High Speed Turning Dynamics

I would like to hear some thoughts on the dynamics of a boat in a high speed turn. Larson & Elison talk about VCG and centrifigal force but nothing about clr. Any Ideas on the seperation of driving moment and CLR . Any ideas on the effects on the crew created by G force if there is to resistance in a turn. Is there anything writen on optimising these thing. any ideas would be appreiciated.
Thanks SG

 

I to would like to would like some info about this. Last year I had a custom boat built and in a turn it would roll in to the point of almost putting the rail under. So the builder put a small keel on the bottom . It solved the turning problem but it feels like the boat wants to throw you out because it grabs the water instead of sliding. Thanks Ron

 

Annecdotally I can tell you that the Krogen Express 49, a "commuter" style semi-displacement design with a partial skeg (slightly less skeg than a lobsterboat), corners almost dead flat, without a pronounced roll either in or out.

 

In a small performance boat though, I really enjoy a boat which banks nicely into a turn. I remember when I built a little catamaran how disappointed I was when I found I had not designed a boat which cornered well - it cornered sharply, but without a nice lean into the turn I felt like I was being thrown out of the boat instead of held firmly into my seat. And I really like the feel of leaning into a turn, seeing the horizon shift a bit and if looking to the side, looking a little downward toward the water. I suppose an aggressive banking into the turn might be more fun at the helm than being a passenger though

-- I wish I had a good reference to link here

 

I agree, Jeff - I just thought it was notable about the Krogen when we sea-trialed her.

The banking is Harry Schoell's reason for preferring a monohull to a catamaran. I would note, though, that I've seen one planing monohull with a pilot enclosure where the roofline interfered with visibility when it was banked into a turn.

In airplanes the proper amount of rudder vs. banking is generally that which puts the g force straight down, so you don't feel pushed either in or out and so that the force remains normal to the wings.

 

Sorry to quibble about this, since it's really not germane to the topic, but the rudder's got nothing to do with turning an airplane. Airplanes are turned by rolling the aircraft with the ailerons on the wings. This points the lift vector into the turn, which generates the necessary centripetal acceleration to curve the flight path. The rudder is primarily used to counter extraneous yawing moments, such as those that result from deflecting the ailerons, an engine failure, or skidding. Many missile designs (AIM-9, for example) use a skid-to-turn stategy, but manned aircraft and cruise missiles use a bank-to-turn strategy.

This does apply to boat maneuvering in a way. When one analyzes the lateral-directional characteristics of an aircraft, the typical approach is to start with the stability derivatives. These are the sensitivity of the forces and moments to changes in the motion, controls, or propulsion.

For example the derivative Ybeta is the change in side force, Y, per degree of sideslip (leeway), beta. Nbeta would be the change in yawing moment per degree of sideslip. Nr is the change in yawing moment due to yaw rate (rate of turn). Etc. There's a stability derivative for each force and moment, for each motion variable.

If you want to figure out how the boat will roll in a turn, you'd have to estimate each of the derivatives and then solve for the solution that simultaneously satisfies each of the equations.

For the example above, in which adding a skeg reduced the roll, here's what was happening. For a given speed, a certain amount of side force is necessary to turn the boat at a given rate, which is equal to m*V*R (mass times velocity times turn rate). This has to be supplied by sideslipping the hull, so that (ignoring rudder forces for the moment) Ybeta * beta = m*V*R. So beta = m*V*R/Ybeta.

There's also a rolling moment derivative, Lbeta, which tends to roll the boat away from the direction of the sideslip. And there's a rolling moment from the boat's buoyancy, which I'll call Lphi (and naval architects would call GM), that is the rolling moment due to heel. For the boat to be in equilibrium in heel, all the moments have to sum to zero; Lbeta*beta + Lphi*phi = 0. From this you can solve for the heel angle: phi = -Lbeta*beta/Lphi.

