

My problem is poor work flow planning for a small detail project like this - which I find kind of odd because I can visualize a building, or a plane, with all of it's subsystems and see how they relate and interact with the people that use them.

Excel is just a nice neat crutch. My paper versions tend to suffer from eraser abrasion fatigue.

#### patrickrio

##### Well-Known Member
Actually................
I started drafting when I was pre-teen. My grandfather was a very good architect and I too was/am pretty good at the paper, pencil and triangle drafting.

My problem is poor work flow planning for a small detail project like this - which I find kind of odd because I can visualize a building, or a plane, with all of it's subsystems and see how they relate and interact with the people that use them.

Excel is just a nice neat crutch. My paper versions tend to suffer from eraser abrasion fatigue.
I am on the cusp for this so I understand. I took my first drafting/drafted descriptive geometry courses before computers entered the classroom. BUT I have essentially never formed a written idea outside a computer since I got my Apple II (with wordstar and visicalc) in 5th grade. My thought processes thus work best with infinite editing ability.

When I have to write or draw or create ideas with only pencil and paper, the ideas don't come out as polished at all.