Canard Calculations

[Steve-S63]

I'm trying to work out a spreadsheet to calculate the specifics of a Canard config based on the Air Force Flyer HL Glider and I've hit a small stumbling block. The wing is a dual taper wing as such:

(1.25" TE Stock has been added to the TE & is used for control surfaces on this wing)
root chord: 8.75"
Mid Chord : 6.25"
Tip Chord : 4.25"
Span to Mid Chord: 5.5"
1/2 span of complete wing: 16.5" (18" - 1.5" for area in 3" wide fuselage)

This gives me a true wing area of 99sq" but the MAC calculations that I have from Ron Van Putte's article on canards only uses tip & root chords. Using only those values the wing area is 107.25sq".

This means that the true area is 92.31% of the area used for the MAC calculation. If I multiply the MAC by that percentage (.9231) would that be accurate for the true area of the wing? Should I calculate MAC for both portions of the wing & then average them? I'm guessing that this isn't enough difference to really matter but I'm curious as to what the proper solution is.

I'm also having trouble with R.V. Putte's V equation for vertical surface area. It seems that no matter what size I make my Verticals I'm getting a value of .09 to .11 where it should be 1. I've even tried making them 2" root, 1" tip & 1" span and still only get .11. If you're not familier with this formula it should be 1 if it's the right size, greater than 1 for too small and less than 1 for too big. I don't see how the size I stated above could be too big as it's only 1.5 sqin. Any ideas?

Thanks
Steve-S

[Sparky Paul]

For a multi-tapered wing, it can affect the m.a.c., depending on the sweep of the sections..
Use this method to get it precisely on...
http://perso.wanadoo.fr/scherrer/matthieu/english/mce.html
You can play with the various dimensions to get a feel for how sweeps etc. do affect the m.a.c.

[adam_one]

I'm trying to work out a spreadsheet to calculate the specifics of a Canard config based on the Air Force Flyer HL Glider and I've hit a small stumbling block. The wing is a dual taper wing as such:
(1.25" TE Stock has been added to the TE & is used for control surfaces on this wing)
root chord: 8.75"
Mid Chord : 6.25"
Tip Chord : 4.25"
Span to Mid Chord: 5.5"
1/2 span of complete wing: 16.5" (18" - 1.5" for area in 3" wide fuselage)
If your canard's wing has only two different panels, you may check the following site:
http://adamone.rchomepage.com/cg2_canard.htm

[Steve-S63]

Thanks for the link Adam One. I now have 3 locations for the CG to be in the current configuration. :p I might do some glide tests before I put the hardware in too see which one seems the most stable. Maybe I'll make a small foam chuck glider instead. With the wing low the nacelles are kind of exposed.

[adam_one]

Thanks for the link Adam One. I now have 3 locations for the CG to be in the current configuration. :p I might do some glide tests before I put the hardware in too see which one seems the most stable. Maybe I'll make a small foam chuck glider instead. With the wing low the nacelles are kind of exposed.Yeah, that's an excellent idea, and as long as the CG location is somewhere between 5% and 15% of MAC forward of the Neutral Point NP, you are on the safe side. The actual CG position is then more a matter of individual flying taste and/or skills than a precise point.

[Steve-S63]

I figured out where alot of my confusion was coming from. One set of formulas was giving the MAC's position relative to the LE while the others were giving the MAC's size itself. I finally got that squared away and now all 4 sources are ball park. I took the web site's numbers & the programs numbers and averaged them (4.00 & 3.92) and I'll use that. It's a little tail heavy w/o any equiptment installed so getting it on the CG shouldn't be a problem. Now to engineer a lightweight landing system to protect the nacelles.

Adam One,
Where did you get the formulas for the multiple panel MAC calculations and can I get them from you?

Thanks
Steve-S

[adam_one]

I've got the formula from Martin Simons (Model Aircraft Aerodynamics) and adjusted it to my java script so that all results can be measured from the canard's LE.
The distance X from the wing's LE to the wing's AC is obtained as follows:
X = (A1*X1)+(A2*X2) / (A1+A2)
Where X1 and X2 are the distance from each panel's AC to the wing's LE and A1 and A2 are the areas of each panel.

[CloudyIFR]

Steve,

I just finished up a spreadsheet (MS Excel) using Martin's book, would you review your CG calculations for me and let me know how they compare to the others programs you used?

Send me an email to suterc@msn.com if you'd like to help me out, I'd certainly appreciate it.

Thanks
Curtis

PS All the formulas are free to view.

[chrisgood]

If additional spreadsheets could be of any help, I have two versions based on Ron Van Putte's calculcation posted at the bottom of this page:

http://www.chrisgood.com/rcplanes/fwiw/index.html

I very much like the Java versions for one and two wing panels at Adam One's page - they are laid out nicely.

Chris

[Steve-S63]

Excellent. At last my spreadsheet is complete. Now to take over The WORLD!! Muhahahahah. hack, cough, hack, darned cough. :p :D Thanks for the info. I appreciate it.

Steve-S


I've got the formula from Martin Simons (Model Aircraft Aerodynamics) and adjusted it to my java script so that all results can be measured from the canard's LE.
The distance X from the wing's LE to the wing's AC is obtained as follows:
X = (A1*X1)+(A2*X2) / (A1+A2)
Where X1 and X2 are the distance from each panel's AC to the wing's LE and A1 and A2 are the areas of each panel.

[U2Steve]

Steve-

You trying to build something like this?


Another Steve

[CloudyIFR]

Chris,

Nice spreadsheet, your calculations are spot on, using Ron's formulas.

I'm using Martin's formulas and get something very, very close.

Question I have is, what is a recommended "Static Margin" for a balance point for a Canard?

