Item 0906
DESIGN: Unicopter ~ Trim, Stability & Control -
Trim - Longitudinal Solution
Drawing:
This is Muse_B
Hover:
The Three Equilibrium Equations:
X:
Z:
ZP + ZS + ZH + ZF = -G.W. * cos(Θ)M:
MP + MS - XP * (zP + zCG) - XS * (zS + zCG) + ZP * (xP + xCG) + ZS * (xS + xCG) - XH * (zH + zCG) + ZH * (xH + xCG) + ZF * (xF + xCG) = 0MP + MS - XP *( zzP + zzCG) - XS * ( zzS + zzCG) + ZP * (xxP + xxCG) + ZS * (xxS + xxCG) + ZH * (xxH + xxCG) + ZF * (xxF + xxCG) = 0 from Access
Rewritten Equations:
TM * (iH + a1S
) = GW * Θ || Not required since (iH + a1S) = 0- TM + TM * (DVH / GW) + TM * (DVF / GW) = -GW
TM * (zM + zCG ) - TM * (xM + xCG ) +or- QT + TM * (DVH / GW) * (xH + xCG ) + TM * (DVF / GW) * (xF + xCG ) = 0
Values:
For arm lengths see: 0899.html
For drag see:
0903.html|
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Values for UniCopter: |
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Gross weight: |
GW |
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zM |
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xM |
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xF |
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Solutions:
TM * =
? poundsΘ =
0 degreesa1S =
not used
Note
Forward Flight:
X-Equilibrium Equations:
XP =
XS =
XH =
XV =
XF =
XE =
Tilt of gross weight
= - GW * ΘZ-Equilibrium Equations:
ZP =
ZS =
ZH =
ZV =
ZF =
ZE
Is this required?Gross weight
= + GWEquilibrium
= 0M-Equilibrium Equations:
MP =
MS =
- MP * zP =
+ MS * zS =
ZP * xP =
ZS * xS =
- XH * bH =
ZH * xH =
- XV * bV =
MF =
ZF * xF =
- XF * zF =
Equilibrium
= 0
Pitch Change between Hover and Fast Forward Flight:
See notes on Pitch Change between Hover and Fast Forward Flight
: in DESIGN: UniCopter ~ Fuselage - Body
This was added by me since it will probably require consideration; Particularly the entry into autorotation.
Could the fuselage's large flat area behind the rotors and over the engine, plus the horizontal stabilizer, plus the loss of the Y-axis component of rotor torque cause a sudden and large nose down pitching upon the loss of power? This nose down pitch could be advantageous if at hover but might be excessive if at high forward speed.
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Last Revised: May 8, 2002