Design > Engineering board
Stunt Control System Geometry
Howard Rush:
OK, I think I've figured out how to calculate this with Excel. First, here are what's to be calculated, some definitions, some assumptions, and the inputs. I included the stuff that's important to me. Tell me what you think. I'm sorry I don't have drawings to include. I'll do them with my 2D CAD program, so I couldn't post them here anyhow.
Calculate:
1. Flap and elevator deflection as functions of differential control line movement
2. Elevator deflection vs. flap deflection
Definitions:
X = 0 at flap control horn axis
Y = 0 at fuselage centerline
Z = 0 at wing chord
X is positive forward.
Y is positive out the right wing.
Z is positive down.
Rotations are positive about positive axes:
Bellcrank rotation is positive clockwise looking from the top.
Flap deflection is positive clockwise looking from the left wing tip.
Elevator deflection is positive clockwise looking from the left wing tip.
Assumptions:
Airplane flies counterclockwise (looking from the top of the circle) in upright level flight.
Wing is symmetrical about X-Y plane and has no dihedral.
Bellcrank axis is in the X-Z plane.
Bellcrank center (intersection of bellcrank axis and bellcrank plane) is on wing chord, Z = 0
Leadouts guides are on wing chord, Z = 0
Flap hinge line is straight and is on the Y axis: X = 0, Z = 0.
Elevator hinge line is straight and is parallel to the Y axis.
Elevator and flap deflections are relative to the airplane X-Y plane.
Leadout attach points on bellcrank are colinear with bellcrank center
All pushrod joints are ball joints; joint location is center of ball
Forward pushrod goes from bellcrank to flap control horn.
Aft pushrod goes from flap control horn to elevator control horn.
Everything is rigid except leadouts, which are perfectly flexible.
Inputs:
X of leadout exit at wingtip
Y of aft leadout exit
Y of fwd leadout exit
Bellcrank-plane pitch angle, positive aft-end-high
Bellcrank leadout-arm radius
Bellcrank pushrod-arm radius
Bellcrank pushrod attach elevation above and perpendicular to bellcrank plane
Bellcrank leadout-arm rotation at zero flap deflection
Bellcrank pushrod-arm rotation relative to a line perpendicular to the bellcrank axis and perpendicular to the leadout arms
Flap control horn forward-pushrod-arm radius
Flap control horn aft-pushrod-arm radius
Flap control horn forward-pushrod attach point rotation at zero flap angle
Flap control horn aft-pushrod attach point rotation at zero flap angle
Flap control horn forward-pushrod attach point distance right of fuselage centerline
Flap control horn aft-pushrod attach point distance right of fuselage centerline
X of elevator axis
Z of elevator axis
Elevator control horn pushrod-arm radius
Elevator control horn pushrod attach point rotation at zero elevator angle
Elevator control horn pushrod attach point distance right of fuselage centerline
Elevator downrig angle from fuselage X axis at zero flap angle
Tim Wescott:
* I think some of your assumptions are immaterial, or negligible (e.g. a reasonable amount of dihedral is negligible, a symmetrical wing is immaterial to calculating deflections)
* To compliment your apparent excess of assumptions, you appear to have left one out. You may want to work in a statement about "simple hinges" assumed -- a cloth hinge rolls the LE of the surface along the TE of the wing or stab; this action is not a simple rotation about an axis. Thus the effective radius (and offset angle, I think) from the instantaneous center of rotation will change in an amount proportional to the surface thickness, and with a complicated relationship to the surface LE shape and wing TE shape. Tell folks to just use a lucky box and hinge the control horn!!
