Foil-Spring Controlled Flapped Foil

What you have described is known in aviation as a down-spring. Ideally, the spring is long and weak so it provides a near-constant down force, independent of flap deflection.

As you've drawn it in your first illustration, the spring will be highly nonlinear because there's almost no arm length when the flap is a zero or negative deflection, and the arm length gets bigger as the flap is positively deflected. If the spring acted on a horn at 90 deg to the flap chord, then it would be much more linear.

To understand the effect of the spring-loaded flap, you need to do a little algebra. For a linear spring, the hinge moment from the spring is
H_spring = l_spring*(K*l_spring*delta+F0)
where H_spring is the hinge moment, K is the spring constant, l_spring is the length of the attachment arm, delta is the flap deflection, and F0 is the pre-load in the spring.

The hinge moment from the flap can be written as
H_flap = 1/2*rho*V^2*c_flap*s_flap*(Ch0 + Ch_alpha*alpha + Ch_delta*delta)
where rho is the water density, V is the speed, c_flap is the chord length of the flap, and s_flap is the planform area of the flap. Ch0 is the hinge moment coefficient at zero angle of attack and zero flap deflection. Ch_alpha is the slope of the hinge moment curve with angle of attack at constant flap deflection, and Ch_delta is the slope of the hinge moment curve at constant angle of attack and varying flap deflection.

You also have the case that the lift on the foil has a similar form to the hinge moment equation:
L_foil = 1/2*rho*V^2*s_foil*(CL0 + CL_alpha*alpha + CL_delta*delta)
where L_foil is the lift on the foil, s_foil is the area of the foil (including the flap), CL0 is the lift coefficient at zero flap deflection and zero angle of attack, CL_alpha is the slope of the lift coefficient curve with angle of attack at constant flap deflection, and CL_delta is the slope of the lift coefficient at constant angle of attack as the flap deflection is varied.

The coefficients CL0, CL_alpha, CL_delta, Ch0, Ch_alpha, Ch_delta can be estimated with a vortex lattice or panel code, or by a 2D airfoil code like XFOIL with appropriate corrections for aspect ratio.

To get the lift, first you have to solve for the flap deflection by equating the hinge moment from the spring with the hydrodynamic hinge moment:
l_spring*(K*l_spring*delta+F0) = 1/2*rho*V^2*c_flap*s_flap*(Ch0 + Ch_alpha*alpha + Ch_delta*delta)

Solving for delta, you get:

delta = [Ch0+Ch_alpha*alpha - 2*F0*l_spring/(V^2*rho*c_flap*s_flap)] / [2*K*l_spring^2/(V^2*rho*c_flap*s_flap) - Ch_delta]

In the limit of zero speed,

delta_0 = -F0/(K*l_spring)

and in the limit as velocity gets very, very large,

delta_infinity = -(Ch0+Ch_alpha*alpha)/Ch_delta

As you'd expect, the spring dominates at low speed and becomes insignificant at high speed. In between, the flap will float at a position between these two extremes.

The lift of the foil with the floating flap is

L = 1/2*rho*V^2*s_foil*[Ch0*CL_delta - CL0*Ch_delta - l_spring*(F0*CL_delta-CL0*K*l_spring)/(1/2*V^2*rho*c_flap*s_flap) + [Ch_alpha*CL_delta-CL_alpha*(Ch_delta-K*l_spring^2/(1/2*V^2*rho*c_flap*s_flap)]*alpha] / [2*(K*l_spring^2/(1/2*V^2*rho*c_flap*s_flap) - Ch_delta)]

I think there are things you can get out of this without plugging in specific numbers. The quantity K*l_spring^2/(1/2*V^2*rho*c_flap*s_flap) shows up everywhere, and is the nondimensional stiffness of the spring compared to the size of the flap. It's a key parameter for scaling a model to full scale.

