RDS Kinematics By Steve Fujikawa

sfujikawa@ase.w1.com
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When installing conventional aileron/flap servos it is important
to set the linkage in the proper holes on the servo arm and the
control horn in order to get the desired ratio of servo rotation
to surface deflection. In RDS, this is set by the angle of the
drive shaft with respect to the hingeline, and the angle of
the bend in the wire. By various combinations of these it is
possible to achieve the desired throw characteristics analogous
to moving the linkage to different holes in a conventional set
up. But since it is difficult to make adjustments once RDS is
installed, we need some way of designing the geometry before
anything is epoxied in place. The following formula is a tool
that can be used to predict surface deflection as a function of
the servo rotation angle, the bend angle, and the drive shaft
angle:

Deflect = arctan[sin(rho)*sin(theta) /
cos(rho)*cos(psi)*sin(theta) + sin(psi)*cos(theta)]

where:
rho = servo rotation angle from null
theta = wire bend angle (45 deg for aileron or 90 deg for flap)
psi = drive shaft angle with respect to hingeline (nominally
45 deg)

Harley recommends a 45 deg drive shaft angle and a bend angle of
90 deg for the flap and 45 deg for the aileron. By holding
drive shaft and bend angle fixed and varying servo rotation from
0 to 90 deg, one can obtain plots of flap and aileron
deflections.



Fig. 1 shows aileron deflection as a function of servo angle for
a bend of 45 deg and a drive shaft angle also of 45 deg. The
plot shows that aileron response is essentially linear, so stick
movements produce proportional deflections, and therefore things
like programmed exponential should work pretty well. There's
also only about a 60% ratio of surface movement to servo
rotation so there's an amplification of servo torque and an
increase in resolution.


Fig. 2 shows flap deflection as a function of servo angle for a
bend of 90 deg and a drive shaft angle of 45 deg. Flap response
is a little more non-linear with slightly more than 1:1 surface
deflection to servo rotation at deflections less than 45 deg, so
there's a little loss in torque and resolution. The effect is
reversed at deflections greater than 45 deg.

By playing around with different drive shaft and bend angles you
can get different amounts of torque amplification/servo
resolution in your installation. For example, using a small
bend angle will get a huge amplification of torque, but reduced
surface travel.

Maximum Deflections for 60 deg Servo Angles
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Since most servos (without benefit of a computer radio) are
limited to a maximum output shaft rotation of 60 deg, we can use
the formula to construct the plot of Fig. 3 for maximum aileron
and flap deflections as a function of wire bend angle (holding
drive shaft angle fixed at 45 deg). Fig. 3 represents how much
the surface would be deflected up or down for a given bend angle
at full stick.



Converting Deflection Angle to Surface Throw
--------------------------------------------
Most kit manufacturers specify throw in terms of inches at the
trailing edge of the surface. To convert deflection to throw
just use the following formula:

Throw = ControlSurfaceWidth * sin(Deflect)

Or to find the required deflection for a given throw use:

Deflect = arcsin(Throw/ControlSurfaceWidth)


Example of Setting the Bend Angle for Desired Aileron Throw
-----------------------------------------------------------
Say you want to set up a plane that requires a max aileron
deflection of 1/2" up and down and you have a servo that has a
throw of +/- 60 deg. The first step is to find the aileron
deflection angle. Say that the aileron is 1" wide. Then using
the formula for deflection angle:

Deflect = arcsin(.5/1)
= 30 deg

Let's follow Harley's recommendation and set the drive shaft
angle at 45 deg. This allows us to use the plot of max surface
deflection above. (To generate a plot for a drive shaft angle
of other than 45 deg is no big deal using the magic formula.)
>From Fig. 3, we find that the required bend angle for 30 deg
deflection is 32 deg (find 30 deg on the Y axis and read 32 deg
bend angle on the X axis). This is good because it gives about
2:1 servo rotation to aileron deflection and therefore there
will be a doubling of servo torque and resolution. A 20 in-oz
servo with an 0.25 deg resolution becomes a 40 in-oz servo with
0.125 deg resolution. Now just bend the wire to 32 deg and
epoxy everything in place.