UniCopter ~
Trim, Stability & Control - TrimOverview:
Calculations and notes regarding the
trim of the Unicopter; and its Absolutely Rigid Rotors.
Trim Analysis:
For general information, see:-
OTHER: Aerodynamic - TrimSee Access database:
FORM: Trim for calculations.The values that are used in the above Form for UniCopter trim have been output from the table [Helicopter] via a Query and this data is on the web page
UniCopter_Trim_Data|
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Trim Conditions: |
Symbol: |
Value: |
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Helicopter pitch angle |
Θ |
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deg. |
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Angle of attack |
α TPP |
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deg. |
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Sideslip angle |
β |
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deg. |
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Flight Conditions: |
Symbol: |
Value: |
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Dynamic pressure |
q |
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lb/ft2. |
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Angle of climb |
γ c |
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deg. |
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, an origin of coordinates that need not be the center of gravity, and for the UniCopter's unique flight controls.The forces and moments used in the following equations can be found in the [Item] section below.
The arm lengths that are used in the following equations Components can be found in
UniCopter ~ Dimension & AreaThe arm lengths that are used in the following equations for Gravity can be found in
UniCopter ~ Weight & BalanceThe arm lengths that are used in the following equations for Flight Control can be found in
DESIGN: UniCopter ~ Trim, Stability & Control - Control - Rotor Coordinate Conversion|
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The Longitudinal Equations: |
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Longitudinal force (forward) |
XP + XS + XH + XV + XF + XE = GW * sin(θ) |
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Vertical Force (down) |
ZP + ZS + ZH + ZV + ZF + ZE = -GW * cos(θ) |
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Pitching Moment (nose up) |
(MP - XP * (zP + z CP - zCG) + ZP * (xP + xCP - xCG)) + (MS - XS * (zS + zCS - zCG) + ZS * (xS+ xCS - 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) |
YP + YS + YV + YF + YE = -GW * sin(Φ) |
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Rolling Moment (down to right) |
(RP + YP * (zP + z CP - zCG) + ZP * (yP - yCG)) + (RS + YS * (zS+ zCS - zCG) + ZS * (-yS + yCS - yCG)) + YV * (zV - zCG) + YF * (zF - zCG) + RF = 0 |
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Yawing Moment (nose to right) |
(NP - YP * (xP + x CP - xCG)) - (NS + YS * (xS + xCS - xCG)) - YV * (xV - xCG) + NF - YF * (xF - xCG) - YE * (xE - xCG) = 0 |
Working Papers:
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DESIGN: |
B321 |
MAKE: |
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BUY: |
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Items:
DESIGN:
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Name |
Item |
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Rotors (port & starboard) [ P] & [S] |
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Horizontal Stabilizer [ H] |
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Vertical Stabilizer [ V] |
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Fuselage [ F] |
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Efflux [ E] |
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Propeller [ ???] |
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Wing (not included) |
n/a |
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Longitudinal Solution |
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Lateral Solution |
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Last Revised; October 31, 2002