* The bellcrank plane pitch angle, as expressed as a rotation around the Y axis, would be positive clockwise looking from the left wing; i.e. it would be positive with the back low. Let's stick to the right-hand rule here: http://www.xkcd.com/199/
* I got wrapped around the axle for a while on "Flap control horn forward-pushrod-arm radius", then I realized that you meant "distance from flap hinge axis to effective control horn pivot". I don't know if you need a foot note, or to reword that, or to just smack me
* It'd be neat if you posted your calculations. I may even try to go over them. :)
Howard Rush:
--- Quote from: Tim Wescott on December 10, 2010, 05:46:45 PM ---
* I think some of your assumptions are immaterial, or negligible (e.g. a reasonable amount of dihedral is negligible, a symmetrical wing is immaterial to calculating deflections)
* To compliment your apparent excess of assumptions, you appear to have left one out. You may want to work in a statement about "simple hinges" assumed -- a cloth hinge rolls the LE of the surface along the TE of the wing or stab; this action is not a simple rotation about an axis. Thus the effective radius (and offset angle, I think) from the instantaneous center of rotation will change in an amount proportional to the surface thickness, and with a complicated relationship to the surface LE shape and wing TE shape. Tell folks to just use a lucky box and hinge the control horn!!
* The bellcrank plane pitch angle, as expressed as a rotation around the Y axis, would be positive clockwise looking from the left wing; i.e. it would be positive with the back low. Let's stick to the right-hand rule here: http://www.xkcd.com/199/
* I got wrapped around the axle for a while on "Flap control horn forward-pushrod-arm radius", then I realized that you meant "distance from flap hinge axis to effective control horn pivot". I don't know if you need a foot note, or to reword that, or to just smack me
* It'd be neat if you posted your calculations. I may even try to go over them. :)
--- End quote ---
* I have some applications in mind for this program that dihedral would mess up.
You are correct about the symmetry. I was thinking of the X-Y plane as the plane of symmetry of the wing, but it really doesn't have to be symmetric. This program would be inadequate for Al Rabe, but covers most anything I have in mind to build.
* Anything I build with cloth hinges won't receive much analysis.
* OK. I should do that to be pure, even though it would make the one in my airplane negative.
* Maybe some linear combination thereof
* I'll send you the file when I write it. The calculations themselves, as I intend to do them, would be embarrassing. However, if you want me to do them in a more rigorous manner, you can tell me how to do the following:
Pick a point on the bellcrank end of the rod: Call it (X1, Y1, Z1). I chose X = 0, Z = 0 as the flap control horn joint, and the Y axis is the flap hinge line, so the flap control horn joint with the pushrod, (X2, Y2, Z2), is on a circle: r^2 = X2^2 + Z2^2 . Y2 is constant and known. For pushrod length L, L = sqrt((X2 – X1)^2 + (Y2 – Y1)^2 +(Z2 - Z1)^2). So there are two equations in two unknowns, X2 and Z2. Gimme a closed-form solution. There are maybe two or four solutions. I want the one (or two) with X2>0 and Z2>0.
Tim Wescott:
I'm still not sure that a few degrees of dihedral would mess something like this up by any great amount, at least the way I think I'd use it. I think that the bellcrank deflection will be off by the secant of half the dihedral, and that the flap deflection relative to the flap horn will be off by the cosine, or pretty close -- so they should cancel. Even if they built up, for a 5 degree dihedral you'd still only be off by a percent or two.
But, if it were really important you could include the effects.
Solving for the flap horn location turns out to be direct, but tedious, if you start from a bellcrank position. Project the bellcrank to flap pivot point onto the Y-Z plane; this can be done with a smidgen of trig if you're starting with angular deflections. Now calculate the offset in the Y direction between the bellcrank to flap pivot and the flap to bellcrank pivot. Use this offset to calculate the projected length of the bellcrank to flap rod onto the Y-Z plane. Now you can find the intersections of the circles described by the flap end of the con-rod and the flap horn, and therefore the two intersections. Then pick the reasonable one (surely z < 0, since that's above the wing centerline?).
The projected length of the flap to elevator rod never changes, so finding the elevator position once you know the flap pivot position is just a matter of inscribing your two circles and finding their intersections.
I don't know if I'm going to actually do the calculation -- the word "tedious" makes me think about all the building projects that I'm not going to have time to get to this winter. But I've outlined it for you.
Howard Rush:
The lad has management potential.
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