PeterF's Chris Golds Northrop B2-A stealth bomber - Page 7 - RC Groups
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Jan 19, 2013, 09:26 AM
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p901P901's Avatar
The flight controls are coupled so each will react to different axis and diffrently to the planes attitude. Everytime I look at this type of design I can see a 3 axis gyro like the Guardian will work to tame this plane. But this will be another experiment to tune.
Chris Gold has got it right and I wonder of how many test he made to get it like this.
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Jan 19, 2013, 01:59 PM
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PeterF's Avatar
Having read Chris Article in Quiet and Electric Flight Inetrnational describing the plane and comments from his accomplice, Robert May on this forum quite a lot of work went into it.

He originally built a 12ft 8in (3.86m) wingspan model powered by 4 x OS46 ducted fans engines. Before this there was lots of chuck glider work to test GofG etc. Unluckily the drag rudders did not operate as rudders, just speed brakes opening and closing together so no yaw control, only very good yaw stability and there was not enough aileron authority. The report was that it had good pitch control but was completey stable in roll and yaw and flew in a straight line until "BOOM".

After that came a Horten IX and YB-49 using drag rudders for yaw control with the drag rudders coupled to aileron, and the drag rudders open >30 at neutral for stability.

Even after all that, the prototype electric B2 (the one I am building) nearly bought it on take off, the CofG was much too far back and it reared up and tip stalled but landed without damage, so the CofG was reset and the plane flew well reportedly with complete stability and plenty of control surface power (and no gyros).
Jan 19, 2013, 02:43 PM
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Kevin Cox's Avatar
Excellent work Peter!
Jan 19, 2013, 09:33 PM
deltas are cool
AIR SALLY's Avatar
what percent of MAC is the C/G on the model? i know what the real one is ,i'd like to compare them.
Jan 20, 2013, 03:51 AM
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PeterF's Avatar
Quote:
Originally Posted by AIR SALLY
what percent of MAC is the C/G on the model? i know what the real one is ,i'd like to compare them.
I do not know about the MAC, but it is 43% of the centre line chord.
Jan 20, 2013, 04:32 PM
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PeterF's Avatar
Just done the MAC calc as far as I can for such a complex planform. I have ignored the fact that the wing shape is different for the body & winf and that there is washout on the wing tips which change the real MAC. On the assumption that the lift is proportional to the chord squared over the whole plane, the CofG comes out at 22% of MAC.

The attached roughly scale drawing is from the Excel calc and is a graph of the measured shape of my plane. The leading edge is at 55 to the root chord, do not know if the sweep is scale or not. The sketch shows the locations of the MAC and CofG.

The reported problems with a rearward CofG on the prototype by Chris Golds was a 48% of root chord or 30% of MAC.
Jan 20, 2013, 04:54 PM
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p901P901's Avatar
Did you project the LE and TE to the centerline of the fuselage to calculate the CG? This would be the root cord length. Not to sure about the TE projection.
I would think the CG would be 10%. MAC.
Last edited by p901P901; Jan 20, 2013 at 05:00 PM.
Jan 21, 2013, 05:03 AM
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PeterF's Avatar
Quote:
Originally Posted by p901P901
Did you project the LE and TE to the centerline of the fuselage to calculate the CG? This would be the root cord length. Not to sure about the TE projection.
I would think the CG would be 10%. MAC.
I calculated the MAC by numerically integrating chord^2.dy over the wingspan and dividing by the total area as per the linked document. As the wing has so many different elements none of the simple methods would work so numerical integration by taking the chord every mm based on my measurements was the only way.

MAC calculation document

I then used the methods outlined in the document to find the centre of area by again intergrating the area moments numerically (chord.x.dx over the span and span.y.dy over the chord and dividing by the total area).

The prototype model flew with the CofG at 43% of the root chord, the rot chord being taken as the centreline. So directly taking the CofG position at 90 to the centreline means it intercepts at 22% of the MAC. See the updated sketch from Excel, which is created using a graph and the calculated points.