When you substitute in the result of the side force equation, you get

phi = -m*V*R*Lbeta/(Ybeta*Lphi)

But wait! There's also a yawing moment from beta, Nbeta, which tends to make the boat track straight, and a yawing moment from heel (Nphi) due to the change in underwater shape, and a yawing moment from the rudder (Nrudder). Which you solve to get the rudder required. Unfortunately, there's also roll due to rudder (Lrudder) because the rudder is below the center of gravity, and sideforce due to rudder deflection (Yrudder), too. Not to mention yaw moment due to turn rate (Nr) that gives the boat its yaw damping, and maybe rolling moment due to yaw rate (Lr) and side force due to yaw rate (Yr), too. In particular, the sideforce due to rudder will be to the outside of the turn, requiring more sideslip, and more roll, than indicated above.

So you have three equations (sideforce balance, roll moment, yaw moment) and three unknowns (phi, beta, rudder) to solve simultaneously. The only difficulty is getting the values of those pesky derivatives. They are determined by the hull characteristics. For example, the roll moment due to sideslip, Lbeta, will depend on the deadrise angle of the hull, with a V'd hull tending to roll more with sideslip than a flat bottom hull.

In the example cited, the boat rolled excessively in a turn because the ratio (Lbeta/Ybeta) was too high or the roll stiffness (Lphi) was too small. Adding the skeg produced more sideforce per degree of sideslip, increasing Ybeta. In addition, the skeg was below the c.g., so its contribution to the rolling moment was opposite of that the hull (tending to "trip" the boat and roll to the outside of the turn). So the skeg lowered the ratio (Lbeta/Ybeta) and reduced the roll.

So that's how you predict how a boat will roll in a turn.

 

Tom, I'm sure that you are correct and I followed your explanation until I derived a headache though I don't see the parallel between an airplane and a boat in turning. In fact, I believe the airplane rudder will be turned in the opposite dirrection to that in a boat when turning to counteract the tendency for the nose to drop.

In the example of the excessive banking boat, I'd guess that it is a deep V hull. The up pressure on the half of the hull outside the turn generated by the skid combined with the down suction of the inside half rolled the boat inward too much. I'd also expect that the turning radius was increased after the skeg was installed. I would also expect that the boat might have a tendency to chine walk and bank sharply into a cross wind. These are somewhat wild guesses since I don't know any specifics about the boat.

 

Well, Tom S, you may very well be right in some of the technical details, but in practice you're at odds with my flight instructor. It was a while back, and I don't recall what instrument it was that gave this indication, but I've been taught that the proper amont of airplane rudder is that which results in the force vector being perpendicular to the airplane. Now sometimes the amont of rudder that produces this might be zero. If that's your point then I don't disagree. I'm not saying the boat rudder and the plane rudder are analogous. What I'm saying is that the same principle might be used to determine the correct amount of leaning for a powerboat at a given speed and turn radius.

 

Well, I was trying to avoid straying off topic and keep the discussion to boats, but if you want to pursue it...

What your flying instructor probably told you was to "step on the ball." In other words, to zero out the side force on the airplane due to sideslip in the turn. So you're right that you are keeping the force vector perpendicular to the wing. It is the right amount of rudder to coordinate the turn.

But that's not what's making the airplane turn. It will turn when banked whether it is properly coordinated or not, up to the point where it is so uncoordinated that the horizontal component of the side force equals the horizontal component of the tilted lift vector. Once that point is reached, you have a steady heading sideslip, but it requires rudder to be intentionally used in opposition to the turn.

Most airplanes with conventional ailerons have "adverse yaw" - the downgoing aileron produces more drag than the upgoing aileron. When you roll into the turn, this difference in drag on the two wings makes the nose want to yaw out of the turn, and the sideslip this yaw generates produces a sideforce on the fin and fuselage. Which causes the ball to move toward the center of the turn. Applying rudder will reduce the sideslip and minimize the sideforce. If you tape a telltale to the center of the windscreen you can see all of this develop.

Airplanes with spoilers for roll control often have "proverse yaw" and require the pilot to hold opposite rudder to coordinate the turn because the drag of the spoiler wants to make the airplane yaw into the turn. Even though this natural yaw tendency "helps" the airplane turn, pilots don't like it because holding opposite rudder feels like an unnatural act.

Consider the lowly Ercoupe - no pedals at all! It has an aileron-rudder interconnect to compensate for the adverse yaw, and it's not a wholy satisfactory solution. But it still turns because the pilot controls the bank.