beating weathercock.pdf

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18/10/13 Beating Weathercock

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Beating Weathercock

Epitome flies rock straight in even relatively high wind conditions, which is something I don't

understand. She is terribly over-stable, but she does leave the launch rod without much speed, so for a

long time I thought that was it; the fins didn't have enough "bite" to cause weathercock. Later I built

Epitome 2, which is even more over-stable and leaves with more velocity, and I thought this example

would weathercock for sure. It didn't, so I've had to go back and rethink things. I'm no aerodynamicist,so this is probably way wrong, but there's been darn little work done by the real guys on passive

stability of subsonic rockets, so I'm fairly sure I won't be contradicting anybody outright.

At first, I thought it might be the Epitome's relatively high lift curve slope coefficients, better known to

model rocketeers as the normal force coefficient. This value tells how much force, called the restoring

force, a rocket's fins generate to bring her back straight from small (less than 10 degree angle of attack)

perturbations. Even if a rocket is properly stable, if this force is too high, the rocket will oscillate back

and forth; too low, and it will "cone", or process about the line of flight. Values for model rockets are

typically in the 10 to 15 range, but the Epitome's are both in the 20s, relatively high. This is surprising,

owing to the canards up front, as they should be resisting the restoring force generated by the main fins,

and without them the normal coefficient should be much higher. A quick check in AeroLab showed that

it would indeed be above 25 after deleting them, and Aerotech's mirage, which is about the same size,

also has a normal force coefficient in this range, and it does weathercock.

Besides, this should make things worse, causing almost immediate weathercock owing to the strong

moment of the restoring force. Yet the Epitomes fly straight up, against winds too strong for anything

else. What, then, keeps them pointing in the same direction?

I think its "keel". Sailboats have large hydrodynamic surfaces sticking into the water to keep them from

falling over in a crosswind. These are more effective the faster the boat goes, and generate a force

opposing the one generated by the wind pushing on the sail. Water is incompressible, unlike air, andkeels are never as large as sails, so sailboats still heel over in the wind until the forces equalize, but at

least they don'tfallover. I think that the canards up front do the same for the Epitomes; they resist the

restoring force so that the rocket heels over in the apparent wind just enough to resist weathercock.

Since a rocket is a free body in space, unlike the sailboat, which is fixed on a boundary layer between

two dissimilar fluids, the forces balance, and the bird flies a straight course from the rod, presenting a

constant, unchanging angle of attack to the relative wind.

I have no math to back this up. This is within the range of the Barrowmann equations for slender

bodied/finned rockets, but I don't know enough about them to work this all though, and even if I did, I

don't think they're designed for this sort of thing. I don't know if canard size and/or number might be important to this

calculation (I suspect they are, but not much), nor the impact shape, placement, etc., might play. Having said all that,

here's how I think it works. While the rocket rotates about its center of gravity, the fins operate on the center of

pressure. Since the canards are much farther away from this point than the main fins, they have a larger moment, so

even though the force they produce is smaller, when multiplied by their further distance, the "restoring" force is

approximately opposite in magnitude to that created by the main fins. In the graphic below, this is represented by the

area of the triangles formed by the normalizing force vectors, the distances from the center of pressure and their dot

product.
http://www.aerotech-rocketry.com/http://www.aerotech-rocketry.com/customersite/products/kits/mirage.htmlhttp://mcfisher.0catch.com/scratch/epitome.htmhttp://www.aerotech-rocketry.com/customersite/products/kits/mirage.htmlhttp://www.aerotech-rocketry.com/http://inet.uni2.dk/~dark/http://mcfisher.0catch.com/scratch/epitome2.htmhttp://mcfisher.0catch.com/scratch/epitome.htm


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As I said at the outset, very little has been done

on the passive stability of subsonic rockets, it

just doesn't have a great deal of application. The

rockets in professional and military use are either

supersonic, actively stable or both. Model

rocketeers are the only people flying in this

region in this way, so other than Barrowmann,

there's darn little out there in the way ofreference material. Chin does have a few things

to say on the subject of active control that might

be semi-applicable here. In the first chapter of

his book Missile Configuration Design, he

discusses the types available to rockets and their

pros and cons. One of these is canard control,

wherein a small set of active canards are placed

near the nose of the rocket and a large set of fins

are placed near the tail. The small canards don't

generate a great deal of downwash whendeflected, so they don't affect longitudinal

stability adversely, and large static stability

margins can be maintained. In other words, the

high passive stability of the missile works to the

canards' advantage; the canards create an angle

of attack, and the large fins try to suppress it by

turning the missile.

There are some disadvantages to active canard

control that would concern the professionalmissile designer; since the control surfaces are

very small, roll stability is a lot harder to achieve and the rate of control movement must be high. But, as Chin points

out, "...for relatively small missiles which do not require roll-attitude stabilization, the canard configuration is probably

the best over-all...", so its probably a good choice for passive keel control on model rockets. Three other types of

active control discussed by Chin also seem to me to be applicable to model rocket passive keel work:

Wing/Tail Control- In this configuration, a second set of large fins are placed near the center of the rocket. For

active wing control the upper fins move, and for tail control the lower fins do, but for passive control, these are

equivalent. As the forward set of fins don't create a lot of lift, this configuration operates mostly on downwash.

The upper fins must change the appearance of the relative wind on the lower fins, causing them to generate a

normalizing force in opposition to the regular one. For passive control, upper fin placement, size, shape, airfoil,

etc., are probably very critical to getting this to work, so IMHO its not going to be as easy to achieve as a

canard keel.

Tailless Control- In this configuration, the fins are moved to the center of gravity, and only their trailing edges


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articulated. Location of the wing is critical, and from a passive standpoint, darn near impossible to achieve, but it

might work on really long, slender model rockets.

Dorsal Control- In this configuration, long, slender strakes are applied to the body of the missile somewhat aft

of the center of gravity. Chin calls this "an 'aerodynamic fix'" and then says no more about it, but this version is

probably a bit more forgiving for passive control (and looks a lot more like the keel on a boat), and I plan to

investigate it more.

Other forms of active control that probably won't work for model rockets include 1) body extension (only useful wherebase drag is significant, i.e., the trans- and supersonic regions), 2) nose flap control, 3) wingless control and 4) jet or

gimbaled motor control. In addition to the problems associated with them in active mode (e.g., they are relatively

inefficient), none of these have a passive analog.

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