Linkage Design Fine Points


The following page outlines some of the finer points of using “Linkage Design”. Some limitations are also described.

Striving for low servo load

In general, it is desirable to achieve the smallest possible loads on the servo while meeting the required surface deflections and rate. Small loads can be achieved by using as much of the servo travel as possible. This has several benefits. By using more travel the servo has better leverage (“gear ratio”) on the surface – a shorter servo arm can be used and servo loads are reduced. This improves the resolution and precision of the control surface position. By using a large angular range of travel, the servo achieves better leverage near one or both ends of the travel. This compensates for the increased surface load near maximum travel and further reduces the servo load.

On the other hand, using the full servo range will reduce the angular rate of deflection of the control surface. This may be noticeable in very high speed models by expert pilots or in artificially stabilized or damped models. The surface rate can be increased by using less of the servo’s range, but this may overload the servo so that a larger servo is required.

It is wise to preserve a small margin of servo travel beyond what is used. This margin can provide for fine-tuning in the shop or on the field to adjust the flight characteristics. This is especially true if you are using a computer-aided transmitter that permits complex adjustments.

Because the load on the control surface is roughly proportional to its deflection it is important to use no more deflection than necessary. Reduced deflection has double benefits. First, the maximum hinge moments are reduced. Second, the gearing to the servo can be improved. These effects combine to give multiplied benefits to the servo torque requirement.

The hinge moment generated by the control surface is roughly proportional to the product of the control surface chord (moment arm) and the control surface area (force). Thus the hinge moment generated by the control surface is roughly proportional to the control surface chord squared. It turns out that control surface effectiveness is relatively insensitive to control surface chord, so reductions in servo load can be achieved by modest reductions in control surface chord. Note that higher aspect ratio tail surfaces can use smaller chord control surfaces without any loss of control power. Care must be taken with long, slender control surfaces to preserve torsional rigidity.

Some airplanes demand extreme downward flap deflections while retaining some range in the up direction. The best way to do this is to use the maximum total servo deflection range. Give some of it to the up direction and the rest to the down direction. For instance, if the servo normally moves plus/minus 40° from center, its total range is 80°. For this flap case, you might use 10° servo travel in the up direction and 70° servo travel in the down direction. Offsetting the flap horn aft will reduce the servo load when the flap is fully deflected downwards. Be sure to check the output box labeled “Max servo torque (absolute)”. This box reports the heaviest servo load over the entire range of travel – this point may not be at maximum servo travel. This is illustrated in the page labeled "plots". Also check the plot labeled “Approximate Servo Torques v/s Control Surface Position” for a graphic representation of the servo load.

Variation in servo load with speed

For a given control surface deflection, the servo load varies with the square of the airspeed. High speeds give very high servo loads!

Some models have two or more speed regimes. For example, hand launch RC sailplanes have the high-speed launch phase and then lots of low speed soaring. It is important to consider how much surface deflection is required during the high speed phase because this phase may yield the greatest load on the servo and size the servo.

A process to evaluate the servo load at different speeds is the following: Prepare a preliminary linkage design that provides the required maximum surface deflections. Estimate the speed and surface deflection required during the high speed phase. Enter this high speed in the airspeed input area. Adjust the current servo position slider to give the desired surface deflection as reported in the “Current Values” block. Note the servo torque. Now repeat this process with the lower airspeed and full surface deflection. Compare the high-speed and low-speed torque requirements. This may lead you to alter your high-speed deflection requirement, or it may point to a speed limit for certain surface deflections. For instance, high flap deflections generate large servo loads. You can use this process to determine the maximum speed at which flaps can be extended.

Servo capacity

Servo torque capacity is usually specified by the manufacturer. It has been my experience that the published capacities tend to be somewhat optimistic. When you determine the servo torque in the program, you may want to leave a safety margin between the requirement and the servo specification.

It is possible to test your servos in the shop easily enough. Mount the servo to a test bench. Use a long servo arm that extends horizontally beyond the bench. Hang a weight or combination of weights from the servo arm. Cycle the servo and see what happens. The torque on the servo (when the arm is horizontal) is equal to the product of the weight and the distance between the connection point and the servo axis. For instance if the hole in the arm is 2.0 inches from the servo axis, and the weight that the servo moves comfortably is 15 ounces, then the capacity of the servo is approximately 30 ounce-inches.

Even when you have made careful measurements in the shop, it is wise to provide a margin in servo capacity. This is due in part to uncertainties in the model’s speed (a powerful effect) and because the program estimates servo load in an approximate fashion. Overloading a servo can lead to motor stall and very high current drains. This high current can reduce the voltage to the rest of the control system and lead to loss of control. Furthermore, most servos deflect (at the servo arm) about 10° to 15° from target values at maximum torque. This offset is reduced to about 3° with some newer “digital” servos. To insure acceptable accuracy and avoid overloading the servo, some modelers size the servo so that its maximum capacity at stall is twice the calculated requirement.

Some servos become stronger when a five-cell battery pack is used.

Servo arm and control surface horn lengths

From a mechanism standpoint, it is desirable to use long servo arms and control surface horns. There are several advantages.

Long arms and horns reduce the load on the pushrod. This can permit a lighter pushrod and gives less wear and tear on the end fittings.

The effect of slop and flexibility in the linkage is reduced in proportion to the arm and horn length.
Long arms and horns reduce the load on the control surface hinge near the control horn. They also reduce the load on the servo output arm and its bearing system.