The lift coefficient is
CL = CL0 + [CL_alpha - Ch_alpha*CL_delta/(Ch_delta -K*l_spring^2/(1/2*V^2*rho*c_flap*s_flap))]*alpha + CL_delta*[Ch0 - F0*l_spring/(1/2*V^2*rho*c_flap*s_flap)]/[K*l_spring^2/(1/2*V^2*rho*c_flap*s_flap) - Ch_delta]

At a given angle of attack and speed, you can trim for any lift coefficient you want by adjusting the spring preload, F0. Allowing the flap to float under the influence of the spring results in the slope of the lift curve vs angle of attack being effectively reduced. Instead of CL_alpha, you get CL_alpha - Ch_alpha*CL_delta/(Ch_delta -K*l_spring^2/(1/2*V^2*rho*c_flap*s_flap)). At very high speed, this will reach a limit of CL_alpha-Ch_alpha*CL_delta/Ch_delta. The bigger the flap, the larger will be the reduction in lift curve slope.

The reduction in lift curve slope at high speed can be useful. From the standpoint of lift, it is like reducing the chord. It will soften the ride and make the craft less susceptible to waves. It will also help with the pitch-heave coupling if the flap is on the forward foil. You probably wouldn't want to do this with the aft foil, as it would reduce the pitch stability and pitch damping.

It doesn't change the effective chord with regard to drag, however. But it could be used to move the drag and cavitation buckets to the operating range.

All of this assumes quasi-steady operation, with the dynamics of the spring-loaded flap being much faster than the dynamics of the boat's motion. Flutter of the flap could be an issue, and you may need to build in some damping to the spring-loaded linkage.

If you're interested in spring-loaded controls, there are other devices from aviation you might want to research. A spring tab is a flap-on-a-flap that is linked to a movable control arm. A spring connects the control arm to the flap, somewhat as you have, but in a more linear arrangement. The tab is linked to the arm, too, so moving the arm deflects the tab in the opposite direction of the flap. The effect of the tab is to change the hinge moment of the flap, using fluid force to deflect the flap instead of the direct control force. At low speed, the stiffness of the spring results in the controls moving the flap mainly through the spring force, and it behaves like a direct linkage. At high speed, the spring is comparatively weak compared to the fluid forces, and the flap is controlled mainly through the tab. Since the force required to move the tab is much smaller than the force required to move the whole flap, the force required for control is much less.

A spring tab is a good way to go for manual control, because it helps to keep the control forces within the capability of the pilot even as the forces on the flap increase dramatically with speed. But any backlash or slop in the spring tab linkage or hinges can be bad news. For a good discussion of spring tabs, servo tabs and the like, see Airplane Performance, Stability and Control by Perkins and Hage. It was written back in the days before fly-by-wire when controls engineers had to rely on the pilot to manhandle the airplane, and both the size and performance of the airplanes were getting to the limits of human strength.

 

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Thank you very much ,Tom-most appreciated!!
UPDATE 10/20/13: Tom, I have ordered a used copy of the book from Amazon. Thanks again for the recommendation!

 

Hi guys, this is avery interesting Post/topic.
Firstly compliments about the idea and about the model. It is veryinteresting, It has a lot of details to experiment. cool! I have design and build a tandem moth (a moth for 2 crew people), in collaboration with the politecnico di Milano. We, compare to a lightweight moth class, have a huge mass to lift out the water and it means a giant foil (1.7m wide). I'm sure we can improve it (a lot), reducing the drag. We decided to use the conventional wand system that is easy to build and precise. It has negative points, for sure, but It has a minimum drag and u can control downforce that is very very important, expecially if u r not well positioned related to you GC.

What about your idea for the flap I think it is very interesting but in any case u have upforce, everytime. How do u want control the down force?
Philsweet - If u r going to study the drag it would be a great thing. Last week, when we tested our tandem moth (find it at www.filippocima.com) we prepared 2 centerboard and rudder sets. One with foils and one without.

 

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Your "2 person Moth" sounds very, very interesting-good luck! Why don't you start a thread about it under "Sailboats" or even here?
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The idea for the spring flap is meant to assist my ama foil(a hybrid fully submerged/surface piercing foil) where altitude is controlled by speed/foil immersion. No downforce required. The point of it was to create high lift at low speed, which would allow the angle of incidence of the whole foil to be reduced- therefore extending the range of speed where no manual angle of incidence adjustment would be required.
At this point, I don't see the spring/flap working on a foil that requires downforce like a wand controlled foil.
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Best of luck with your boat-please tell us more!