To make sure I have this right, I have taken the planform and considered it as a simple delta wing with a tip chord of zero at the outermost point of the wing. This sort of balances out the areas outside of the delta shape and the cutouts, and the delta I have taken has 98.4% of the area of my model, so pretty close for a cross check. I have then calculated the location of the MAC and the MAC using the cross strings method. The result is in the second sketch, the delat shape is in orange with the rough MAC chord lines. These are very close to the integrated values I came up with. The simple MAC is 6mm (1/4") shorter and 11mm (1/2") inboard. The key is it confirms the numerical integration was OK.

Is your point about the 10% MAC an observation that a flying wing such as the B2 ought to balance at 10% MAC or from my graph that the CofG looked more like 10% rather than 22%.
Jan 21, 2013, 09:47 AM
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p901P901's Avatar
Thanks for the document will use for future reference.
Looking at you drawing CG looks about right, but the CG at 43% root cord is not. Its the math that was used is confusing. So my statement about CG at 10% MAC may not calculate in your math (need to look at your document more). Multiple panel wings formulas calculations that are 25% MAC for each panels so panel areas multiplied by MAC is used for each panel. NP= (Area a x X1)+(Area b x X2)+(Area c x X3)/ (Area a + Area b + Area c) X1, 2 and 3 is measure form the LE of the innermost panel. MAC = (Area a x MAC)+(Area b x MAC)+(Area c x MAC)/ (Area a + Area b + Area c).
My past experience with flying wings is that the distance from NP to CG is all the leverage you have. So if these to points where close t. he pitch moments would be very sensitive. So there has to be some sort of static margin for flying wings to keep the nose heavy. Conventional aircraft has a Static margin 5-15 percent ahead of the NP because they all have tails. Flying wings need more because they have no tails.
Last edited by p901P901; Jan 21, 2013 at 10:13 AM.
Jan 21, 2013, 10:18 AM
check for reversed controls
alpea 41's Avatar
The flyers of the LX model have difficulty getting the C G forward enough . Better to be too far forward
Jan 21, 2013, 10:47 AM
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PeterF's Avatar
The 43% of centreline chord is what is on the plan so that is what I stated first, I am new to all of this theory, empircally it flew at 43% of the centreline chord. If my calcs are correct and the MAC is in the right location then I have a CofG 3% in front of the NP if this is at 25% MAC but as you say, I may not have the maths perfect.

If again I assume my MAC is correct, the setting the Cof G to 48% of the centreline chord brings the CofG to 30% of MAC and behind the 25% NP. No wonder it reared up when it got to flying speed.

What this is teaching me is that as I put it together forward CofG is critical and I must not think that it is only part of an inch backwards it'll be OK because it wont and for early flights moving it furtehr forward than the plan may be a good idea.
Jan 21, 2013, 01:52 PM
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Yes that looks to close to the NP.
I need to run the numbers to see if using the 3 panel method will work for this design
Jan 21, 2013, 03:21 PM
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As I solved the calcs by numerically integration I essentially split it into 1238 panels each 1mm wide (1238mm for the half wingspan). This needs numerical inegration because you can not come up with a simple formula for the whole TE as a function of span that you could integrate properly.

On the graphs I have plotted each square is 200mm x 200mm (approx. 8" x 8") so the span is 2476mm (97.5") and the length is 1001mm (39.5"), but the centreline chord is 980mm (38.5"), the rearmost portion is the rea wing tips.
Jan 21, 2013, 05:29 PM
deltas are cool
AIR SALLY's Avatar
22% MAC sound like a safe C/G ,im sure the computers on the real deal help ,so since the model does'nt have any the 22 % should be a safe bet.
Jan 22, 2013, 05:29 AM
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PeterF's Avatar
Found on the net some calcs for the B" from Aero Eng students at Virginia Tech Aerodynamic calcs for B2 and that has a page where the shape of the wing has been plotted from an on line 3 view drawing along with the resultant calcs for MAC and MAC location.

If I scale the quoted 86ft wingspan down to my models size then my calc for MAC length and the MAC spanwise location agree with my calcs within 5mm (1/4"). Additionally, within a few mm the model agrees with the planform and measurements in this analysis, the same 35 (to one decimal place) LE angle and centreline chord. It seems that the Chris Golds plan is a good outline vs the full scale.

You can download the program he wrote to generate MAC from Aerodynamic tools and look under Planform Analysis. The program works but I do not have the numbers for my model with me at the moment to cross check.
Last edited by PeterF; Jan 22, 2013 at 06:08 AM.


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