B306
OTHER: ~
Flight Dynamics - Trim
Overview:
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General trim information related to intermeshing helicopters is on this page. |
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Specific trim information: |
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Notes:
The material in these
trim sections is primarily from Prouty's 'Helicopter Performance, Stability and Control', chapter 8. The drawings in this chapter should be referenced to clearly understand the variables used below. These algorithms are modified to suit the two-rotor intermeshing helicopter, with additional modifications to suit the UniCopter's rigid rotors.The SynchroLite and the UniCopter use the
body axis system. The centerlines of the two masts are perpendicular to the X- axis, therefor the rotors do not have an angle of incidence [i].a1s
and b1s are not applicable to the UniCopter because its blades do not flap.
Trim Analysis:
The aerodynamic
forces and moments in the body axis system that are acting on an intermeshing helicopter are due to the following components [identifying subscript in blue];Non-aerodynamic forces and moments;
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Physical Parameters: |
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Distance between Origin and C.G., on X-axis |
xCG |
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Distance between Origin and C.G., on Y-axis |
yCG |
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Distance between Origin and C.G., on Z-axis |
hCG |
FORM: Trim
in the Access database has the computerized coding for the following calculations. It is only for the UniCopter.
The Six Equations of Equilibrium:
The following six equations are from
[RWP1 ~ p.483]. They have been modified for; two main rotors, no tail rotor, and the origin of the coordinates need not be the center of gravity. They are valid for a conventional intermeshing helicopter such as the SynchroLite. The UniCopter's equations differ slightly because of the unique flight controls and its equations are located on UniCopter Trim|
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The Longitudinal Equations: |
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Longitudinal force (forward) |
X: XP + XS + XH + XV + XF + XE = GW * sin(θ) |
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Vertical Force (down) |
Z: ZP + ZS + ZH + ZV + ZF + ZE = -GW * cos(θ) |
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Pitching Moment (nose up) |
M: (MP - XP * (zP - zCG) + ZP * (xP - xCG)) + (MS - XS * (zS - zCG) + ZS * (xS - xCG)) + ZE * (xE - xCG) - XH *( zH - zCG) + ZH * (xH - xCG) - XV * (zV - zCG) + MF + ZF * (xF - xCG) - XF * (zF - zCG) - XE * (zE - zCG) = 0 |
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The Lateral Equations: |
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Lateral Force (right) [Sideslip] |
Y: YP + YS + YV + YF + YE = -GW * sin(Φ) |
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Rolling Moment (down to right) [Dihedral] |
R: (RP + YP * (zP - zCG) + ZP * (yM - zCG)) + (RS + YS * (zS - zCG) + ZS * (-yM - zCG)) + YV * (zV - zCG) + YF * (zF - zCG) + RF = 0 |
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Yawing Moment (nose to right) [Weather cocking] |
N: (NP - YP * (xP - xCG)) - (NS + YS * (xS - xCG)) - YV * (xV - xCG) + NF - YF * (xF - xCG) - YE * (xE - xCG) = 0 |
Longitudinal Trim Solutions:
Hover:
X:
Z:
ZP + ZS + ZH + ZF = -G.W. * cos(Θ)M:
(MP - XP * (zP + zCG) + ZP * (xM + xCG)) + (MS - XS * (zS + zCG) + ZS * (xM + xCG)) + ME - XE * (zE + zCG) + ZE * (xE + xCG) - XH * (zH + zCG) + ZH * (xH + xCG) - XV * (zV + zCG) + MF + ZF * (xF + xCG) - XF * (zF + zCG) - XE * (zE + zCG) = 0The above 3 algorithms have been copied to UniCopter's 0906; for expansion and solution, but not (yet) copied to SynchroLite.
Forward Flight:
Lateral-direction Trim Solutions:
Hover:
Y:
R:
((dRP / d b1S) + (TP * cos(VM) * (yP + yCG)) - ((dRS / d b1S) + (TS * cos(VM) * (yS + yCG)) + (TEY * (zE + zCG)) This algorithm needs cleaning up.N:
(QP * cos(Ya)) - (QS * cos(Ya)) - (xT + xCG ) * TEY = 0The above 3 algorithms have been copied to UniCopter's 0907; for expansion and solution, but not (yet) copied to SynchroLite.
Forward Flight:
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OTHER: Dynamics - Trim - Sideforce, Yawing and Rolling Moments |
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DESIGN: SynchroLite ~ Rotor - Disk - Centers, Radii & Moments |
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DESIGN: SynchroLite ~ Rotor - Blade - Composite - VR-7b - Centers, Radii & Moments |
Introduction Page | SynchroLite Home Page | Electrotor Home Page | UniCopter Home Page | Nemesis Home Page | AeroVantage Home Page:
Last Revised: February 4, 2007