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Control surface sizing?
Hi everyone, does anyone have a link to a site were i can find the science/maths behind control surface sizing?
I would just use a calculator but im writing up a project for my degree and i need to show my working out. Any help will be appreciated... 



Cromer,Norfolk, UK
Joined Nov 2006
2,505 Posts

Given that control surface size is dependant on many factors, there is no one equation which dictates it. Factors involved would include;
Aircraft role  Aerobatic, training, 3D etc Wing section  Flaps in particular, different sections are designed to use different size flaps as a % of wing chord Control method  In full size, nonpowered controls have to be sized to keep stick forces to a level suitable for a range of pilot arm strength Aircraft speed range  Slower flying aircraft need a larger surface (normally) Drag  The trade off point between a wide chord surface moving less, and a narrower chord surface moving more Altitude  Thinner air, needs more control surface authority to maintain control at higher altitude  More surface, less movement For general sport/aerobatic models, the main deciding factor is how much response is required. So, off the top of my head, I would work to the following rules of thumb; Elevator/Stabiliser Trainer  20% of total stabiliser chord Sport Aerobatic  30% Aerobatic (non 3D)  40% 3D  60%+ Rudder/Fin Trainer  1015% average fin chord Sport Aerobatic  25% Aerobatic (non 3D)  30% 3D  75%+ Aileron Trainer  20% Wing chord Sport Aerobatic  25% Aerobatic  25% 3D  35%+ More specialised models, especially F3b/F3f tend to have wing sections designed for specific aileron/flap sizes. Control surface sizes on gliders, especially slope models, tend to be 510% larger than those on an equivalent IC model, principally due to the need for control, even at low speed, with no propwash etc. So, there it is, control surfaces are designed to a multitude of criteria, and I would suspect that there is no one mathematical method to determine them. I would guess that probably 90% of model aircraft are designed on a precedent basis. Because it is so easy to alter movements, or use a stronger servo, or even change control surfaces fairly easy, in our world, we can work on the "that looks about right" principal with a good deal of success, without recourse to mathematical design. 



You should be able to analyse it by looking at the net force on the surface with incidence, and relating that to a moment around center of gravity, and translating that into rate of change of attitude..how that stablises into actual speed of roll, or amount of yaw, or G in a loop, is beyond me until the 2nd cup of coffee..








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You write above : .. need to show my working out; but basically you ask here total strangers to do the work for you. Designing and sizing of control surfaces is a very involved business if you want to derive methods for calculation. Most textbooks on aerodynamics have a large section devoted to that subject: Stability and Control. So I would suggest you start there first. If you get stuck with some details you can come back for help here anytime. A little hint : find a graph which shows the polar of a thin symmetrical section with various deploiment angles of a 25%  40% flap. It shows all the relevant coefficients in comparison to an unflapped profile. BTW it would be advisable that you first calculate the sizes of the horizontal and vertical control surfaces including the flaps or rudders in the fixed position. All the best W. 




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Best regards W. 



Cromer,Norfolk, UK
Joined Nov 2006
2,505 Posts

Agreed Wendi, but the problem is that in the case of models certainly, 99% of the time, the control surfaces sizes are based on what works, which is itself largely based on experimentation, so there simply isn't an "equation" that is used.
It might BE possible to derive an equation using mathematical constructs, but that equation would have to have too much variable data to be workable. I do agree though with your first reply with regard to asking for help, and I do sometimes wonder when people ask these questions. If person X is doing a degree, they presumably have access to a university library who will be able to order books in on virtually any subject. As well as having access to the internet, and more than likely, access to a wide array of research papers and technical papers and abstracts. 



A Tentative reply.
Since you are writing a paper to be submitted relative to your degree, you are trying to meet a requirement OF SEVERAL FOOTNOTES AND/OR SOURCES for the information that you presented.
I have attended seven Universities and have writen several papers with referenced information. I find that the people who read your papers DO NOT pay much attention to your sources. So go ahead and write your paper and throw a number of footnotes to them. They are looking more for FORM than true research accuracy in undergrad courses. The profs wont know what you are talking about half the time. ** You have asked an impossible question by the way. As others have said,"there are many variables", too many for one equation to cover. If I were you I would measure the control surfaces of a number of kit planes. Chose trainers, 3D, scale etc. Pay attention to something called "Tail Volume". You know that a short fusalage usually will have tail surfaces that are a greater percent of the wing area and visa versa. 


Cromer,Norfolk, UK
Joined Nov 2006
2,505 Posts

You could do a useful piece of research here actually.
"A single equation be applied to the size of RC aircraft control surfaces" On that hypothesis, examples of popular models could be measured for; wing section, chord, tail volume, tail moment, CMo etc Then, using the results of those measurements, you could try to devise an equation which fits the facts. That way, you could either prove or disprove the hypothesis. In either event, you fulfill the objective of the research. 



Thanks guys for all your help. The airplane im designing is a F5D pylon racer designed to fly at times as quick as 250mph. I have already calculated the required aileron percentage as that has to do heavily with the airfoil section.
What im really after is the required size for the actual horizontal and vertical stabilizers. They have already been designed as i have worked off from a paper which had used percentages from the actual wing area to calculate the size of these components. I just didn't think that stating percentages would have been enough to support the design theory. As said before, there are many variables which can go in to the equation. I also really don't think that such an equation has been derived for model aircraft. Ill do a little more research, if nothing comes up ill just source the paper which im basing it on. Thanks to everyone for their help... Abdullah. 



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Thanks... 




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Flieslikeabeagle 



USA, WA, Edmonds
Joined Aug 2008
1,883 Posts

Tail volume is a relatively simplistic calculation that isnt as accurate as some others.
I had a stability and control book written by Jan Roskam that gives 1 long equation for each stabilizer surface. Determining all of the variables in that equation was fairly difficult though. 



I have no doubt that the tail volume coefficient isn't the entire story. After all, one could start from scratch by trying to solve the differential equations for fluid flow around a rigid body, and try to get all the way to sizing flight controls from there.
But the tail volume coefficient and associated information might well be sufficient for the OP's needs. It certainly seems to be sufficient for a lot of RC model design. There is some good info on RC model design here: http://www.charlesriverrc.org/articles_modeldesign.htm The following two references might also be useful; they're designed for the lay person, so the math level is not high enough for an engineering student, but they still contain a great deal of good information: http://www.amazon.com/ModelAircraft.../dp/1854861905 http://www.amazon.com/BasicsModelA...7918677452345 Flieslikeabeagle 



Try also searching 'static margin'.
Also buy a copy of Model Aircraft Aerodynamics by Martin Simons it really should be a standard text. S Ps Flieslikeabeagle  the best screen name and avatar? PPS Sorry, just realised Flieslikeabeagle was also recommending MAA by MS. 
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