 

Thank you for the suggestion, I will.
That sounds good! I would be great to have an auto trim flap. U should find the right CG position at every point of sailing. we had trouble with it.

we had a test towed by a rib (see attached picture). There was no wind and we had to find a lot of setting to have a good foiling

 

Cool

Congrats
That's cool. I think in the first test, with a little porpoising, your model is going down, try to locate your foils carefully.
Good luck,

 

Yes It was our first test
It is towed and we r completely outside the CG. In addition we had the foil without negative so it was like if we pushed the lift up botton continuosly

 

What is the "negative"?
If it is the negative pitch due to sail forces, then yes - the test was viced by the towing point too low. The actual aerodynamic driving force will be around a boat length (judging from the photo) above the towing point in the pic, giving a much smaller (if any) bow-up moment.
Cheers

 

one thing you have to be very concerned about in any dynamic system with any springyness, whether part of the control system or just from flex of the various componets, is that you run a very high risk of flutter.

Tspeer mentions the flutter hazard, but usually any spring loaded controls are abandoned because the risk of hitting a harmonic and the forces become very large very quickly and damages the system. You need to have some means of dampening the movement in a controlled way, sometimes the right amount of friction in the system does it, other times you need specific amounts of dampening with a specially designed dampener.

Like always, when dealing with the dynamics of moving fluids, be they air or water, complexities always manifest themselves in very unanticipated ways with usually negative consequences.

 

Sometimes it could be possible to control the entire foil with a spring, instead of flaps. That's much easier to compute, as the lift and momentum coefficients of airfoils ar well-known.

It's interesting that, at least in the simplest case of a symmetric foil section, there are settings that produce the same lift for any speed.

Assume that we have 2 foils of areas S1 and S2, and a distance between CoE of each foil and the center of mass is x1, x2, respectively. The fore foil is spring-controlled, while the rear one is fixed.

The equation for the lift force reads:

Fl = p*c (alpha*(S2+S1) - delta*S1) (1)

where
p = 1/2 rho v^2
c is a slope of the lift curve (for symmetric foils the zero-angle lift is zero)
alpha is the angle of incidence for the entire system
delta is the relative angle of the fore foil

The momentum with respect to the center of mass is:

M = p*c (alpha*(S1*x1-S2*x2) - delta*S1*x1) (2)

and the spring equilibrium condition reads:

k*delta = p*c*S1 (alpha - delta) - F0 (3)

k, F0 are constants.

Let's analyze a system with conditions:

x1*S1 = x2*S2

F0 = Fl*S1/(S1+S2)

When substitute them to (2), we obtain:

M = -p*c*delta*S1*x1 (4)

The equation (3) leads to:

(k + p*c*S1) delta = p*c*alpha*S1 - Fl*S1/(S1+S2)

p*c*alpha = Fl/(S1+S2) + (k/S1 + p*c) delta

When substitute p*c*alpha to (1) we obtain:

Fl = [Fl/(S1+S2) + (k/S1 + p*c) delta]*(S2+S1) - p*c*delta*S1

Fl = Fl + delta [k*(S1+S2)/S1 + p*c*S2] => delta=0

which also means that M=0 (from (4) )

So, in the equilibrium state with M=0, the lift force is always equal to Fl, regardless the p factor (i.e. the velocity). Moreover, we have positive stability in this state: more lift produces negative pitching moment.

I tested this many years ago, building a catapult-launched model glider. It really proved to fly straight at any speed until it finally stalled due to energy loss.

Perhaps the similar system can be useful in boats, I never thought about it.

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What I am sure about, that the spring-controlled wings (or flaps) can be useful in foil-assisted boats, like DSS system. I made a simple simulation of a foil-assisted hull with a fixed foil. It became unstable, when the foil lift exceeded 30% of displacement. When the wing was spring-mounted, I was able to reach the lift above 80% of displacement without instability.

regards

krzys