I've never built nor flown a Canard but assumed that 10% for a first flight would be sufficient and safe as in a conventional tailed airplane. Is this assumption correct?

Thanks
Curtis

PS My spreadsheet is very close to completion.

PPS Steve, the spreadsheet I sent has a minor error in it. The distance from the Canard to the Wing is slightly off, it's been fixed. I'll get you an updated sheet when I get home in a day or so.

[chrisgood]

I have a swept-forward canard I just modified this weekend with a new canard setup. I have been using both sets of calculations (my spreadsheet and AdamOne's Java webpage) to calculate where the CG should be on the new setup. My spreadsheet says 18.9 inches from the canard leading edge. To get that value from the Java webpage, I have to set the static margin to 26%, which is too much. I am thinking about 20 inches from the canard leading edge, which makes the static margin 15%. The total CG range is less than 2", but I am still going to narrow that down with a small 1/3 scale balsa glider version I am building for a test flight this afternoon. I will let you know where the CG comes out for a stable glide out on the 1/3 scale version. From that we can get the static margin for this canard. You should be able to apply that to your canard.

The canard I am working on is here: http://www.chrisgood.com/rcplanes/canard/index.html

The previous version (different canard config) flew, but was a bit nose-heavy. Here is the way it looks after I changed it over the weekend.

Chris

[Sparky Paul]

A static margin of 10% should be adequate. It's when it gets less that handling can become "interesting".

[adam_one]

The Aerodynamic Center AC of both the wing and the canard can easily be located with accuracy, whereas the location of the plane's Neutral Point NP is much more difficult to obtain accurately, hence the use of empirical formulas such as Ron Van Putte's formula for the CG.

If the two wings have different aspect ratios (different dCI/d-alpha), the NP will be closer to the one that is slimmer (more efficient) and since the rear wing operates in more or less disturbed air, the NP location will also be affected by that.
Further, both the fuselage and propeller blast will affect the location of the NP as well.

Following is the complete formula used by Martin Simons to calculate the neutral-point of an aircraft:

NP = h0 + ns Vs ( as/aw) (1 - (de/da ))

where:
NP - neutral-point
h0 - aerodynamic center of the wing, typically 0.25
ns - stabilizer efficiency typically 0.6 (0.9 for a T-tail)
Vs - stabilizer volume coefficient
as - lift curve slope of the stabilizer
aw - lift curve slope of the wing
de/da - change in stabiliser downwash angle versus change in wing angle-of-attack, typically 0.5 to 0.33

However, if one understands the major factors that affect the NP location, one can add a "fudge factor" and get a "safe" starting point for the flight test.

[Steve-S63]

Sort of, but w/o the central vertical. I must have gotten it right, even though it's nose heavy and just plain heavy (18.8oz w/battery), as it flew rather well in 20-30 mph winds yesterday. Not enough throw at low rates though so I'm going to turn those up a bit. I'm probably not going to paint this one silver as it's overweight already & the battery is too far forward (that's what I get for balancing it & cutting out the battery bay before installing the landing gear I suppose). I have another airframe & piece of TE stock so I'll find a way to hollow out the fuse to save weight. More pics are in the 'FF airliner conversion Pt.2' (http://www.rcgroups.com/forums/showthread.php?t=350314&page=2) in the foamies section.

Steve-S

Steve-

You trying to build something like this?


Another Steve

[chrisgood]

To verify the CG, I built this small scale model of the full size plane and trimmed it for best glide. Best glide should be almost on the neutral point. This experimental neutral point from the scale model agreed exactly (EXACTLY!) with the equations at the AdamOne's canard web page. Thank you! I have the CG set for approximately 10% static margin and will fly tomorrow.

Chris

[Sparky Paul]

Chris, that's a perfect example of the 'try the chuck glider first" to get the c.g.
Well work bookmarking/saving.
Expect it to be referenced in the future. :)

[adam_one]

To verify the CG, I built this small scale model of the full size plane and trimmed it for best glide. Best glide should be almost on the neutral point. This experimental neutral point from the scale model agreed exactly (EXACTLY!) with the equations at the AdamOne's canard web page. Thank you! I have the CG set for approximately 10% static margin and will fly tomorrow.

ChrisYou are welcome. :)
It was a good idea building the smaller test model and using the calculation as a starting point.
The actual static margin is often an individual preference depending on one's flying technique and experience.
I guess that 10% is a good starting point, allowing for a possible inaccuracy in NP calculation.

[chrisgood]

It flies! The forward swept wing canard flies very well. Two (successful) flights on Saturday and two more today. The first flight on Saturday did not go well. I had the CG set where the programs and the test glider said it should be. No good. The plane left the ground and immediately went straight up and flopped on its back. It made it about 75 feet in the air before coming back down. It landing directly on its spine. I kept full throttle to have some elevator authority until it got back to the ground. It broke the rudder off and the firewall came loose. CA, accelerator, spare balsa, and a little fixing time at the field at it was ready to go again. I removed a chuck of lead from the tail and tried again. Second flight was perfect. Pitch trim was almost dead on. So I flew it again. The only problem was that everyone had gone home, so no one saw it fly. Everyone in the club say it crash, but no one saw it fly. Back out today for two more flights.

I'm still trying to figure out how the equations and the test glider could be off. The equations and test glider agree with each other perfectly, but the full size version required a forward CG. I'm guessing it is the washout and incidence that I have the main wing. It may be shifting the aerodynamic center forward enough to require a farther forward CG. Total offset from the predictions is about 3", which was plenty on this plane to cause unstable flight.

Chris

[adam_one]

Regret about your first flight.
It might have to do with the prop located in front of the canard making the foreplane more efficient than the formula allows for.
I have a pusher canard and it flies well with the CG located 10% of MAC ahead of NP.