On the other hand, long arms and horns can create extra aerodynamic drag and can make pushrod routing problematic due to the greater sideways motion of the pushrod. It can also increase the friction in a pushrod-in-a-tube installation.

Use the pushrod force outputs to get a feel for the loads on the system. If they are too high, increase the servo arm and control horn lengths.

Some thoughts on the Rotary Drive System

The rotary drive system can provide aerodynamic benefits in reduced drag and noise.

A rotary drive system works by twisting a bent shaft within the control surface.  As the shaft rotates, the angle of the bent shaft changes and the control surface follows along.  The main variables in the design are the angle of the main part of the shaft with respect to the control surface hinge line and the bend angle of the shaft.  A main shaft that is perpendicular to the hinge line provides the least control surface deflection.  A main shaft that is parallel to the hinge line results in a control surface deflection equal to the main shaft throw, regardless of the bend angle of the shaft.  A typical angle between main shaft and hinge line is about 45 degrees.  In such installations, the control surface throw increases as the bend angle of the shaft increases.

An important design consideration is the support of the shaft and its connection with the control surface.  One mode is to firmly support the main shaft in two places - the servo and at a point very near to the control surface hinge line.  In this mode, the bent portion of the shaft must interact with the control surface only at its tip, where it must be able to slide spanwise in a precise slot or between two parallel plates.  The advantage of this mode is the longest possible moment arm to interact with the control surface and possibly increased precision. 

A second mode is to support the main shaft in a vertical slot located near to the control surface hinge line - this permits the shaft to move vertically.  This means that the bent portion of the shaft must interact with the control surface in two places - near the hinge line and near the tip of the shaft.  In this mode, the vertical support of the bent portion of the shaft is provided within the control surface, not within the fixed portion of the wing as in the prior mode described above.  The advantage of this mode is that the main shaft does not have to go right through the control surface hinge line - less precision is required.  On the other hand, the leverage of the bent portion of the shaft on the control surface is not quite as good so friction and slop may increase slightly.

The following comments apply to a design using the first mode described above:

It is possible to reduce the need for precise alignment by increasing the diameter of the drive shaft at its tip (where its force is exerted on the plates) so as to provide clearance elsewhere between the shaft and plates. This avoids binding. Such a diameter increase could be provided with a short sleeve of brass tubing.

Ideally (in a geometrically unconstrained situation), the brass sleeve would be replaced by a ball bearing in order to reduce friction. Please note that the program does not consider friction in the calculation of servo loads. In the case of the rotary system, friction could significantly increase servo loads – be sure to use an ample margin between calculated loads and servo capacity.

Much of the load on the rotary linkage is transferred to the airframe where it passes through the wing rear spar area. It is important that this load is supported with a rigid and slop-free bearing. The magnitude of this load is inversely proportional to the distance the shaft protrudes into the control surface. This is analogous to the length of the control surface horn. It is desirable to extend into the control surface as far as practical in order to reduce airframe loads and reduce free play. It is also important to provide a rigid and slop-free hinge in the neighborhood of the rotary shaft in order to transfer the actuation loads from the control surface into the airframe.

Other, generally applicable comments:

Rigidity of the control surface deflection is also influenced by torsional deflection in the shaft. This is controlled by the length of the shaft and, most powerfully, by the diameter of the shaft. For greatest rigidity, mount the servo as far aft as possible. On the other hand, the servo should be mounted far enough forward that it does not protrude from the wing surface, in which case much of the aerodynamic benefit of the system could be lost. Also, there may be dynamic reasons to mount the servo farther forward in the wing so as to inhibit flutter.

The rigidity of the system is most powerfully controlled by the diameter of the shaft. The torsional rigidity of the shaft is proportional to the fourth power of the diameter, so small increases in shaft diameter have large effects on rigidity. The program calculates the approximate deflection of the control surface due to shaft torsion for the maximum trailing edge up and down cases as well as the “current” position. The program assumes that the shaft is a solid cylinder of steel. Aluminum shafts are about one-third as rigid for the same diameter.

We are unaware of a theoretical measure or rule of thumb to define the limit of control surface flexure. Concerns that might arise from too flexible a system include “blow-back” (surface position imprecision) and control surface buzz or flutter. Such a buzz may drive the entire surface into flutter, and this can lead to catastrophic structural failure. Until a better measure is deduced, we would estimate that maximum surface flexures of less than a degree are likely to be acceptable for most models.

Harley Michaelis has extensive experience with this system and offers excellent hardware for sale on his web site. Take a look at it before attempting your own design!

Program Limitations and Notes

“Short Pushrod” and “Perpendicular Axis Pushrod” calculate the intersection of two circles and a circle with a sphere, respectively. Both of these solutions find two intersection points. The program, however, chooses only one of them assuming that the control surface horn point is always below the baseline formed by the hingeline and trailing edge. This is a minor limitation. While it is possible to devise a linkage in which the control horn crosses above the baseline, the linkage will not be very practical and will have weak leverage.

You will find that the program cannot solve impossible problems! For instance, if you have too long a servo arm, it is possible to jam the control surface horn to the limit of its travel. In this event you will see that the control surface illustration partially disappears.

The calculation of control surface hinge moment is approximate in the interest of simplicity. Control surface moment is dependent on many variables. The three most important: airspeed, control surface chord and control surface span, are used by the program. Other important variables not used include control surface chord fraction, air density altitude, Reynolds number, exact control surface design, and surface aspect ratio. The hinge moment used is an approximation based on information in Hoerner's Fluid Dynamic Lift.

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