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First pass elevon mixer design

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addaon

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Feb 24, 2008
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Location
Kanab, UT
I've been on a mission to design my control system, making it as simple as possible. I might have made it too simple now, but I think this is the minimal mixer.

First off, goals. For cockpit ergonomics (30° seat angle) and style, I want a side stick or side yoke. For that fighter-like feeling, I want low travel with pretty high, progressive stick forces. As the design is a flying wing, both pitch and yaw control is through the elevons, so a mixer of some type is required.

Required "aileron" deflection is approximately 12°, symmetric. Required "elevator" deflection ranges from 18° upward to 6° downward. By hinge moment analysis, hinge forces for asymmetric (aileron) deflection are about 0.36x lbs/°, while hinge forces for symetric (elevator) deflection are about 0.31x lbs/°, with x determined by airspeed and linkage mechanical advantage. So, with these numbers, maximum aileron-axis force is approximately 4.32x lbs, and maximum elevator-axis force is approximately 5.58x lbs, giving a 1.3:1 maximum force ratio.

From Hodgson's article in "Contemporary Ergnomics 2001", this best fits force gradient 3 from page 88. Although not the first choice, this gradient does give acceptable pilot performance. This gradiant has a maximum push force of 10.2 lbs, a maximum pull force of 18 lbs, and an assymetric maximum lateral force of 14 lbs inward and 11.53 lbs outward. By targeting an 18 lbs maximum pull force, we get a 13.9 lbs symmetric maximum lateral force and a 6 lbs maximum push force.

Hodgson only discusses maximum force, and not force per unit stick deflection. Other sources seem to broadly agree that forces per unit stick travel should be approximately twice as high in the elevator axis as in the aileron axis. For a sidestick design, aileron-axis travel is limited by clearance to the cockpit wall and the pilot. For my short-throw design, I am targeting maximum aileron deflection at 3" deflection from center position. At 13.9 lbs maximum lateral force, this gives 4.6 lbs/inch. Thus, we wish the elevator axis to have a force gradient of about 9.3 lbs/inch. With 18 lbs maximum pull force, this corresponds to 1.94" (will use 2") maximum deflection aft of center; with 6 lbs maximum push force, this corresponds to 0.65" maximum deflection forward from center.

From the above, we can determine that the elevons should deflect 4° per inch of lateral stick movement, and 9° per inch of longitudinal stick movement.

Note that, although targets have been in terms of absolute forces, travel ranges have been designed based only on force ratios. The "natural" hinge moments of the elevon are somewhat too light to provide the desired forces at the desired positions. As such, anti-servo tabs will be used to increase control forces to the desired point, reaching maximum control forces at maximum deflection at Va. Each tab will also be electrically actuated as a trim tab, with differential trim applied by the two-axis autopilot for control.

So, we've now defined how the stick should move, and what it should make the control surfaces do. Next is to determine how to do it.

Let's look at the right elevon first. Consider a side yoke, with a mounting point for a push rod some ways up on the vertical stick. The attached push rod runs down the wing at an angle of 25° behind spanwise, and attaches to a single bellcrank. The bellcrank rotates the push rod action to run straight back via a second push rod; the second push rod connects to the elevon two inches below the hinge. The second push rod must thus push 0.03490" per degree of elevon travel.

When the side yoke is pulled back one inch, the elevon should deflect upwards 9°, as determined earlier. Assuming no stick movement around the lateral axis, the push rod will push by 1/sqrt(1 + 1/tan(25°)^2) = 0.4226 inches. So a push rod deflection of 0.04696" should cause a control deflection of 1°. Assuming no stick movement around the longitudinal axis, a horizontal movement of the mount point by one inch will cause the push rod to push by 1/sqrt(1 + 1/tan(90°-25°)^2) = 0.9063". But this should only cause 4° of control deflection, so only a 0.1878" movement is appropriate. Therefore, the mount point should be mounted vertically 0.1878/0.9063 = 20.7% of the way up the stick. That is, if we have a 12" long stick on the side yoke (which rotates about 15° to either side of center), the mounting point should be just about 2.5" away from the center of rotation.

The connection to the left elevon is similar to that for the right, but there is a complication. The nominal (stick centered) angles of the pushrods must match for the two elevons to get symmetric control, but the push rod for the left elevon must travel an additional 20" or so across the fuselage to meet the stick. As a result, the attachment point should be about 8.5" further forward than for the right elevon. Up until now, the side yoke has been effectively L shaped, with a vertical portion acting as the stick and having the mounting point for the right elevon push rod partially up it, and a horizontal portion passing through a pillow block bearing and having stops on it. If the bearing is in front of the vertical stick, the side yoke can be extended to a U shape, rising up again sin(25°)*20" = 8.5" or so in front of the rear vertical. The rear vertical acts as the control stick, and extends a full 12" or so above the bearing; the front vertical extends only the 2.5" or so necessary for correctly locating the left elevon push rod attachment point. The two push rod attachment points thus slide and rotate in sync, being rigidly attached, but the placement of the attachment point for the left elevon is forward such that the push rod angles are the same.

The bellcrank is pushed 0.04696" per degree of desired elevon travel. The second push rod must push 0.03490" per degree of elevon travel, so the ratio of radii on the bellcrank for the first and second pushrod connectors should be 1.3456 : 1. As usual, the greater the radius the more linear the action will be. All push rod ends (for both the main and second push rod) have movement slightly out of axis, so spherical rod ends are needed.

Attached diagram might need some squinting to see what I'm trying to illustrate.
 

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