Stability of ...diamond planform

[Waccky]

howdi yall,
I am new to these boards, but after scoping out the forums, i realise im not sure where best to put this question except here, as i am designing a UAV.

i am working on the "stability and control" of the designed uav and we have gone for a planform that looks similar to a diamond with a v tail.

however, after some manipulation, i have hit a wall...

i have assumed the NP is at the AC, by saying the lift produced by the fuselage will be negligible, and i have calculated the NP using:

Xn= lr/4 + ((2*b)/(3PI))tan(angle of quarter chord)

where lr = root chord
b = span
PI = 3.14159 etc

I used this equation as the i am using, "the design of the aeroplane" or something similar to that says it should be used when the taper ratio is less then 0.375 ... but our ratio is in fact 0.

After this problem, i am not sure where else i am to be heading, pitch stability and with what equations ... as many of the textbooks i have indicate the requirement of a tail plane ... ie for conventional aircraft... =(

Thank you for any help.

Waccky

[Sparky Paul]

"taper ratio is 0"..
For a diamond, the taper ratio should be quite high... ?

[Waccky]

the planform looks like
http://img62.imageshack.us/img62/4266/uav1we0.jpg
although some sizes are wrong, and i have yet to put in a v tail...
since i have drawn it to a point, the taper ratio would be zero as the tip chord is very small, isnt it? :confused:

[Sparky Paul]

Using this procedure...
http://perso.orange.fr/scherrer/matthieu/english/mce.html
And assuming a tip chord of 1...
the m.a.c. comes out as shown.

[Sparky Paul]

Lockheed's first cut at stealth was a diamond.. designed by the electrical engineers to give the least possible RCS... the aero guys named it "The Hopeless Diamond", and added a few things to make it flyable.
Northrop's X-47A was a diamond.
It morphed into a flying wing after testing..

[Aceshigh84]

Don't really know how extensive your knowledge of aircraft stability is but if you want a easy measure of pitch stability use what is called static margin. It is a measure between the neutral point, which you have calculated, and the CG. SM=(Xnp/mac)-(Xcg/mac). Most full scale planes have a static margin around 5-10% but models are usually higher 10-20%. This should give you an idea. If you take another look at your text books the equations can be easily converted for flying wing use by just dropping the portions of the equations with the tail contribuitions. The problem you will run into is that you don't truly have a flying wing because your V-tail will act like a closely coupled horizontal tail and unless you find a text that deals specifically with that design shape none of the empirical assumptions in the normal textbooks can be used. If you don't have access to some basic CFD program you should probably use the static margin equation, shoot for 10% and testfly some foam models.

[Waccky]

I have my static margin of around 7%, but the textbooks dont relate that to much, the ones i have anyway... does that mean the control surfaces on the wing should be approximately 7% of the MAC?

Thank you again =)

I have calculated pitch values for my aircraft to be:
Mq = -0.73639 rad^(-1)
Zq = -1.66111 rad^(-1)
where Mq is pitching moment derivative due to rate of pitch
and Zq is the lift force derivative due to rate of pitch

But my question is what are those values in real terms, i.e. what they correspond to? :confused:

=)

Waccky

[Aceshigh84]

Static margin is just an easy way for the designer to get a feel for how "stiff" the plane is in pitch. It isn't used as much more then that. In order to determine how big your control surfaces should be you need to find your control power. Control power is deffined as the change in angle of attack due to the change in the angle of elevator defflection. In this case, just as a starting point you want your control power to be between -1 and -2. The values are negative because a upward deflection of the elevator is considered a negative deflection(because it produces negative lift) and when you deflect the elevator upwards you get an increase in angle of attack. You can calculate control power with the following equation delta_Aoa/Delta_de = Cmde/Cma. That is the change in the coefficient of pitch moment due to change in the elevator deflection divided by the change in the coefficient of pitch moment due to change in the angle of attack. The control power varies significantly with static margin mainly due to the change in Cma and very slightly due to a change in Cmde so when you calculate your control sizing make sure you have your cg where you want it. It is VERY hard to fly a plane with an overly large control power.

As for your rate based values they are just some of the stability derivatives that are plugged into the longitudinal stability matrix in order to calculate dynamic stability. Just looking at the signs of the values I can see that there is some dynamic damping to longitudinal distrubances which is good. Unless your really know what your looking at I wouldn't worry about them at this point. Get your static longitudinal stability figured out first. Also, watch your significant figures. Those values are empirically based hand calcs and deffidently don't need them that exact. If you are doing this for more then just fun and you show your numbers to someone who knows what they are doing they won't take you seriously. Keep them to two decimal places or so.

Matt

[Waccky]

hmmm ... thanks AcesHigh for the help, and others too =)

Ive got some photocopies of a book im gonna troll through, thinking i need to produce 3 graphs, one for each axis, focusing on the statics first ... =)

Thanks again everyone

Waccky

[Sparky Paul]

The ultimate test would be to make a chuck glider of about 18 inches span, with your proposed c.g. and see if it can fly.
If not, move the c.g. around.
You're bound to need some reflex on the elevons, if you don't use a reflexed airfoil.

[vintage1]

The ultimate test would be to make a chuck glider of about 18 inches span, with your proposed c.g. and see if it can fly.
If not, move the c.g. around.
You're bound to need some reflex on the elevons, if you don't use a reflexed airfoil.

Actually a paper dart will prove a lot at about 30 seconds build time

Ok took me nearly 3 minutes to get CG right with two paper clips. This is stable

[Waccky]

hmm ... Ive currently "calculated" the elevator angle for trim sticked fixed as approx 3.4 < angle < 6 ... in degrees =) is that too small?

im also trying to work out what hinge moment trim curve actually shows, or what it is in real terms, i have calculated the values, with Ch v Cl graph ... but i am actually unsure what it really shows

In Performance and Stability of Aircraft book, it just shows the slope as being positive, without explaining what the values mean =(

[Aceshigh84]

Those text books arn't going to spell it out for you. You have to think about what the stability derivatives mean and then the numbers and plots will tell you how they interact. You shouldn't need to calculate hinge moment unless you are worried about your servos' strength. Your trim seems reasonable but getting trim right is a difficult proposition without more complex analysis methods. You have taken this about as far as your going to get without some empirical data specifically on your general design, a wind tunnel test, or come CFD. Unless you want to go down that route, take what your know, build a model out of some fan fold foam, throw some electronics in it and test fly it.